:. :.: MATERIAL USED IN MUSICAL COMPOSITION A SYSTEM OF HARMONY BY PERCY GOETSCHIUS NEW YORK G.-SCHIRMER UNIVERSITY OF CALIFORNIA AT LOS ANGELES GIFT OF MRS.MATTIE H.MERRILL . / TENTH EDITION REVISED AND IMPROVED. THE MATEEIAL USED IN MUSICAL COMPOSITION. A mm OF BiRMOKY DESIGNED AND ADOPTED FOR USE IN THE ENGLISH HARMONY GLASSES OF THE CONSERVATORY OF MUSIC AT STUTTGART, BT PERCY GOETSCHIUS, Mus. Doa, ROYAL WTTRTTEMBERG PROFESSOR. NEW YORK: G. SCHIKMER LEIPZIG: FRIEDRICH HOFMEISTER. ENT? STA. HALL. 1909 COPYRIGHT, 1889, BY G. SCHIRMSS. COPYRIGHT, 1895, BY G. BCHIRMER. MUSIC LIBRARY MT SO Or TO ^ PROF. DR. IMMANUEL FAISST V TUI8 BOOK IS INSCRIBED, IN TOKEN OF THE PROFOUND ESTEEM f\ AND ORATITUDE OF ITS AUTHOR. 213637 CD Preface to the second Edition. (Partly adopted from that of the first Edition). I he Author is not inclined to the sanguine belief, that such a subtle and imaginative Art as that of Composition can be acquired by those not possessed of the innate faculty, by simply studying from books. But it is certainly true, that even those who are bom to com- pose are not exempt from the necessity of a careful training, systematic arrangement and studious development of their ideas. It is therefore essential that the musical student be guided in his studies by some Method in which the primitive laws of the Art (a8 instinctively rec- ognized by Genius) and the subsequent experiences and inventions of distinguished minds (as transmitted through Classic productions) are comprehensively and truthfully recorded; and that Method which most lucidly, concisely and systematically imparts such information is the one from which the scholar will derive the greatest benefit. In opposition to the still popular impression that such books as these are only written for the use of Composers, and that only those who intend or hope to become Composers ever need to study Harmony, the Author avers his belief that none of the many branches of musical discipline is so indispensable as that which treats of the Science of Music; and he therefore wishes to be understood as having prepared this Treatise more particularly for the Musician in general, than for the very small minority of composing Musicians. It is encouraging to observe, that, at the present time, when the Art of Music is becoming day by day more universal, and steadily advances to a higher rank than that of a mere accomplishment, its disciples are awakening to the conviction that something more is necessary than a mere knowledge of the names of the notes, and that it is presumptuous to profess to "interpret" what they, themselves, do not more fully compre- hend. And it is also encouraging to note that, for this very reason, the desire to become ac- quainted with the hidden beauties, and to understand and follow the inner workings of the Art, is becoming of late more eager, and the study of Harmony and Composition is being pros- ecuted with more earnestness than ever before. But the Author's experience tends to the conviction that the necessity still exists for a work which, by maintaining a medium between VI the extremes of too superficial, or needlessly profound treatment, will prove an efficient and entertaining guide through the difficulties and subtleties of the Science of Composition. The desire to contribute in some degree towards meeting this want, has been the Author's incen- tive in preparing this Treatise. The scholars in whose hands this book is to be placed, are assumed to have com- pletely mastered all the elements of Notation ; to be reasonably expert in Piano playing,* and in reading at sight (for which the easier Sonatas of Mozart or Haydn may be offered as tests ; and to be somewhat familiar with current Classical Literature. If this is not the case, they are urged to devote a few months to the acquisition of this indispensable knowl- edge, before commencing Harmony; for neither from thin nor from any other book can th* study of Composition be successfully pursued, by any scholar whose attention is still partly engrossed by the Rudiments of Music! This Method of harmony ie based npon the Method of Prof. Dr. Immannel Faisst, for a detailed account of which the Author is indebted to the interest and kindness of Dr. Faisst himself.** The present Author's knowledge of Harmony was obtained solely through this channel, and he takes pleasure in avowing that what he has since learned is due to the influence of Dr. FaiBst's incomparable mode of instruction. But in the preparation of this book the course of instruction received by the Author has undergone many, in part radical, modifications. It was necessary to adapt it to a style of teaching and a manner of study in which English-speaking nations naturally differ from the Ger- man: The order and division of Subjects have been slightly altered: An entirely new collection of Examples and Exercises (excepting such as bear Dr. Faisst's name) has been invented: In carefully investigating doubtful questions, and pursuing original researches to a satisfactory issue, older views have been changed or relinquished, and many new ones advanced Chief among these as defining the main stand-point assumed in this Method in distinction to all others, and as indicating the source from which the laws of harmonic action, and logical tests of euphony are deduced are paragraphs 12a f, 24, 48 50, 51, 90 93, 165a f, 220 a g, 211. The Author lays claim, furthermore, to the originality of the treatment of the Rules of Melody (9 13); of Part n, Divisions C and D; of Extraneous Modulation! * The reason* for adopting the Piano-forte at the most convenient medium for the practical study f Harmony, are given in the coarse of the book ** See the following Preface VII /5 -280289): of 309312 (Progressions of the Chord of the Diminished Seventh): of Part in, Section 5 th (Harmonizing of Melodies with Modulations); of 337; of Part IV, Sec- tion 4* k : of 383: of Part V, Section 2 nd : and of Appendices A, B, C and F. The present completely re -written Edition differs from the first one in the follow- ing respects: The different subjects of study have been more distinctly and methodically system- atized; the explanatory notes and illustrations are more copious, while many intricate or speculative points have been either omitted altogether, or materially simplified; the Exer- cises, also, have been made easier, so that every ordinarily gifted scholar may have the gratification of correctly solving them, with a fair amount of application and patience; and finally, three different kinds 'sizes) of type have been adopted throughout, by which the scholar will be guided in his choice of a more or less comprehensive and severe course of study. The smallest type has been used for exhaustive explanations, or matters of general information, and can therefore be passed by, in the case of such pupils as deem them un- necessary, or who may chance to be in haste with their studies. What is printed in large type, on the contrary, is absolutely essential for every scholar, and must be thoroughly stud- ied. The Course of Study is divided into Lessons (weekly, or semi -weekly) in such de- grees as the Author has found to be most convenient in his own practice; but it is left to the judgment of the teacher to modify this division as occasion prompts. It will oftener be found necessary to devote the time of two lessons to one alone, than to merge two lessons in one: haste is of little avail in the study of Harmony. Each lesson terminates with an Exercise, or a set of Exercises, and a synopsis of the fundamental principles of the subject under treatment. The Author recommends working out all the given Basses and other Exer- cises, upon the ground that "practice will make perfect". But here, also, omissions may be made. The adoption of the given Positions (upper figures) facilitates the solution of the Basses very materially, of course, and they are really intended only for the use of weaker scholars. Those who are ambitious to profit most by the given Exercises will simply ignore all such auzittiaries , t. e. will copy out the given Basses without paying any attention to the upper (Position) figures. The Fundamental principles should be memorized. The references to other paragraphs (which may appear at first glance unnecessarily profuse) have been made with the studied purpose of impressing certain points more deeply upon the scholar's mind, by dint of frequent repetition. Therefore the scholar is required to make conscientious use of them, despite the slight interruptions they may cause. In the other references (to other works the Author has limited himself as much as possible to such Compositions as are accessible to every scholar, and, with very rare exceptions (in favor of some particularly striking examples), to Piano-forte music alone. The printed The abbreviated denomination of all the Chords, according to the numbers osed in this "absolute" figuring; e.g. the Two-seven-one; The regard paid to the emiuent influence, which in all Chords (above all. in the Concords) the condition of the Soprano exerts upon the admissibility and effectiveness of the Choral-progressions; and, in consideration of this influence, the investigation and judgment of all the diatonic harmonic-progressions, with regard to every possible Soprano -position; furthermore, in the same connection, inciting and guiding the scholar to a melodious pro- gression of the Soprano, in every kind of Exercise; The institution of rules for voice-progression, which are not limited to a succession of two tones, but apply to the connection of a protracted series of tones; The application, throughout, of each part of the harmonic material, in a three- fold manner; a) in working out figured Basses; b) in the invention, by the scholar, of original Phrases and Periods; in both cases with special regard to the acquirement of these simple, elementary forms in regular con- struction. for which reason, the suitability of the momentary chord -material for Semi- cadences is also indicated; e) in harmonizing given Melodies, chiefly in these elementary forms, or in other related forms proceeding from them; The determination of the relations existing between the laws of rhythmic pro- gression, and the prolongation or change of Chords and Bass tones; Many rules of voice-progression for special combinations of Chords; particularly ra reference to covered, interrupted, and oblique consecutive octaves and fifths; The distinguishing between different kinds of parallel fifths, according to their size, and the condition of the voices; Precise definition of the harmonic relations and general use of the different 6 /4 Chords of the key;* Thorough exposition of the free resolutions or progressions of Discords, and their nse; also the free resolutions of Suspensions; Regulations respecting the practical application of the diminished Triads, and their Inversions; of the Chords of the Ninth, and Inversions; the Chord of the Seventh upon the 7 tt step in Major, with its Inversions; of the Altered and Mixed Chords;** The derivation of the Chord of the Seventh upon the 4 th step, from the Chord of the Ninth upon the 2 d ; The distinction between, and separate treatment of, Diatonic Modulation (based upon the fundamental principle that certain Chords are common to different keys) and Chromatic or Enharmonic Modulation; Diatonic Modulation to remote keys, direct and indirect; precise exposition of the different chromatic Chord-progressions,*** and their modulatory significance ; * Dr. Faisst distinguished between strong and weak Six-four Chords. The present Author deter- mines their relations and nse differently. ** Dr. Faisst regarded the Altered Chords as borrowed from a foreign key. * Thii the present Author has very considerably condensed. Tke Author. XI Rules for determining the admissibility of False-relations: Detailed treatment of Harmonic and Mixed Figuration; The transition from the harmonic (homophonic; style of writing to the polyphonic, by means of inharmonic tones. All these characteristics, which I believe to be peculiar to my Method, have been adhered to with more or less fidelity by Mr. Goetschius in the present work. But. while it would be groundless to regard each individual point in the presentation and treatment of these subjects in this book as proceeding from me, (inasmuch as Mr. Goetschius has de- viated in many respects), it would be still less just to overlook what he has done to com- plete certain parts of my Method, and present it in a fitting shape for practical instruction; besides the addition of those parts, in reference to which he in his Preface lays just claim to having advanced original views, the significance of which will not be denied even by those who are unable promptly and easily to appropriate them. May this book then, which has been prepared with so much intelligence and assi- laity, prove to be a successful guide to very many, in their musical studies. Dr. IMMANUEL FAISST. 8ttgart, Oetolw I8tl Explanation of signs. The reference -figures usually in parenthesis* apply to the paragraphs, unless their reference to tfc is explicity indicated by Ex. Care must be taken not to confound these figures. -0- signifies "bad"; t or tt doubtful. - The Roman numerals I, II etc. indicate Triads ("Common-chords") of which the corresponding Scale- tep u the Root. When a T or 9 is attached above, it signifies a Chord of the Seventh or Ninth. When 1, 2 or 3 is attached at the lower right-hand_ corner, it signifies the corresponding Inversion; and o signifies In- complete, $. . without the Root. Thus: Vj = the Chord of the Seventh on the fifth step, in second Inversion. When an Accidental is attached, it signifies that the Chord is Altered. The figures 3, 5, 8, 7 or above given Bass notes refer to the corresponding Interval of the Chord (i. . the "Position"), and are reckoned from the Root. When + or - are attached, they signify high and lair Position, respectively. The figures below the given Bass notes agree with the traditional "Bass figuring'', and indicate the upper intervals from their Bass note. A line after a figure (or alone) (e. g. 6 ) signifies that the note in question, or the former Chord, is held. When a slur ~~ precedes a Bass figure, it draws the Chord back to the preceding Bass note. Only used in Suspensions). When a figure is crossed through (6) it signifies that the corresponding interval is raised. Accidentals in the figuring refer to the figure which follmot. A soli- tary Accidental refers to the figure 3. Single Capital letters in the Examples in Modulation refer to the corresponding Major Key*, tttm to the Minor Keys. Org.-pt. *= Organ-point. 8. = Suspension. 8. Ch. = Suspension-chord. A. or Ant. = Anticipation. A. Ch. Anticipating-chord. ' ' ) Simple Neighboring-note. f Unaccented Passing-note. Accented Passing-note PART I. DEFINITIONS AND RULES. 1. The study of musical Composition embraces the consideration of the three essential factort of Music, namely: Rhythm, Melody and Harmony. Rhythm. 2* Rhythm is the principle of motion, and treats firstly of the division of the time required for the expression of a musical idea into absolutely regular and equal Units, of which the most convenient and commonly adopted representative is the "Beat". Secondly, Rhythm treats of the grouping together of a certain number of these Units or Beats in symmet- rical Measures (Bars). This grouping is effected by means of a regularly recurring emphasis (Accent), laid upon the Jirst Unit of each group. The Beats are absolutely similar in size or duration but differ in quality, some being heavy and others light. This is the most essential principle of Rhythm, as it establishes a distinction oetween the beats, and gives the otherwise monotonous and meaningless series of similar strokes a recognizable, plastic form. S. a. The rhythmic groups consist of either two or three Units or Beats, and constitute the Simple Measures or Bars of written music. When there are two beats in a group (heavy and light beats in regular alternation) the rhythm is Duple: Ex.1. When there are three beats in a group an irregular alternation of one heavy and two light beats) the rhythm is Triple: ft f 1*3 ! M fr ft l! The following kinds of Time are examples of simple groups or measures, in Duple and Triple rhythm: \ 'i. e. a group of two anits of the value o! Quarter-notes, ; $ fa group of three units of the value of Eighth-notes] ; | or (J; [alia breve) ; | ; | etc. b. Compound measures are combinations of these simple groups. For instance, two groups in Duple time: | -(- |= ^ or C (ometimes called Quadruple or Common time); or \ -j- \ |> I H- f -f- | = $ ; | -}- | = | (not to be confounded with | I) etc. I Mode* of Accentuation. Simple measures hare only one Accent, Compound measures hare an Accent for rhythmic group that they contain: rr r 1134 1-4 123 456 78* 1-6 7-9 The only difference between simple and compound time is, obviously, the number of Bar-lines. The first accent of a compound measure is the strongest, as the exponent of the Jirst of the two or three groups which compose the measure, and is called the Pr unary accent, the other accent or accents are Secondary. Modes of Accentuation. 4. a. The accent which falls upon the first unit of each group is called the Natural or Grammatical Accent, and is fixed by counting. But an arbitrary stress, or emphasis, may be imparted to any individual beat, for diversity of effect. These accentuations are called Rhetorical or Artificial, and may be produced as follows; 1 st , dynamically, by simple Gmphasis; 2"*, metrically, by a tone of longer duration, representing the sum of two or more beats, or fractions of beats ; and 3 rd , harmonically ', by a change in the com- bination of tones. Thus 1.4, Dynamic accents. Metrical accents. % Harmonica! accent*. A A A - *- i sfz tfz -4=3=f 0' 0- b. Those rhythms are most natural, comprehensible and agreeable, in which the dynamic and metrical accentuations coincide with tne natural accent, that is, fall upon the first unit of a rhythmical group; if not constantly, at least for inch a period, and in uch frequency, a* to render the rhythmic intention unmistakable. a. The measures a, b, c, d, are perfectly regular, and satisfactory in their effect; at e, the primary and econdary accents are exchanged. At f, g, n, I, the metrical accent does not coincide with the natural one, to the detriment of the latter ; such rhythms as these, in which the metrical accentuation is violated ('. 0. in which heavier notes occupy lighter Seats, or fractions of beats are called Syncopated. See 353. Bach irregular rhythms are undeniably effective, when understood. In order to be comprehended M irregularities, they must be used in connection or alternation with sufficiently marked regular rhythm. Melody. The Scale. 3 Melody. Melody if any succession of single tones . arranged in natural and logical order. It i& commonly called the Air or Tune, and is the most important element of musical com- position (at least, from a certain stand-point), as it constitutes the continuous Motive or Thread which indicates the Design of the tone -structure, and to the support and devel- opment of which the elements of Rhythm and Harmony are subservient. The Scale. 6* One of the simplest , and at the same time most complete and gratifying , and consequently most common tone-successions is the so-called Diatonic Major Scale, consisting of 7 (or 8) whole and half-steps (generally called whole tones and semitones) in the following order: C-major. 8 PJ -J. 3 B~ ^ 7 _ -fc 1-^=2-^= 3 ,^- &) ' r ^ 1|. 1 3 ft 6 liult* vj JttloUy. b. The Inactive tones, which, as the scholar will readily perceive, represent the harmonic fundament of the Key, are *cientifically defined as the "Harmonics" or harmonic "Attendant-Tones" of any single funda- mental tone the Generator), assumed in musical theory to be the Tonic of a scale. The "Harmonics" arise from aliquot division* ($, J, ^ etc.) of the vibrating body which, at it* full length, produce* th* fundamental ton*. (8e* 22). fii. IL IS Tonic, The first Attendant-tone is the reproduction or corroboration of the Fundamental, in the Octave; th* econd tone is its Fifth (Dominant of the Scale; the third again reproduces the Tonic; the fourth is it* Third the Mediant of the Scale); and the fifth one reproduces and confirms the Dominant Up to thi* number the Harmonics, which are so distinct as to be easily detected by a practiced ear, appear in the natural Major Scale as Inactive tones. The sixth Attendant-tone does not appear in the Scale, and the seventh one again corroborates the Tonic. It is easy to understand why these tones, the !*, 3 rd , and 5 th rteps of the Scale, which proceed so naturally and directly out of the Tonic, should share its nature as Inactive centre (or Axis) ol the Key, around which the other, Active, elements of the Scale operate, and towards which they tend as being their point of rest. 6. The tones which lie between these Inactive steps are Active (i . the 7 th , 6ib, 4* h , and 2nd _ E X . 10), and the tendency or direction of each one is denned by its proximity to an Inactive tone; being naturally most strongly attracted by that Inactive tone which lies nearest. d. The proximity of the 7 th step to the Tonic defines the tendency of the former upward, The 6 th step, lying nearer to the Dominant than to the Tonic, proceeds downward tc the former. The proximity of the 4 th step to the Mediant defines its tendency down- ward. The 2 nd step, which lies equidistant from Mediant and Tonic, has but a slight tendency, and may proceed downward or upward, to either. Thus: Si, 12. This rule i* illustrated in the following examples: Mendelssohn. ^"j j J jjjL j ,h ij; ^f ^^. I - rM>- H^l ' J r<-?P e *^ =i n " 4 * 7 y J^J 4- J 781 Brahms. * -H H-^- -&-j^ 4 u d. - ^-p-^ ? *-gJ* "* ^jgg 7 31491 , r *> jV ,, ^ p etc.' 6 Brahms. ^fr^ Lji i_U CT ==9 i-^^sL^ ^T ''' 7 These are the natural or inherent tendencies of the four Active tones of the Scale. They may, however, be counteracted by approaching them from the opposite direction. In the descending diatonic Scale (Ex. (i) the TW> step is pushed down from the 8 th ; and in the ascending Scale both the 4 th and 6 th step* are pushed upward from below. Rule* of Melody. 7 Moreover, an artificial tendency or impetus may be imparted to any step of the Scale, Active or la- active, by the following means. 1. By approaching it diatonically from either direction in rapid rhythm (139; 159); 2. By so arranging the accompanying notes that it becomes a Dissonance (164); and 3. By chromatically raising or lowering it ;246a). In this way the tendencies of the Active tones may be counteracted, or intensified; and the Inaetrr* tones may acquire tendencies in either direction. Ex. 14. f t Ml I ' I The natural tendencies are the strongest, and should therefore generally be respected in preference to the acquired tendencies, whenever there is a possible choice; especially in prominent parts. 13. Beside* these special rules of melodic progression, there are a few other melodic characteristics which may be regarded as favorable if not essential features. Thus: The melodic succession is frequently based upon some harmonic combination. This mode of construction conduces to the strength, concreteness and unity of the Melody. Ex.15. b.11. a. Beethoven, Sym. III. b. Beethoven, Sum. V. i h 3 r-h i ~ n r-T*r- ri~ *-*- -^-P 1 :; zz Lf*0f*^ =u ^ * ^ 1 h ^-^ [.equivalent to ' ^zr i qz * B E 7 _^ 7 [^ 7 7 7 | Weber, ^ono^a 7Z (This is a characteristic of the classical period, represented by Haydn, Mozart and Beethoven, but* unfortunately, fast disappearing before the stormy inroads of modern "originality"; there are but very few living composers who endeavor to retain this logical, transparent and satisfying style of melodic concep- tion. Rubinstein belongs to this rare class). It is often employed, on account of its concentrated character, for the expression of vigorous, bold and lofty sentiments; as in patriotic songs, national hymns, and the like. Stctr-tpangled Banner. -f> ; - & f J-2 i .R^fa _^ J. * I '-tr-r S3 :te.is=i_-; 8 Harmony. Intervals. D. A Sequence is the repetition of a certain melodic or rhythmic figure upon a different step* Melodic* which contain Sequences are consistent in design, and symmetrical. Beethoren. 1.17. (This melodic formation is a characteristic feature of RafFs music.) Harmony. 14. Harmony, in its narrowest sense, is the Combination of single musical tones; in it* widest sense, the Succession of such harmonies. 15. The combination of two tones constitutes an Interval, a term which must be applied not only to the "Space" between the tones, but more particularly to the "Relationship" established by joining them together. Intervals. 16. Intervals are always counted from the lower note upward, as the diatonic Major Scale goes, and are determined by the number of steps of the Scale included by the two notes. Eighth. Prime Second. Third. Fourth. Fifth. Sixth. Seventh. Ninth. Tenth. - y or 1 1 ^ ^ i o n -/rv Unison. ^, 75T- ^ ftp- The first eight are simple intervals; the last two and all that follow (beyond an octave) are compound consisting of an octave and a second, octave and third, etc. Such intervals are always reduced to simple ones, and called, with omission of the octave, simply "Second", Third", etc.; for, as already observed, these terms indicate strictly the relationship between the letters, which is always the same without regard to distance, as long as the letters do not exchange places. Thus, c D 1 is a "Second", whether written mnd even 'D C -/r\ a -\- hut slightly different (2t.) 17. These intenrals, which follow the natural diatonic Major Scale, and therefore represent the simple Scale -relations of the several steps to their Tonic, may be called Natural or Diatonic intervals. They are divided into two classes, namely: Perfect and Major. The Unison, Fourth, Fifth and Octaye, from the tonic of any Major scale, are called Perfect. The Second, Third, Sixth and Seventh from the Tonic are called Major. Intervals. Perfect: Ex.19. C-mjor. 8** Major: ^th -gi\r I3rd; Ex.20. Thal is to say: the interval e-f (for instance) is a fourth, because f is the 4 th letter or step in the Scale of C; and it is a perfect fourth, because it exactly agrees with the natural Scale of C, and because "perfect" is the term used to qualify the Natural or diatonic 4 th . The interval *-fl /r\ ff 8 would be counted along the Scale of E, and, as jt is the 6 th letter from , it is a Ugt^n tixth] furthermore, a major 6 th , because it exactly agrees with the Scale of E, and because "major" is the term applied to the Natural sixth. 18. a. A Perfect interval, when extended by an accidental (if $*), the letters remaining the same, becomes Augmented; when contracted by an accidental (;}, b, |? W> it becomes Dimin- ished. For example : Perfect 6 a . Augmented & tk . Diminished 6 th . 21. It is obvious that, if the letter were to be changed, the quantity of the interval would be altered Therefore the y& (Ex. 20) must not be regarded as equivalent to a(?, nor g\? toyjtl b. A Major interval, when extended by an accidental, becomes Augmented, precisely like th* perfect intervals. When contracted it becomes, not diminished, but Minor (N. B. I). e. A Minor interval when contracted becomes Diminished. Thus: Major 3 rd . Augm. 3 rd . Minor 3 rd . Dimin, 3 rd . 33 % ff^ Eg yrfz From this it appears that the perfect intervals become diminished by an* contraction, whereas ih major intervals must be contracted twice to become diminished. 19. Why the perfect intervals are so called will be proven in '25. The other intervals, unlike these, admit of modi- fications which do not so seriously affect their harmonic quality but that they constantly appear in two distinct dimensions, differing by a chromatic half-tone, and called respectively Major ('-greater") ana Minor ("smaller"). As has been shown, it is the Major dimension which agrees with the Scale of the lower tone, as Natural interval. 22. \l \ 1-1 3B . _. U^, u^> 1 i^ <& How the augmented and diminished intervals are obtained from these is very obvious. 20. In determining the quantity and quality of a given interval, the scholar must always start out from the only infallible criterion, the diatonic Major Scale (16) ; and erect it upon the lower of the two notes. The step, or letter, of the Scale, occupied by the upper note, gives the quantify. If th 2 10 Intervals. upper note corresponds exactly to the scale in question , the interval will be perfect or major, these technical terms being synonymous with "Natural", or u as the Scale runs" (17). If, however, th upper note differs chromatically from the Scale, the interval will he minor, augmented, or diminished, .<. according to the alteration (18). For example: quantity, a fifth; tne tf-Maj. Scale: Scale-note being changed, however, from d to djf , the natural "perfect 5 th " has been increased to an "augmented 5 th ". And again : 2345 (/)|7-major Scale), quantity, a seventh; being altered from to efr, the natural "major 7 th " has been decreased to a "minor 7 tw> . In a case like the following : :rn *^~~ *here the major scale of the lower note is impracti- cable or inconvenient, the simplest process is to cancel an equivalent accidental from each note. Thu: The mode often adopted of determining the quantity and quality of an interval by the number of included half-tones is not only too mechanical, out really unreliable; for the same tones mav be written in different ways, as different intervals {<. . harmonic relationships), without their undergoing any change in actual distance apart For illustration : is equal to eight half-tones, and so i* ; but the former \ minor 6 th in one Key, while the latter is an augmented 5th j n another. Exercise two. fD^ and the A. Erect the Dimin. Octave, Minor Second, Dimin. Third, Perfect Fourth, Augm. Fifth, Minor Sixth, and Dimin. Seventh, upon each of the Notes E, A, D, G, B, Fit, C/^1 X "CT > t*< * C?, Dj?, andBp: Augm. Octave, Major Second, Minor Third. Dimin. Fourth, Perf. Fifth, Augm. Sixth, and Min. Seventh, on the notes U. C. F. D. E;. ft* B. And determine the Names 1 J {, \ n \ 1 i n of the following Intervals i 3E=i & \ yy> Tf?5 . i \ ?i* ^> "K^ it, -] 1 t- jfi !T cs \ir "^^~ -s y& $?&- ^ a ^ IO '1 S r Tone-relations. \ j Fundamental principles. After a wide skip the Melody turns. The 7 th step of the scale proceeds upward. The 6 th and 4 th steps proceed downward. Intervals are counted upward. The perfect and major intervals agree with the diatonic major scale. Tone-relations. 21. The vital principle of musical Art is Tone-relation. Every combination, every progression, every obligation is based upon and defined by the correlation of the tones. A solitary tone haa (ordinarily) no more meaning than a single letter or character of speech has ; both acquire a signification only upon being associated with other characters, whereby a certain Relationship is established, involving mutual obligations and evolving action. . a. The classification of the intervals and the determination of their various grades of intimacy is not a matter Ex, 23. -- - - , -j- pulsations . These sound-waves are generated , f .... forward and backward vibration of an elastic body at an inconceivably high rate of speed. A pianoforte-string which makes 261 full pulsations in a second of time produces the sensation (or tone) we name c 1 the middle c of the Pianoforte. w. Another string say a violin-string also vibrating 261 times in a second will, of course, produce exactly the same tone, representing the interval called "Unison" with the first one. This mathematical proportion of 261 : 261 or 1 to 1 need not be regarded as an 'interval" at all. C. Another string of exactly half the length of this one will vibrate (all things being equal) exactly twice as fast, or 522 times a second, and will produce the next higher c i'c 8 ). The simplicity of this division of the first string, exactly in the centre, and of the mathematical proportion of the two velocities to each other, 261 : 522 or 1 to 2, is a self-evident proof of the simplicity or intimacy of this tone-relation (the Octave). The tones must blend and produce consonance, because there is no conflict between sound-waves which enter the ear together at the rate of one to two. d. This interval, the octave, is of no great use in active Harmony, as it merely alters the regis'er of what is prac- tically the same tone, so complete is the agreement. In order to obtain a new tone, another division of the string must be made, which will result in the next simplest mathematical proportion, namely 1 to 3. One-third of the first string (e 1 ) will vibrate three times as fast as the whole string, or 783 times in a second, and pro- duce the tone g\ 1. "2. 3. Unison: 8 th / _^^ _ __ i / ( \r & rW Whole string : Vi f string : i9& / 3 of string. 1:1 1 .- 2 23. From these simple experiments the following facts are deduced: The Unison and Octave are the most simple and intimate tone -relations, but the perfect fifth is of the greatest significance in Harmony, as it represents the simplest mathematical proportion and consequently the most intimate relation which can exist between actually different tones, and therefore constitutes the basis of all tone - combination. The perfect fifth is the standard of measurement in Harmony, and may be called the Harmonic Degree. 24. The group or family of tones collected from the whole Realm of Sound to form a Scale or Key consists of seven members, which conform to the relation of the Harmonic Degree, and is obtained 2 12 Tone-relation*. 25. by projecting the same upward from the tone which if to be the Tonic or Fundamental of the Seal*. As follows, for C-major : 1) The Harmonic Degree is projected downward once, so that the Tonic may appear as tipper tone of tha relation, an well as lower; but with this exception it is successively transferred to ht " f 3 u* 1 J. Octave (Root). 3rd . .J. Octave. J /!, Root. sz Root. giRoot. Exercise four. Erect the six Triads of (7-major in successive order J, II, HI, IV, V, VI), in their three Positions, according to the following model: Octave Position : Position of the 3 rd .' Pot. of the 5 tt : 5 J J // 43. 4 4 a. The Root must always be in Bass. Strict regard must be paid to the compass of the parts (Ex. 34) and te their relation! (42); and to the duplication of Intervals (43, 44). The following examples are wrong: . f-:^=E=.=t= f F n i H- r u - *2.Kule2. 43. Ex.37 c. Ex.37 d. Ex.34. 20 The Rules of Part writing. Fundamental principles. The average compass of vocal parts lies between C and G in some register or other. The uppermost tones impress the ear most strongly. The principal tones of the scale Tonic, Dominant and Subdominant) should be doubled. The Fifth of a Triad must not be doubled. - The duplication of any Root is justifiable. The "Position" of a Chord is defined by the Soprano. The Rules of Part-writing. 46. The mutual operations of the parts in producing a series of Chords and expressing a musical thought (as seen in Ex. 35) are guided by the following four fundamental laws of Voice-progression. Rule I. a. The parts should move as naturally and connectedly (. e. horizontally) from one harmonic interval to another as circumstances will permit Wide tkipt should be avoided , aa they tend to obscure the movements of the individual parti, and endanger a correct apprehension of the harmony. b. A tone which is common to two successive Chords generally remain* in the same part and octave. C This rule applies most especially to the middle parts , which must be kept subordinate. The outer parts (So- prano and liags), which are more independent and have a more important object, should not be subjected to great restraint ""-J-J.J*. .fj JrJ-^ 40. N. B. Each of these measures is an example by itself, and is not to be connected with the one that follows. Role II. a. No two parts (neither Outer, Middle, Adjacent or Parallel parts) should move in parallel motion (*. e. direction) from one perfect fifth, to another; nor from one perfect octave or unison, to another perfect octave or unison. In other words, parallel or con- secutive fifths, octaves and unisons in the same pair of voices are strictly prohibited. Successive fifths sound badly. See Appendix A. Successive octaves do not offend the ear; but, when two different parts have the very same progression at the same time, the separate individuality of each part is momentarily lost, and the effect is meagre, weak and blundering. Successive unisons are still less excusable, for thereby one part disappears entirely. Parallel seconds and tevenths are not included among the foroidden intervals in the Rule, because they are so obviously incorrect, that the prohibition would be superfluous. Parallel fourths , which are certainly very disagreeable in themselves, are not likely to occur alone, and whatever accompanies them generally justifies them. El. 41. Parallel motion in r r+f f+f The Rules of Part-writing. Parallel or Consecutive fifths and octave* 21 11.42. The Scholar will recognize -which parts are represented in this Example, by the direction in which tht stems are turned. The other parts are purposely omitted. b. These faults arise from leading the parts in the same direction; therefore the most effectual mode of avoiding them is, naturally, to lead the park as much as possible in contrary motion (. . two in one direction, and two in the opposite; or one against three), especially the Outer parts, which, when they move in parallel direction (both ascending or both descending) are apt to carry the mid- dle parts with them. The danger is greatest when all four parts move in the same direction. Rule III. The parts (or, more exactly, any two parts) should be led as much as possible in parallel thirds or sixths, as progressions of this kind are the surest guarantee of euphony. Comp. Ex. 41, measures 2 and 5. Bach. Si. 43. This applies to short progressions as well as to a protracted series of Chords, and is applicable to any pair of parts, not necessarily adjacent ones. Eule IT. a. The Leading- tone must progress diatonically upward to the Tonic, in whichever part it chances to lie; but especially in the Soprano, that being the most prominent part. Ex. 12. b. The downward tendencies of the 6 th and 4 th steps of the scale must also be respected, in prominent parts. Ex.12. C. The Leading-tone must never be doubled. (43.) The general Exception. 47. These rules of harmonic progression refer only to the transition from one Chord into another (new) one, and are not valid for the mere repetition, or change of form, of the same Chord. Hence, when a Chord is simply repeated, it may be desirable to change the location and arrange- ment of the tones, even with skips (contrary to Rule I) , in order to avoid monotony. And in such cases parallel movement in all four parts (see Rule II, b) is not objectionable. 22 /rt J- T/ic general exception. ^- U4- -j- -J-r- ftv-- > I g " 9 t r i i i is preferable to _jE_jZ 1 ! r i 1 - ^ 2 * P *- -*- -f 1 -r r i -r -r- 1 Thus: In regard to Rule II : repeated fifths, octaves or unisons must not be considered in the sim* as progressive fifths, etc. The following cases are right : i 8. a - - 8 . As to Rule IV : the Leading -tone may be transferred from one part to another when the Chord fa* which it is contained is repeated, without necessarily ascending. (Compare Ex. 44.) Thus: ^Eff L --f\ i-, ^ \jfel ^ r r etc. As to Ex. 12 : the tendencies of all the Active tones are nupended during a repetition of th Chor4 in which they occur, similar to the above treatment of the Leading-tone. Fundamental principles. The voices must move smoothly. Parallel 5 th ' or 8 V>tance of its Root from the Tonic in Harmonic Degree*. This deter- mines the extent to which it supports and confirms die Key, and is also a test of its frequency and recognizabUity. The Qualification of the Tones, Intervals and Chords. 23 fc. The quality of a Chori-lnterTOl ia defined by its distance from the Root of its Chord, in thirds (31). C The quality of single Tones varies according to their connections. As Soots, their relative importance it shown in Ex. 24. In other harmonic or melodic capacities they are qualified as in Ex. 10, and at b. above. 49. a. Of the Triads, the I, V and IV are therefore the strongest and most independent Then follow the II, VI and HI, which are dependent. Ex. 32). fo. Of the Chord-intervals, the Root, which identifies its Chord, is the strongest The Third is lighter and more flexible, and is therefore regarded as a better (in fact the lent} Interval of the Chord, for the practical purposes of composition. The Third also defines the mnde (major or minor) of its Triad (34). The Fifth of the Chord is a very weak, "soft" Interval, almost entirely devoid of harmonic strength, and one which, as shown in 44 b., may sometimes be dispensed with. It bears the same secondary relation to the Third of the Chord that the latter does to its Root, and is therefore third in importance in its Chord. This may be casually offered, at this place, as one of the reasons for the prohibition of consecutive firths (4rt. Rule II}. The "Fifth of a Chord" must not be confounded with the perfect fifth as Harmonic Degree, t. e. as grade of relationship between two independent tones (Hoots, or Key-notes). Q The Seventh and Ninth of a Chord , being dissonances, possess characteristics which distinguish them as the most unstable and dependent of all the Chord-intervals, but which, at the same time, impart a certain keenness and force to them which the Fifth altogether lacks. (0. The difference in the mode of treatment of these various musical members may be expressed, in general term*, as follows : * The Independent Chords are treated with greater freedom than the Dependent ones, as regards the manner of their introduction and progression. b An Independent Chord-interval may enter and progress with a wide skip , while those which are Dependent require to move more smoothly, and are often limited to step-wise progression. C. Not only a skip from a Dependent note or Chord-interval, but also a skip to it, is incorrect. d. An Independent Chord-interval should be doubled ; those which are Dependent, seldom. (Ex. 37). 6. An Independent Chord may be prolonged almost indefinitely, while the Dependent Chords are generally of short duration. ! Hence, a protracted succession of Dependent notes, Chord-intervals or Chords, or even a single succession of such as are sensitive, is dangerous to the Key. A judicious interchange of Independent and Dependent tones produces the best Melody; a judicious interchange of Independent and Dependent Chords produces the beet Harmony. 1. In this Method of Harmony the Author proposes to divide the Chords of a Key into three distinct Classes or Elements, quite similar by themselves, but differing essentially from each other. The distinction will be explained in the proper place , and will be strictly maintained , excepting in the case of a few rare Discords of exceptional character. The Scholar will soon learn to assign each Chord its rank in the Class to which it belongs, and will have but three primary laws of Chord- tuccession to consider and respect, instead of regulating the movements of each Chord separately. The three Classes will be named : Tonic Class, Dominant Class (or the First Class of non-tonic Chords), and Sttbdomiliaiit (or Second) Class. (165. 220). PART II. THE COMBINATION OR CONNECTION OF CHORDS. Division A: Concords.. Section I rt : Triads. The Tonic Triad, L it. This is the fundamental representative of the Tonic Class of Chords (51). It is the Alpha and Omega of the Harmonic system. It can progress with equal facility to (that is to say, can be followed by) every other Chord in its Key. 53. The Position of the Third is the best, in general. (Ex. 39). The Octave-Position U heavy; that of the Fifth somewhat weak. (Comp. 49 c). The Dominant Triad, V. This is the fundamental representative of the Dominant or First Class of Chords (51). 54. a. The V contains the most important melodic note of the scale, t. e. the Leading-tone. Thii appears in no other Triad but the III, in which it is the unimportant Fifth. b. Hence the V, in order to satisfy the tendency of the Leading-tone, must naturally progress to such Chords as contain the Tonic note, t. < . first of all, to the Tonic Triad. e. In noteworthy contrast to the Ten:; Triad, which is characterized by its ability to progress directly to every other Chord in the harmonic system , the Dominant Triad is distinguished M the Chord into which every other can, and in truth, must progress, as the medium through which the Tonic (the Object of all harmonic succession) may eventually be reached. 55. In the Dominant Triad there is but little choice of Position ; the Soprano can take any Interval, th Octave being perhaps the least frequent. 56. The relation between the I and V (the Harmonic Degree) is a sufficient guarantee of the facility with which they may be connected, '. e. may progress into, or be followed by, each other. Thii succession of Chords (I V or V I) is the most common in Music, as is obvious from their su- periority over all other Chords. The connection I V. 25 57* The following Examples illustrate the combination of the I with the V in each order. The choice of Chordt determines the Bast part, which takes the Root. The Melody (Soprano part) is next found by deciding which Position each Chord is to take ; this depends partly upon the tone which lies nearett to the first Soprano note (Rule I, 46), and partly upon the general rules of Position (53. 55; In these Examples the possibilities of the Soprano are exhausted by progressing systematically from each of the 3 Positions of the first Chord to each Position of the next, in the order of then proximity. The Middle parts are then added generally the Alto first) by completing each Chord as in Exer- cise 4, but with strict regard to the fundamental rules of paragraph 46. Each "measur^' is an example by itself! No special Rhythm ia intended; unless marked with an accent (v) it will be understood that either Chord may occupy the accented beat of the measure. The signs -Q-, ft, T, (T), dqnoit- the quality of the example in question, and are self-explaining. The Scholar should try to discover the reason for each distinction. The given references, and the lines drawn between certain notes, indicate when the errors lie. to. 47. The connection I V (C-major). From the OctaY6-position of the I : Ex.48. Ex. 41 n 3 (T) ~ : T=f J J good! lV 44b. b. From the Position of the Third of the I 1 J J ^ f-F - J J-i 1 f e. From the Position of the Fifth of the I- i 5 3. 1V 4 f=f *J-HK* '1 26 The reversed succession, V /. 1) Rule Ib (46\ *2) Rule IL *3) This measure illustrates (in Soprano and Bass) a noteworthy modi- fication of the error shown in Rule II, namely: successive octaves in contrary motion; and at *4) the same kind of successive fifths is exhibited. In the case of octaves, the difference in direction is usually a sufficient excuse, even in prominent parts. But successive Jiftlus are just as objectionable in opposite as in parallel motion, excepting always when one of the tones is in a Middle part, where it is less noticeable 12x. 47, No. J, Tenor and Bass). *5 Rule lib. *6) Rule la. *7) Both objectionable, on account of the wide skip in the conspicuous Soprano part to the sensitive Leading- tone (5Uc). In Ex. 47 7 the same skip in Tenor (middle part) is of no account *8) The repetition of a Melody-note is slightly monotonous, but by no means wrong. 68. The object of these and all subsequent Examples is : firstly, to furnish the scholar with a sufficient (if not exhaustive) illustration of the harmonic progressions, as a table to which he can refer in working out his Exercises ; secondly, and perhaps chiefly, to afford him a test to which he can apply his ear, and according to which he can and should cultivate his musical sensibility. Therefore the Example* mint be ttudied at a well-tuned Pidno (or some other manual instrument fty being played through slowly and thoughtfully , each correct me sure several times in succession, first emphasizing one part and then another, and, if possible, humming or softly singing the Soprano part (Melody) each time. The explanatory notes which follow each Example should also be carefully studied. The third ob- ject of the Examples it to afford the Scholar material with which to construct original phrases, if he desires. 69* The following general roles for the Soprano may be deduced from these examples . A* Two Octave- Positions in succession in Triads are dangerous (Ex. 47, meas. 9, 10). b. Two Positions of the fifth in succession hi Triads are always bad (Ex. 49 6, 7). C. A wide skip (i. e. beyond a 3 rd ) to or from the Leading-tone is objectionable in the Soprano (Ex. 487, 8; and Ex. 512). d. The repetition of a Melody-note is somewhat monotonous (Ex.49 1). The reversed succession, V L 60. A. From the Octave-Position of the V 8 I *9d. Ex. 50. m ?T h. From the position of the Third: 3 , Me. \ Pule IVa. f=F W J n J j=[ P^ oie. C. From the position of the Fifth: Ex.61. m r / PP J. J. t= etc. EX. 52. ^9 * f w . 'x j ^ ^ V 1 f J J- > r i i + ^ r>* ^ -* r i *W ' ^^ ? < ^-p ^i * r !r , H f i The Perfect Cadence. 27 * 1) The Tenor takes the Leading-tone downward to the Dominant, instead of upward to the Tonic accord- ing to rule. This irregularity is allowed in a Jlii/ille part inot in Soprano Ex. -M 3j ; but only when, a* indicated in 1 2 e, it is preceded by a higher tone : that is, when it U pushed downward from above. See Ex. 53 d. 61. a. Although the Chords I and V stand each in the relation of a Harmonic Degree to the other, it does not follow that their connection ia equally natural either way. The natural arrangement of Chord-Roots above the Tonic (with one apparent exception, to be accounted for later on) as seen in Ex. 24, proves that their inclination must be dottmivards in Harmonic Degrees, in order to reach the Tonic, in which their obligations are fulfilled. Consequently the succession V I (Exs. 50 52) is more natural than T V (Exs. 47 49). fo. This progression, in which the CJiord falls one Harmonic Degree, we will therefore distin- guish from all other Chord-successious by the term "Normal" or "Regular* Progression. Exercise five. Combine the I V in G-major; the V I in .Bb-major; the I V in U-major; and the V I in Z>i?-major, according to the foregoing Examples. Fundamental principles. The Tonic Triad (I) can progress to any other Chord. Every Chord can progress to the Dominant Triad. The Dominant Chord is characterized by the Leading-tone. Successive octaves in contrary motion are allowed, but not fifths. Successive Positions of the Fifth are bad. * Middle parts are less noticeable than Soprano or Bass. The Regular or "Normal" Progression of a Chord is a Harmonic Degree downward (from Root to Root). The Perfect Cadence. 62* a. Cadences are the interruptions or momentary pauses in the rhythm, which are necessary for separating the different melodic and rhythmic members or Sections of a composition, and which indicate, by the manner of their appearance and recurrence, the Form, or Plan of construction, upon which the composition is based. All Cadences fall Upon accented beats. The Cadence- Chord, in order to interrupt the rhythm, must be a heavier (longer) tone than the preceding one. b. The Perfect Cadence, or full stop, which occurs at the end of the piece, or at the close of a large Section, consists of the Tonic Triad, in Octave-Position, on an accented beat, and preceded by the Dominant Triad (in any Position) 28 The Phrate. El. 53. The Tonic notes in Bcu (I) and in Soprano the Octave-Position) bring both the Harmony and Melody to a satisfactory conclusion. The V must, however, precede them, as the identity of the Tonic Class depends upon the Leading-tone, which only the V contains. The following Example illustrates different forms of the Perfect Cadence: b. The Phrase. 63. a. The smallest limits within which a harmonic and melodic thought may be adequately expressed is the Phrase. It is distinguished from larger forms in having but one positive rhythmic interruption, namely: the Perfect Cadence at the end. b. It may be two, four, or eight measures in length; seldom an uneven number, as 3, 6, or 9 measures. It commences with the Tonic Triad, in any Position, and upon an accented or unaccented beat at option; and closes, as already stated, with the Perfect Cadence (V I) upon an accented beat (either accent) of the second, fourth, or eighth measure. 64. The outline of a Phrase of two measures, in C-time, may be then as follows : El. 54. r I 'Cadence' U J fe 5E i- es 55 ~f~ ' 7 i 1 \ J -FT i -| H r -*-' f 1 "^ 5 y 1 1 C V yv m J si (CD i ' 1 ^ r J -j 5 ^- JJ I | IP-t: i. i -1 75 -i ,F '/, ife 65. a. The unoccupied beats (denoted by |||) may be supplied with the Tonic and Dominant Triads in the following manner, the Melody-notes being chosen according to Rule I (46): Ex. f U) y u^- F r K i . 54 a.) J ^ I j * r ^ c> 3tc_ r 4 =t= =22_ v i / r / r The Phrase. 29 Hie regular alternation of I and V in Ex. 54 c would misplace the Perfect Cadence, by bringing the I upon an unaccented beat, thus : To aToid which, one of the Chords must It repeated: n /., 1 J 1 I . u J J fy fpS \ j 1 1 1 f \ 1 ' ' ' 1 1 1 J 1 ^ t^ a * 75"". b. But the repetition of a Chord in the course of a Phrase is subject to certain rules of Rhythm. A repetition like the following, from an unaccented to an accented beat, would displace an accent, and occasion what may be called a "Rhythmical Halt": Ei. 56. jfcrC* V H = i j -V i- -^r- J i i i * i | ) i I 1 x ^n-* 1 - ^^ r- because the rhythmical outline, which is J | J J J-j-J* [)-, i t Tarianee with the prin- ciples of metrical and harmonical accent, as expounded in 4 a. (which see). Hence it appears, that a Chord may be repeated from an accented to an unaccented beat, but not from an unaccented to an accented one; for the impression of a new rhythmic group (indicated by its Accent) , should be supported by the announcement of a new har- monic combination. In other words, to prolong a Chord beyond its beat is to impart a metrical accent to that beat ; therefore it is clear that only such Chords as occupy naturally accented beats ('. . down-beats) may be prolonged (by Repetition, or by Ties). 30 The Phrase. a. An exception to this rhythmical rule is always admitted at the very first Accent of a Phrase. Thus 67. uG * J J. i SS^E w~ 1 ^-5 ggb i */ i ' ii i J i 1. !)" ( V 1_ / , 1 1 F* 1 Especially when the natural accent is supported by a met- rical accent, by making the first beat (the true Accent) a longer note, thus 1) This first unaccented beat (called sometimes "the Up-beat") is simply a preliminary beat, and ii never included in the actual rhythmic progression. But it must be deducted from the final measure, never- theless. This exception is also allowed at the first accent of a new Phrase, or distinct melodic member of a Phrase, and in Sequences, where it is possible that the first Chord of the new Phrase or Motive or Sequence may coincide with the last Chord of the preceding Phrase or Motive ; because these two Chords, in their relations to their respective Phrases or Motives, have less rhythmic connection with each other. For example: Haydn. Ei. 58. 67* The Melody (Soprano) of these examples may also be constructed in the following ways : 59. /^ (** ^-" J J J -7^ * J ^ - &* (Ex.55 ) ^r r or 2 | 2 ^ -.ei_ ^* r r 3 -ffi- 5 bbJ 1 A-r W ^ -40 &- - V D * y (Ex. 55 b.) * r * etc. ^v-jv 1 F- & 1 68. But they are somewhat less smooth and natural than the construction of the Soprano as shown in Ex. 55. In this manner, however, the Soprano should be repeatedly tested and improved until the very best Melody has been found that the Bass (or the given Harmony) will yield. A melodic progression like the following, involving a "Perfect cadence" anywhere in the court* of a Phrase, would be obviously incorrect : Ei. 60. jU^> J r-^- * J ^ Sr Ex. 55 b.) -f~i-- )' T*> *- ^ '-..turf, r- r V i i, v /, The Phrase. 31 Hence it is advisable to avoid the Octave-Potitton of the Tonic Triad in the coarse of a Phrase, especially on the accented beats 'but always excepting when it is only a Repetition see 47.) 69. After tke Melody has thus been determined, throughout the Phrase, the addition of the middle parti is an easy task Ex. 55 b, when completed, is as follows : Rule IV. dt J"" 4 " I j .' J ' _B f ^ YF ""* m. j A V ] J A " 1 1 i 1 i r r -' J ~^v V A i EZ / * f ** 1 1 1* 1 U -f P - t H- f d nol 1 1 j ! i * J V J * * ^^ ^^ | Xi 1 I -* A u n Exercise six. The following given Basses, indicating certain harmonic progressions in Phrase-form, are to be supplied with Soprano, Alto and Tenor, as shown above. N.B. The Soprano must be written out complete, before the Middle parts are filled'in. The Ban notes are successive Roots. The numbers above the notes refer to the PcmtfotT^Soprano note) to be taken; the sign + before a number indicates the high Position; the sign -, the low Position. The last Bass ("Numbered Bass") is to be written out in the given Key and treated like the others. a. ft* e +3 4~"\ * *t 5 8 3 3583-8 53 -3853835 ^ ff C* * d. +385 353 5 8 J A- Mi JOI. 1 / / F 111 F 7 f / 1) Value J " M J N. S. These Phrases are not to be tested at the Piano until after they have been carefully and com- pletely worked out at the tablet Those Scholars who prefer to work independently of the given Position*, may of course ignore them, and choose their own Melody (perhaps a number of different one*). In thi* 59 and 47 must be carefully consulted. Fundamental principles. All Cadences fall upon accented beats. The Perf. Cadence is made on the I, in 8ve-Position, accented, and preceded by the V. A Chord must not be repeated over the bar, or over an Accent. Avoid monotony in the Melody, but also too many wide skips. 32 The Subdominant Triad. IV The Subdominant Triad, IV. 70. This is not the fundamental representative of the Second Class of non-tonic Chords (51), M will be subsequently seen. But it is one of the most important of the Class, on account of its perfect-fifth relation to the Tonic note. It is a broader, heavier, more "masculine" Chord than the V, and it* characteristic feature is, the possession of the 6 th and 4 th Steps of the Scale (the tones with down- ward tendencies) which distinguish it from the Dominant Triad (54 a). 71. The Position of the Third is preferable to either the Pos. of the Octave or that of the Fifth. 72. The IV bears the same relation to the I that the V does (a Harmonic Degree) , and therefore its connections with the former are as natural and convenient as those of the V. (56.) The Scholar if referred to 57 and 58! 73. The combination of the IV with the I is as follows : Ex. 62. IV L a. From the Octave position of the IV; ne. 8 a Vstn b. From the position of the 3 1 *: /r / Rui*ivi>. C. From the position of the m wr 69 d. r^r* SEE " 5 ws-^- 7F I 595. 1) The 4 th step moves upward in Soprano, because approached diatonically from below. *2) Whea approached from ub<>r?. its natural inclination is strengtheced, and it must move downward! And so, also, with the 6 th step. *3) This is quite objectionable, whether the Octaves are parallel or opposite, because the 4 th step skips upward in Soprano, contrary to its natural tendency. Compare Ex. 479, lo. *4) The upward progression of the 4 th and 6 h gteps in the Middle parts is not very bad; still, the following measure (*5)) is better, notwithstanding the doubled Mediant (e] in Sopr. and Alto. This proves that the rule nf correct melodic pro- grettion is more significant than the rules of duplication J In other words, the melodic successions must be correct and smooth, even at the cost of other general rules. This applies, as usual, principally to the Soprano part. 74. The reverse of this connection , '. . from the I into the IV , coincides with the Normal Pro- gression (61). The Subdominant Triad, IV. 33 From the Octave position of the I ; b. From the position of the 3** ; C, From the position of the &**. b.63. I-IV. |59c. f 500. s^ CD 8 5 595. 3E r *1) The ikip to the Fifth in Soprano, though but short, is disagreeable. *2) The skip here ii not M bad, because, though both tones are Subordinate steps of the scale, neither of them is a Fifth, nor the Leading- tone; the following measure is better, because the skip is shorter. 75* In regard, then, to wide skips in the Soprano, the following may be added to what was given in 59 c: a. If either tone be the. Leading-tone, the wide skip will be objectionable. (Ex. 48 7, 8; Ex 51 2). b. If either or both of the tones be the Fifth of the Chord, the wide skip must be avoided. (Ex. 49 6, 7; Ex. 523, 4; Ex. 6211 ; Ex. 6310, 13). C* Any rational ikip is allowed where a Chord is simply repeated (47). But see 11. How the quality and nature of the Chord-progression affect these rules will be seen later on. (Ex. 76 ; Ex. 82). 76. The fact that a Phrase can not very well consist of the I and IV alone, proves that the IV is inferior to the V, which in the foregoing Exercise teas used with the I alone in constructing simple Phrases. The individual harmonic character of the IV, (its heaviness and, in a certain sense, dullness, renders it less frequent than the other two principal Triads (I and V). It is most effective near the final Cadence, where its breadth ia very appropriate, as suggesting and supporting the impression of completion and repose. The following Phrases are therefore somewhat unnatural : . a. i b% i fck i -1 - 3 I- - 4 '-* J H T 1 ^* =5=*- \\ ^ r r r . 0- -4^ -0 * f I * i -0 i ft- I r f , I -* F f- L r I* P I IV I IV I Cadence. I IV I IV I IV I IV I Cad. Not to this one , however , which consists of the Tonic Triad in alternation with the Dominant aad Subdominant Triads : i. . the progression* I IV I and I V I, with frequent repetition*. r*~ ^- J 'J Jil 1 ' \ Ji'l ' '; IV 1 ^=n $f^-J-===fd ' - - a. -a _^ E "* J J b. m r L - f ' 1 11 f r "r r r -JJ I IV I V I IV I V Cadence. Th consistent and symmetrical construction of thii Melody is shown by the brackets and slurs. 8e 1SV 5 34 The Subdominant Triad, IV Exercise seven. The scholar is to supply Ex. 64 b and Ex. 65 with middle parts; and to work out the follow- ing Basses as before. Review the remarks before and after Exercise six. Complete the Soprano before filling out the Middle parts. KV^V*V ram* -8 83+83 f-| m 1*1-1 r-^ n \~~^J D .-4 . I" r^-r i * f -ir^-r * j .; * \ --4411 f 1 1 6. Firace. /. Db-Major. +8 - - -JF- -/-/- -F-/- -F-F- -/-/- -ZF-J F- -/-?- - ntP *1) The figures slurred together indicate that the Chord is to be struck twice in the upper parts, in differ- Positions. This is done for the sake of the Rhythm. *2) This somewhat irregular repetition of the I vuli j. uxiLiuiio. AIUB IB uuuc lui uic oaivc ui LUC J.VUJTI.UUI. *- i mo Duuicniiat uic^uiax icpcuuv/u ui uic A (prolonged from an unaccmted beat 66) is less objectionable than usual, because, being the second beat in Triple time, it is not prolonged to a stronger beat. "3) The wanting Melody-notes may easily be found by - ' ' _U . t TJ..1. Tlf V IA& \ trict observance of Kule IV b. (46.) 77 > That these simple Triads may be and have been effectively employed in Phrases, devoid of all is proven by the following extracts from two of the most romantic Composers. a. Andante tost. rH P 7 -m 9 * f- j Jj j : ; j i 5 i **** . ... g * ; t t* * ^ v ir 4i^ i a ^-4 ^ -S J-9 *( ^^55 r 'rTfr 1 ' f -J 'P ^ T zr -r r r -f f m I IV S3 j?-^ff ., fe-t-tM. Wagner. "Rheingold". -w w JL 5 rfft * These rhythmical discrepancies are justified upon grounds which will be explained in due ti Combination of the Subdominant and Dominant Triads. 35 Fundamental principles. The Subdominant Chord is characterized by the possession of the 6 th and 4 th Steps. Smooth progression and correct melodic direction are the most essential rules of Part- writing. Wide skips in the Soprano part are objectionable if either tone is sensitive (Leading-tone, or Fifth of the Chord), except in Repetitions. In Triads, the Position of the Third is usually the best. 78. Combination of the Subdominant and Dominant Triads. Having in the foregoing examples illustrated the combination of the Tonic Triad with the Dominant and Subdominant Triads respectively, it now remains to consider the combination of these latter (non-Tonic) Chords with each other. This involves a new phase of Chord-progression, because the IV and V are not only not related to each other by a Harmonic Degree , but are not even related by coincidence of tones ('. . they possess no tone in common) . Lying in opposite directions from the Tonic, they are two Harmonic Degrees apart, or, when placed nearer together, one step. Thus: IV IV V 79. All Chord-progressions of this kind, where there is no common tone, are recognized by their neighboring Roots (i. e. lying side by side in the Scale), and will be distinguished in this Method as "Foreign Progressions". See Appendix B. 80. Foreign Chord-progressions are more difficult than any others, because of their lack of a common tone as natural connecting link. Hence , greater care must be taken to avoid disco nnectedneM, forbidden parallels, etc. In a word, the rules must be applied with more rigor than usual: ft. Wide skips are almost entirely prohibited, in every part ,- and b. All three upper parts should mote in contrary direction to the Bass. 8, 8 * 1) This may be admissible , because skips in a Middle part are not so noticeable as in Soprano, but it i very exceptional *2) Doubled Leading -tone. *3) Allowable, because the Fifth of the first Triad U omitted. * 4) This measure is wrong, because the ear will not follow the Tenor in its skip from > down to g (which belongs properlv to the Bass), but associates the c with the following i/ of the Alto, so that parallel 5 thi are distinctly hearu. This peculiar and comparatively rare error, which aminds like successive -T ths: without their actually appearing in the same pair of voices, is called "Ear Fifths ' '. They are worst in Foreign Progressions, 36 Combination of the Subdominant and Dominant Triad*. 81. ft. Tht reversed combination, V IV, is extremely unnatural, and therefore barely potsiblt ; becauM the Leading-tone in the V is BO suggestive of the Tonic and the Tonic harmony, that the IV (in which the Tonic is but the Fiftk] sounds disappointing and disagreeable, especially when the Leading-tone is in the Soprano ; when it is in a middle part the progression is less noticeable, although hardly less objectionable and peculiar. b. All Chords are attracted by the Tonic Class, which they must ultimately reach; and that Chord which naturally lies nearest to the Tonic (the V compare 220) is attracted so strongly that it can progress nowhere else, legitimately. Hence the canon of harmonic movement The Chords of the Dominant Class progress legitimately into the Tonic Class; not into the Subdominant. Nos. 4 and 5 of the following Example exhibit a peculiar connection in which this irregular pro- gression can be utilized. Its application and explanation must however be deferred for a time. i^l m ^ ? s=e ^F j ^ j F IV 1 1) The direct succession of "Leading-tone" and "Fifth" (the most sensitive Chord-interval) in the prom- nent Soprano, is what makes this example worse than the following ones, where it appears in a middle part. Exercise eight. In the first Bass the Positions are purposely omitted. It may be worked out at the blackboard, with the Teacher. a. Falsst. &.,,*' ... f^=f=g= -__] n j-i=* -35 d. 3 -8 5 - 3 -fc-zt-F i- - g -^ 1 1 ^ ^ ^ ?T- 5=QE L^- ^P =1 1 ^ &U4 -^ ^ttz^=S^=t= Lw_J e. D-maior t*^t~^>" -3 3 6 F^M^ 8 [T > r P| J tEE / /r r / /r ft 5 -' s rr f r r^ p *1) The 'Toreign Progressions" are indicated by brackets throughout this Bass. The Melody is found according to 80 a. b. 2) The irregular progression V IV. *3) Value f The Principal Triads in the Minor Mode. 37 Fundamental principles. In Ff,reign Progressions the Roots of the Chords occupy neighboring steps of the Scale. In such progressions no wide skips are allowed, and the upper parts move contrary to the Bass. Dominant Chords progress, legitimately, only into Tonic Chords. The Principal Triads in the Minor Mode. 82* The origin of the Natural scale was shown in Ex. 24. The three principal Triads are drawn from this scale, and prove to be all major Triads (see note to Ex. 32) , lor which reason the scale is called "Major". The so-called "Minor" scale is a modification of this "Natural", or Major scale, and may therefore be called an "Artificial" scale. It is constructed simply as follows* A, The principal Triads of the Major scale are transformed into minor Triads , by contracting their Thirds (Ex. 21, and Ex. 3t) , fe. The Minor Scale, reversing the natural process, is then drawn from thete Chordt. Thus: Prin. Triads, Major. Prin. Triads, Minor. Minor "Scale" of C. ix.69. IV C* This process defines the Signature of the Minor scales. In this instance, C-minor, it is three flats. That Major Key from which the Signature is borrowed (the Minor scales having no independent Signatures) is called the "Relative" or "Parallel" Major, (in this case J?r?-Major) ; but it has nothing to do with the above derivation from C-Major, which may be called, in contradistinction, the Original Major, or the "Opposite Mode" (See 26S.) 83. It is very noticeable that the above Minor scale sounds more satisfactory in the descending than in the ascending direction. This is owing to the fact that the last interval in the ascending scale must be a half- step ; in other words, that the Leading-tone, in order to acquire and retain its superior and characteristic melodic force, must lie as close as possible to the Tonic note. Its upward inclination depends upon its proximity to the Tonic (comp. 12 c), and, if the interval were to be widened to a whole step, as in Ex. tiy, it would be robbed to a great degree of its peculiar melodic influence and function in the scale 84. Therefore this minor scale, being only an "artificial" scale in any case, submits readily to an ulterior modification by which the Leading-tone maintains its half- step proximity to the Tonic, and the Dominant Triad remains a major Chord, as in Major. Thus: minor, minor, major! True scale. (Harmonic.) 70. 213637 3S The Principal Triads in the Minor Mode. 85. That the descending scale in Ex. 69 (with b{? instead of bj) sounds well, and that both scales in may be made to sound better (as Scales), onlv proves that this "artificial" scale is subject to still Ex. 7L Ex.70 > proves tnat this "arunciai" scale is suojeci to still other modifications But these other changes are only necessary where the independent melodic progression of the individual voices is concerned, and will be considered in the proper place. The function of the 7** step of the scale, a Leading-tone, is a vital factor in Harmony, and must be respected. Hence the scale in Ex. 7u is called the 'Harmonic" Minor scale, and is the same both in ascending and descending direction. 86. As the 6 th step in Minor lies a half-step nearer to the Dominant than it does in Major, iU melodic tendency downward is intensified so that it equals that of the 7 th step upward. la consideration of this fact it may be called (in Minor) the "Dominant Leading-tone". The 7 th step may be termed, in distinction, the "Tonic Leading-tone", or simply "Leading-tone" M heretofore. 87. a. The Dominant Leading-tone mttst progress downward, and it is better not to double it b. It is strictly forbidden to progress from one Leading-tone to the other, in any part. gt* 7 tt ytt gtt Not only because each of the tones would progress in the wrong direction, but because the succession involves a very unnatural chromatic interval (an augm. 2 nd ) which it is impossible to sing exactly true, and which sounds abnormal and incoherent. This error is best avoided by careful attention to 87 a; or Rule IV, a and b. This succession may be produced on an Instrument, it is true, but it always sounds unnatural, and is only appropriate in certain cases, where a weird dramatic effect is desired. 88. The Chord-Progressions in Minor are of precisely the same quality as in Major (56, 61, 72, 74, 78, 81) and are executed in precisely the same manner, and according to the same rules. (8 7 a. merely emphasizes a former rule.) 89. In effect, the Minor mode is more sympathetic and agreeable to the sense than the Major; its greater number of half-steps make it a more graceful and melodious scale. The beauties and advantages of Minor will only be appreciated by the scholar after he has acquired a thorough comprehension of Major, in which scale the natural and regular workings of harmonic bodies can be studied with greater profit. Exercise nine. Tbe Signatures show that the following Basses are in Minor. The accidentals below certain bass tones refer to the Third of the Chord (in Bass No. 1, f$, the Leading-tone; comp. Ex. 70) and are rendered necessary by the absence of the corresponding accidental in the Signature. See Remark to Exercise eight. Falsrt. 6. -8 ,. } The SuborditMte Triads. e. r **> - r ' p f r 1 d. L_L K J '1 1 II --I : ( -s*=- 5 5 e. 8 8 i 3 3 4 fi 5 + 8 S ^^J_4_ * * g ' PS-minor. ? 2 / v 1 iv- - F / IV if 7- f-l-f- -^-F-^.H-/ I 8, *4 1) 87 a. 2) 80 b. *8) Rhythm ? f, of course. 4) The bracket , , indicates that both Chords belong to one beat. The tie signifies here, ai elsewhere, that the Chord is to be held, not reiterated; the Rhythm of this measure is therefore J_JJ J or J. /J_ *5) The Bast *nd Soprano of this second example are to be written out (and played) in erery other Minor Key. Fundamental principles. The Minor Mode is derived from the Major Key of the same Tonic. The Harmonic Minor Scale differs from the Major at the 3 rd and 6 th Steps, which an major in Major and minor in Minor. The Dominant Chord is alike in both Modes. The 6 th Step in Minor must progress downwards. The two Leading-tones (6 th and 7 th Steps) must not succeed each other in the gam* part. There is no essential difference in the treatment of the Major and Minor Harmonies. The Subordinate Triads in the Major Mode (see Ex. 32). These three Triads should not be regarded as entirely new and independent Harmonies, but merely as new formt of the Principal Triads. Aside from the relation which they bear to each other and to their Tonic (as implied in 48 a, and illustrated in Ex. 72 a) there also exists an intimate and significant relationship between the separate Subordinate and Principal Triads. Each Subordinate Triad alone is accessory to one particular Principal Triad, in the connection com- monly known as "Relative" major and minor. Namely : the accessory of the I is the VI (repre- senting respectively C-major and^-minor); the accessory of the IV is the II (representing .F-major and Z)-minor), and that of the V is the III (G'-major and JS-minor). 91. An exact analysis and exposition of this harmonic relationship is neither necessary nor possible at this moment. It will develop itself naturally in the course of the succeeding lessons. The following example U a sufficient illustration for the present* 40 The Subordinate Triads. 93. a. (Ex. 14J r/ 7/7 6, Relative* HI e. 3 Rrlafitie.1 [=/f % %" i I P * TV I % Relatives / PJ .related IF n P 277 ^ o ^Z~^ 6 Principal. Subordinate. *1) The "Relatives" occupy corresponding places in the two species of Chords (Prin. and Subord.). 2) The "Relatives" represent Parallel Major and Minor scales, t. . . with the same Signature. See 82 e. 92. To iff own Principal Triad (called the Parallel or Relative Triad) each Subordinate Triad i* closely related, usually acting as substitute for it and deducing most of its harmonic regulations from those of its Relative. Hence they are to be regarded as joint represen- tatives of the same harmonic Class or Element; i. e. the I and the VI together represent the Tonic Element or Class of Chords, the IV and II the Snbdominant Element or Class, and the V and III the Dominant Element or Class. In other words : the VI is ft Tonic Chord, the n a Subdominant, and the in a Dominant Chord. See 51 1 The harmonic intimacy is strongest between the Subdom. Chords IV and II* 1 ); weakest between the Domi- nant Chords V and III ; and medium between the Tonic Chords I and VL *1) Probably because the II, being the first of the Subord. Triads, and lying nearest to the Prin. Triads In the order of Harm. Degrees (Ex. 72 a) is most closely allied to the latter in Quality. This _ also account* for the inferior degree of relationship between the V and the remote HL See also 220. / The Changing-dominant Triad, IL 94. ft. This is in reality the fundamental representative of the Subdominant or Second Claw, aj will be seen later on. Comp. 70. b. The best Position (Soprano note) is that of the Third. C. The Octave Position of a Subordinate Triad is more objectionable than in a Principal one, because undue pro- minence is given to a subordinate step of the scale , in placing it thus in both outer parts at once. Still , th Octave Pos. of the II is not forbidden, because it is the best of the Subord. Triads. d. The Position of the Fifth is very objectionable in this Triad. 95. Either the Third or Root may be doubled. No Interval can be omitted. Review 43, 44 a. 96. Being a Subdominant Chord, the n contains the 4 th and 6 th steps of the scale See 70. Great care must be taken to lead them downwards, especially in Soprano. 97. The following Examples illustrate the Proyrctsion* of the II , in the order of natural preference. The Examples, hereafter, will be condensed as much as possible. The scholar is again referred to 58. ft, The Normal Progression, n V (61b). J j J M - ^ *' **- Ex. 73. II-V. r j j 3^S better * m js The Changiny-dominunt Triad, II. 41 No. 3 is not wrong, despite the wide skip in Soprano to the Leading-tone (75 a) ; chiefly because it U a skip downward, and the Melody in turning back partly equalizes the distance. The skip ujitrnr-l to the Leading- tone is always wrung excepting in Repetitions !). No. ;"> illustrates a case which is very common in Harmonic and Melodic progressions, namely, the "Deferred" (or intercepted) Resolution.* 1 } The 4 th step in Sopr. reaches the 3* a tndirn-tly, after one conremmit tone has been interposed. No. 4 is doubtful because the correct progression is evaded altogether. No. 9 is a curious exception to several rules, which will be elucidated later. For the present, the suggestive lines in Sopr. and Alto will suffice. That this same melodic violation of Rule IV b (and yti) was not allowed in Ex. 67 - 9, 10, is owing to the relation between the Chords there, Foreign Prog., and here a Normal one. * 1) The term "Resolution" is applied to every obligatory or desirable progression which fulfils the obli- gations of a Dependent tone. See 166. b. To the Tonic Triad : a Foreign Progression (80) . Ex.74 n-L Ex. 75. ,f JgJ,J J.J .J. 1. 96. *) 13 6. n^-r Ife-. .-1 ^ ^g :Lt - -4-*arm-**-*- \ n**-- S*5E V f i a i i y ^ 80 a. ^ f- s 2 f '' 1 J O: ^ S E=3=3E -+S- - =- k=J * w ~~f *~ -^ S g > 7 I-*H r 1 ' r h -r- -i- 1) In every Foreign Progression excepting IV V (Ex. 67, where both are Prin. Triads) H suffices to lead two upper parts contrary to the Bass; the other one moves in 3 rd * parallel with the latter. *2) Comp. Ex. 622, 3. - To the remaining Prin. Triad, the IV. This progression of the II, into itt own Relative Prin. Triad, is not good. When the two repre- sentatives ol the same Class (Ex. 72 c) are connected, the Subordinate Triad should follow, not precede, its own Principal Triad. In other words: of the two Parallel Chords, the Principal Triad comes first. Thus, the IV can progress to the n, but the II cannot progress to the IV. And the same applies to the other Classes; I VI is correct, but VI I is wrong; V III is allowed, III V ii incorrect. o * y y \ i 1 1 h 1 T ~jr 5 i * i 2 - i*""* ft J 11 1 i i f f ^ ^ ( J ^ J i r ! 1 _*. *-^\ ^ ~f f -t -t- f- , f - -t\ , L r_ II IV re exception to 54 c. - VI I III V 98. The Introduction of the II ia exhibited in the following Examples ; arranged, as before, in the ord of preference. ft. By its Relative Prin. Triad, the IV. , J 51 J 5! ^^T -H -i | j i I 0i I > Ex.76. IV IL IV II 1) Compare Ex. 739. 42 The Changing-dominant Triad, II. This Progression is to be regarded as almost tantamount to a Repetition, because the Chords are Parallel (simply different forms of the same Class). Hence, greater freedom is allowed here, and in all similar cases, than in any other connections, excepting actual Repetitions. This accounts for the wide skip in Soprano in Nos. 4 and 5, and even justifies No. 6, where a wide skip is made from the Chord-Fifth (75 b). It also excuses the Pos. of the Fifth of the n (No. 7) which is barely possible in any other connection (94 d). b. By the Tonic Triad : a Foreign Progression. Ml I ' , !*), I 5! , 6 JBx. 77. i n. e Ex.78, v n. 1) Ex. 74, Note * 1 ). *2) These wide skips are less objectionable than usual, because both tones (/ ) are Principal steps of the Scale. By the remaining Prin. Triad, the V. This Progression (V II) is the counterpart of Ex. 68 (V IV) because the IV and n are Paral- lels, and in each case the V does not progress as it should, to a Tonic Chord (81 b). Nevertheless, the Progression V II, although at variance with one of the vital principles of Harmony, may be more readily effected than the former, on account of the relation of a Harm. Degree which the Triads represent The first measure of the following example shows the most rational connection, similar to Ex. 68 4,5. tJ ^ Mid 1 J W *1) This Soprano is wrong. Only when the V progresses to a Tonic Chord, does it have the effect of a Dominant Chord. In this measure it sounds like the I of oth Chords are Subordinate. In this case the n can not be used as sub- stitute for the IV (92). Ex. 8H, No. 4 is doubtful, notwithstanding the relation of a Harm. Degree. because there are too many weak Chords in direct succession (See 50 f). 46 The Mediant Triad, III. b, The Foreign Prog, of the III into the IV (104 b) is more favorable and common than its Nor- mal Prog, into the VI. C It displays an advantage of the Foreign Prog, which must not be overlooked, namely: the convenient proximity of the Chords (lying side by side in the Scale,, in consequence of which the Bass part makes a smooth progression. Where there is a choice between the upper and lower neighboring Chords, there u always some important consideration to decide the direction. Thus, the II lies as near to the III in the Scale as the IV does E but the progression into the former is out of the quet- /// // /// IV tion, as baa been seen. 108. The 7 th step of the Scale, as Fifth of the IE, is not to be regarded as a genuine Leading-tone. As is shown in Ex. 86, its progression is generally diatonically dowmcardt, invariably so when the IV follows, in which case it lies in the Soprano, and can not progress to the Tonic on account of parallel fifths with the Bass. This eccentric action of the characteristic tone of the Scale u a striking proof of paragraph 103. Exercise eleven. Falsst. ft. 1) To be worked out with the Teacher. *2) 96. 8) Position of the Third. Se 68. *4) Pa* of the Third. 100 b, 8j loti a. 6) Iu6 c. 7, lo b. The Subordinate Triads in Minor. 47 Fundamental principles. The best Position for every Triad is that of the Third ; but especially for the Sub- ordinate Triads. The Octave-Position of the VI is forbidden. In the in the Leading-tone usually progresses diatonically downwards. The Subordinate Triads in the Minor mode. 109. The Intervals of these Triads are determined by the Harmonic Minor scale (Ex. 70), from which they are derived, and are as follows . C- minor. Ex.87. VI II III 1 10. The VI is a major Triad , the II a diminished, and the in an augmented Triad (see 34) . The latter two are Discords, (although only three-tone Chords) , because they contain respectively a diminished and an augmented Fifth (30 a). Therefore their consideration must be deferred until the next Division. 111. The VI is treated, in Minor, the same as in Major; excepting in its connections with the II and ffl, Ex. 79, 83, and 86) which are regulated by the rules of Discords. Review 87 a, b. Exercise twelve. "-*- -R7&J-3 i ** f- 1 f~? | t-f r r ^ Faisst. ^4j 4-^ 1 jj IJJl=ib * f f ^ :-^-E 3 58* * y n ^V^ ')3 -f 1 ^ ! -1 1 * 5 a 5 . 35 i i Ps-^ B B i\ i 853 -35 o * ?5^** ^* ' ~m~f r ? F ^ p n. P - - - Jt X rf S ' 1 f ^ p 1 F-t 5- b r i ^ r j* M-?- -^ X X A X roA 1,1 * 8 i i 1 . 1 ' r^ -3 S X "^X \~l~i 1 -* * IgSElE -f-*-t -^J-fnJ ^^3-^ -*-~r * i *1! Exercise 7, note *1). 48 The Period. The Period. 112. The next larger form of musical composition, after the Phrase, is the Period. This ii the conjunction of two Phrases of similar length and character. Each Phrase has its own Cadence, and the two Phrases represent the relation of Question and Answer (Thesis and Antithesis). The first Phrase, called the "Antecedent", has a Cadence which is rhyth- mically as strong as the Perfect Cadence, but harmonically and melodically incomplete, so that the continuation of the musical thought into a second Phrase is rendered possible and necessary. Imperfect rhythmic interruptions of this kind are called Semicadences, and can be made in a great variety of ways. The second Phrase, called the "Subsequent", constituting the end of the Period, has the Perfect Cadence. Compare 63. 113. A Semicadence coincides rhythmically with the Perfect Cadence, in falling upon an accented beat of the 2 nd , 4 th , or 8 th measure, but differs from it harmonically. As a rule, any combi- nation of firm Chord* (only excepting the Perfect Cadence itself, and the unstable III will con- stitute a Semicadence. But the most common and appropriate Chord for the Semicadence it the V ; preceded by the I or any other suitable Chord (IV, PI, VI). A "Cadence" embrace* at least two Chords, and often more; but the seccnd (or last) one, that which occupies the accented beat, is called the "Cadence-Chord". 1 14. The Subsequent Phrase begins upon the same beat of the meaaire as the Antecedent, and the two Cadences fall upon corresponding accents. The following Example is the outline of a Period of 8 measures, in '/ 4 time, with the Domi- nant Semicadence: Ex . 88. | Antecedent phr. 4 measure\ \ ^Subsequent phr. 4 measure*. , g , -fl-HI ^ F ^* &*- \ \ .4--I I-U-I ,> 1 ft' p | I 1 J \ r "I J I J 5" ^ 1 1 ==^ ==- -f | -t-rr~ - 4 f -*3V 1 ^L*. . (V VI III IV I VI V) Semi- (I y rj r Z VI HI IV VI) ^P** cadence^ tadoice^ 1) This Semicadence, I V, is harmonically the reverse of the Perfect Cadence V I) and therefor* constitutes the most consistent Antithesis to the latter that can be found. This is also the case in Bass a of Exercise 12, and in most of the Periods that follow. The V may, however, be preceded by any other gond Chord (113 . A Semicadence upon the IV is heavy, and therefore seldom used; its Relative, the U, although a Subordinate Chord, is better. The I can be employed as Semicadence -Chord, but not in Octave -Position Comp. 68. Exercise 12, Bass r . It is not very good, however, as it furnishes too little contrast with the Perf. Cadence. Its Relative, the VI, is somewhat better. The III, as already intimated, is too weak for such a prominent and important place. The Scholar can easily substitute these different forms of the Semicadence for the one given in Ex. 88 , and judge of their comparative effect and appro- priateness. 2) Here the unnatural Chord-Progression V IV (Ex. 6S) in turned to account at a point where the narrow relation of Chord to Chord is overbalanced by the broad relation of Phrase to Phrase. The Triad* pertain here to their separate Phrases more directly than to rack other, and their lack of connection rather aids than interferes witn the Form, in heightening the effect of the interruption where the Phrases are separated. Ex. 58 is a similar illustration of the relation between "Chord-Progression" and formal "Strnc- .ure". The Period. 49 8) This longer note is necessary for the Cadence- Chord , which, in order to interr*.*pi the Rhythm, must embrace two or three beats, according to circumstances (see H'2 a). The length of tht Cadence-Chord depends upon the -,ccent it occupies, and whether the Antecedent Phrase began upon the accented or un- accented bet (Comp. the last Chords of Ex. 54 a, b, and c). The longer it is, the heavier or itronger tb Cadence. Exercise thirteen. Complete Ex. 88, in A^- Major. And point out the erroneous Chord-Progression* in tht following incorrect Bass- The Form? Also the erroneous Positions and melodic progressions in the following- fee Also the general errors in the following. The Time? Cadences? Form? Chords? Positions ? Duplications T Consecutivest The Teacher is recommended to work out the second of these given Basses (in which the hnrmonit progressions are correct) with the Scholar, at the blackboard of course, after the errors in Position have been pointed out by the pupil. Fundamental principles. The Subordinate Triads in Minor are derived from the Harmonic minor scale. The Semicadence marks the end of the Anteeedent Phrase: (in other words, of any Phrase which is not complete in itself). Any firm Chords, with a rhythmic interruption, will constitute a Semicadence. The best Semicadence-Chord is the V. The Inversions of the Triads. 115. "Inverting" a Chord means, simply, placing some other Interval than the Root in the lowermost part. Thus the Triads, which have three Intervals, may appear in three different shapes, as re- gards the condition of the Bass, namely : 50 The Inversions of the Triads. l gt , as original Triad or fundamental Chord, with the Root in Bass; 2 nd , as First InYersion, with the Third in Bass ; and 3 rd , as Second Inversion, with the Fifth in Bass. Fundamental Chord; I** Inversion; Inversion. Ex, 89. / -U- gy a J - * Third. \ ZT= Fifth. H J S3 Root. 2) 1) Spoken: "Tonic triad. 1 st Inversion"; of more conveniently "One-one". 2) Spoken : ''Tonic triad, '2 nd Inversion"; or more conveniently "One-two". 116. a. The word "Inversion" applies, then, to the lowermost part (Bass), just as the term "Position" applies to the uppermost (Soprano); excepting that the Inversions are numbered 'first" and "second", instead of taking the distinctive title "of the Third" and "Fifth", as in the Position*. t=t. r b. It is obvious that merely changing the Chord-Interval in Bass can no more change the funda- mental Harmony than the same procedure in Soprano (45). Hence, the Chords in Ex. 89 are all designated "The I", because their Root is in each case C, the l il Step of the Scale, though at one time there is e, at another , and finally g in Bass. In other words, the Inversions are merely new forms of the fundamental Chords. Still, the alteration in Bass affects the quality and charmo- ter of the Chord to a still higher degree than the change of Position in Soprano, as the Bass it essentially a harmonic part. 117. In order to distinguish the Bass notes as Third or Fifth of the Chord, from the Bass note as Root, certain figures are attached below them, which indicate the interval or intervals from the Bass note to the attendant upper tones, and define the shape and general denomination of the Chord. Thus : Triad. Chord of the Sixth.**) Chord of the Six-four. 9 *) El. 90. n 3 t*~V -\ r i \ 0\ fr* ^ &> 5 6 f r W' (Third 35 1 V' -( Fifth) or j 6 4 (3) 6 4 e 4 J U 1 The figures intervals 5 and 3 are always understood, unless contradicted by B and 4 respectively: therefore they are usually omitted. The figure interval b signifies duplication, and is usually understood in Triads. 2 go called in analogy to the figuring in Bass, 6. *s Agreeing with the Bass figuring ^. Ex. The Chords of the Sixth. 51 Exercise fourteen. Attach the names (in Roman numerals) to the following Chords, M indicated in the first measure. (When there are no Figures, the Bass note ia a Root. When marked 6, the Bass note is a Third, the Chord is a I 6t Inversion, and the Root, and name, is found a 3 rd below. When marked 4, the Chord it a 2 nd Inv., and the Root, and name, is found a 5 th below. See 35.) Ufa- Major. / IV, F/i 1 , b 3 3 , f2 . s & & &&. 6 6 4 B -Major. 6 06 4 4 6 66 4 1 & a a 6 6 4 * 6 e 4 66 66 4 4 666 6 4 4 6 4 6 And indicate the following Chords in figured Bass notes, as above: Z>-Major I 2 HI IV, V 2 II, VI It VI, III 2 IV II, V t VI 2 III, IV, II; and the same Chords, in reversed order, in Grj?- Major. Section 2 nd . The Chords of the Sixth. C- Major. R l\ t J, J/t III, 1) These Chords will be limited principally to the Major mode, at present, for reasons intimated in 110. Only those Examples in which neither the II nor the III, or their Inversions occur, can be applied to the Minor mode also. 118. The first Inversions appear most naturally and most frequently as substitutes for their respective fundamental Triads. The Third being a lighter Interval than the Root (49 b), it follows that the 1 st Inversions are lighter and more flexible than Triads. Therefore they are best adapted for smooth and graceful harmonic successions, in moderately animated tempi. The Principal Chords of the Sixth. 119. The chords of the Sixth are classified, like the Triads, as Principal and Subordinate Chords. The Prin. Chords of the 6 th are, naturally, the first Inversion of the three Prin. Triads. 120. a. The hest Position for every Chord of the 6 th is that of the Octave (i. e. Root in Soprano, see 120 d), hecause the Root, when taken from the Bass, should be given to the next hest part (Soprano), in order that the quality of the Bass tone as Third (in- stead of Hoot, as the ear is always apt to assume) may be unmistakably defined, and the Chord be distinctly recognizable. 52 The Principal Chords of the Sixth. b. In the Principal Chords of the 6 tk , however, the Root, being a Prin. tone of the caU, can lie in a middle part without endangering the identity of the Chord, in which caat the Soprano may take the Fifth. C. The Position of the Third should be avoided, because it doubles an inferior Chord-interval, in the outer partt. ' ' I '. I 121. a. As a rule if w 6e* to double the Principal tones of the Scale. b. But in Chords of the Sixth almost any tone (excepting the Leading-tone) may be doubled in order to obtain smooth voice-progression. It is least desirable to double the Bass notes (t. e. the Third) in Principal Chords of the 6 tk . C, No Chord-inter cal is ever omitted, in any Inversion. 122. a. The inverting of Triad is attended by the following advantages: It facilitates the combination! of the Chords to such a degree that almost any of the foregoing forbidden Progressions become possible, when either or both Chords are inverted; b. As seen in 121 b, it simplifies the rules of duplication; C. It simplifies the rules of melodic progression so that successive Positions of the 5 th or 8 th are allowed when one (especially the second 1 Chord, or be Soprano are less objectionable than in Triads; when one (especially the second 1 Chord^ or both Chords are Inversions; and wide skips to the 5 th in lei u. It conduces to the melodic smoothness and beauty of the Bass part, which has precisely the same melodic choice of Root, Third or Fifth as the Soprano has. Compare the Basses in the following Exercises with those of the preceding ones. 123. The following tables exhibit the Progressions of the three Prin. Chords of the 6 th into Triads, in the order of preference. The Pupil is again referred to 58. El. 93 I.. The Principal Chords of the Sixth. Ex.94. Ex.95, iv,. WJ i ' ' ' 0) i ~f 6 / 6 yi 6 n 6 HI 6 TV 777 1) Major and Minor (Comp. Ex. 91, *!)). *2) 122c. Appendix A, b. *S) 59 d. *4) Major only. 5) See Ex. 78 and compare 122 a. *6) Rule IV a (46). 124. The Introduction of these chords is effected according to the same principles as their Pro- gressions , and can be found and studied by simply referring each measure of the above Examples (i.e. playing the second Chord before the first). But particular attention is called to the following exceptional cases : Ex.96. Ex.183 4.1 3 |1) ,* ^*), \\ 2 v 1 3 t ~ ! \ ^=| ^n" Good. 4- 4 ~$ V' L/ A! m r rl 1 _P Ex.93 9. -0- ^Ti * *~ '*! i 1 1 r Ex.93 10. GW. 1 I -- -*- T Ex.95 4. Ex.94 6. 1, /T\ ^^F ' 1 *) > -*- , f -*~ * f - r -> * - -* f | - - 77 6 A UU i i 6 6 VI 7, 1 ( 77 |7F /Ft 1 rt ' v *1) These measures show under what circumstances the Position of the 3 rd of the Ii may be not only admissible, but necessary. As already stated, the 4* h step should progress diatonically downward when- ever it is possible (particularly in Soprano). *2) See Ex.75, and compare 122 a. *3; Ex. 73 3, note. *4) See Ex. 68, and compare 122 a. 125. From the foregoing Examples it is apparent that Chords of the 6 th prefer to progress and to enter smoothly, i. e. with as few wide skips as possible hi the Bass part. Compare the first 2 or 3 measures with the last onei, in Exg. 93, 94, 95. Exercise fifteen. A. Hawses. The pupil is again reminded that the figures beloic the Bass part are always reckoned upward from the given Bass note, irrespective of the quality or denomination of the Chord; whereas the figures above the Bass refer to the Position, and are reckoned from the Root. 12()d. See directions given at Exercises 6 and 8. N. B. Complete the Soprano of each Bass, before filling out the Middle parts. Define the " form" of each Bass (Phrase or Period). The Principal Chords of t/ie Sixtn. Ifr-Minor. ? /-F,-/ -F-F/-/I -fF-/-7F.-/F -F -F/-/F-/I- -/F-/-JI- -F-/-/F,- *) 1) 120m. -- 2) 80b *3) RuleIVb{46), tad 120 b. *4) 122 e. 5) Exercise 9, note &}. - 6) ValueT B. Transpose (at the Piano, at sight) the following two fragments (separately) into every other Major Key: * s-rri-r^ @ i /, r ft / / A r h i Observe closely the Positions and Chord-progressions, and the transposition will be an easy talk. Fundamental principles. The best Position for a Chord of the 6 th is that of the Octave. The Pos. of the Fifth is admitted in a Principal Chord of the 6 tfc . Any Interval may be doubled, excepting the Leading-tone. No Interval is ever omitted in an Inversion. Inverting a Chord facilitates its combination with other Chords , and simplifies its treat- ment in very many respects. The Subordinate Chords of the Sixth. The only good Sub. Ch. of the th is the II 4 . The VI, and III, are extremely rare. 126. These Chords are limited almost exclusively to the use of the Octave Position; becaui* their Roots, being Subord. tones, must, in order to be recognizable as Roots, lie in a prom- inent part 120. The Subordinate Chorda oj the Sixth. 55 127. The exceptions are: ft The II,, which may take the Pot. of the Third (best when the three upper parts lie close together), i b. The HIi, which, when followed by the IV, may (like the III itself) take the Pot. of the Fifth. 106* These exceptions are rare, and not obligatory I Ex. 97. 3 1^ hih p4- *T-n J 8 | 1 /r-r -J - $3 * r * r- ! w- i[ [ 1 i t - i\ -r-r- i 2 a _ p n i h. 1 i r T 6 ~ ' TT T 6 ' rr. 6 u 1) Admissible i compare 108. C. In Repetitions, of course, any Position can be taken: 47. 128. The Progressions of the three Sub. Chords of the 6 th to Triads, are u followg: Ex.98. Hi. 5: t^ 1 i=t ma. 107a. J/ 6 F 8 Ex.99. VI,. Ex. 100, m.. ^ 60f. 730,. ^ n * m * iv * I Ex.97 4. 730. J J. 107a. & Ji^JT 104. ^ nil i III 8 6 IV 6 129* The Introductions will be found, as before (124), by playing each of the above reversed order. The following exceptional cases deserve special attention: 56 The Subordinate Chords of the Sixth. Ex.78. ,,o J J I . - JJ-! , JJ. ! ^ a_ i 1- ^_ -- P=^ ^ ^ Ex.98 2. f | JL JL r~v. m Ex.98 . . j ri ( -^-*-- ts'^S -8 * 8 > u O . r +8 r^ "^ sT^~~ *~ "Fr~ S^5 -< * J-^- -- mi -4~4r- --& j ^j j - i j * i r -i i r i ij -0 * j r J 00 6 | 6 '6 # 6 # #6 M) -. . - o J?b-Major. [H^ /-5-/-F|-y-r t J/-/JQ-//-F/1-F/-F/I . r/-Fi-Z-/F,-F-/// ; - F/-//1-F-7 *) 1 126. *2i This line denotes that the Soprano note U to be held. *3) 127b. ) 46, Rule IV, b. *5) Also write out this Bass (alone) in any six other Major Keys. Fundamental principles. Subordinate Chords of the 6 th must take the Octave Position. The movements of Triads are regulated chiefly by ''Chord-relation" Thj movements of Chords of the 6 th , by the proximity of the Bass notes. Consecutive Chords of the Sixth. 57 Consecutive Chords of the Sixth. 131. The Progression of a Chord of the 6 th into another Chord of the 6 th (instead of into A Triad as in the foregoing lesson 123, 128,) is one of the most graceful, natural, and common Chord-combinations, and can be effected with the greatest ease, especially when the Bass moves smoothly, as explained in 130. Here the advantage of Inversion is again exhibited in a very striking degree; for when, as in successive Chords of the 6 th , both Chords are Inversions, wider skips are admissible in Bass, and the Chords an connected without regard to their relations (see 122 a). For instance: the TVi'ad-Progressions V IV in n are entirely wrong; but as Chords of the b th (Vi IVi IIIi IIj) the racceMion u unquestionably correct. Thua : 0- -0- -0- good. -9: ^ 0To =r- & & ' may precede * 6 6 56 66 ) S ) ) 56 6 6 6 6 A. 3 r/fc?rli: 1) 137. SJ 139 a. 8) 132 a, and c. *4) Rule IV b (46). *5) 139 b. 6) Ex. 107, note 1). 7) The line denotes that the Soprano note is to be held. *8 This Bus illustrates the diversity of Rhythm explained in 140. *9, 106 a, and c. The Six-Jour Chords. 61 Fundamental principles. In successive Chords of the 6 th the Soprano usually runs in 6 tki with the Bass ; and one part must move contrary to the others. The couplet 65 or 56 must be placed in some single part, generally Soprano; and the first tone must not be doubled. Rapid diatonic tones run on in the same direction. It is desirable to diversify the rhythm of the parts. A tone should not extend into or beyond a stronger beat than where it began Section 3 rd . The Six-four Chords. (Ex. 90). 141. These Inversions stand upon the Fifth of the fundamental Triad, as shown in 115. The quality of this Chord-interval, as defined in 49 c, has been repeatedly tested in the foregoing Example* (paragraph 59 b, 75 b, etc.), and its quality and harmonic characteristics are most apparent, and exert the greatest influence upon the Harmony, when it lies in the Bass part, as supporter of its Chord. 142. Consequently, a. Six-four Chords are not employed independently, but must be placed in certain connec- tions with other and stronger Chords, as accessories of the latter, as Embellishments, or as Intermediate ("Passing") Chords; b. They can not occur in direct succession, because of the successive Fifths in Bass (com- pare 59 b ; and C. They can neither enter nor progress with a skip (in the Bass part, of course) d. For this reason, also, they are not classified, like Triads and Chords of the 6 th , at "Principal" and "Sub- ordinate" Chords. The only distinction that can or need be made is as follow! El. 108 C- Major. 7 2 777 2 7F, Fj F7 2 1) See Ex. 91, note *1). *2) The 12 , when accented (as is commonly the case), is Semi-independent. The rest are all depen- dent, and seldom occupy accented beats. The weakest 6 / 4 chord is the 2. 143. a. The Soprano-Position of a 6 /4 Chord does not enter into consideration, being always regulated by the Chord with which it chances to be connected. The Soprano usually has either the interval 6 or 4 (Third or Root of the Chord) very rarely the Bass note. b. The Bass note is always doubled, (as just intimated, not in Soprano but in a Middle part). In this Section particular care must be taken not to confound the terms "Bass note" and "Hoof I 62 The Combinations of Six-four Chords. The Combinations of Six-four Chords. First Connection. 144. In general, the Six- four Chords can appear in three different connections with other Chords. Firstly: a */4 Chord may enter from or progress to the Triad upon the same Bass notei i ^ g^H^I 1 V K ~_ J"' " tr '==' The following Example illustrates the Ij in this connection. The pupil is again referred to 58. =M Ex. 109. ^ f> B 5 3 3435 6 5 5 4343 rt 4 3 E i r *1) Major and Minor. *2) The figures 3 denote the Triad, and are necessary on account of the figures * As is seen in measures 1 and '2 the Soprano almost always takes either the melodic line 505 or 343 (but compare the last three measures), and the Bass tone is doubled in one of the middle parts. When this connec- tion is prolonged, as in measures 4 and 5, the Soprano may change from one row of tones to the other, to avoid monotony; this change is usually made after 3, not after 4'; wherever the 6 th it, the 5 h will fol- low (as in Ex. 1U3J, and similarly, the 4th j g followed by the 3 rd . 145. This connection of the ^ Chords is not allowed in the following rhythm . I * g ^ because it occasions a Rhythmical Halt to repeat a Bass tone from an unaccented to an accented beat, whether the Chord changes or not. This rule supplements the rule given in 66, which see. 146. a. Not all of the six Chords can appear in this connection. The following table shows that, besides the Ij (Ex. 109), only the IV 2 , 112 and VIj can be combined with the Triads of their respective Bass notes. With the V 2 and III 2 it is impossible. The II|. ThelVt. The VI* Them,. Ei. 110 a. *1 The V] can not be used in this connection on account of the false melodic progressions involved (46, Rule IVa, b.). *2, With these Accidentals the " Chord is not a V 2 , but the I> of tf-major or minor. *S) Here it u a IV* in Z>-minor. *4 There is no legitimate Triad upon the Bass note of the HI] (37). The Combinations of Six-four Chords. 63 b. The connection of a J Chord with the Cftorrf o/" f/* jrp ^-*fq ^^ = ?] ;r r \ =f= p n =^i=fl d < -r \ i^r rixr 1 43 0505 4 4 I 5 # 5 4 * = B^K 34 -?-, ol n _ 4 t +3 ^ ^r 1 ^ r s tone (associating Connections 2 nd and 1 t ). I 66 The Combinations of Six-four Chord* Thus: In this group the V Chord almost always occupies an accented beat (or, at least, the accented fraction of the beat), and represents the same kind of inter- cepted Chord as in Ex. 114. Thus: ; r A \ I i A ! f nj r i f r r r '65 43 JM. It is more usual to retain the same Soprano note in the 4 Chord as in Nos. 1 and 2) than to exchange yokes (as in No. 3 , as it indicates the connection in which the Chord enters. 153* There is here an apparent violation of the rhythmical rule enunciated in < 6, because the ^ Chord upon the Accent is a repetition of the preceding, ui accented, Chord. This exception is accounted for on the ground that Six-four Chords are so vague a form of their fundamental Triads, that they do not represent and suggest the latter, but seem, especially when accented, to indicate the Triad of their Bass tone. 164. a. Therefore a Chord may always be repeated over the accent without producing a Rhyth- mical Halt, if it becomes the second Inversion. b. Hence it is, also, that a ^ Chord, when occupying an accented beat, evinces a decided pre- ference for the progression into the Triad upon the same Bass tone, no matter in which connection it was introduced. When a !/ Chord is unaccented, it matters but little in what connection it enters and progresses. e. This progression is only obligatory with the Tonic % Chord (I,), which, when accented. must progress into the V: But it is not obliged to make the progression at once, sometimes quite a number of Chords the other connections (same Root or neighboring Bass tone) intervene. Thus /t r. i t r. it v. it v. i t r. Ex.116. -/r The Plaaal Cadence. 67 3 +3 Exercise nineteen. **) &**) r^VMP X 2-c- "^ ' ___ l r**~i * 1 1 r ' i! t5l i- * ;j- - p ^ .!L:g: '^ f ~^r~- -Vi- _ ^=Ui=^t=r: : 5 05 5 6 05 565 *) 05 05 65 05 65 65 43 43 43 43 343 ' 43 43 43 43 43 e. y- 4 n =3 < , = r=r- J J 1 ^ 6 5 6 6 6 * 6 +- 6 -* in -4- = 8 L) 6 5 6 6 43 4 4 34 4 43 4 3 * -3 +3 -j ( 4 l n E3P =i +5 *) Fa [8 St. 8 X( 4^ 6 4 65 43 6 50 i 05 43 r i_* *_ . _! * 4 6 05 4 43 * 6 50 4 34 4 *) -f -H -3 5 ^3 r"< ^ r** -8 / ?r r* i + rr^ri 3 -3 5-? 8 **) "* f r i* ^ * -^ i 65 65 -i 65 * 6 ^ 6 8 f! 5658 ir f i ! Eg 65 65 3 ^^ 65 05 6 65 6 43 4 343- 43 43 43 43 *1) Note to Ex. 115. *2) Plagal Cadence ; gee 155. *8) The irregular rhythm in the first tiro measured of this Bass, caused by the longer note ( f ) upon the weaker 2 nd beat, is made good, partly by the continuation of the rhythm in the upper parts, and partly by the repetition in the following measure, which corroborates the figure and equalizes the measures. Hence the general principle: " Itepttittons and Sequences justify most Licences." But the repetition must, of course, be symmetrical; i. e. it must occur at corresponding parts of the measures. Thus. Good: Irregular. Good : Irregular. a i n E 1 i -^ i i n f- 1 0444- | 4 *- \-0-f * i \ \-*4-0-i4 kJ-J *-* 4) 120 a. ) 1:<7. 6) Exercise 18, note *4). *7) The Soprano note is held. *8) Play the Bast and Soprano of this first Phrase , at sight, in every otter Major Key. Each Bass when completed, is to b analysed as in the preceding Exercise. The Plagal Cadence. 155. The Plagal Cadence is a short succession of Chords (generally not moie than two in number) affixed to the Perfect Cadence , to make the relaxation of motion more gradual. To prevent the effect of the Perf. Cad. from being counteracted by this continuation of the rhythm , it is necessary to retain the Tonic note in Soprano (or both Soprano and Bass) during the plagal ending. Therefore the latter must consist of such Chords as contain the Tonic, i. e. the IV or VI. The most common of these is the IV, which, by its natural breadth, deepens the impression of repose, and confirms and strengthens the Perfect Cadence. Like every other Cadence, it must close upon an Accent, and for this reason it can only appear in Com/o/ind Time (3b), the Perfect Cadence falling on the Primary, and the Plagal Cadence upon the Secondary accent (3 c) . 68 Six -four Chord* as Passing -chord*. Ex. 117. f\ 1 "l 1 *" i A I ^~i V ' i 1 t I l v f J sp S3 Q3 * m zj d fa\ / AV-YY * ^v <*v 2 i 4 k - r a I 1 ! eel. PlagaL \ J 1 1 \ 'i r ! r vr ! J 1 r , ! *-*- f V 1 J 1 r { \ TT Goo J J r 5' ( v 3 ^=- _^ ^_ ^* T~~? I 2 " ^~T -^5 4-^ * ^* IF lifrrlr 565 143 -j J ^ P H / 6 6 4 I 65 6 4tf 4 ISE 6 ft * 4 3. 4 * -*-*- 666 6 4 4 15 56 65 4 4* J-J tf >*t +3 f - 1 ^ 3 ' bfc^J 6 65 L ^v p *>) H 66 4 6 6 65 6 * 6 65 e 6 4 65 56 6 565 343 1) 4) = ^ 65 6-65 56 43 43 6 6 4 666 4 6 6 65 43 *) c\\ )- b 3 \ i S F -& .^ J J . I ^ a /*> ' 6 6 4 656 4 8 b 4=f^ 6 5 4 8 6 5 6^5 4 3 r J * f 6 6 ' 64 35 46 53 1 a ' ^ r ^^ ^ ^ >-. j 1 r f- | j J .. r*3 *'^- ^ =H t 6 4 1 $*~ 666 4 56 34 fr U 6*6 4 U- 6 4 J * II The Tonic Six-four Chord at Cadences. 71 1) See 157 a, b. 2) See 159 a, b. - 3 137. *4) See 158 a, b, 5) Here the weaker notes (J) occupy the first half of the measure, instead of the unaccented second beat, on account of the Plagal Cadence, which must end with a heavier note (155). *6) Exercise 18, note *4,. The Basses are to be lysed, as before. 160. Before concluding this Division, attention is directed to the importance of the Tome \ Chord at the Semi- cadence and Perfect Cadence, where it is very commonly used in connection with the V (compare 154 c), partly in order to embellish, and partly to lighten the Cadences. Thus: O. Semi-cadence. 6. Per/. Cadence. J . J. J- J .. *. K. K J Ki. .. . I , _4 i * * + Kx. 122. E 1 4 tr 4 r r ^ 1) Compare with Ex. 88, bar 4. Further Examples will be found in the two preceding Exercises. Exercise twenty-one. Transpose at the Piano, at sight) the first of the following Examples into every other Major Key ; and the second, in the same manner, into every other Minor and Major Key. i Closely observe the Positions and the Bass figum. Division B, Discords. 161. A Discord is a harmonic body which contains one or more dissonant Intervals. Review 25 b, c. 162. The simplest Dissonance is the interval of a Seventh, which arises naturally from adding one higher 3 rd to the Intervals of the Triad. See 29 a, 30 a. The result is a four-tone Chord, named Chord of the Seventh, after the Dissonance which it contains (see 32). 163* The Chords of the 7 th are the fundamental four- tone Chorda, corresponding to (and derived in ft certain sense from) the Triads, or fundamental three-tone Chords. But they can not be classified 72 Discords, and their Classification. in the same way as the latter, on account of the peculiar obligations connected with their Disso- nance, in fulfilling which, their original independence AS fundamental Concords is to a certain de- gree sacrificed. 164* A Dissonance has, as the term indicates, a harsh sound which the ear will only accept on condi- tion that it be reasonably brief, and that it be justified by the intervals which precede and (especi- ally) follow it. By itself, a Dissonance is meaningless and unsatisfactory, and urgently demands a progression which will fulfil its tendencies and obligations. This impression of Incompleteness and Expectation characterizes the dissonant Intervals, and imparts an activity to them which is of great advantage in animating the Harmony. The Classification of the Discords. 165. a. The Discords are divided into Grades or Classes, representing their proportionate degrees of importance, and consequent frequency. These Classes are determined by the distance of their Roots from the Tonic, in ascending Harmonic Degrees (perfect fifths). 7** class. &* class, f* class. El. 123. 4 th cltut. f(T\ 1 / ? \ ) X-* "^ Ch. dom. Disc. - Submed. Disc. Med. Disc. ^7* tj ** nnm. Ducordt. \ / Tonic. b. This table shows that thev* we only four fundamental Chords of the Seventh, or, in other words, Discord Classes. The Discords which stand upon the other three* steps of the Scale (4 th , !*, 7 th ) are derived from these, in a manner which will be seen later on. e. The Tonic-Class is not numbered the "First", because it is exclusively composed of Con- cords. No Tonic Chord can become a Discord, without losing its chief Tonic characteristic, Repose, and becoming a member of one of the four Discord Classes ! d. Hence, the Dominant Chords constitute the First Class, because they rest upon the first per- fect fifth above the Tonic note. And, similarly; the 2* d Class have the 2 nd perf. fifth above the Tonic, as fundamental tone, and to on. e* The Third and Fourth Discord Classes are so rare that they hardly enter into consideration ii Harmony. They are exclusively dissonant. f. Therefore it is apparent that the Tonic Class, (exclusively consonant) and the l ft and 2* 4 Classes (both consonant and dissonant) represent together virtually the three Elements of the whole System of Harmony. See 51 and 220. The Resolution of a Dissonance. 73 The Resolution of a Dissonance. 166* The Progression which satisfies the requirements of a Dissonance (164) is called its Resolution) and the Chord which follows a Discord and affords such satisfaction is the Resolving Chord. 167. a. Every Dissonance in Music is resolved diatonically, in the majority of cases down- ward: Ex. 124 a. The progression with a skip is very irregular, and can only be justified in Repetitions : Ex. 124 b. b. The Dissonance of a Seventh cannot progress upward: Ex. 124 c. e. The interval of a 7 th should not progress into an Octave Ex. 1 24 d d. No dissonant Interval should ever be doubled : (50 d). a. mm. fa.124. J i r-Aj-, J J 1 jj J 1 I I 1 1 V i^ ""* ^ 2 !]ES .&) (7^^ ie?^z) E2CBZ\ Xr. { & i* w vO & n^ t s> f- jS^ lt.fi* ^ ^ n^"^r/ J '7 3 r '7 '5 r 1 ', '. 1 " IT 4 168. Dissonances very often prove to be a modification of some consonant Interval, and the manner or direc- tion of their Resolution depends chiefly upon the nature of the modification. Augmented intervals have an upward tendency, diminished ones progress downward. The Seventh of a Chord must he regarded M a depression or contraction of the Octave, and therefore it is always resolved downward. The 2 nd , M in- version of the 7 th , derives its progression from the latter. Dim. & tk . Augm. 6 th . Dim. 8 7 Dim. 5'*. Augm. 5**. Dim. 7 tt . 1 7 ' r ^C f ^ T^ r Section l rt . The First Class of Discords (Ex. 123). A. The Chord of the Seventh upon the Dominant i-G > & " ^t~ ETC ^t 5^ J^J u ^& VL' C^ C^"^ 1 Cr* */ 7 7/i minor. ^j* ^ ' *s 7 '3'8\ i) Spoken : 'Dominant-seventh", or "Five-seven"'. 2) Ex. 90, note *1 , *3) 170 h. 1 74 The V and its Resolution. 169. The Chord of the Dominant-seventh is obtained by adding another (higher) 3 r * to the Interval! of the Dom.- Triad (162). The new Interval, the Seventh, is the Dissonance, requiring resolu- tion 164). The Chord of the Seventh is employed in place of the simple Triad V, whose natural tendency towards the Tonic is strengthened by the addition of a Dissonance. The construction and treatment of the Chord is the same in Minor as in Major, with the usual exceptions (Ex. 71). 170. a. There is no choice of Position, . e. the Soprano is optional (55). The Seventh may lie in any part. b. The Fifth may be omitted, and the Root doubled. c. The Seventh progresses diatonically downward, and is not to be doubled (167d). 171. a. The resolution of the V into the I (or Inversions) will be called Normal, because it corresponds to the Normal Progression (61 b). b. The resolution into the TI (the Parallel of the I) will be called Deceptive (see note to Ex. 84). e. Both the Normal and Deceptive Resolutions are Regular, because both lead into Tonic Chords (81 b). Normal Resolution. Deceptive Resolution. J j|J.Ji i jij^iii , i J -Jif t V4n J i * ^i I J I * m J H I , I . ^ W \-H H- ^11 * J : Ex. 125. 7 ^ fr ' ' b 1) Separate measure, as usual. Alike in Major and Minor. *2 See 167 e. This error may be termed "Unequal Octaves ", and is quite as disagreeable as actual parallel Octaves. The simplest way to avoid them is nut to double the Resolving '-fane of the Seventh, excepting when the two tones enter in opposite directions, as at *8), which is admissible. The error is most palpable in measure 7. *4 The parallel -> thf in the middle parts are also "Unequal , because the first one is diminished and the second one perfect. For this reason they are not altogether wrong, as the rule only applies strictly to successive perfect o* h . The admis- sibility of such doubtful progressions depends almost always upon the second interval, and when, as in th above case, th^second 5 th a e) is perfect, the consecutives had better be avoided by leading the Tenor from 6 to e, as in measure 9. The Introduction of the V. 172. Dissonances must not only be resolved, but some consideration must also be taken of the man- ner in which they enter. 173. The most natural and regular modes of introducing a Seventh are: a. Diatonically from above (i. e. the Seventh is preceded by the next higher tone), and b. by Preparation (*. e. preceded by the same tone, as Interval of some other Chord). c. On the contrary, the Introduction diatonically from below, or d. with a Skip must be regarded as a licence, the admissibility of which depends princi- pally upon the quality and grade of the Chord. In all Chords of the First Class thet* irregularities are allowable. For illustration : The Introduf tion of the V 75 o. Diatonically from above. b Prepared. From &/ou?. El. 12A. d. With Skipt. ^ j^. i . fl V ^ |5 7 8767 m 1) In Major and Minor. *2 See Ex. 125 5. *3) The skip to the Seventh from above to much more objectionable than from below, because the part must continue in the same direction (contrary to Ex. 9), in order to resolve the Seventh 174. From this it may be deduced that it is only proper to skip to an Active tone which requires resolution, in the direction opposite to its tendency. For example: the skip may be made in any part upward to any Seventh, to the Dominant Leading-tone (6 th Step in Minor), and to all Diminished tones, because these resolve downward; and the skip may be made downward to the Leading-tone, and to all Augmented tones, because they resolve upward. Thus: ttej: See Ex. 73, note to measure 3. Exercise twenty-two. JL Write out the V of every major and minor Key, with its two Resolutions, on one stave, as follows: -maj. O-min. B. Transpose (at the Piano at sight) the following fragment, into every major and minor Key: 1 l-fi J -H 1 i 1 \- i- E* ^ & ' (v) r ' O gy P=P r (= !x P ^ I V VI V I Closeb observe the Chord-Progresrions (Bass) and the Positions (Soprano), and the transposition wffl b easy. 1C* 76 The Introduction of the C. Basses. (From here on, the 3 upper parts must be made together, M H is not practicable to define the Soprano alone, as heretofore, on account of the Dissonance). . +3 ) +8 8**)3 +7 )*) 4. * 87 66 4 +8 p^j-lj f . 1 I r ^ f j-^ 3i *^ 'a ' ^ ^ " J ^ ^ * - ,_ 67 al 65 85 43 t 87 65 76 5 *4 tf 65 43 6 ' ^B tf 4 3 3 '-)$ f f l ~~i~ -^f^^H-j 1 ^j i H j ^>- 1 m 4^ /. i 57 -3+3 8-3 0007 4 "i 1 ; ir~ 8) 7 05 1 43 7 3 J'Tjj ,T- J J * * * * 07 87 H C 43 7 Falsst. -n 07 8 7 7 56 66 657 4 3 667 01 4 3 1 705 7 * 348 ff' +3 G-Maior. % ~/~ -/i-/r F-/-/I- -f/r/jrF.F- -F/-/I-//J- -y-/-_F- -;i~/F /irFi-fc -/FC'~/F- -V-/.-F- ** " ii n ^~ ~ ~ ' ~ ~ ~ - ~ ~~~ ~ ; ~ ~~ t) 1) 157 a, b. 2) 170 b. *3) 160. *4) Ex. 128 d *.*) Ezerciae 18, note 4). *6^ Ex. 120. 7) The upper parts may all be held. See also Exercise 19, note *3). *8j Ex. 107, note *1). *9) Exercise 9, note *"> . After working out these Basses, they are to be thoroughly analysed, with special reference to the manner in which the Dissonance is introduced (173), and the mode of its Resolution (171). Fundamental principles. Discords are divided into Glasses, agreeing with the distance of their Roots in Har- monic Degrees above the Tonic. Tonic Chords are exclusively consonant. The Seventh of a Chord is resolved diatonically downward, and is not doubled. The Fifth may be omitted, in Chords of the 7 th . Unequal octaves are wrong Unequal 5 tbs are wrong when the second one is perfect The Introduction of a 7 th is regular when it enters diatonically from above, or if prepared. - All rational Licences are admissible in First-Class Chords. The Inversions of the Dominani-Seventh-Chord. 77 The Inversions of the Dominant-Seventh-Chord. 175. All chords are inverted in the same manner, i. e. by substituting some other Chord- Interval for the Root, in Bass (115). A chord of the 7 tk (4-tone chord) has, obviously, three Inversions, as follows: l t Inversion, \ _ u ^_ f with th Third in Bass; rion, 1 , , ( wit > as before < sion, I I wit 2 nd Inversion, J " I with the Fifth in Bass; Ex. 127. 3 rd Inversion, with the Seventh in Bass; The Inversions are figured and named exactly according to 117. Thus Chord Chord Chord of the Seventh. of the Six-five. of the Four-three. ^9) Chord of the Second. ^T) ^ ^* '*' * J (gj g 1 4 4*) 3 3 ? *1) As usual, those figures which are understood, are generally omitted. *2) The pair of adjacent notes^ which invariably appear in the Inversions of 4-tone Chords, always represent the Interval* 8 and 7, that is, Root and Seventh; thus In other words, the upper of these two tones is the Root, and consequently defines the Chord. There- fore the names of the three Inversions merely indicate the intervals from the Bass note to this pair of tones. cies, the Leading-tone, which has an Accidental. ones. 5*3, and 2. *3) Spoken: "Five-seven-one": first the Name or Root of the Chord, then its Spe- 'ies, and lastly the number of its Inversion. *4) In Minor, fuller figuring is necessary, on a: count of 176. The Inversions are lighter and more flexible than the fundamental Chord, and occur frequently as modified forms or substitutes for the latter. The 1 st Inversion is perhaps the most com- mon (118). The 2nd Inversion is weak, like the 4 Chorda, but not in the same degree. The 3 rd Inversion is the most dependent, but is very unique and effective, because of the prominence which the Dissonance assumes in the Bass part. Therefore it is a very useful Chord. 177. The Inversions are treated, in general, just like the Chord of the Seventh. The excep- tions are- a. No Interval should be omitted (121 c); b. The Inversions are limited almost entirely to the Normal Resolution (into the I and Ij). The Deceptive Resolution (into the VI) is attended with difficulties naturally incident to these weaker Chord-forms. c. The Introductions, on the contrary, agree exactly with those of the fundamental Chord. Review 1 73. Hereafter the Examples will, wherever practicable, embrace both the Introduction and Retrlution of the Chords. 78 The Insertions of the Dominant-Setenth-Chord. Ex.12*. noj Ex.129. Soi-mal Resolution. Q 1?3a - I J im. , j 'f "ft ,7jj / J 1 *<-r-' i- J 1 , ^tt * > * J ! i v i O-+TJ ^T~ ^**t***m =?=**= {ft rie3 -f *^J -f f I f 1 1 1 rrf J ! 1 J 1 Li ^ ii 1 J ! 1 J rj ^ r r PS ^ . 2 1 * F i ? f - .* 5 ,* * r 1 -f P E 7 r*W 1 100- / i_ft 35 **> ^ .S: I I f=f 1 1 Deceptive Res. rr U4 itt: j3 3bJ FaFJ, 34 3- 20 o 2 a 2 6- a (J - 1) - ig equivalent to ~ , the interval 6 being usually doubled. *2) 4 - = 4 - , the interval 4 5 DO ^ 4 T being doubled. *3 See Ex. 125, note *4). These Unequal 5 h * are good. *4) Either the I or I } can follow the V.). The I is best, as it obviates doubling the resolving-tone e. *5) The upward progression of the 6^ h Scale-step in Soprano is justifiable here. *6) It is obvious that no other Chord than the Ii can follow the Vj on account of the resolution of the 7 th in Bass. *7) The Unequal 5 ths in Bass and Alto are doubtful, but not altogether wrong. *8 A ;t Chord is treated in general the same as the 4 Chords, but somewhat less strictly. The skip in Bass is not absolutely wrong. Compare 1-12 c. *9) These Chords are too weak to occur in direct succession. A 4 Chord can never be employed in the independent capacity nf a direct "Retolu- tion". 142 a; 1 77 b. *10 In Minor as well as Major, excepting where the 6 th step moves upward. Further illustrations of the V and Inversions : Beethoven. j j. P---*?; JJ m Beethoven. 1_ f, F, F /F, 7, 7F It F, 7 Fj F t 7 77, 7, F 7 178. ft. The rule of the Rhythmical Halt (145) is subject to one other and final exception, as followi. An unaccented Bats note may be prolonged over the bar or Accent, on condition that it becomes a Dissonance at the following accent (or full beat) ; for this change in the quality of the tone ii sufficiently striking to compensate for its inactivity. Thus: The Inversions of the Dominant-Seventh- Chord. 79 /fc=^ (ffl p -& f-H -ft: ^ : V \ 1 -1 J 4- j _P ij y^ FE= ^ ht^i IF 2 b. In summarizing the rules of Rhythm as applied to Chord-progressions, it appears then, that* A Chord may be repeated over the bar or Accent when it becomes a 2 nd Inversion (154 a ; and A Bass tone may be repeated over the bar or Accent when it becomes a Dissonance. Exercise twenty-three. A. Write out the Vi of F, G, B^ D, E^ A, E, A\>, D^ B, Gfr Majors- the P^> of Eh , ?>b, f> c t> /(ft c, b, 87 4S |9; !' " 8 4 1 -3 ! ' B ' r J , * r n b^?-tt ' ' * " 05 4 6 43 S r M "^1 1 i | T * 20 6 7 S S -*-^ 207 ' ' i-j i i *- 6 -f- 4 -^ H 4 ^E 3 ' ;- i-'.r>- -f f-f - f f r r- ^ ^ r -J H -^ ^^ # * f 664 3 J * ^ 65 ! i ^ rf . T^ 040 6 354 -* i i f- 65 4 3 ' ' r j 60 87 5 ^ " 1) The Positions are reckoned from the Root! 120d. *2) 106 a, *3) Ex. 128, note *1 note 1). *5 Ex. 128, note *2j. 4) Ex. 107 Fundamental principles. Inversions are lighter and more flexible, but weaker than fundamental Chorda. In an Inversion, no Interval is to be omitted. The Deceptive Resolution of the inverted V is objectionable. A Bass tone may be prolonged over the bar or Accent, if it becomes a Dissonance. Irregular Resolutions of the Dominants-Chords. 179. The majority of licences in the treatment of dependent Chords and Intervals appear at Repetition^ where, as has been repeatedly shown., all rules are nullified. See 47. 180. The licences which attend such Repetitions are of two general classes, namely : a. The Resolution of the active tone or Chord is Deferred by the interposition of other forms of the game Chord, "modified Repetition"), or by the casual intervention of a foreign Chord, ("Digression" or "indirect Resolution"). b. The obligations of the active tone are Transferred) in some rational way, to another part, in the same or in a different Register. Irregular Resolutions of the Dominant 7 th Chords. 81 181. a. Hence, when the Chord remains the same, any convenient Interval or Intervals may b* interposed between the Seventh and its Resolving-tone. (Deferred Resolution). b. When the Chord is repeated, it may change its form, its Position, and the disposition of ita Intervals to any reasonable extent; whereby the Seventh is likely to be transferred from one part to another, without any other restriction than this: being a tone with downward tendency, it is most apt, even when the Chord remains the same, to progress to a lower tone. C. In all of these Deferred Resolutions the Seventh is ultimately resolved, in the part where it last appeared. a. Deferred resolution. , , , . & Transferred Distonanc*. EX.ISL 78 =T^ =F 3 tQt 4 - J T 1 ^ = ''TT^ 1 7 3 143 2 V Ft 5 1) Major and Minor. *2) The 7 th moves upward, in apparent contradiction of 167 b; but in reality the g is only an interposed Interval of the same Chord, and does not interfere with the ultimate reso- lution into e. *3 Here another form (Inversion) of the Chord intervenes, before the Resolution takes place. *4) The " th is transferred from the Alto to the Soprano, and is resolved in the latter part, the one which assumes its obligations. Ibl c. *5) The 7 h in Soprano, though transferred to the Bass and resolved there, should progress downward to d or b, and not upward. See 181 b. The following measure u less exceptional, because the 7 th in Tenor it taken up by the Bass in the tame register. The Passive Resolution. 182. The "Digression" or "Indirect Resolution" (180 a) consists in interposing a foreign Chord before the proper Resolution takes place, and is therefore more unusual and dangerous than the above "Deferred" Resolution. The foreign Chord must be reasonably 6ri*f, and must be in some vmy connected with the Discord whose progression it interrupts. 183. a. The foreign Chords which intervene between the V and its regular resolving Chorda are the two Subdominant or Second Class Chords IV and II, in both of which the Seventh of the Dominant occurs as consonant Chord-interval (Root and Third respective- ly), ihus constituting a connecting link. For example: If II 82 The Passive Resolution. b. This Chord-progression may be termed a "Passive Resolution" because the 7 tt , in becoming a consonant Interval, is actually resolved ; not by its own act, however, but patsively, through the other parts. Reference to Ex. 123 shows that this progression is the transition from the Domi- nant or 1 st Class into the 2 nd Class, and therefore exactly the reverse of the natural progression into the Tonic Class. It corresponds to the irregularity in Ex. 68 and Ex. 78, but is more justi- fiable, because of the connecting-link which the Seventh affords. 184. The consonant condition thus gained by the 7 th does not compensate for the actual regular Reso- lution. Hence: a. The Passive Resolution is usually only a Digression from the Discord and directly back to it (perhaps in a new form): in other words, the foreign Chord is interposed between 7 7 77 the Discord and its Recurrence. Thus: V (IV or II) V: or V (IV or II) V t or V,. Compare Ex. 68, measures 4, 5. b. Much more rarely, it is interposed between the Discord and its resolving Chords. Thus: V JV or H) I or VI. Compare Ex. 114, note *2). e. Rule L The Seventh must remain stationary, i. e. in the sfme part d. Rule II. The Seventh should not be doubled or otherwise disturbed, during its transient consonant condition. Passive Resolution. Ex. 132. J=J^J Ineorrtci. ^ J-^ Exception*!. Rule L Si HE jJ; JZu/ J/. tf 1) 184 a. *2) 184 b. *3) The "*> must remain in the same part, irAn Me Harmony ehnnyttt Compare 181 b. *4) The/ in Alto is wrong, because it doubles the passive Seventh. *5 These meas- ures, in which the passive "^ changes parts, are exceptional, but admissible, because the tone remains is the same regiaUr. Other Irregular Resolutions. 83 185. Besides the above Licences there are two other irregularities which are peculiar to the Chord of the Dominant-seventh : a. The 7 th may be resolved diatonically upward, when the Bass part moves parallel vnth it, in 3 rds ; and b. The Seventh may be doubled, when one of them progresses to another Chord-interval, before the other is resolved. Thus: a. Ascending Resolution. **) Doubled Seventh. - . 6 r- i 7-5 /t 3 7 - 1) Major and Minor. *2) This licence is limited to the Chores Vj I ( ; in no other case would the Bass move with the ascending 7 th , in parallel 3 rils . It is not to be confounded with the first measure of Ex. 131, where the 7 th progresses upwards but returns to its resolving-tone. In the above Example tht Resolution does not take place in the same part, but is transferred to the Bass. *3) These 5 thi an allowed. See Appendix E, d f. Exercise twenty-four. A. Basses. (To be analysed, after being worked out, with special reference to the above Licences). .. +75* 1 ) 3 3 5 & :=* -5 35 75 6 2 - 66- 87 4 ) 56 '*) * 8 ) 34 ,87 57 6- 9~ 5 ft 6 4 7 6 5 C. *) +3 '* m 3 f 4~ m - 66 65 6- 43 5 57 #- 87 672 6 40 Cr ^7ftjk n | * g J~ ~ j j ft _ |^r ] 5 T p g M^-oJL p [* J j Ji j f ! 5 8 ft 6 6 - 6 ft 7 * 32 445 *2) 4tf 8 ' 8 * ) ) 8 7 n f~\ ^ ^] p r r * i i 1 ^n 6 6 ft ft 6 8 514 4 4 3 5*5 6 -B 7 56 32 3 5 % L 34 5 007040 54 0*057 3 54 3 32 48 FalsuU +7 L :i | i ^fc^^ s 6 66546 382 54 6- 4- 34 232 4- 8 - * 7 $ * 6*6 84 84 Irregular Resolution*. ft * rr^f . 3 1= t~ ?,,f F 1 II * * tf 2 44365 3 4* * -5 * f ) ^7 +ip 7 e ft 4 4 ft .. f f TTJ *~* < g 466-65 S 4 56 4 3 f ' 'If 46404 aa i a s ".r^Fs ~~*~ J ig it 1 6 7 4 6 +*- 4 r^56 8 34 i u g; * 75 ^r- 6 2 6-4^ SEE 3- 7- 34 3 - 1) Ex. 131 b. *2) Ex. 107, note *1). *3) As usual, die rows of figure* indicate the Bourse of tk parts. M) 184 e, d. *5) Ex. 133 b. 8) Ex. 120. *7) Ex. 133 . B. Play the following Chord-progressions slowly, at the Piano, in different Major and Minor Keys. At first, with the right hand alone; afterwards with both hands, in ordinary "open* 4-part harmony. I-V-i-I || V.-V-i; || V t -V-VI || V_I 2 -V 3 -V 2 -?|| V-IV.-V-Tll v,- iv 2 - H v- n 2 - v H v- iv t - i 2 -v- v,- Fundamental principles. When a Discord is repeated, it may change its form so that the Dissonance is trans- ferred, or its Resolution Deferred. A Dissonance is always resolved, ultimately, where it last appeared. The Passive Resolution of Dom. Discords is effected by Subdominant Chords. If a Seventh cannot move diatonically downward, when the Harmon o changes, it mutt stay where it is. The Passive Resolution is most commonly interposed between the Discord and its Re- petition (possibly in another form). The Dominant Seventh nay be resolved diatonically upward, when the Bass accom- panies it in parallel 3 rd8 . B. The Incomplete chord of the Dominant-seventh, or, the Triad upon the Leading-tone (37). 186* ft. The Root i* the Interval upon which the identity of a Chord naturally depends; but when the other Chord-Intervals are of such a nature that they define their Chord beyond a reasonable doubt n-ithout the Root, the latter may be omitted without endangering the identity of the Harmony. The Incomplete chord of the Dominant- Seventh. 85 b. This is naturally not often the case in three-tone Chords, but is quite common in those of Jour tones, and almost obligatory in those with five. When applied to the Chord of the Dominant- Seventh the result is as follows. Inversion*. Figuring. Positiont. cry ? | <2 [ If ^ 'I i J 8 n o ^ & \1 "W ^ -" Z7 i5? & y_ nl'\ and is indicated by the 0. The Inversions are not reckoned from the actual Root, but from the apparent Root the Third of the fundamental Chord). *2) The Positions also are reckoned from the lowest tone of the Triad, exactly as in ordinary Chords. 187. a. The Incomplete V is the Triad upon the Leading- tone, with its Inversions. b. Like the V itself, it is alike in form and treatment in Major and Minor. But see Ex. 71 C. It is a Diminished Triad, because its Fifth is diminished (34), and therefore a Discord (161), though but a 3-tone Chord. The diminished 5 th is the Dissonance. 188. The reasons why this Chord must be regarded as a derivative of the V, instead of as an independent Choid with the corresponding designation 'VII), may be demonstrated as follows: l stl y, because it contains the Leading-tone, which is the chief characteristic of the Dominant harmonies, as Bass tone, or apparent harmonic basis (54 a): 2 n <%, because its most natural progression (Resolution) is into the I and VI, in which point it corre- sponds exactly to the V (171). This is naturally owing to the tendency of its Leading-tone, and to the coincidence of its Dissonance (the dun. 5* h ) with the dissonance of the V: 3 rdl y, because the comparison of this Chord with the V discloses a similarity of effect not to be found or expected between different Chords. 189. a. The Dissonance, being no longer an actual 7 tk , is not obliged to resolve diatonically downward, but may especially when approached from below) progress diatonically upward. b. Either the 5 th or 7 th of the original Chord (3 rd or 5 th of the Triad) may be doubled. When the latter (the Dissonance) is doubled, the two tones generally progress in oppo- site directions. C. The best and most frequent form of this, and every other Dim. Triad, is the Chord of the Sixth ( Vj). The Triad itself is rarely used. The j| Chord is better than the Triad, and stronger than other (consonant) Jj Chords. It occurs in the usual three Connec- tions f!44 etc.). 7 d. The Resolutions correspond to those of the V complete, *. t. Normal, into the I (Ij); Deception, into the VI; Passive, into the IV and n. For example* Chord of the 6 th ( Ex. 1046. Ei. 135. 6 / 86 The II in Minor. Ex.131 The Triad ( ^J. The I Chord (Q^). \ ! . . I ^ *1) The Mediant (3'' 1 Step) is very often doubled in connection with these Incomplete Chords, as it con- duces to smooth progression. *2) The Leading-tone may be casually doubled, when each moves dia- ttnically. opposite to the other, as here. *3) The skip from the Dissonance (/) is justifiable, but very irreg- ular. Compare *" . *4; ].*". *5 The Unequal 5th in Bass and Alto are allowable. *6 159b. *7 The skips in Bass from the Dissonance, in this measure and the next, arc irregular and unusual, but excus- able on the ground of 189 a, and the Quality of/ as Subdominant note (7b). *8) The two successive 4 Chords contrary to 142 b) are allowed because one is the !> (Ex. 108) and the other a Discord (189 o). 190 The II in Minor. This IB also a Diminished Triad, and consequently a Discord (See 1 10). It belongs properly to the 2 n * L/.ASS of Chords, as its Root is the Changing-Dominant (Ex. 123), therefore its treatment at this place is premature, but justified by its importance. It resembles the Incomplete V in general character and treatment. In structure it corresponds of course to the Major II : 191. a. This Dim. Triad differs from the Q V in being a fundamental Chord, and not a derivative. There- fore it is used more independently and more frequently than the former. b. Its treatment is very nearly the same as in Major. The Dissonance (dim. 5 th ) is, at the same time, the Dominant Leading- tone (86), and is resolved diatonically downward to the Dominant; consequently, the Resolving Chords will be such as contain the Dominant note, viz. the V, V or I. The Passive Resolution into the IV (which contains the Dissonance as consonant Interval) is effect- ive, as transient progression. e. As before, the best form is the Chord of the 6 th (189c). The Triad itself is very rare. Tht 2 nd Inversion is, as Discord, stronger than ordinary Chords. Chord of the **. The Triad. Ex. 137. Minor). The II in Minor. 87 The 9 Chord. rr r-f ) J. J. J ^ 00 00 /.OOv, 44 4 * 2 4 4 4 STo o *1) Compare Ex. 136, note *8). In .flf c>r, where the Hi is a Concord, this iuccession is palpably inoomeC Majw. 5*1) Exercise twenty-five. 3 +3 * 4 ) ft Tf 8 ,35 00006 65 **) 4 46 43 6 60 0060 00 >7 ) !* *) S -5 ue 50 67 4 05 05 06 PT~ 5 i 3 * TTT rrf~Ti p r P f F~ ~j i 1~ i 1 1 5=| 4 * c -* ^-H- ~f r := ~ ' ' r r i J J J =^= 60 000 05 10000- 4 60 0-00 57 34 Minor. e +8 S m '-^B^ 50 5- 4 Jf- 4 06 ft 8 C 6 57 565 4 4 #- 343 - tt 8 3 1 n ^ R^F*q -J ; j I ^ | /j | J^" 8 ^i ! ; '^ M *ti 1 jjr- 1 w i i ! 1 ^f- , ^, r^ *^f J J 1 t ' * "ii * ^c 05 6 56 * 6 6 6 87 4* 442 #- 0-Oft 00006 ^5 6 57 4 * 1) Ex. 134, note *2). *2) Ex. 120. *8) Ex. 107, note *1). *4) 106 a. *5) Ex. 10S. ) Rhythm J j ^!. *7) The #ass c// J Soprano of this Phnwe are to be tranipoied and played at fight in a number of different Major Keys. 88 The Chord of the Ninth upon the Dominant. Fundamental principles. The Triad on the Leading -tone, in Major and Minor, is an Incomplete V, and is treated accordingly. 7 There are two legitimate Diminished Triads in Harmony: the V Incomplete, and the II in Minor. The best form of a Diminished Triad is \isjirst Inversion. The diminished Fifth is generally resolved diatonically downwards. C. The Chord of the Ninth upon the Dominant. 198. a. This fire-tone Chord (see Ex. 29) is obtained by adding another higher third to the Intervals of the V. b. The new Interval is a Ninth from the Root , and its most important characteristics are : firstly, that, being related most directly to the Seventh (upon which the last third is erected) it must always be at least 9 tones (a 7 1 ' and a 3 rd ) from the Root, and therefore can never be contracted to a 2f*. Thus- 7- , and, 2 nd1 *, that it cannot appear without the Seventh. Consequently, c. the Fifth must be omitted in 4 -part Harmony; not the Seventh, nor the Third. No Inter- val can be doubled. 193. This is the first Dominant Chord which differs in Major and Minor. In the former mode it has a Major Ninth, in the latter a Minor Ninth. Hence, a distinction is made in its treat- ment in the two modes, as follows- a. In Major, the Ninth should always be placed in the Soprano. b. In Minor, on the contrary, the Ninth may lie in any of the three upper parts; but, afl stated above, never less than a 9 th from the Hoot ') I 9r i 9) tt=3& V Minor. -9 *-t InMqjor (193 a): TZ In Minor (J93b): TT ^J r l) Spoken ; Tive-niM". *2) Always figured % on account of 192 1* 2dij. >) 192^ - '4 1 fintly. V Introduction and Resolution of the V. 89 Introduction and Resolution of the V. 194. a. The Introduction of the Ninth is similar to that of the Seventh, as shown in 173. i strict, when entering diatonically from above, or when prepared; free, when entering from below, or with a skip (from below). Ex. 139. b. The Ninth is resolved exactly like the Seventh, diatonically downward; or, if a Passive Resolution, by remaining , usually in the same part. The two Dissonances, (Seventh and Ninth) are very commonly introduced and resolved together, in the same manner; but not necessarily. e. The Normal Resolution is effected by the I (I 2 ). The Deceptive Resolution is not possible. The Passive Resolution is effected by the rV t or IV 2 ; not by the II. Review 171, 183. Introduction. Strict (comp. Ex. 126 a, b, c) : Kx.139 Ex.140. riKVn i 1 r-r i 1 hi r-J-rt-, i i i n Kail rW- r^- J J S^Tf 1 Jj i i ^ j 1 1 |J-J ! 1 : 1 J ^ : r = * f t \ i i i -f I 10 9 10 9 TV 9 ? r 87 7 _ " 7 1 1 " Fr<: *1) When the 9th i s introduced diatonically from above , the Leading-tone moveg contrary to its natural tendency. It is Chord-repetition. *2 A skip of a seventh is hardly possible in any other connection than in Chord-repetition, as here. 3) Unequal octaves. *4) Comp. Ex. 126, note *3). Resolution. Normal.- Partial: Passive t 3 987 765 343 98 7- ^ f-f\ rT^ f r IV 1) The 9 is resolved alone. 12 90 Introduction and Resolution of the V " 19o. There are a few Licences in the Resolution of the V which are to a certain extent peculiar to flve- tone Chords, as follows : a. The ordinary Deferred Resolution (see 181 a), and the Trantferred Dittonane* (see 181 b). b. The Exchange of Dissonance*. C. When one Dissonance progresses to another, or, in general, when any Active tone prcgresset to another Active tone of similar obligations , it evades its own Resolution , the progression of the last Active tone sufficing for both. This is another example of Transferred obligation. See 180b. , and the resolution of the latter suffices for both. *8) The 9 h is merged in the lowrr Leading-tone and evades its ordinary resolution. The progression upward into the Leading-tone would, however, be very irregular. In all of these cases, excepting the Passive Resolution, the Discord is merely repeated in another form (179). "* ] t-T Exercise twenty-six. i\ i) Falsst. 6. +B 1 1 J P =* 1 J^ --i u 3 i -g P--T i ^Edt^ 1_ 987 765 343 rJ- ji_r__l ( p_ e 98 7 ft 7- -\ *~ 56 B -* f 67 7) 4 a 3 =P=F 08 5: T" C i i \ i^ IT L Oft m a ) -j -j 98 < t * T^ 44^ ^^a 1 J 87 B- rf. |1 W-M 050 36 7 M) ) S3 65 2 8 43 7 58 65 ' 56 43 1 ft *j i rj j , ff P*b 07 75 *^ -*--*- 87 65 43 -*1 ^-h-^ t- 06 75 & 1 57 SEsS 98 6 75 5 6 79 ^5 6 08 W 6 07 7- q- G ffissal 8 6 9 87^ * J^ The Inversions of the Five-nine. 91 1) ) to*ffi-? B- 1) I ^ 9 *- 1 f 1 i* p r N * * t -r-r i J- ("' * 1 S *^S- Ll * 1 ' L_LJ f -L_J. 98 6 5 65 2 6 9 65 78 7 43 34 3 -8 3 +9 -f 5 t 65 97 65 43 75 43 3- f Cd i NJ 86 7 6 * 56 5 4 7 3 4 3 F * 1~' -p ^' i * ?- 8 7 6 4 3 9 \ * t *- <^L *-*--^ ^- 6 2 6 6 898 8 6 65 9 4 7 43 7 *) 65 43 " T ' * : 95 65 7 -* ^ 1 98 87 * 7- 1 *1) 193*. *2) Ex. 103. *3) These unusual groups of figures indicate, as before, the course of the parts. *4) Ex. 120. *5) Ex. 14U, measure 6. *6) Rhythm J J . *7) Work out this first Bagg in A- Minor also, with a different Melody, according to 193b. Fundamental principles. The Ninth, as Chord-interval, must always he at least 9 tones from the Root. The Ninth never appears without its Seventh. In Major, the Ninth of the V must be in Soprano. The Ninth is introduced and resolved exactly like the Seventh. When one Dissonance progresses to another Dissonance, or to another sufficiently Actirt tone, the resolution of the latter suffices for both. The Inversions of the Five -nine. 196. It is obviously impossible to inyert the interval of a 9U> ( because it exceeds an octave (26). But, as the Inversion of a Chord merely affects the Bass part, and does not necessarily involve an inversion of all the intervals , it follows that complete Inversions of the Chord Five-nine may nevertheless be obtained , in the usual manner. But they are peculiar, and difficult to handle, on account of the inconvenient 9-tone interval, which can neither be inverted nor contracted (192b). The following Example exhibits the possible forms: Ex. 142. 1) The 2d Inversion can only be employed in five-part harmony, as the 5tk (the only omissible Interval) lies in the Bass itself. *2) The 4th Inversion, involving an inversion of the nine-tone Interval, U an absurd- ity. *3) The Resolution of these Chords corresponds to that of the V itself. 92 The Incomplete Chord of the Dominant-ninth. D. The Incomplete Chord of the Dominant-ninth, or, the Chord of the Seventh upon the Leading-tone 197. It must not be assumed from the above paragraph that the Chord of the Dominant-ninth is only available in its original, fundamental shape. On the contrary, that is the very form in which it is most rarely found or used, because it is too bulky, and subject to too many restrictions. This is the case with every Chord of the Ninth, hence the rule: A. Five-tone Chords are, as a principle, not to be used in four-part Harmony in their Complete form, but must be made Incomplete (by omitting the Root. See 186 a, b). b. The only exception is the V, which, by virtue of its superiority as First Class Chord, u occasionally used Complete. (Q 198. The Incomplete V is the Chord of the Seventh on the Leading- tone (comp. 187 a) with its Inversions, and differs in Major and Minor, like the V itself (193): Maj. J/i'n. i 9 V 1) Spoken "Five-nine, Incomplete", and figured as usual 1,\, \, and 2. See Ex. 134, notes. The V in the Major Mode. 199. The Chord of the Seventh on the Leading -tone is called, in Major, the "Ambiguous Seventh", because it is more suggestive of the Relative Minor Key than of its own Major Key, and unless carefully handled, with strict regard to the conditions of its Key, it causes a disagreeable conflict of Scales. This ia owing to the fact that, as the Leading-tone cannot be a Root, the ear naturally assumes the lowest tone of this Chord of the Seventh to be some other Step, and consequently in some other Key, namely, the Second Step of the Relative Minor. Thus C-Mtyor: In order to hold this Chord in its Major Key (where it is a Chord of the Ninth), and counteract its tendency towards the Relative Minor (in which it is a Chord of the ScYenth), it must be treated like the original "Ninth", and not like an ordinary "Seventh". The rules are as follows. 200. a. The 7 -tone interval from the Leading- tone to the Ninth represents the original 9-tone interval, thus therefore this interval, in Major, should not be in- El. 143. :- The V in the Major Mode. 93 verted (as Second; compare 192b). In other words, the Dom -Ninth, in Major, must never C-Maj. I A-Min.\ i H lie below the Leading-tone, thus b. The most effectual mode of avoiding this error is, to place the Ninth in the Soprano (193 a). C. The Major Ninth may, it is true, also lie in a middle part : but only when the Leading-tone is in some lower part (according to the above rule), and when the 9 th is introduced ttnctly. d. No Interval can be omitted in these Incomplete Chords, and consequently none can doubled. g The following table illustrates the manner in which the V Incomplete and it Inversions may be erected in Major: Major. 1) These forms are exceptional See 200 c. *2) Ex. 142, note *2). 201. The Dissonances (7 th and 9 th ] are introduced in the same manner as in the Complete V, but perhaps somewhat more strictly: x. 144. Major. Introduction: JLJ. + *1) When the 9 th enters diatonically from above, the Leading-tone is generally doubled. This is entirely correct in this connection, as it enables the interval 7 to enter from the interval 8. Comp. Ex. 126, measure 1, 2. *2) These parallel th8 are particularly objectionable, and apt to occur. They are best avoided by doubling the Third of the I, as seen in the preceding measure. *3) 200 c. 202. The Resolutions, also, coincide with those of the Complete V, i. e. Normal, into the I, I,; Passive, into the IV (VI); Deferred, by other forms of Dominant Discords (195). 94 Th V t Major Mode. El. 145. Ibjor. Resolution. -& 184 b. IV 1) In the Normal Resolution, these parallel 5*1" are of course still more dangerous than in the Intro- duction, because the former is one of the obligatory progressions. See Ex. 14J, note *2). As before, they are generally avoided by doubling the Mediant, as in the next measure. *2) Comp. Ex. 140, measures 4 and 5. ) Comp. 185 *4) Comp. Ex. 136. note *7). Exercise twenty-seven. i i^: 3 ) , 6**)-*) -r-ifn 1 1 .1) M) rni r j : pi S8t 0. 75 +S ' i ~ ! ~~\ 64 6 6 6 4 7 6 66 43 4- 6 32 6 7 6 668 7 6 87 75 -3 +5 irr 1 V - 7 86 000 05 7 5 43 40 3 00 4 57 040 3 77 007 86 5 6 34 3 ^p.y?^ _< I J Tff ^ r I,' j_-j 4 ' -i i 7 6- 34 3- 65 7 43 ' ! ' ^ 07 -~ \j * r 059870- 43 7 43 0- 4 70 54 50 67 *1) 200 b. *2) The Positions are reckoned the same as in ordinary Chords of the 7*k, without regard to the actual (omitted) Root See Ex. 134, notes. *3 Ex. 145, note *1 . *4; This Bass, after being worked out, is to be played at sight, with its Melody, in a number of different Major Keys. *5, 200 c. 6) Rhythm J* . The V in the Minor Mode. 05 The V in the Minor Mode. 203. a. The Chord of the Seventh upon the Leading-tone in Minor is called the "Chord of the Diminished 7 th ", because it contains that peculiar interval (in C-minor, lt\ <&}. C-Minor. Figuring: Ex. 146. ' Q ' L -~ -^=*^ - ^- b. One of its most significant features is, that the contiguous intervals are all of the same riza (at least, on the Pianoforte), namely, three half-slept, as shown in the following Example: Ex. 147. C. Consequently: All the forms (Inversions of the Chord of the Dim. 7 tk must sound exactly alike, as they constitute each time a group of "three times three half-steps". This can best be tested at the Piano; It is impossible to distinguish the separate Chord-Intervals from each other, and there- fore the restriction in regard to the location of the Ninth in Major (200 a, b) is un- necessary, These Chords are the most flexible in the whole Harmonic System, and accommo- date themselves with unusual ease and readiness to other Chords. Hence they are very important and useful Harmonic bodies. d. The difference in the denomination or artnal size of the intervals (according to the letters) is necessary for the identification of the Chord and Key. In the above Example all the adjacent tones constitute minor :i* a -- excepting b frfa, which it an augmented 2 nd , and represents the figure* 8 and 7 M hown in Ex. 1-7, note*2), which see. 204. The rules are, then, as follows: a. The disposition of the Intervals in the four parts is entirely optional. The ninth may lie in ami part, even in Bass. Otherwise the treatment is nearly the same as in Major. b. As in Major, no interval is to be omitted, and none doubled. C, The Introduction of the Ninth diatonically from above is impracticable, on account of the false progression. See Ex. 71. d. In the Normal Resolution, the parallel 5 th8 are not as bad as in Major (Ex. 145, note*l), because one of the 5 th8 is diminished. Still, it is advisable to avoid them, as in Major, by doubling the Third of the resolving-chord I). 96 The V in the Minor Mode. Ex.148. MlDOt. Introduction. 104 C FT f rr -u 3 m ** -j. 4! S ^-- n j ti 5464 34 3 - 3 - JoJ 204 J C6 4 ^ j=t r o ~~ 3 l) These skips to the Leading-tone are good. Bee 174. Ex. 149. Minor. Resolution. ' '/ l sr 3 > r \ 1) I/ /j j=i . 1 1 t^ 6 /, ^^ /r t i*^- * r 3/1 ^Si /r * J_4. n -y-*- *)/! * Chopin. ft- his) *fe *"l IVY J The V in the Minor Mode. 97 1) 204 d. *2) These skips from the Dissonances, in Bass, may be justified on the grounds of 203 c. See also Ex. 136, note *7). 3) The 3i Inversion of the Dim. Seventh is somewhat weaker than the others, on account of the 9 th in Bass, which though admissible, is unfavorable. Especially the Normal Resolution (into another weak Chord, the I2 ; is objectionable. Therefore the following measures are prefer- mble. - *4) Passive Resolution. *5) The irregular progression in Soprano (contrary to Ex. 71) ii correct, because it is merely Chord-repetition! tractive than the latter. Exercise twenty-eight. These Minor Basses are all to be worked out in a number of different ways (i. e. with different Sopranoi* according to 204 a). The given Positions may be used for the first solution, and then muit be ignored altogether. 77 565 66 3 -- - if * 6 ft 6 4354 3 if +5 *V 8 ) -3 * +3 _}' H *> " ~~* i* -y i J~~| j f*~ t~^~i F^T" ft -* 1 -i oil. 454 6**""^ 2 3 Z 43 g _^ -- * eJ -* * * * -j ft 4^7 6 ft 6 6 6*6 53 5545 . r <* 45 . i n^ F =2 6 3 i " ^ J r <* ? CZ 6 4 8 6 5 * 3 - p^-f._....r.*_4- r _ i U_/ ^-^J 1 - J^-ri- M=t 4-t^ f. * . . * *--\ frri.. 6 * 67 if- 67 547 6 5 * 6 6 if 6 3 656 5- if 3Z 434 -3 -8 6 if 4 6 C if 4 r i i I 8-7 3C 3 3 6 & 6 65- 4Jf- -^T^rf5 i i t - -r > u i 3 i^-a- J i | ^ f- -* p-fe- nr~^ :i"|, ^ - r^ [- ' it L^" [ g 4-C" 1 '|P '/fc^ 4 -H- ^ -j-'i-J J 1 J 1 6 4 6 5 6 676 78 7 Z 5 4 . 6 6 C 7 3434#4ifr 3 54 S * -5 * 8 ) -1-3 *7 3 +8 -S 7 < 6 4 a 8 ! " 6 ft 7 4 6 2746 ft 6 53 73 5 it / +3 -*3 -8 -^+5 -8 3 +3 3 ^7 ? if ,6 6 & 5 4 b & 7 05* *4) 6666 6 '4 543 4 45 ; 45 * S 4 6 8 3 6 7 5 1) Exercise 27, note *2). *2) Rhythm J J*. *3 Comp. Ex. 149, meas. 4. *4) Comp. Ex. 88. note *2 . 98 The Discords of the V* Clot*. Fundamental principles. Fire-tone Chords, with the single exception of the Dominant-Ninth, are not tui Complete in 4-part Harmony, but Incomplete (without the Root). The Incomplete V is the Ch. of the 7 th on the Leading-tone. The Incomplete V in Major suggests the Relative Minor Key, and is only possible whea the Ninth lies above the Leading-tone. The Major Dominant-9 th is best in Soprano. The Incomplete V in Minor is the Chord of the Dim. 7 th , consisting of equidistant intervals , and is very useful , attractive and easy to connect. The Chord of the Dim. 7 th and its Inversions all sound exactly alike. The Ninth in Bass is unfavorable. The First Chord- Class, or Dominant Element, embraces the Discords V, V, V and Y, and the Concords V and III (92). Section 2 nd . The Discords of the Second Class. 806. The fundamental tone of this Class is the second perfect 5 th above the Tonic, or, the Second step of the Scale. Review 165. Therefore the 2 nd Class embraces the Chord of the 7 th on the second step, the Chord of the 9 th on the second step, and the Chord of the 7 th on the fourth step, as Incomplete Chord of the 9 th , in Major and Minor. Major. Minor. El. 150. *) ) t* > t/ O >) Spoken: Two-seven"; "Two-seven-one" etc., and figured as usual, 7, 5,3, 1. *2) The U is only available in -4-part Harmony without its Root, as IV (See 197 a); *S) Called Tonr-ceren*' instead of* Two-nine, incomplete" 1 , on account of its relation to the Triad IV. 207. To this Class belong also, as Concords, the fundamental 3-tone Chord n, and its Parallel the IV, which is actually an Incomplete Two-seven ! Compare 92, 93, 94 a ; and see 220. II II 7/oor/F The II and its Inversion*. A. The II and its Inversions. 808. JL These Chords are not quite as common as those of the First class, but they are barely lew important, especially in modern Harmony. They are treated, relatively speaking, almost exactly like the Dominant Chords, only a little more strictly. The principal external distinction is, that the II has a minor Third, while that of the V is major. Moreover, the 2 nd -Class Chords do not contain the Leading-tone (like the First Class), but the 4 tb and 6 th Steps of the Scale (see 96 and 70). b. The Seventh (Dissonance) is resolved diatonirally downward, or remains stationary (Passive Res.\ and is not doubled. In the II itself, as fundamental Chord, the Fifth may be left out; but in the Inversions, no omissions are possible. C, The Normal Resolution is effected, as usual, by the Chords which lie a perfect 5 th below, namely, those of the First Class (Dominant). This fundamental rule must he accepted in its most comprehensive sense. Every 2 nd -Class Chord it normally resolved into any and every l st -Class Chord, Concord or Discord. The same is true of all the Discord Clashes, each of which obtains its Normal Res. by progressing into the preceding Class : the 2 nd into the I- 1 , the 3"* into the 2"^, an( j tne 4th m t the 3" 1 . d. The Passive Resolution, for which this Discord-Class evinces a decided preference, if effected by the Tonic Chords (I or VI), which contain its Dissonance as consonant Interval: EX.15L D g g : (Comp. 183). y % s 77 J 77 P7 e. The Seventh should be introduced strictly, as a rule (173 a, b); rarely with a skip, nevei diatonically from below. h 100 The IV and its Inversions. T T=-T f-f J: p i 7J-! d=J: J-J J/J, *1) Major and Minor. Separate measures, as usual *2 Normal Res. *3j This is the first cae ef different Din-ord* in tuccessmn. The Resolution into the Dominant T* h or 9 th is more favorable for the Key, than into the Triad. *4) Passive Res. *5) After the Pass. Res. it is best to return to the same Chord-Class, as here. Compare 184 a. *6 Ex. 128, note *1). *7) In the Pass. Res. no other part hould run into the Seventh. Here the Soprano is wrong; the preceding measure is right. Comp. Ex. 132, note *4). *8 The 2 nd Inversion is the weakest form, naturally; it is better (stronger in Minor. 9) When the Bass progresses upward into the Leading-tone, the Seventh may skip downward to the Domi- nant, or move parallel with the Bass in 3 rd *, as in the next measure. See 185 a). *10) The Pass. Res. of the Seventh in Bass is very doubtful. *11) The last two measures are exceptional *12) In the // tf- telf the Fifth may be omitted. B. The IV and its Inversions. 209* ft. The assignment of this Chord to the Second Discord-Class, instead of assuming that it is aa independent (say 3 rd ) Class, on account of the Principal tone upon which it stands (the Subdomi- nant , is justified by all of its harmonic movements, by its sound, and by the analogy with the development and arrangement of the First Discord-Class (Compare 188, 197 a). b. The Dissonances (7 th and 9 th ) are treated like those of the Dominant The introduction is perfectly strict. f No Interval can be omitted, and none doubled (200 d). d. The Chord is the same in character in Major and Minor. The Ninth may lie in any part. fa. 152. ' '"i ,1-6- * r ' 1 r-f- 1-4 t 1 | J J^ J^ , -V -*^0 B -^-rf ^ ^ i ^* -+~*-z-j- * s | 1* , * ? t f t m ED f r ^ 0f c k. _ ^ _ f f J \ /t\ 1 \l^ 1 1 1 1 * 1 - f J J J ',' T 1 j.^ ~~j^*~ i i * ^ fi 1 56 5- * 3 '7 r, 2 r, 6202 i 5 The Digression into the next higher Class. 101 1) These parallel 5* hs are even more likely to occur than in the analogous Resolution of the ^ (Ex. 145, note *!)}; they are best avoided by progressing into the Discords V or V. *2i Passive Res. *3 Ex. 144, note *1). - *4) Partial Res. See Ex. 140, meas. 4, 5. *5 The treatment of a 1^ is lew trict, when accompanied by the Ninth. Comp. Ex. 145, meas. 13. 6) The 2nd ^fl 3rd Inversions (Seventh and Ninth in Bass have no Passive Resolution. Comp. Ex. 151, note *10). The Digression into the next higher Class, flO. The Digression or Passive Resolution of the First-Class Discords (explained in 182, 183%, which review) may also be made into the Discordt II and IV, as well as into the Concords U and IV. In this case the progression again represents the reverts of the Normal Resolution (see 183b), being the upward instead of the downward direction: in the mosi literal sense, a "Digression" from the natural order of harmonic succession. Thus : 1t P1-100 -' , ._ instead of: V (V) TYmio. Plaaa _^^__^__ Si A 211* When First-Class Chords ascend in this manner into 2 nd -Class Discords, the rules of the Passive Resolution must be strictly respected,, namely. a. The first Dissonance Dom.-7 th or 9 th ) remains in the same part. Furthermore; b. The progressions of the parts must be smooth; and C. After the Digression, the frsi Chord must return, in the same or in a different form See 184 a; 184 b is not possible in this case. Ex. 153. Ei. 151 111 7 7 A 7777* "<<& * 9- & 97 v ii v v iifyi r ii r J & I / r *v iv *1) Major and Minor. *2) The second Dissonance, in this connection, usually enters from below. contrary to 208 e. 3) See 211 c. Two Pass. Resolutions in succession are not possible. In general, comply with Rule III (46j. Further illustrations of 2 md -Class Chords: ! Ex. 155. , Mendelssohn. fo^r; 4 1^, ^ ; J -j J ' tf * ^ M 1 v i 1 ^f-r TV * ( r r t ~r r r -i t^- i ' ? r =J=^H P j 1 ' 1 7 7 7 7 7F // IV s *' f F~~5~7T* //i //i r -1 1 102 The Digression into the next higher Class. Mendelssohn. JL Basses. Exercise twenty-nine. To be analyzed as usual, after being worked out, with special reference to the Resolutions. The gin Positions [upper figures may be ignored, if desirable.) ft. n:.!j 6 I 07:267 B 6 ft 0650 34 4 : 76 0- 07 54 65 4ft 5 3 'f ^ ^i-*~ 3 *) ^3 f ( P~ -M 9 f -j 5 2 1 ( -^ * 1 I 56 2 6 ^5 5 * 657 ) 4 3 L-U r f . 4-35- u 6 7 67 5 4 3 43 * " ' 47 r ' +S ( + ? * "*' r 50 o- jr S 4 05 4 1 3 -4 f *. 67667 4 *- 56 * 6 "Hi 34 4 3 3- -5** J 1 f*~*~~ ' 76 tf 45 6 6- 56 23 2 65 78 7776-* S S 7 6 347 64 6^ if 7 7& 7 52 3 5- 8 656 4* 14 106 The Discords of the 4 th doss b 6 +3 8 48 3 ^ -3-8 a 3 r j j i j J- -* ~& * * == * 6162 6 4 67 S S S S 44 HandeL d. 7 76 6 44 0m , til) ^** ..... .... , f . .J 87 * ~ 6 65 4 Falsst. *) ; J' J J; i* * r'T'"^ * * b L ^3 f F i j d V ~~i-r 2 J ! i i J^ t-fl L * " '' t d^-lL^ 1 -y 1 6 6 i 76 6 -r 54 564 -7 8 1 6 6- 87 2 6- 4- 65 65 43 7 ^ 8 S ^- p * r / ~~FT~T I. * J-i 1 & U i 666 68 3 46 7 2 6-462 1" 56 6 4 6 6 3 3 5- 5 '" * r , 8 , 5 * 0= /* ' f- f * - *-**- 1 1 l-s ! J * * U ' 46 466-776 35 > 65 ft -. + 7 +8 LT r > ~r~r~^~^i r- ; 6- 266777 65 B 4 3 Forsyth. 5 _ -* *--*- -f-f ^^ r u r r r . r i T -f- 6 6 6 76 4 56 6 4 4 4 64 3 32 a- * +8 r **V fr ' rr ^ i * - j j [ 6467 8 65 fl 6 07 7 ft 7 43 * ft 8 _| ! p_ F 1 I &-' . 7 6- 6-67 65 65 3 r^ P^,-C f . i j c [ , r | r ! SEE 6 87 462 5 65 '35 1) Omit the Fifth. *2) Rhythm J ^ 6406 6767 565 35 4 3 343 . S Exercise 18, note M). 1) Ex. 157, note *2). Fundamental principles. The Tonic Chords , when impaired by a Dissonance , cease to be the Harmonic basis of their Key. The Dissonances of the 3 rd -Class Chords cannot remain stationary. B. The Discords of the 4 th Class. 817. This exceedingly unimportant and rare Class of Discords consists of the Chords of the 7 tk and 9** upon the Third Step in Major and Minor, and the Triad III in Minor. The Chord of the Ninth is, as usual, almost entirely useless in 4-part Harmony, and, when its Root b removed, the original V re-appears. This proves that the circle of Chords which constitute a Key is herewith completed, and that, M stated in 92, 93, the Mediant Chords are remotely related to those of the Dominant. Major. Minor. -"i 1) When followed by the I, the III is not an actual Chord, but only a combination of Grace-notes resem- a Chord. Comp. Ex. 1 57 , note *3). *2) The "Digression" from :< rd -Class into 4' h -Clas8 Chords u possible in Major, but very inferior, and rare. The m, m and III in Minor. 219. a. The III in Minor sounds, and is treated, very differently from the Major ffl. Its Dissonanc (the Augm. Fifth), being the Leading-tone of the Minor scale, must ascend to the Tonic. (See 7 also 16S). The best Resolution is the Normal, into the VI (or VI). The Irregular Resolution is dangerous, on account of the upward progression of the Leading-tone ; only the IV 4 is possible. The Dissonance may lie in any part, and is introduced ttrictly. Ill f Minor). III! I El, 162. ^f^^-^-=^=s= JiJ .- a; !_. r~ u Lt,J J 1 J ^~l ' ' J | J ^ J || __ . R \ 1 f t_ + * j_ A I H 1 ^ r u i* f-- c r M ^E-flM- 1 rr tfr am 1 **} VI VI IF v *^- n ^t.m 1 j **)S ~] j~ 6 n ^ J r ] j 1 -f 4 i * JI-0-J -*<< Fl! I, / 'F' 1) The line through the figure "> signifies, as before 'Exercise 18, note *5 , that the corresponding note h rmised. *2 When an Accidental stands alone, in the Bass figuring, it refers to the figure 3; see Remark iefore Exercise 9. *3) The progression of the III or IIIi into the I or V ia not 'harmonic" (Ex. 161, 108 The III, III and HI in Minor. Ex. 163. b. The Chord of the III in Minor is of but little consequence. 7 C. The III is not absolutely useless, probably on account of its resemblance to the V. treated like the III itself; the Seventh and Ninth resolve downward. /// (Minor}. liiM Exercise thirty-one. The Pogitioni may be ignored. KTinnr E ? r T j- * j * * - "" S / * 1 * ' 1. : q 5 56 b * f * f"~*: 64626 6 76 34 5 34 45 -jCLd A 667 45* 8- - 86 - 86 8- 6 # 87 7 7 6 ft 6 7 6 6 57 38 5- 5- 65 3 2 * tf- l) Ex. 120. 2) Omit the Fifth. 3) 132*. 4) Ex. 107, note 1). Analyze thete Bassei, M before. Table of the Harmonic System of a Key. 109 Table of the Harmonic System of a Key. 220. The following table illustrates the arrangement and relations of the Chord* within each Key; (Compare 51, Ex. 72, and 165 a to f) Dominant Snbdominant Tonic Class: or or First Class: Second Class: 03 s hi I V IT 6 YI (III) II c w and Inversions. and Inversions. and Inversions. /3rf Class. 4> ClassA | 7 7 7 7 OB V II VI III V 9 (II) (VI) (HI) Xi * e V M IV \ I III in / To Minor. and Inversions. and Inversions. a. The Chords in parenthesis are very rare. b. The Classes are a perfect Jifth apart: 165 a. C. The Tonic Class is Inactive, the others are all Active : see also 52. d. The Normal (Regular) Progressions or Resolutions are made by each Class one Grade from right to left (towards the Tonic): 61 b; 81 b; 208 c. 6. The reversed progression (away from the Tonic) is the "Digression": 210. This, and the progression of two Grades (215; 218) are both Irregular. f. Every Regular progression is complete in itself, and entirely cancels the obligations of the Class. Every Irregular progression, on the contrary, is only a Partial Resolution , or none at all, and demands justification by subsequent Resolution. The best and common- est moie is, after every Irreg. prog., to return immediately to the former Class: Ex. 68, measures 4, 5; 184 a; 211 c. g. The movements of the Triad III are eccentric. Synopsis of the fundamental principles of Rhythm, Melody and Harmony. 221. These are general fundamental principles, not absolute rules. Many exceptions are possible, (chiefly in favor of smooth voice-progression) which have already been explained in the respective lessons. The most striking ones are repeated here, in connection with the rule. The pupil is re- commended to memorize these paragraphs, as they embrace all the important rules: especially NOB. 2, 6, 9, 10, 11, 12, 18, 19 and 27. 110 Synopsis of the fundamental principles. Rhythm. 1* A long note, or a long (repeated) Chord can only stand (t. e. commence) upon an accented beat 2. Consequently each new measure or half-measure (wherever there \ an accent) should com- mence with a new Chord and neio Bass tone. The two exceptions are given in 178 b. (Another not uncommon exception is explained in 340 and 351). 8. Strong (accented) beats cannot be subdivided (say into * or ' notes) unless the following (weaker) beat or beats are also similarly subdivided. 4. The Rhythm of the several parts should be as different as is consistent with the uni- formity and regularity of the whole. Melody (Soprano part). 5. After a wide skip the melody should turn; excepting when the Chord is simply repeated. The Active Tones must progress according to their natural tendencies : the 7 tu step up- ward, the 6 th and -4 tb steps downward. Excepting when approached smoothly from the oppo- site direction, in which case they may move diatonirally contrary to their tendency. 7. Triads usually take their Third in Soprano. Chords of the 6 th take the Position of the Octave. In Dominant chords the Positions are optional, excepting in the Major V, which demands the Ninth in Soprano. The Triad VI never takes the 8 Te Position. The Triad II seldom takes the Position of the 5 th . . It is dangerous to skip beyond a 3 rd to sensitive tones such as the Fifth of the Chord. The Leading-tones, and the Dissonances, may be skipped to from the direction opposite to that of their tendencies: to the 7 th step, from above; to the 6 th step, and to Sevenths and Ninths, from below). Harmony. t. The whole System of Chords within one Key is divided into three Primary Elements or Classes, viz: The Tonic Class, exclusively consonant, consisting of the I, the VI, and their Inversions; The Dominant or First Class, consonant and dissonant, consisting of the V, V", V , _Ji _& V and YO, and indirectly, the III; The Subdominant or Second Class, consonant and dissonant, embracing the II, IV, tl and iV. The extraneous 3 rd and 4 th Classes are very rare. 10. The Voice- Progressions must be as smooth as possible. The choice of a Chord or an In- version often depends solely upon its proximity, and the facility with which it can be reached, not only in Bass, but in all the parts. 11. Successive perfect 5 ths and Octaves must be avoided. 12. The parts should be led as much as possible in parallel 3 rd * and 6 th *. 18. The Root of any fundamental Chord may be doubled. In Chords of the 6 th , double which- ever tone will give the smoothest voice-progression; excepting the Leading-tone, which can but very rarely be doubled. In ^ Chords the Bass tone is doubled. Synopsis of the fundamental principles. Ill 14. The Fifth may be omitted in the I, IV, V, V, V, H, VI. In no other Chords are omission! allowed, in 4-part Harmony. 15. Sevenths and Ninths are resolved diatonicatty downwards. 16. Inversions are more flexible than fundamental Chords, but weaker; hence, they require smooth progression in the Bass part. Inverting a Chord facilitates the Chord-progressions, and simplifies the treatment of the Fifth and 8, in Soprano. 17. All the Triads may be freely used, excepting the III. All the Chords of the 6 th may be freely used, excepting the III, and VI,. The Chords must be used sparingly; the best are the I 2 and IV 2 . The I 2 is very important at the Semicadence and Perfect Cadence. Every form of the V is good. The V Incomplete and other Dim. Triads should be used principally as Chord of the 6 th . The V seldom appears Complete ; other Ninths never. The V Incomplete is not good in Major, but excellent in Minor, where every pos- sible form can be utilized. The tl and Inversions may be freely used. The iV, and all 3 rd and 4 th -Class Chords, should be avoided. Movements Of Chords (within same key). IS. All Dominant Chords must be followed sooner or later by a Tonic Chord (1 or VI). They may be prolonged by Repetition in different forms, and it is even possible to interpose a Second-Class Chord (II, IV, II between the different forms, but the Tonic Element will eventually follow. Peculiar exceptions to this canon of Harmony are explained in 297 b, and 31 4 3. 19. The Tonic Chords may progress with the utmost freedom into any other Chord. tO. Subdominant Concords prefer to progress into Dominant Chords, but may go directly into the Tonic Class. Second-Class Discords prefer the Passive Resolution into Tonic Chords. 21. In general, the best progression is the Normal, downward one Harmonic Degree. 22. A Subordinate Triad cannot progress into its own Principal Triad. 23. Chords of the 6 th prefer to move smoothly, and connect very readily with each other. Irregular Concord-progressions are often rectified by making the second Chord an Inversion. 24. Chords of the ^ can be connected with Chords of the same Bass tone, same Root, and neigh- boring Bass tone. Unaccented ^ Chords generally progress diatonically. The Tonic \ Chord, when accented, must ultimately reach the V. 7 25. The Inversions of the V progress into the I, not into the VI. 26. All Chord -progressions may be classified as Regular or Irregular. In the latter case justi- fication, and subsequent Resolution, are necessary. 19. All rules are nullified when a Chord is simply repeated. 112 The Harmonizing of Melodies. Division C. The Harmonizing of Melodies. 222. In Harmonizing a Melody, i. 9. assigning to each separate Melody-tone its appropriate Chord and B*ss tone, it is only necessary at first to decide which of the three primary Elements or Chord- Classes the tones represent (51), for the whole body of Chords is embraced in these, as has been seen. The three Elements are represented most directly by the three Principal Triads I, V, IV, (see 220), in which all the steps of the scale are contained. 223* The following table, in which the primary harmonic basis of each Scale-Step is defined, must be thoroughly memorized in the Key of C, and then applied to all the other Keys, by transposition: Ex.164 C-Majoz. Principal Triads: I V 2 JF I 3 5~ 5 - 5 _ ^3 or. Scale- steps: Steps of the Scale: 1. 2. 3. r~ f) 2 p ' 4. I. e. 7. A gr- V ~ ft -(iQ J J- *r- ,' ^ J Ai/F F r IV r* JF r Prin. Triads: 1) The Tonic note (in the Melody) occurs in two primary Chords, the I and IV; and the Dominant note occurs both in the V and the I. At these places, of course, choice must be made between the two Elements ; but all the other steps of the scale represent, originally, but one primary Chord. The pupil should learn thus to associate each Scale-step (not by Letter but by Number with the Principal Triad in which it occurs, and with which (or with one of its Derivatives] it must be harmonized. For example, the 6 th step ;in C the tone a, in G the tone , in .Fthe tone d, in A-namor the toney, etc.) must be accompanied by a Subdominant Chord of the Key in question. And so forth. 224. The application of this table to any given Melody defines the Harmonic Basis, from which the BOM part is deduced, similar to the manner in which, in the foregoing Exercises, the Soprano part was deduced from the Harmonic Basis indicated by the figured Bass. For example: Ex. 165. Harmony : \v\iv I IV V JI V V il \IV \IV 225. When choice must be made between two Elements , as at the Tonic and Dominant notes (e and y in this Example), and, in general, wherever a choice is necessary between all the possible Chords of the same (or perhaps of another) Element, the following former Rules will serve as a guide : a. The very fir ^ Chord must be the I, the last two Chords the V and I (63 c) in Triad-form. b. The rules of Chord-progression as stated in 221, Nos. 18 (19, 2U), must be respected. c. The rule of Rhythm as stated in 221 , No. 2 must be respected; t. e., accented beats must be new Chords. d. The Chords must not be so chosen that any two successive Melody -notes would be the Fifths of the Chords (59 b). Successive Octave-Positions are less dangerous, because they can easily be rendered harmless by Inversion. It is generally unwise to make a note which enters or progresses with a wide skip, the Fifth of Chord (75 b). Applying these rules to the above Melody, tte result is as follows: The Harmonizing of Melodies. 113 EK. 166 JL 3 J_ - ~m j | y ^ tg 4 - * i 7 F 2) 7 7F F 7 F F 7 *) *1) The V is cancelled by 225 a. *2 The IV is impossible because it would make successive Positions of the Fifth not only with the preceding Chord, but with the following, also '225 d). *3) The IV is can- celled by 225 b: the'V, on the preceding beat, must progress into the I. *4) The IV is cancelled by 225 a. Ex. 167. 5"\ / rrt ^ 7F F 7 f n frm *1) The IV is cancelled by 225 a. *2) The I is not impossible, but the V is preferable, according to 225 o. 3) The IV cannot follow the V; nor can it be repeated at the following accented) beat. - *4) The IV is cancelled by 225 d, as it makes 5* hs with the succeeding Chord. *5, The I is cancelled by 225 c, in view of the following beat. *6) The IV cannot follow the V. *7) The V cannot progress into the IV. *8) The I and IV are cancelled by 225 a. 226. When the Harmonic Basis has been found in this manner, it is next necessary to define the Bast part. This, which is simply a choice of Inversion, is regulated by the following former Rules a* When the Soprano has the Third of the chosen Chord, the Bass generally takes the Root (221 7). And when the Soprano has the Root, the Bass takes the Third (221 7) ; except at the very beginning, and at the two Cadence Chords, where the Root inSassis obligatory (225 a). b. But the rule of smooth voice-progression is an important criterion for the Bass part, at well as for the Soprano. See 221, No. 10. That is to say, the Bass should take that Inter- val of the chosen Chord which lies most convenient, as a rule. C. The use of the Fifth in Bass (2 nd Inversion is to be deprecated. See 221, Nos. 24 (and 17). d. Each accented beat should take a new Bass tone (221, No. 2). Applying these rules to Ex. 166. the result is: 8. Ex. 168, Ex. 169. 1) 226 a. Root in Soprano, Third in Bass; and vice versa. *2) Here the Chord is very appropriate and convenient, on account of the adjacent Bass notes. See Ex. US. *3) It weakens the Cadence to UM the fi Chord here. 4 The following examples are wrong : "* -H-r+J J-ii*U J i J J J . i J i '6 66 4 4 4 4 44 *1) The 5 Chord should not progress with a skip into a new Chord. *2; Two 4 Chords in succession an forbidden (H2b). *3> 226d. *4 22(5 a, last clause. 15 114 The Harmonizing of Melodies. Exercise thirty-two. i.. Harmonize the following fragments of Melody, at the Piano, at sight, using the three Prin- cipal Triads and their first Inversions. Ex. 164 should be placed where it can be seen and referred to. The left hand can take the JBast /*, and the right the three upper parti together. (7-Major (and Minor). "i m tf-Major.**) .F-Major. *1) May be either V or I. *2) Cannot be the V, because the IV follows. *3' Change the Chord at these Accents (225 c). *4) Cannot be the I, because the I follows, over the bar (note *3). *5) Cannot be the I, because the next (accented) beat must be a I. *6) A Melody is harmonized according to the Scale -steps of the key it is in! The Scholar is recommended to play each of these melodic fragments in C-Minor also, and to extend the Exercise by writing them out in different keys, and harmonizing them M before, at sight. B. Add the Bass and Middle parts to Ex. 167, and harmonize the following complete Melodies, with Principal Triads and their Inversions. The Bass pan should be completed first, before the Middle parts are added. . <* I I I . I I II ^^ Om i |i i -J ; , j 4 9 + Li u &* <-+- hi - m- * V4 ) 1 i j j ^ .y j y a a/ i J r*^-' ^3. *>* r * _ i j j ^^^-q fr i . ,TI ;,. I E FJ =f] ~ f~ t -f- -f ^r I-.* |J*<- ^pj= j J j i i ^ f J J -i- := F5 1 : 1 1 11 ; t; ^ k_ r- f] j ==!= -t-- 4= ^= 4- * i -i- ) 1 * * *--^ * * 3^3 t) 8) E fc4 = A = m =rf - r, ^- L lf O - ^jjff^ ~f ' f f * * J ^ ^ .*) .**) :== g *> F% t 2-r !L E 1 * f f=5 -J-- 6 (- r* -j-j -B I -j- -- ! 1 r | . ) If * J J J^_J J| Mj|j.l 1 J|J J 1 J Fyp ri ^ > nr ' * -*- -* *^-* *~r=J^- 1) 225 c, 2) Must not be the I nor I f , but the 7 (e/ 4 Chord* see 160 ! *3) When the Melody-note* are such that a Chord must be repeated over the bar, exception 154 a must be resorted to: i.e. it must become a 6 /* Chord on the accented beat. Attention is also directed to 1 54 b and c. *4) Where the V is gives successive Positions of the Fifth. This irregularity, like that at note *4), is rectified by inverting the 2 d Chord, or both Chords. 221, No. 23. S 7) Ex. 88, note *2). The Harmonizing of Melodiet. 115 Fundamental principles. The 3 rd Scale-step, as Melody-tone, is harmonized with the I; the 6 th Scale-step with the IV; the 7 th Step with the V. The Bass note must change at each Accent. Each Accent must be a new Chord, excepting when it is the 2** Inversion of the preced- ing Chord. Root in Soprano, Third in Bass; and vice versd. Irregular Chord-progressions, and false successive Positions, are rendered les objec- tionable by inverting the Chords. With Subordinate Chords. 227. The application of the Subordinate Chords, in harmonizing a Melody, is regulated chiefly by the principle that they only appear as substitute* for their respective Principal Chords. This is strictly true of the VI and HI, whereas the II can also be used independently. Compare 94 a, and 220. The details of their use are as follows : 228. a. The VI can be used in place of almost any I, but especially when the latter is in 8 Tt Position (the 1 ?t Scale-step as Melody-tone . Not, however, when the I is in the Position of the 5 th ; and, of course, not at the very beginning or end of the Phrase (225 a). Ex, 170. Ei.lTL Ex. 172. Both Inversion* ( VI ^ and VI i must be avoided. I VI I VI I VI b. The III is only used in harmonizing the Leading-tone, when it descends diaf onieally ; in which case it cannot be the V (as ordinarily), without involving awkward voice-pro- gressions. The III, may also* be taken, almost as well as the III; but never the IIIj. m V T7 VI V VI III IV \V IVi 111 I c. The II, on the contrary, can be used not only like the VI) as a substitute for its Prin- cipal Triad, the IV (when the latter is in 5" Position), but may also be employed as an independent Chord, in larmoniziny the. 2 nd scale-step. In the latter case it is more likely to be the II, than the Triad II itself, according to 226 a. - - The II 2 must be avoided. 8 3 3^5 2nd step 2 1 r H 2 1 1 f-*rf 2 3 1 2 3. 2 1 i i-j- 7 I r -^- IV 11 IV II II III //,/! Hi VI L (I2) V I S 'II VI) I77l V V // V HI IT *1) Whether the 2 nd Scale-step shall be harmonized with the II, or, u before, with the V Ex. 164), depends chiefly upon the Melody-ete which follows. If the 3 rd Step follows (wb : ch must be the I), then 116 The Harmonizing of Melodies. the V should be taken , because the II does not progress to readily into the L *2) At these Melody- notes it must be the II , on account of the Rhythm (225 c). Applying these rules to Ex. 166, the result is as follows: Ex 179. 0. , | J J J 1 2*4 2*4 L'iJ j .,.. , * i i _JJU ui . | A 9 t=az \-^ \ .. *:r * -A Sk' r-- = ^ * _sZ.'- . J v/ ^ - '#) r/ 5 . II cv 3 *"F *"** /-^ a*-' *-^ ^ v*^* -f^V" >L A 1 ' -t f f * i i /^ * 1 1 4- ^ 6 I 1 1* 1 6 6 .6 6 *ft *1) The It ( in Bass) is better than the I itself, notwithstanding the Third in Soprano, because it affords smoother voice-progression ; see Ex. 98, meas. 6. But the la is also good. *2) Both II and lit are good. When applied to Ex. 167, the result is as follows : Ex. 174. i ' a -* ^-B-*- 1 1 J A\ 1^ J 9. 4 p ^ h*-j H (D *!) *) r/; a (IV) (I) 11 VI 5 ^r_C.. *_ '-V^! j ^ !* 1 p ' I ^ ' i 6 r i * >A^ *1) The upper Bass notes are possible, but dangerous, on account of the parallel motion with the So- prano. The combination is foreign; see Ex. 84, meas. 5. *2) Neither the II nor lit would sound well here. *3) Must be the It (not the I itself , because the VI precedes. See Ex. 96, me**. 4. *4) Must be the VI , as the I would not sound so well after the IL 229. Just as the 7 th step (Leading-tone) , when it progresses diatonically in the wrong direction, is not harmonized with the V, but with its Parallel the III Ex. 171), so the 6 th step ("Dominant Leading-tone"), when it progresses diatonically upward, instead of down- ward, will not be harmonized with the IV, but generally with its Parallel the IL Thus: Ex. 175. 6 th ISt iiinv ii r i iv u v (V) (IV) 230. It is sometimes very convenient to harmonize certain sections of a Melody with Succes- sive Chords of the '*; especially when the Melody is smooth (diatonic). The Chords succeed each other without regard to their relations (see 131). Still, this style of Bass must not be used too freely. As a rule, the Outer parts should move as much as possible in contrary motion, instead of parallel, as here. For instance- Harmonizing successive tones together 117 Ex. 176. ( 1) Had better be atE9c (-J-*-*^ Z 4*- + J_ JxJ 1 a,. ffp 4 ^ *> Ex. 165. J t Hi 5 nil iPitzzi) !.? i i ^4 f f k^-l : M j 1 1 | f 1 6 6 666 66 the V, as momentary interruption of the 6* h *. Harmonizing successive tones together. 231. If an accented Melody-note and the following tone (or tones) represent the same Element or Chord, they may be slurred, as follows, and harmonized together: =- ^ =- M ) > Ex, 177, m *2) / FJ /Fjjrr j F- vi iv *1) The 57 and ths in the two upper parts. See 221, No. 12. *8) The Harmony of this measure might be I I, Ij, and th repetition of the I in the next measure would not be incorrect, because the 2 nd measure is lighter than the !. Exercise thirty-three. The pupil is first referred to 238. Complete Ex. 175, t76, 177 and 178. And harmonize the following Melodies with the following Chords: I -I, 1 2 ; IV IV, IV,; v_ V, iV.) ; II II,; VI; III (III,). ^ ffiE *) Falsst. ^ *: Melodies, with Dominant Discords. 119 Faint. S H rr-mLc *) 8, 1) 228 a. 2) 228 c. *3) As Cadence Chord, must be the V not the III *) 228 b. ) V or Hi. *6) Ex. 175. 7) 231. Observe the slurs. *8) 160. *9) 232. *10) In Minor, the choice of Chords is more limited than in Major. The III cannot be used at all, nor is the II itself good (191 c). The only Subordinate Chords that can be freely used in Minor are th>- VI and II\. *11) Can be the same Chord throughout the measure, but must be repeated (perhaps with Inversion), not held, on account of the Rhythm. *12) Exercise 32 B, note *6). *13; Ex. T9. "14;Ex. Fundamental principles. The VI is only available as substitute for the I, at the 1 st Scale-step. The II may replace the IV (at the 4 th step , or may be applied to the 2 nd Scale-step. The descending Leading-tone is harmonized with the HI. The ascending 6 th step is harmonized with the II. Tones which belong to the same beat or accent may, if parts of the same Chord, be slurred, and harmonized together. A Melody-note, repeated over an accent, generally becomes ft '/4 Chord With Dominant Discords. 234. The employment of Dominant Discords not only improves the Harmony, but also facilitates very much the harmonizing of certain Scale-steps. The Dissonances of the Dominant ,the Seventh and Ninth) are the 4 th and 6 th Scale-steps. In the foregoing Exercises these Steps demanded Subdomi- nant Chords (IV or II), which, however, are sometimes noticeably inappropriate. At such places, the advantage of substituting a First-Clas (Dom.) Discord for the Second-Class Concord* (IV of II) is ob.ious. 120 Melodies, vrith Dominant Discords. 235. The Five-seven can be used, equally well in Major and Minor- l stly , and in general, wherever the Concord V and its Inversions are possible. Which form of the Chord is used, .whether the V V, V 2 ^, or^ ), will depend partly upon the progression of the Bass part (see 226 b), partly upon the Melody-note, (which will seldom, if ever, be doubled in Bass], and partly upon the following Melody-tone. 2 Bdl y, and in particular, the V can be used in harmonizing the 4 th Scale-step, when the latter descends. For illustration. 4 3) L. i 0**1 , ^^ 3iU+Vj,, J..JI, 4d =z : ==*4=n|=f^=- :/ :7~ir~& dtvj- rVidizrfczr, F- or Inv. **) or Inv. rj j r*| j 1_^ i i^_ FF or Inv. 1) Not the V 3 , because the Seventh cannot be doubled in Bass and Soprano. *2) Not the VI: see 177 b. *3) The Incomplete V should be used as Chord of the 6>: see 189 c. *4) Not good, on account of the Rhythm. *5) This is the one possible case where the ascending 4**> step may be harmonized with a Dom. Discord; but it is rare- Bee Ex. 133 a. *6) See Ex. 131 a. *7) Passive Res. see Ex. 132. 236. The Five-nine, as stated in 1 97, should be used almost altogether in its Incomplete form. And a distinction must be made as usual between its application in Major and Minor. a. In Major, it can only be used, safely, in harmonizing the 6 th Scale-step, when it des- cends. This places the Ninth in Soprano, and ensures the admissibility of any legitimate Inversion Ex. 143). b. In Minor, the V (generally Incomplete) may be used 1 I'* 1 *, and in general, wherever the V and its Inversions are possible. (Kx. 181.) 2 nd1 ?, and in particular, as in major, in harmonizing the 6 th Scale-step (descending). For illustration: Ex.182. 1 Major and Minor. 6 5 1) Minor. Maj. (Min.) Major. 9 7 9 7 9 7 F F F F F F Almost any form - - *) 9 9 99 J+JUMM-^^ r r Ex. 171. f 7JJ < r *1) Not good, on account of the Rhythm. *2) The Passive Res. is a little dangerous. *8) Possible, but of doubtful quality. H; More likely, in such rapid time, to be the same Chord (V V) and tarn* Bast tone, than the usual III IV. Melodies, with Dominant Discords. 121 837. As stated in 229, the ascending 6 th Step is generally harmonized with the II instead of the usual TV. But the IV may be used, even in this case, if the following tone (the Leading-tone) is har- monized with a Dom. Discord, instead of with the Concord V. The hest of the Dom. Discords for this purpose is the V|, which then progresses either into the I or VI (Ex. 181, meas. 3): Ex, 183. J.Y 7- *1) The V itself if dangerous. K t IV f 3 IV V 7F ft 238. The following general principles and directions should always be borne in mind, in determining the harmonic basis of a Melody 1. Always look forward. Never define the Chord of any melody-note without considering its relations to, and possible influence upon, the following tone or tones. B. The attention should be directed chiefly to the Accented beats. The unaccented notes are of less importance, and must accommodate themselves to the Chords which the accented beats require. 8* Mark, at the outset, all those Scale-steps which can be relied upon with reasonable certainty, throughout the Phrase. Namely: the very first Chord (I); the Semicadence (gen- erally V, or f^V) and the Perfect Cadence (V I, or V I, or I 2 ^ I) ; the 3 rd step (I); the 7 th step (V etc,^ ; and the 6 th step (IV or ^ ). 4. After doing this, sing (or play) the Melody through once or twice in correct time and rhythm, and endeavor to discern its harmonic basis by instinct (by "ear",, applying slurs where successive tones (of the same beat or accent evidently or probably belong to the sjime Chord. 239. The following table, in which the most natural and probable harmonic basis of each Scale-step is again shown, as summary of the rules of this Division, should be thoroughly memorized : f*fifef.. 9* i 6 n ^ r~i * r .,rd. ^tt ^^ II EH3CZ " fi ' 5 th step in C-Major a to ay, or raising the 2J step d to , as I of C- Minor, the preceding ab becomes a legitimate Scale-tone, and the Chord is authentic in C-Minor. See 243 d. *3) This is the Chord of the Diminished Seventh, the use and advantages of which, in Major, were intimated in 205 , which see. *4 The altered tone may lie in any part. *5) Compare 243 a. *6) This example is wrong, because the a, which is about to progress chromatically into ab, is doubled in Bass, where it progresses with a skip. When the duplication progresses diatonically , as in the Bass (and Soprano) of the following measure , the irregularity is rectified : See 246 e. *7) The chromatic progression can not b divided between two parts, as here between Bass and Soprano. 246 e. 120 The Altered Chords in Major. 247. a. The raised 2 nd step, when alone, can only occur in Chords of the First Class ; '. . Domi- nant Chorda. b. The raised 4 th step can never occur in any other than Second-Class Chords; i.e. in the II- IV- ti IV. C, The 2 nd and 4 th steps may be raised together; but (on account of the 4 th step) only in a Second-Class Chord. Compare 247 a. Ex. 187. 0-Major. a. Raised ? M <* step : 6. Raised 4** step: C. Raised 2** and tf* steps: -^ *1) Spoken "Five-altered"; the it indicate* that the Chord contain! a raised Scale-step. "2) It will b noticed that most of the Altered Chords of the 2 nd Class progress into the Ij ( 6 /4 Chord . *3) The progres- sion into the V re-establishes the original Key, and is therefore admissible; but it is rare, and does not sound genuine. The chromatic progression, in this singular instance, will be divided between two parts, because the raised step must ascend. *4) In this case the^J can hardly be termed a raised 4 th step of C. This progres- sion will be elucidated later. *5] The two sharps above the II indicate that the Chord is "double-altered^ *6 This Inversion of the Altered II is somewhat rare. The Passive Res. of the Seventh in the lowest part U irregular- See Ex. 151, note *!<)) 248. The following alterations are much lets common: a. The 5 th Step may be raised ; but only in th I or L b. The l t Step may be raised, in the I or VI (VI). C. The 6 th step may be raised, but only in connection with the raised 1'* step, ne?er alone. d. The raised l t step, or l t and 6 th steps, must be followed by a Dominant-Seventh, not by the V itself. The Altered Chords in Major 127 O. Raised Dominant. 6. Raised Tonic. c. Raised Tonic and 5<* ttep. I "7 J KT *'' j? "< ^ f n r 78* 7 F/ t F Intr. and Ret. / F tone 1) Thus marked to indicate that the Fifth is raised: Comp. note *3). *2) The resolution of the Altered s (upward into c) renders the IV necessary, as Resolution of this Altered Chord. This is not directly contradictory of 243 c, because the IV does not unmistakably confirm the y$ as Leading-tone of ./-Minor. 3) This notation denotes that the Root of the I is raised. Comp. note *1 ). *4) 24bd. See note *6). 5) When the VI is Altered, its Seventh will remain stationary contrary to TLx. 158. *6) If the V itself were to follow, these Chords would both be in G-Major, as H and 1 1 The V, on the contrary, re-establiahei the original Key (C). In the following additional illustrations of the Altered Chords in Major, the numbers aftei Mendelssohn's name refer to bis "Songs without Words": 1. Mendelssohn, No. 9. 2. No. 41. No. 16. 3b. fs r^.11 s No. 16. No. 36. iJ=J, BeethoTen, S'ym. Ab. 9. S * m t^F^ E3 ^~ oF 8 5 713 /F J7, 128 The Altered Chords in Minor. B. In Minor. 49. The Alterations of the minor Scale tend chiefly towards removing the unnatural chromatic-interval progressions, from one Leading-tone of the harmonic scale to the other (6 th and 7 th steps). See Ex. 71. For this purpose the 6 th Step IS raised in the ascending scale, and the 7 th Step if lowered in the descending scale. These alterations nullify the tendency of each original Leading- tone, and are the modifications upon which the Melodic Minor Scale is based. See Ex. 69; Ex. 70 ; paragraph 85. N.S. N.B. Ei. 190. C-Minor. y +. m * .* Transpose this Example into every other Minor Key. These Alterations prove conclusively that a Key may embrace tones which are foreign to its Scale , or, in other words, that a Scale may, under certain cir- cumstances, contain the same letter in different notation (242b). "While it may be a matter of opinion, which of the above tones is the legitimate Scale-tone (whether a? or oj, b% or b?) it has never been contested that they bth appear, and are both necessary (in their respective places) in the same minor Scale! From thi* the inference may be naturally and correctly drawn : that if C-Minor, for a sufficiently good reason, can have an a 5 or ft 7, th'en C-Major, for an equally satisfactory reason, may take an o? or/^, 7 43 5- 43 q 635 5415 -if 4- J -i-4?- ^J__i_^_ 05 706- 5 43 * 4- 43 ~*\ 1 _l 3 +8, 5 {IT} ^. HJMKP-^-- h ft 4 0- 0^837 065 ^0 JS*^ 8 * 2 7 S ' ^ 8 52 87 5 3 3*53 5- 65 l) *J* *^ * 4 * |l 3 * / | 8 r> 3 ^ flT -5 -3 6 +5 XJ 9 ; u (^ ^'~^ *~~ -tj^j Ler~~*~r~r F L/~~^ 1 ~~^~ ~^~ 3 -^-Fi =r-p ^--*- *- 0- ft ^ft if - 6 S5 ft b0 87 3 iTl ^fe* 1 * J n^* j 1 ^ 1 r ^ ii 050 bO 0- 0- 6 8 t b65 65 4 q 4 54 05 45 49 3 3- 1) The Accidentals in the Bass -figuring refer to the figure that follows. *2) A line through a figure signifies, as usual, that the corresponding tone is raised. *3) A solitary Accidental always refers to the figure 3. *4j Ex. 107, note *lj. Fundamental principles. An Altered Chord must be followed by a Chord which confirms and re-establishes th original Key ; otherwise it becomes a Modulation. In Major, only the 6 th step can be lowered; but almost every step can be raised. The raised 4 th step can only occur in a Second-Class Chord. The raised Tonic, or Tonic and 6 th step, must be followed by a Dominant-set-erc^A. In Minor, the 6 th and 4 th steps can be raised; the 7 th step, and the 2 nd step, may be lowered. 17 132 The Mixed Chords in Major. Section 2 nd . The Mixed Chords. (244). A. In Major. 256. a The distinctive feature of the Mixed Chords is the interval of an augmented 6 tfc , which they all contain, and which results from associating or "mixing" characteristic tones of different Scales, in the same Chord. For this reason they are generally called "Chorda of the Augmented 6 th ". b. One of the most important rules for the treatment of Mixed Chords is, that this interval (the augm. 6 th ) should notbe inverted. Thus, the interval f^ d (in Ex. 19S) should not become the dim. 3 rd d /"jj. An exception is allowed when the inverted tones lie mor* than an Octave apart, but it is very rare. For example: augm. 6** dim. 3 rd dim. 10 th L Ex. 197. 257. a. There are two kinds of Mixed Chords in Major: I* 11 *, those of the First Class, containing a raided 2 nd step, in conjunction with the Seventh (or Seventh and Ninth) of the Dominant Compare 247 a Ex. 198. C-Mjor. 1) The augm. 6 th arises from the association of the Pom.-Seventh of one Key (/, of C-Major) with tha Leading-tone of another <12, of e-Minor). *2 Ex. 197, meas. X *3) The raised step generally liet in the Soprano, even when the Major Dom. -Ninth accompanies it; comp. 193 a. b. This same augm. 6 th is sometimes used (especially by Schubert) in a Second- Class Chord, II or II; but it is evidently not quite genuine. Further, C. The 2 nd step is sometimes lowered) in the Dom. Discords. This, also, is of doubtful quality. Finally, d. In some extreme cases the Minor Ninth (lowered 6 th step) is associated with the raised 2"* step in these First-Class Chords ; but the Discord is very harsh. Harsh. Ex. 199. II I 1) These Chords are more likely to be Mixed Chords of the Relative Key (^-Minor) : See Ex. 204. *2) The lowered 2nd 8 tep usually lies in Bass. These two Chords are probably in -F-Major (Ex. 201). 258. The Mixed Chords of the First Class all resolve into the Tonic Chord (I, and Inversions). Thai' The Mixed Chords in Major. 133 Ex. 198. Ex.200. OMajor. *1) The raised 2 nd step may enter with a skip, but only from above. Comp. 174. 269. 2 ndly , those of the Second Class, containing the lowered 6 th step, in conjunction the raised 4r th step, or raised 4 th and 2 nd steps. (Comp. 247 b.) a. , 1X b. Ex.197., !) Ex. 20L C-Major. : IV , IF I/ 1) The Mixed IV sounds best in this Position (Seventh in Soprano). The Second-Class Mixed Chords, also, resolve into the Tonic Chord (258). Thus: El. 202. 1) The lowered step generally lies in Bass, and one of the raised steps in Soprano; Comp. Ex. 198, note *3). *2) This irregular interval-progression (c df] is allowed; especially in a Middle part. *3) Ex. 197, meas. 3. This irregularity is less objectionable in this Mixed Chord. *4) The resolution into the Dom.- Seventh is possible. Comp. Ex. 1S7, note *8). *5) Comp. Ex. 201, note *1). 260. The raised 2 nd step, in these Second-Class Mixed Chords, is often erroneously written as if it were the minor Mediant: e. g. in C-major, e? instead of d$. See Mendelssohn, No. 34, measures 3S and 39: instead of Bee also No. 42, measure 4 (fb for e#); and No, 38, meas. 14 fb for d$). This common error is probably owing to an instinctive reluctance to associating d$ with ob when ev appears to be so much more plausible and natural; or it may also be owing to a thoughtless confusion of the Major and Minor Modes. C-Major cannot have an e?, as that is the very tone which distinguishes it from C-Mmor, as seen in Ex. 186, meas. 1, 2. The difference lies simply in the proyreuion of the Chord, to which, in analogy with 243 c, ths notation should conform. Thus Z is a C-Major Chord, and progresses to th , I of C-Major LExr.202 is a C-Minor Chord; and progresses to 'Ae I of C-Minor If in G -Major, then, of course, the e? will be right: 134 The Mixed Chords in Major. Ei. 203. Additional examples of the Mixed Chords in Major : 1. Booth. Symph. 9. 2. Schubert. .(, g g S=jbC- 5 |ZZgZjJfc> > a Lyt^t i r ffr f taaL(~ !!' >_ -ft * J \ 1 \ i i ; z* ? 257*. 247 c, 259. Schubert. 4. Beethorcii. Op. 18, Nal. B. In Minor. 261. There is only one group of Mixed Chords in Minor. They contain a raised 4 th step, and are consequently Second-Class Chords (247 b). The augm. 6 th results from the asso- ciation of the raised 4 th step with the original Dom.-Leading-tone : Ex. 204 a. Compare these Chords with the corresponding Altered Chords (with raited 6 th step), in Ex. 1 92 a. They resolve either into the I or V. Thus : i. q a . Ex. 204. C-Minor. < te Ex.197. tii& 7i ~.With~ Inversions'^. The Mixed Chords in Minor. 135 1) The inversion of the augra. 6* h is least objectionable in these Mixed Chords of Minor. *2 These irregular interval-progressions are allowed. *3) The Resolution of this (the most frequent) form of th 7 & IV into the V involves inevitable parallel 5* 1 ". Therefore it ia wke to progress, as a rule, into the L 4) Compare Ex. 202, note *4). 205, Additional Examples of the Mixed Chords in Minor : -/. Mendelssohn* No. 40. 2. No. 22. V TT> fv J m- te-9 * f g J - -JT- .. _ "* ^i~ ' ^ C T t p S ^ >^ <) i S*, fcfc b 8 :: c s d /, F F /F t v Major. Exercise thirty-six. 7~6 87 54 SB- * t3 +7 53 6 rrr- r > i . f r i < Tn 5 +38 3 1 E T7 fll 5 +5 *> t ^ f 1 1 L^x.; o \- - u_j f, \ * **- f- ^-r f ' * 87 7 7 ^ t- L 65 65 4-46 43 43 4 5 - 4 JI p e o & i 8-137 Si'! [ojtf ^'"'jn i ^ i i .T" J J r-r- an i +8 -3 ^J| || r~- ** * 1 _J 87 87 8 -7 + 51; 5- 3 jf . 3 *) . i p * j * f s * Jii *_<* * \~ 0- 0700 o " 6 4- R6 4 A 32 6 *) 5 *l) S _ _^ ; ^ 5 L2 p-4 ! ' 1 L^. e - o B ZZ 4 a --' =T-T (56 857 Ir h * ( ^4^t 1 ! 1 1 6 676 5 ? ; 5 6 65 6 87- 3 e 3 43 5 6 -ff 3 E ^~ J *^ J - t ^ 6 ft 1 4 J }>7 I 5 136 The Mixed Chords. +3 . .^: 7-3 Minor. ft- 5- 66 43 4 if- S5 7 6- 66 _ Faisst. 4 tf 3 +8 3 -a fcfy-b-^ __4 ! f - -rr- 1 1 taH E> J h* 5' -f t \ |> ^ ^ . 1 3 J 1 1 hH i i j * 3 r i- 6 6 14 4 3 4 I- 3 ' ' / ^ u 87 b6 65 6 5- 4C 8 1 1 \ * T T e q 7 e 6 4 f * ft 8?7 665 M 3- a 7ft- 6 4 3-4 4 3 3 Faisst. if P^ ^r ,pt 8S7 6 7 4 tf 6 7 6 ft * i ft- 5 7 6 5 5676 6 4 87 4- if - 4 if 5 4 3 65 43 fc 4# 1) Do not overlook the Resolution of the Seventh 1 2) Rhythm J J^. *8) Ex. 107, no 4) Rhythm J^. - These Basses must be carefully analyzed, as usual. The Positions may be ignored. Fundamental principles. All Mixed Chords contain the interval of an augm. 6 th . This interval must not be inverted, unless the tones lie more than an octave apart. There are two kinds of Mixed Chords in Major: the Discords of the First Class, with raised 2 nd step, and Second-Class Chords with lowered 6 th step, combined with the raised 4 th , or 4 th and 2 nd . steps. Mixed Chords generally resolve into the Tonic Chord. The Mixed Chords of Minor belong to the Second Class, and contain the raised 4* tep. PART III. MODULATION. Section I rt : Key-relationt. 162. Modulation treats of the process by which a transition is made from one Key or Mode into another, This transition is effected, in general, by inflecting one or more tones of the first Key upward or downward, whereby the location of the half-step* is changed , and, consequently, the harmonic and melodic relations and tendencies of the original Scale - tones and Chords are changed to conform to a new Tonic basis. No modulation is possible without such inflections, and although foreign tones may be introduced, as in the Altered and Mixed Chords, without entirely changing the Key, such Chords, as stated in 243 e, are really incipient Modulations, and are only prevented from effecting a complete change of Key, by vigorously maintaining the original Tonic impression. S63. a. All the 24 Keys in Music have exactly the same rotatory series of Letters A, , C, D, E, F, G, A, B, etc. The difference between them is, that they start at different points in this series of Letters ; and therefore, in order to preserve the fundamental arrangement of whole and half- steps fas shown in Ex. 6,) it is necessary to inflect certain of the Letters by Accidentals ($, Jj, p). For example, in the scale of C-Major, which commences with the Letter C, there are (according to the universally adopted notation) no chromatic inflections, and the half-steps lie between E F (steps 3 4) and BC (steps 7 8), thus: C D IS^F Q A 'B-C. In a Major 1234 5678 scale starting at G, the half- step B C would be in the right place (steps 3 4), but the half- step E F would lie between steps 6 7 instead of 7 8. To rectify this discrepancy the Letter F must be inflected upward (by the sign $) : thus, ( Scale C: C D E-F G A B-b b etc. (Scale G: C D E >$-0 A B-C D etc. 456 .7 71 8 . 2 1 3 4_, 5 In the Major scale starting at F, the half- step R Fis correct (steps 7 8), but the half -step B Clies between steps 4 5 instead of 34; to rectify this discrepancy the Letter B must b* inflected downward (by the sign fr) : thus, J Scale C. b b E-F & A B-b D etc. 1 Scaled; C D E-F G A-B? C D etc. 5 6 J 8_, 2 j} 4_, 5 6 Hence, the scale of C-Major is called the Natural scale; (/-Major is called the scale of One Sharp; and F-Major the scale of One Flat. b. It appears then, that by introducing an/ft into the Scale of C-Major (as substitute for and inflec- tion of the Letter/), a transition may be effected from C-Major into (/-Major. And, by substi- tuting 5j? for b, a Modulation may be effected from C into /"-Major ; and so forth. IS 138 Relationships between the Keys. C, The origin of the Minor Key, and the relation of Minor to Major, which (as the similarity of Signatures proves) is only a distinction of Mode and not of location in the Modulatory system (Ex. 206' , is explained in 82 (83, 84, 85), which see. The Major mode (like the Major Triads) must be adopted as the basis of modulatory action and relation. The Minor mode is merely accessory to the Major. 264* The first step in the study of Modulation is to. acquire a thorough knowledge of the Relationships between the Keys, '. t. of their relative location* in the modulatory system. These points decide the practicability an4 quality of the various modulatory transitions (see 270). ft. The relationship of Key to Key agrees in many respects with the relations of the corresponding Triads. But in general it is more correct and convenient to define the degrees of relationship, firstly, and chiefly, according to the number of tones which the Scales possess in common; and secondly, according to certain important coincidences, or points of contact (of single tones or Chords). b. The notation of the Letters, and consequently the number of common tones, is indicated by the Signatures of the Scales (263 a); therefore the degree of similarity or Key-relationship becomes directly apparent by simply comparing the Signatures. This applies to , and includes, the Minor Modes as well as the Major. C. The relative locations of the Keys (and their Signatures) are exhibited in the following chart of the modulatory System: Explanations : The outer circle represents the Major Kevs, the inner one their Relative Minors. N. B. Hereafter the Major Key-notes will be printed in Capital letters, and the Minors in Small letters. The Signatures between the circles belong to both the Major and the Minor Keys. The distance from Key to Key, along the circles, is a perfect fifth, or Harmonic Degree. That this is the interval-distance between adjacent Signatures is explained in 2M a. and proves that Key-relations are only magnified Chord-, or Tone-relations. The difference in the site of the right and left half of the circle is owing to the actual difference between/^ and gV, and is a trifle exaggerated, to make it more noticeable. This will be explain** 1 in Enharmonic Modulation. fa. 201 Relationships between the Keys. 139 265. a. The Relationship of Key to Key is simply a question of distance, according to the above table, or "Circle", of Harmonic Degrees. It will be observed that each Key (Major and Minor) is attended or surrounded by five adjacent Keys. These are called the Five Next- Related Keys, and are directly accessible. For instance, the five Next-related Keys of C-Major are. (r, e, a, d, F (in any order). Of ^t-Major: D, b, f%, E, cjj. They can b found by reference to the table, or by comparing the Signatures (264 b.) b. The 5 Next- related Keys of any given Scale are also definable as those whose Tonic Triads occur on ths several steps of that Scale; (in Minor, the descending Melodic Scale). For illustration: From D-major. M **) From a-minor. *1) Ex. 807. *2)DJ el f$I GI AI 11 al Gl FI 1) Not the Tonic Triad of any Key ! *2) Comp. with Ex. 206. 266* The Next-related Keys are designated as foUpwa : I** 1 ', the Dominant Key ; 2 Bdly , Subdominant 3 rdl >', ,, Relative 4 thj y, ,, Relative of the Dominant (Dominant-relative) ; and ,, ,, ,, ,, Subdominant (Subdominant-relative). Thus From C: From a: Dominant Key Q, Subdominant F, d, Relative n , c, Dominant-relative 9 Q, Subdominant-relative 99 d. F. *1) The Signatures of the 5 Next-related Keys do not differ from that of the Principal Key by more than one Accidental. The Relative Key has the same Signature as the Principal Key ; the Dominant (and Dom.- rel.) have one sharp more or one flat less ; and the Subdom. (and its Relative) have one sharp less, or one flat more. 264 b. 9G7. Besides these five Keys, there are a lew others which, on account of certain important harmonic or melodic coincidences with the principal Scale, can claim a remote degree of connection with the latter, and can be reached more readily than the other Foreign Keys. They may be called Remote- ly -related Keys, and are as follows : l rt1 *, the Subdominant - Minor from Major, and, reversed, the Dominant- Major from Minor; for example C'-Maj. and /-Minor (instead of F-Major); orf (7, etc. This relation- ship, although "Remote", because there is a difference of 4 Accidentals in the Signatures (comp. C and f- * and 4 flats), is quite as intimate as any Next-related Key, and the Modulation from one Key to the other is as easy and natural as if they were actually next- related. For this transition the term "Stride" may be adopted. The following formula is easily memorized The Stride is a Harmonic Degree, downward from the Major Key-note, and upward from the Minor, and with a rliange of Mode. ^> -Gd 140 Relationships between the Key 9. Thus: G e (and, of course, * G)\ d A; a B, Fb? (not *ijl The Harm. Degree Li * perfect fifthl) ; * F\ 9$ S\f (with necessary change from sharps to flats) ; Ap $, etc. tc. The Stride -relation i baaed upon the coincidence of the I of Major with the V of the MLnot Key, the two most important Triada. Thua 168. 2*y, the Opposite Mode of the same Tonic. For example, C e, a A, fj A^, etc. etc. This relation is baaed upon the coincidence of all the important Scale-tones (Tonic , Dominant, Leading-tone, etc.). and is a very common Modulation, though more difficult than the Stride. The relation is "Remote", because there is a difference of three Accidentals in the Signatures. 169. 3 rdJ 7, those Keys in which there is a coincidence of the Mediant and Tonic notes (Inactive tones) possess a mutual relationship, which, though more cencealed than the other modulatory links, is very significant and useful. For instance : C (Tonic-note c) and A? (Mediant-note also ); or C (Mediant ) and E (Tonic ). Between Major and Minor Keys this relationship is elo$t; be- tween Major Modes it is Remote. Thus: Next -related: Remotely-related i Med.-Tonic. Ton.-Med. Ton.-Med. Med.-Tonie. Ex. 20S. Ztt ^_^__^ 5" * ?P <^ -.1 ei -$& 1 <5> - -fc* | a C - and reverted A 1 ? E These are called the Mediant-Modulations, and can be made quite easily, upon certain condition*. - There are a few other Remote relationships, in which, as above, the Keys have some single significant point ' f contact; but they are not of sufficient importance to demand specification. See later. Keys whick are neither Next-related nor Remotely-related, are termed "Foreign". First Rule of Modulation. 270. A Modulation may be made directly into any of the 5 Next-relafed Keys; and also by the u Stride". Into the Remotely-related "Opposite Mode" and "Mediant Keys", a Modulation may be made directly, but only upon certain conditions. The Foreign Keys can, aa a rule, only be reached indirectly, through the intermediate Related Keys. Exercise thirty-seven. Make a table of the Related Keys (Near and Remote] of every Major and Minor Key, according to the following model. Ex. 206 is not to be referred to until the table is finished! Prin. Key C(Maj.) (Min.) O 9 Next-Re Dom. lated Key Subdom. t: Dom. Rel. S-D.ReL Remotel Stride /-Related Opp.Mode Keys: Ton.-Med. Med.-Ton. O 9 D d F f C e a et By et( j. i d c C At E 1, The Mediant Keys from Minor are ^ex^-Related: Ex. 208. The process of Modulation. Fundamental principles. Modulations are made by inflecting certain Letters by means of Accidentals. All the Keys have the same series of Letters, but with different signs. The degree of Relationship between two Keys depends upon the number of Tones, or the quality of the Tones, which they possess in common. The Signatures, which indicate the condition of the Letters, define the degree of Re- lationship. The five Next-related Keys differ from their Prin. Key by, at most, one sign. The -Stride" a harmonic Degree downward from Major and upward from Minor, with ehange of Mode) is tantamount to the Next-related Modulations. Next-related Keys may be reached directly; Remotely-related Keys, conditionally ; Foreign Keys, indirectly. Section 2 nd . The process of Modulation. 271* The transition from one Key into another can only be effected, legitimately, through the Leading- tone of the desired Key ; or, in other words, through those Chords which contain the Leading- tone. Because, as shown in 8 b, this is the characteristic tone of a scale, and the one which mutt progress more or less directly into its Tonic-note and Chord. 272. The Leading-tone occurs in all the Dominant Chords (First-class Concords and Discords), and it is through these that the desired Key must be entered. The best among them for this purpose are: the V (which is almost absolutely characteristic of its Scale), and the Chord of the Diminished Seventh ;V,); which, as stated in 205, can be used equally well in Major, as Altered chord (Ex. 186, note * 8 )), and in Minor, as Legitimate Chord; and which is distinguished not only for its beauty, but also for its flexibility, and the ease with which it connects with other Chords. The Modulation into (r-major, for example, would be made through any of the following modulator) 7 Chords : EX.209. G-Major. NfcqgJ^^/E^^gg^gt Resolving into: ~ f F Fo F V or any Inversion. B 1) The V may, of course, be used with the Major Ninth, but it is much more difficult to handle. (See 199,. These very same modulatory Chords would also be used in entering (/-minor (as well as G-mtijor}. Because, as is obvious, the modulatory act is directed toward th Tome, or Key-note, which is the same in both model. 142 The process of Modulation. 273. This important rule is illustrated in the following Modulatioi Dom. Key; 266); from C-Major into G-Major (tht b. 210. Ko r, The sign ** indicates where the entrance into the new Key (the "Modulation") is effected. 274. ft. Modulations that are made, in the above manner, with a First-Class Chord, are the most direct and positive. b. But it is also possible to enter the desired Key through one of its Second-Class Chordi II IV-- it; 220). in which case the Modulation will be somewhat less abrupt, and still as 2 nd -Class Chords resolve directly into those of the Dominant) it will be scarcely less reliable than the former. C. Of the remaining Class of Chords, t. e. the Tonic Class (see 220 , only one single form can be used in effecting a Modulation; namely: the 1 2 (Tonic- ^ Chord) of the desired Key, upon an accented beat. It is entirely contrary to the fundamental principle of Modulation, to enter a new Key with one of its Tonic Chords, but the accented 7 2 is a very important exception. By virtue of its in- timate relation to the Dom. Triad, and its obligatory Resolution into the latter (154 c), it estab- lishes its Key completely. These more gradual transitions are illustrated in the following Modulations from (7-Major: Kx.211 3^ : *-*- ^ n ) y-U ^T W 3E i i fe ^ The process of Modulation. 143 *1) The new Key is indicated by a 2 nd -class Chord; but it is evident that the Modulation is not plrtf until the Dominant Chord, with the Leading-tone, appears (271). *2) The I? must stand on an accented beat, otherwise it has no modulatory power. *3) The Examples, hereafter, will be in consecutive Phrase- (or Period-) form- not in separate "measures", M heretofore. 175. The act of modulation consists mainly in obtaining the desired Key, it is true ; but it is also im- portant to decide at what point, and upon what Chord, the original Key may belt be left. a. If the last Chord of the original Key is one which also belongs to the prospective Key (in another harmonic signification, of course), the Modulation will be gradual- there cannot possibly be any CJiromatic progressions: and the Chord, being common to both Keys, is reasonably certain to connect readily with the following modulatory Chord. For instance : L 212. C 11 I 1) This Chord, the last one in C-Major (as VI), may also be denned, prospectively, as the II of G. Consequently, the progression into the following characteristic (Dominant Chord of G is as simple and natural as i? no change of Key were taking place. Such Modulations are called Diatonic, because, In the absence of any chromatic change, each separate Chord-progression (before, during, and after the change of Key) obviously pursues the track of a diatonic Scale. *2) Here, on the contrary, the last Chord in C (the lit) does not belong to the next Key (#-major), and therefore the chromatic change of f into ffy is necessary. Such Modulations are called Chromatic. They are more abrupt and striking, and consequently more effective, than Diatonic transitions. *8^ Not only this last Chord, but also the two or three preceding Chords, belong to both Keys. The change of Key, in such cases, is made almost insensibly. 876. a. The simplest, most general and most important rule, however, is, that it is always best to leave a Key at one of its Tonic Chords (either I or VI) ; simply because these Inactive Harmonies, especially when they occupy accented beats, convey the impression of completion and fulfilment, and rather suggest than hinder the digression into a new harmonic circle; comp. Ex. 10, and paragraphs 52, 54 c, 220 c, and 221 No. 19. For illustrations of this rule, see Ex. 210, Ex. 211 (all excepting No. 4), and Ex. 212 No. 1, in all of which cases the latt Chord of thefint Kty is either the I, Ij or VI, (though not invariably on an accented beat). 144 The process of Modulation. b. 213. b. If the Tonic Chords at the close of the first Key belong also to the desired Key, their progression into the Mcxlulatory Chords of the new Key will be Diatonic (as in 275 a) ; otherwise the progression will be Chromatic. For the treatment of the latter see 246 e, and 294. The following Periods illustrate these principles of Modulation, both Diatonic and Chromatic . Mendelssokm. 1m AndanU. * M x flb ' 7 77 7 7b 7 7 7t 7 CI dV 9 7 CF laVVIGV leV I aV I Oil V IFVICIIV a Tonic Chord (Q70 a). And, as it progression is Diatonic. *2) 274 c. . , , . -,. but the V. This is chiefly owing to the unaccented beat ; it is the preceding Chord, upon the accented beat, which appears to conclude the former Key. and this it the Tonic Chord of that Key. *4) This is the I of the first Key, but, not belon t f 7 7 F ) F. 77 J ? M) 7F f V f f JF <{ 7 > F ^ \IlJ 11 (1I>?) (HIT) (V?>) ditto (11) V V 12 VI (Vof)(Voff a 1 1 I 1 1 -tt-^ ff-^~ ~lt~^r~ Step 1 : 2 : minor : 3 : 45 : 44 : 43 : 42 : 5 -. *1) See alflo 178 and Ex. 181. And compare the whole table with Ex. 184. 6: min. 7 The process of Modulation. Exercise thirty- eight. 1-15 A. Pi ay the following Chord-progressions on the Piano, in the usual manner (the Bait alone in the left har.dj : CI FV t I||CI-GV I||CI aV 1 1| C I eU, V I || CI V VI dV I||GI CV 3 Ij GV I||al V t I | e^ IV t V |T|| F I RV- I 2 d V I g V 1 1| b I V I A II 3 V t I U B* Modulations into Next-related Keys. Each Bass, after being worked out, is to be analyzed, as usual : the Keys, their Relationship, the modulatory Chord, and the species of Modulation (dia- tonic or chromatic) must be marked. Do not Overlook OF neglect the Accidentals! The Accidentals make the Modulation see 263 a. b. +5 8 -* + 6 6 5 - 6 87 * * 8 3) 6*66 5 2 v 4 2) 53 +5 3 87 4 it A +3 F*y-f- /v - 1 & * J 1 1 : 1 1 J . <^)-s]r3 -|- - 1 L - t-^ 65 6 43 ^^t 4 * \v=^ \-!2 1 1 43- J f % 4- *- ^6-6^ 2 i 7 i 1 1 1 3 87 87 6 ft i7 bs-a 4 rcy r v , 1 , 1 -\ "I 1 r- \ ^7 ^ 4- t TT: *~f3 - ^1 p: j>j,rj ^*^t -2_^dl_ r * *- . , < , ^^^^ -^-it- f n . - 1 r 1 f 'r . 1 i i i , i * i . ^^J-lH-rT7 n) Ex. 107, note *1). *2) Exerciie 35, note*2), and notes 1) and *3 ako. S) gee 246 e. *4) The Melody-note is sustained. *5) For the treatment of these Unflgured Basses, see 277 and 316 b. A modulation takes place at each *. As a preliminary exercise, the student is recommended to harmonize Melodies b e and g of Exercise 32 B, as Bass part (one or two octaves lower), altenng, if necessary, the first note to a Tonic, and the note before the last to a Dominant. - *6) Here, and in all subsequent Lessons, the pupil should also make a number of Original Basses (with upper parts), applying the material of the Lesson, and imitating the given Basses. But they must never exceed a ^Measure Phrase ! 146 Altered Chord*, as Modulatory Mediums. Fundamental principles. Modulations are made most naturally through the Leading-tone of the desired Key. Consequently, the best Modulatory Chords are those of the First Class (Dominant). Second-Class Chords, or the accented I 2 , may precede the Dominant Chords of th new Key, in more gradual Modulations. The best point at which to leare a Key is where one of its Tonic Chords (I or VI) occurs. Especially at an Accent Diatonic Modulations are smoother, but less striking, than the Chromatic. Altered Chords, as Modulatory Mediums. 278. It is evident that the Altered Chords, standing as they do upon the boundary line between different Keys, must constitute a very natural and efficient medium between the Keys to which they artn.iliy belong as Altered Chords), and the Key or Keys which they appear to represent as Legitimate Chords . The dis- tinction is defined in 243 d, to whicn the Scholar" is again referred. This interesting phase of modu- latory transition is illustrated in the following Exam ties: Schubert. El. 214 CII 7, Extraneous Modulations Mendelssohn. 147 1) This Altered Chord the raised 2 d and 4 th steps: 247 c) is purposely used three times in succession; twice as Altered Chord in C, before it is transformed at x into the Legitimate VQ of e-minor. This is done to prove its identity as Altered Chord of C, in comparison with its subsequent signification in e. *2) It is true that this Example (and the following one also) might be demonstrated exactly according to the preceding lesson, without considering the Altered Chord. Because an Altered Chord, when it progresses in this way, ceases to be "Altered'. Still, the fact remains, that the transitional Chord At x might be (and, in truth, actually was) an Altered Chord in the preceding Key, wherefore the Key-relations are more palpable, and the Modulation more natural, than if this were not the case. The succeeding Examples Nos. 3 to 10) cannot be accounted for in any other, or simpler, way. *3; Lowered 2 nd step: 255. *4 Here, the transitional Chord enters as Legitimate V of the original Key, but progresses as Altered IV (with raised 6 th step: 251 ; of the next. *5, and *6, Lowered 2 nd step. *7) This is exactly and purposely) the reverse of No. 1; and, as there, the Altered Chord is used first as actual V of e, before being transformed at x into the Altered II of C. It is plain that this modulatory Chord (at x) cannot be analyzed in any other way than as an Altered Second-class Chord of the desired Key: Compare note *2). *8) The transitional Chord is Mixed, in both Keys. *9) A raised 4* h step in C, and a raised 6 th step in a. '10) Raised Jnd and 4th g tepi in C, and raised Tonic and 6 th steps in F: 248 c. Extraneous Modulations. (1. Through Next-related Keys.) 279. A Modulation is called extraneous when it extends pott the Next-related Keys] or, in other words, into a Key whose Signature differs by more than one Accidental from that of the abandoned Key. The fundamental rule for such remote Modulations is . to progress in successive stages, through the intermediate (Next-related) Key or Keys, along the lines of the "Circle of Keys" (Ex. 206); that is, through the Signatures which occur successively in the direction of the ultimate Key. For instance, the Modulation from (7-Major (1 sharp) into ^4-Major (3 sharps) would be made through the Key of 2 sharps, thus : G D A, or G 4 A. i) ) *1) It is not necessary to adhere to the same Mode: on the contrary, it is advisable to alternate mow or less regularly; between Major and Minor, as at *2 . From C (natural scale) into A^ (4 flats), through 1, 2 and 3 flats, thus: C F B^ E^ Ab: orCdBl e Ab (Ex. 2152): or C F g E$ A^, etc. And from E (4 sharps) into bb (5 flats' , through 5 # , '6Jf or 6t>, thus : E B F% or 0/ 4f> : or E 9% F% oT*?? 4?, etc. For illustration : 19* 143 Extraneous Modulation*. I. J C Exercise thirty-nine. . * 8 ^^^^^^S^U-^j S8S28 8 7 , -eS^nr b5 4* , b4 a 1) Altered U of J*nd Altered 1^ of d. All the Modulations in this Bass are made through Altered Chords, and must be analysed accordingly (27^). *2) During the first three meas. this Bass modulates in regular Degrees "downward '', . e. adding a new flat each time: At *.), instead of keeping on into ' nais. it tunu back into 4 flats, and then resumes the original downward direction. This is done to avoid Extraneous Modulations. 149 the monotony of several successive Modulations in the same direction. At *3) the monotony is again broken by the ''horizontal" Modulation into the Parallel Key. *4) Compare note *2>. *5 The Si<*nature (5 J) is omitted, on account of the subsequent Mod. into the flat Keys. *6 ; Here the Notation is changed fruin ~$to 5?; the Key is the same. Add Short Original Basses. Extraneous Modulations. (2. Direct.) 280. There are cases in which, contrary to the above fundamental rule of extraneous Modulation (through intermediate Keys), the Remote Key is reached directly. The most common of these exceptions are the Keys which are Remotely -related, namely, the Stride, the Opposite Mode, and the Mediant Key*. The Stride. 281. See 267. This transition is generally made in the ordinary way, leaving the first Key at its Tonic Chord (the I, but not the VI, in this case), which is at the same time invariably a Principal Triad of the desired Key. Thus, in the Stride C /, for instance Ei. -/y- : and H72te->g= ^ or, also, ^ 3 ^ and reversed. o-J o i '1 i i ** ^ 7 / 2^" /- C - !) x 7b = /r/ * 3-* X X Ij I*8H e ^ J , * y0 7 ^- -T0 ^^-^j-{7^ j (^ - -T-. 3 $' * J , * -0- -0- 1 ' ' r ' J J II ! >J ~?i *~ i r L_ f- * 1 * r ^ * 1 ' T ^ t ? *-! * *- f? f i | j*5 3 r ||**- ~ *9 m m '0 2 * f~ s r~ 1*^0 m * * --4-4 1r ^p-^ ^r- p- pr 1 l i 1 I- ' ' Allegro, -r-r 1 ficn :-/, r i 1 ' \ 1 el-SP-I eri Schumann. f 1 X 1 U | y n y y i 1 iff \ . J ^H wfT\} \? U A * *s ? - ^..li, ""^ ^* ^ s ^~ t ^T~ \S jy / Hr * 1? * '* *Z A P f irS ai e. W -^b. ' ! 8) vj I I L *S 1 T 0* ^., '; U 2 ^ f * -^ r 251 * 1 ^-^-?^u 4 i i _- 1 ^_ ' *i Ab rr tr v ^. V ^^ ir ^ O/ V J.~ J.J. -tf f>7V^ FI 1) An Altered Chord (lowered 6 th step of C:. *2) The facility of the Stride is strikingly shown in thii Example, where it is made forward and backward in three beats! Such rapid Modulations, from beat to beat, will be specially considered, a little later on. When, as here, the I of the old Key is at the same time the Oominant Choni of the new one , there is no need of delaying the Modulation. *3) In this unique and exceptional example of the Stride, the order of Chords U reversed; t. e. the first Key is abandoned at its V, and the new Key is entered through the I. 150 The Opposite Mode. The Opposite Mode. 282. a. See 263. This change (not to be confounded -with the Relative Key 82 c) is generally made through the Dominant Chords, which are common to both Modes. The Altered Chord* with lowered 6 th step m Major) are also available, and extremely auspicious. Thus: C F F 7 t v r 9 7 cV Q II IF Or, the Modulation may be made by a direct chromatic change from the one Tonic Triad to the other. Thus: b. This Modulation ia very different from the Stride, and is far from being as natural and easy as the latter. It is of a peculiar character, and is not everywhere appropriate. The change from Minor into ^lajor is often employed at the md of Minor Pieces, in order to obtain a stronger Perf. Cadence ,'on the Major Tonic); see Bach,' Well tempered Clavichord , Prelude and Fugue Nos. 2, 4, 6, etc., the last measure of each. It is aho frcijuentlv used, either way, for the sake of abrupt and striking contrasts; and, more rarely, as a meani of reaching other remote Keys more quickly (Ex. 217 3;. C. When the Dominant Chords are used for the Mod. into the Opposite Mode, they should appear on accented beats, and be prolonged as far as the rhythm will permit, so as to sepa- rate the conflicting Mediants (Maj. and Min.) as widely as possible. 1% Allegro. Beethoven. Op. 31, No. 1. 2. Andante. l !, Ik I / VI -? i. r\ \ 1*. i u-TL L Schubert. ^ rT* F i v j&tByi ' \rt-i ^ \rt-i +* 3. Allegro. Sehvbert. 4. Adagio. Brahms. The Mode. 151 & Vivace. 8**<~ Lisit. *1) As this Chord is common to both Modes, it ia simply a question whether the Mediant (the distinctly* Letter in this case d) shall be Major or Minor in the following Chord: Compare Ex. 18 >, notes *l) *2). *2) Here the Opp. Mode is obtained chromatically. *3) The Stride. *4) Here, the Opp. Mode serves to shorten the distance between U and B?, which, according to 27!, would require the intermediate Keys G, C and F (or their Relatives). *5) IV of o-Minor, and Altered IV of ^4-Major. See also Ex. 2211. 283. The exchange of Mode, indicated at note *1) above, is liable to take place after any Dominant Chord, at any point in the Phrase. The coincidence of the Dom. Class of Chords in both Modes is often turned to advantage in this way, for many reasons. For example - El. 217 b. 1. Allegro. dB=5s e r /3 JT3 , , 1 -- J- Beethoven. Op. 73. f J. r Minor! Min.! -( ( ^ Min.! r 1, 36 38, 40 41, 4546, etc. The direct Extraneous Modulations into the Mediant Keys are subject to special condition, which will be considered later (287). 152 Direct Extraneous Modulation. 184 As the Stride is almost exactly equivalent to a Next-related Modulation, it is ^vident that its application as intermediate Key, in Extraneous Modulations, conforms sufficiently to the fundamental rule given in 279. Its use in this capacity is very advantageous, because it shortens extreme distances materially (being a transition of 4 Signatures) , and relieves the monotony of regularly succeeding Signatures. For instance, instead of the long-winded and monotonous successions: C F By Ey ^7 Dp G\f, the same end may be reached thus: Cf DJ? G\?', or: C F 4J? Gfy. (The! indicates the Stride). Also, from C to FJ, thus C*BF*. From D to F, thus: D y F (Ex. 218 2). From C to A, thus: C m E A, (pott the desired Key, and back); or: C d A (Ex. 218 1). X, c 'd A ** '** --' "^ Beetnoiem *t- 1 F; in the Tenor as lowered 6 th step of A would prolong the impression of the former Key (d) and make the Mod. smoother. Maj. Min. / i - Strifes Signa- tures. l 5 i 4; | ** * t> In determining the route to he taken in an Extraneous Modulation, it is first necessary to ascertain the distance and the direction , according to the table on the margin. For instance: from A? to ft is six degrees npicard. If, as here , the distance exceeds three degrees , it is advisable to shorten the Modulation by using the Stride ; but otherwise it is not necessary, and the route may be taken, as usual, through successive Signatures. In a remote Mod. upward from a Major Key, the Stride can not be employed directly, for obvious reasons ( the Stride is downwards from Major, ; therefore a trans- ition must first be made into a Next-related Minor Key, from which the upward Stride will be possible. The same applies inversely to a remote Mod. down- ward from a Minor Key. For example- from C to g%, thus- C or C-i--0jj. From/jf Exercise forty. A. Indicate, in Letten (as shown above) the thorktt potnble which may be taken in effecting the following Extraneous Modulations. Occasional reference to Ex. 206 , and to the table on the margin, u not deprecated. Only the Stride, not the Opp. Mode., is to be used in shortening the distance 1) Extraneous Modulation. 153 From C tc E?: e , F: m * 9 From d to 7 : ' l It must be remembered that 6i? and GJ are identical 2) Not directly ; the Opposite Mode is not to be used here. From ^7 to O: ^ n : A /I * 7? ~ . fib E: B /:*) _ ^07 : -B C. B. Basses : To be worked out, and analyzed as usual. The Positions may be ignored. "*3+3 8 6. _g 3: S k A > 1? O / 6 655 8 5 7 3. 5 38 # 5 c * -5 87 48 4 865 8 43 nrn A a 6877i>7f5 7 7 b S6 6 S 7 i I M a bi ft 87 5 - fl65 6 87 *- * - 4B 65 rf. -3 Schubert. -<^f 2 i ^a i- ",':. n . 1_ 61 -M- 4 1 -H*- 2 87 E3E R -I 1 be b~7 4 f e eb? ^ 6 05 43 *4) 53 c f i f f A. Wagner* 43 qe as 5 # 1) CJ}-Major is substituted for cj}- Minor. *2) SimHar to note !). c for C, and F for/. *8) fV of , Mixed. *4) See Exercise 38, Note *5). Add Short Original Bosses. 154 Modulation in Sequences, and at Cadences. Fundamental principles. Remote Keys are reached, as a general rule, through the intermediate Next-related Keys. The only Remote Keys which can be reached directly, by ordinary and legitimate means, are the "Stride" and the Opp. Mode. Both the "Stride" and the Opp. Mode are employed in shortening the distance to a remoU especially the Stride. Modulation in Sequences, and at Cadences. 285. ft. The reason assigned in 2 76 a for leaving a Key at its Tonic Chords was, that the latter fulfil the melodic and harmonic obligations of their Key, and therefore leave no obstacle in the way of an exchange of basis. And, analogously, preference is given to Accented beats, because these are inactive, constituting the points of rest (more or less pronounced), upon which, as was seen in 62 and 1 13, all Cadences, ultimate and transient, must be made. b. Nowhere is this impression of completion stronger than at the Cadences, and at those places in the course of a Phrase where a more or less distinct interruption of the Rhythm* (perhaps only a mo- mentary pause) marks the end of a separate section of the form, at the "joints" so to speak) between the various Members, Motives and Figures, of which the Melody consists: (those points at which, in playing, the finger is raised, or, in singing, breath may be taken . Hence it is, that Modulations are very frequently made at these points; and it is so natural to begin a new Melodic Member with a new Key, that these transitions are often very abrupt, and, especially when extraneous, are made without regard to the ordinary and legitimate rules of Modulation. 286. According to this principle, Modulations may be made in Sequences; i.e., as repetition of a melodic or harmonic series oi tones or Chords a certain interval higher or lower (See 1 3b). The original Member and its Sequence are, of course, separated by a "joint", and their symmetry is an additional justification of the change of Key. The Modulation may (not must) be made from the last Chord of the first Key (whether it is a Tonic Chord or not) directly into the I of the next Key , without strict regard to its connection with the former, and without the intermediation of the Leading-tone, which is so indispensable in ordinary Modulations. Compare 274 c. Such an abrupt change of Key may more aptly be termed a modulatory Leap, than a genuine "Modulation". Mendelssohn. Schubert. &L 219. T/ie Mediant- Modulations. 9, Mendelssohn. 155 fcfl srogression , or a partial Sequence (in only one or two parts) is all that the ear demands. See also " i. 2214. There is an analogy between these Examples and Ex. 88, note *2). The Mediant-Modulations. 287. It is at such points as these in the course of a Period, and, particularly, at actual Cadences (Per- fect and Imperfect) that the Mediant-Modulations, and other kindred transitions of a peculiar nature, can be made with ease. 288. a. The Remote-relationships called the "Mediant Keys" in 209 (which see), are based upon the coincidence of the Tonic note of either (Major) Key, with the Mediant note of the other (Major) Key; and therefore the transition will only be justifiable, strictly speaking, when it is made precisely at this point of contact, by .transforming either the Tonic or Mediant note of the first Major Key into the Mediant or Tonic of the other, inversely. b. As these tones both belong to the Tonic Chords, it is necessary to make the Cadence upon the I of the first Key (very rarely, the VI), and progress, as intimated in 286, directly into the I (more rarely into the IV) of the next. C. The connecting-tone usually remains in the same part Thus Ex. 220. :# 1221 i Schumann. 2. Cad. i it u CI SI XI i tf* u Ton\\-Med, -9& tic. -TT 4 Tonic- j Schubert* 8, Lento. Chopin. ^ : ^Ci j"^*- ^^ J.^ ^5^4 : : Ton. AI D/ 20 156 Other Cadence-Modulation*. * Allegro. * 1) This interesting example of the Med.-Tonic Modulation is not made at a Cadence, but in rupted courie of the Phrwe. This is possible, but rare. Other Cadence-Modulations. 289. a. The Cadences or "joints"' in a Phrase or Period are such exceptionally auspicious moments fo r raodulatory changes, that still other Remote Keys, whether related (in the ordinary sense; or not, can be directly obtained with comparative facility and good effect, at these places. It is simply necessary, or at least desirable, to maintain some single (but significant and palpable) connecting link, as shown above. b. Thus, the Dominant note may be exchanged for a Mediant, or reversed; and it is quite common to transform either of the three Inactive tones of the first Scale (Tonic, Mediant or Dominant) into an Active tone \7 th , 6 th or 4 tb step) and resolve it accordingly. The most usual of these last forms is : C. to transform the Tonic note (in the I) into a Leading-tone (in the V or III). For example: Dom.-Med. Med.-Dom. Dom.-Ldg-tone. Dom.-6 th ttep. Ton.-Ldg-tone. Further: (Major Keys.) 1* Allegro. A U *? Ex. 221. Cad. Mqj. AI - Mozart. &+* + *. Mendelssohn. Cad. 3, Mod. Schumann, Min. o aa ^J^T S3t 3/ed. -Dom. **Y Other Cadence-Modulations. 157 Schubert., 5* Adagio. Beethoren. 7) 1) Opp. Mode; '. e. the Major Tonic is exchanged for the Minor one, at the Cadence. *2) The Mediant is exchanged for a Dominant (instead of a Tonic, as in Ex. 2-203). The new Key (d- Minor) is Next-related to the former one ; but it might just as well be the remote Key, D- Major. *3) Also an exchange of Bom. and Med., and an Extraneous Modulation. 4*) The Altered IV (lowered 6 h step'. *5, At this Pauge, which interrupts the Rhythm as completely as if it were a Cadence, the Tonic note of the first Key is trans- formed into a Leading-tone. *6 Here, also, the Tonic d? becomes the Leading-tone c. *7) The Dominant of the first Key is transformed into a 6 th step, in the course, of the Phrase, (owing perhaps to the slow Tempo). Exercise forty- one. Modulations in Sequences and at Cadences, into Related and Remote Keys. To be worked out and analyzed as usual. The Positions may be ignored. *) 3 & c e a JT e be e 6 *= 6 t> e S6?e 4 b3 b5 6 57 b3 4 t* 6 p5 4 3 4 _ 65 >7 6 75 4 53 76 7 * 6 46 6 6 6 6 7 34 S3 t 2 4193 ff 65 19 865 b7 f 65 7 61 B43 44 65 54S 4* I 57 -3 ^S 66 6 6 Q7 57 * 4^' 5-7 FA'ii " i. ' '""-"-' = s r H g f Jl * I ^ ?- >H;r-gi tfiH i ' 1 1 *1) Sequences should be made as nearly alike as is practicable. Comp. Ex. 219, Note *3). *2) See Exercise 38, Note *5). Add Short Original Basses. 158 Chromatic Progression, as a special modulatory agent. Fundamental principles. Modulations are most easily effected at those points where separate Members of the Melody join; t. e. where interruptions of the Rhythm, or actual Cadences, mark the end of a Section of the Form. Modulations are therefore often thus made in Sequences, without strict regard to the Key-relations, and the legitimate means of transition. At Cadences , the Mediant Modulations and other Extraneous transitions may be made through single-tone transformations. The Inactive tones muy be mutually exchanged; or they may be transformed into Actire tones. Section 3 rd . Chromatic Progression, as a special modulatory agent 290. a. A progression ia chromatic when the same letter is inflected upward or downward by an Accidental, thus: g g, or g $?, and reversed. b. The result of such an inflection is much greater than it appears to be, and can only be correctly appreciated by comparing the two tones as Key-notes, which, according to Ex. 206, indicate their actual distance apart, in harmonic degrees (perl 5"'*). This test proves that every chromatic progression is actually a leap o/seyen degrees; thus G (1$) and G? (6 flats;; or A? (4 flats) and A$ (3 sharps,. 291. Hence, it is evident that Chromatic Chord-progressions must be classed among the most peculiar and unnatural* 1 ) movements in Harmony; and many unique harmonic successions, which cannot be explained according to ordinary and natural musical principles, must be ascribed to the subtle and seductive agency of "Chromatics". The change (for which there can hardly be any theoretical justification) must be accounted for and excused on purely practical grounds, namely: the apparent distance t. . to the ear) is so short, being but a half-step, that the ear, far from experiencing any difficulty, rather evinces an inclination to follow and apprehend the progression. *!' The terms 'Chromatic' 1 and "Diatonic" are directly opposed to each other, and as Diatonic series con- form to the arrangement of tones in the Natural Scale Ex. 2.~> , it follows that Chromatics are "Unnatural. 292. Abundant opportunity has been afforded, in the foregoing examples, of observing the ordinary use and application of Chromatic progression , because there was no sufficiently important reason for adhering exclusively to Diatonic successions: see 246d; Ex. 212b: 276b; Ex. 213, No. 2; and Exercises 38, 39, 40. But, as intimated above, there are certain special uses for Chromatics, and certain peculiar harmonic effects which can only be produced and demonstrated by chromatic means. 293. Chromatic Chord-progressions (that is, Chord-progressions in which one or more of the parts progresses chromatically) may be distinguished as Simple or Compound. In a Simple chrom. Chord -progression the Chord does not change its /arm. In Com- pound progressions there are diatonic as well as chromatic successions, so that the Chord assumes a new shape. For illustration : Rules of Chromatic progression. 159 O* Simple. \ , r 1 ) 6. Compound. EK. 222. ii= =d ? J 1 i i i i i i p^ sr V * t^- 1 4 or -< b* - * * Ir' i ? J T =J !| y-j?0 ks-i J_^ ! i 5 5 b b 5b5 i 3b3 5 b4 i 2 -< t ll ^ r Lp fc 7 5 * ^ E ^_ __ 1) The simple change of e into c7 does not alter the form of the Chord, which is the Triad'c ^ i/or nrf a/*er the chrom. change. *2] Simultaneously with the chrom. change eefy in Soprano, there is a diatonic progression o 6 7 in Basg, whereby the Chord-form is changed from a Triad to a Ch. of the Second. Rules of Chromatic progression. 294. a. The chrom. succession must be made in one and the same part. (246 e). b. If the note which is about to be chromatically changed happens to be doubled, it should progress, in the one part, diatonically opposite to the chrom. progression in the other part. e. The chrom. progression should be approached, if possible, in the same direction. Thus: d. The parts should all move as smoothly as possible. 295. The violation of 294 a (i. e. when the original note is in one part and its chrom. change in another) occasions the so-called Cross-relation. But, though false in principle, there are many exceptions, and many excuses for its occurrence. For instance; (a) when one of the parts involved is the Bass ; (b) when the original note (the one to be chrom. changed) pro- gresses diatonically; (c) when separated by a Sequence, or any other joint in the Phrase, (d) when in different parts but in the same register. For illustration: Croat-relation. (a) (ft) - i I*) I . I I I (c) BeethoTei. fix. 223. ICO Chromatic Chord- progressions. *\) These two examples, in which the chrom. change is divided between two separate parts, are entirely wron" *2) Admissible, because the Bass part, in which the Cross-relation occurs, is, to a certain extent, independent of the 3 upper parts. *8) The examples at (b) are all allowed because the original tone moves diatonically. *4) Sequences. Compare Exercise 19, note *3). *o) N\ lieu the chrom change takes place in the same register, the ear will not detect a Cross-relation. But this licence must be limited strictly to Instrumental music. See also Ex. 2146. *6) These Cross-relations all occur on the same beat of three successive measures, and therefore closely resemble those at (c). Another jx-ciiliar instance is given in Ex. 227 5, which see. Chromatic Chord-progressions. 296. The entire system of chord-succession is divided into two radically distinct domains, the Diatonic and the Chromatic. To the Diatonic domain pertain all relations and associations between any two chords which belong to the same key. Here, the quality and permissibility of the chord-successions may be, and are, determined by natural harmonic principles, because their relations are defined from a common centre (their Tonic). These rules of diatonic chord-succession are given in Parts I and II (for example, 221, nos. 18 to 27) ; they are iucontestably necessary and just, and cannot be violated with impunity. "Diatonics" is the domain of harmonic Law and Order. To the Chromatic domain pertain all connections between' any two chords which belong peculiarly to different keys. Here, no natural law of chord-succession can be laid down and defended, because the chord relations cannot be defined from a common centre ; any imaginable succession is possible, and it is difficult even to systematize, in some degree, the almost inexhaustible multitude of possibilities in this domain (see . etc.) " Chromatics" is the domain of harmonic Lawlessness. While the chord-associations in the diatonic sphere are the unconstrained consequence of natural conditions, the chord-associations in the chromatic sphere are a direct violation of these natural conditions, and are effected by artificial means (i. e. by means of the apparently delicate, but in reality most powerful, chromatic "lever," which inflects the chord in such a way as to destroy its contact with its Tonic and cancel its obligations to the latter). A. The chromatic inflection may be made in either direction (upward or downward). b. It may be applied to any chord-interval (Root, Third, Fifth ; seldom Seventh or Ninth, and chiefly downward, in these Intervals). C. It may be applied to almost any two chord-intervals at once, or even to all three (of a Triad) at once. In this case the inflections are generally made in the same direction, but it is also possible to inflect one Interval upward and another downward ; and, if all three are inflected, the chord must be inverted. d. It may be applied to any chord; best, to a Tonic chord (major or minor, see Ex. 224 a) ; or to a Subdominant or Dominant Triad (see Ex. 224 b) ; or to the Dominant- Seventh or Dom. Ninth (see Exs. 224 c, and 226) ; or even to other 4-tone chords (II 7 , IV 7 , VI 7 ). 6. The chrom. chord-progression may, finally, be either simple or compound, usually the lattei (see 293, Ex. 222). For illustration (raised Root, raised Third, raised Fifth ; lowered Third, etc., etc.) : a I D V e IVd C VIE IV O II A I F IIIcZ VI Ch romatic Chord-progressions. 161 The almost infinite range of possibilities afforded by chrom. inflection is left to the investigation of the stu- dent, who is recommended to proceed systematically in pursuing the interesting quest. The rules governing the technical act are given in 294 ; the guides through this maze of " wandering" harmonies, the determination of the choice, and extent of their use these can be dictated only by the taste, tact, and good judgment of the student. But see 297 and 298 ; and also 286, 288, 289. The above tables are illustrated in the following Example : fm >0 0. ^Tr^' 1 1) The chrom. progressions &t a. are made from Tonic-Chords. In this first case, from the Major Triad o-e-g, as I of C. *2) From a Jftnor Triad (a-c-e) as VI of C. *3) Minor Triad, as I. *4) Major Triad, as VI of Minor. *5) The chrom. progressions at &. are made from Dom. or Sub- dom. Chords. In this first case from the Major Triad g-b-d, as V of C. *6) IV of 0. *7) H of a This Example shows that an Inversion may also be taken. *8) V of a-Minor. *9) IV of a-Min. 10) The examples at c. conform to 296 d, and 297 b. In this case from the V of C. *11) V of o- Min. *12) V () of a-Min. *13) V of C. (Might also be regarded as the II of a-Minor, if the preceding Chord were the I of a). 162 Chromatic Chord-progression*. 297* Among the many curious and exceptional results which attend the use of Chrom. changes, thert are two which require special consideration, namely : a. I* 1 *: Chrom. progressions are not necessarily limited to the Next-related Modulations, but sometimes lend immediately, and easily, into Remote Keys. Such irregularities , though possible results of chrom. agency, can of course only be admitted when carefully and ob- viously justified by circumstances. For instance: These Remote Modulations are all made according to 296 a (and 276 a}, from a Toiiic Chord. *1) The Opp. Mode. 2i This Mod. is analogous to 289 c: the Tonic (in Bass; is transformed into a Leading-tone. '8) A Mod. of six Degrees, the remotest that can be made. *4) The Altered fi of I). *& Can just as well be C$-M(tjor (with e in Alto). b. 2 nd >: By means of the chrom. inflection, even the Dominant Discords may be turned aside from their strict obligations to the Tonic of their Key, so that instead of resolving themselves (as has been hitherto emphatically demanded: see 221 No. IS , they progress into other Keys! This is indicated in 29Gd, and Ex. '22 \ c. The conditious upon which this extraordinary (but quite common modulatory proceeding is allowed, are, firstly, that the Dom. Discord should be led chromatically into another Dominant Discord (i. e. of the other Key), whereby it will appear as if its own obligations had been merely trans- ferred to a counterpart-Chord of another Key; and, 2 nd1 ', that the obligations of the first Dom. Disc, must he fulfilled as nearly as possible. that is, that the Seventh or Ninth, or both, should progress downward, and, if possible, the Leading-tone upward. e. There are, naturally, a few exceptions to these rules, which, in common with some other strange harmonic successions, must be placed, roughly, to the account of "Chromatics". T *J e followin fcble illustrates the progression from the principal Dominant Discords (V, V a , % V o) of 0-*jor, into those of every other Key, in the order of preference: Chromatic Chord-progressions. 163 Ex. 20. '9 17 9b 9? 7 7 7 7 CFFF CFo-FF CFo-FFo CFoFFo CFaF aF ) *) *) 979 7 , 7 6F ^7F 3) 1) These Chords, excepting *5), can be connected in any Inversions. *2) The Seventh is resolved diatonically downward. *3) The Dom. Discords, it will be remembered, are the same in Major and Minor. Therefore this may also be c- Minor, and f-Mmm- (and A-, D-, B-Majr, etc.) *4] Ex. 224, note *13). *5) These progressions are only good in this arrangement of parts. *6 Passive Reso- lution of the Seventh. *7i The Seventh progresses chromatically upward: this is "Enharmonic"' change, which will be explained a little later on. not good. *8) An 298. When one Dom. Discord is led chromatically into another, in this manner, the second one is generally resolved into its Tonic Chord. But it is also possible to progress again, chromatically, into a third Dom. Chord, and so on. Such continuous Chrom. Chord-progressions are least confusing and dargerous when they constitute more or less exact Sequences; and, in any case, some thread of connection must be pursued in some part or other, as, for instance, the descending progression of the Soprano in Ex. 227 1, in regular chrom. succession; and the regularly ascending chrom. succession in No. 2 (Bass), No. 3 (Soprano), No. 9 (Bass) ; and the Bass-sequences inNos. 6 and 4. For illustration : Ex. 227, 164 See Ex. 223, note ). Chroma tic Chord-progression* . Bcotheren. 6. HandeL 8 Cases of this kind, where the of one Key progresses chromatically into the I of another Kej, are Tery rare, and difficult to justify : see 297 c. 199. The above Examples contain Passing Modulation* of the most transient kind. In almost every case the Keys are represented by no more than nne single Chord. This Grade of Modulation corresponds, in fffeet. to the Altered Chords, but should not be regarded as a contradiction of the principle enunciated in 43 e 'which review). It remains a fact, that one isolated Chnrd does not completely and unmistakably define a Key, but is dependent upon the Chords which precede and (especially] which follow it, for its identification. This is proven in Ex. 214. But when ,_ as in this Example, the adjoining Chords are chromatic, and therefore neither confirma- tory of the middle Chord nor of each other, then of course there is no alternative but to define each ingle Chord, by ronjrrture, according to the Key which it reasonably suggests. The choice between the two Opposite Modes is almost always quite optional; comp. '283, and Ex. 226, note *3). Finally, when the succession is as rapid as in Ex. 227 No. 8, it is a question whether arty definite change of Key can be felt at all, or whether the whole is not a series of Passing-Chords". For interesting examples of chromatic succession the Scholar is referred to Bach. Chromatic Fantaaie, meas. 3'5 -U : Chopin, Etude Op. 10 No. 3, mcas. 3841; Schuniauu, Novellette Op. 21 No. 3 meas 43 -19, Wagner, Overture to Tauuhiuser, measures 1730. Ch romatic Chord-progressions. 165 Exercise forty- two. A. Pltrr Ex. ?26 on the Piano, extending each measure to four Chords, by striking the I (in any form) ber'ore the first Chord, and resolving the second Chord into its Tonic (I or VI, in any form). Example 224, note * 10 J, will serve as a model for Ex. 226, meas. 5. B. Make two tables, exhibiting the progression, /*, from the I of C- Major (in any/ormj into the V or T (at Dim. 7 th ) of every other Major Key; and, 2 nd1 ", from the I of a- Minor (= VI of C) into the V or V Q of all the other Keys. Thus: -C a-F C-G C-D Table I. r j etc. Table IL r _&L_ 3fc=^= etc. C* Basses with Chromatic Modulations. To be analyzed, as usual. P*V, ; b ^ * . .. t_ ~f l * t h ^ 7-6 S -a * 6 b5 4 B3 8 d m 65 43 7 HBb 63 4 b2 "T-y" *t- b7 SO g6 tf-t 63 B6 V b4 ! b3 : re >4 : U c r- 15 >3 2? LjL* : ^J k^j Ij ^ 1 1 J g r C IF* g 87 -8 1 'i i r ^__i - _j.jsi_ *-*^ ' s< 4 ft 96 ft 6 B7 ft^O B Q4 64 B 53 b5 5 fit ^ T ffx5 B B7 fi TJ "6 ffxftffS 5 b3 >5 5 4 *f4 3 if 3 ' ft 96 76 b5 L 57 tt 95 3?5 S3- 3 *1) See Exercise 38, note *5). Dom. -Discord at each *. Review Exercise 35, note *1) *2) *3). Add Short Original Basses. Enharmonic Modulation. Fundamental principles. A chromatic change is equivalent to a progression of seven harmonic degreef The chrom. change should be made in one and the same part. The Cross-relation is allowed, when the first tone moves diatonically. Through the agency of Chromatics, Remote Keys may be obtained directly; and the Dom. Discords can be diverted from their Tonic-resolution, and led into Dom. Discords of othef Keys. In continuous chrom. Chord-successions, the Keys must be defined by single Chords. Section 4 th . Enharmonic Modulation. 300. A progression is Enharmonic when the next higher or lower Letter is so inflected as to agree in sound with the original tone, thus: gfy -f\ g a|?; fdfa c? ^ fff* *&& abb; etc. 301. a. It is usually called the Enharmonic "Exchange" 5 or "Change"', upon the universal assumption that it is not a "Progression"' ; and this assumption is practical. y justified by the location of the tones on modern Pianoforte* (and other instruments', where both Enharmonic tones are produced with the same tchite or black key, and therefore are made to correspond exactly in pitch. Still, there is an actual difference, and, consequently, it is theoretically proper to call it a "Progression". w. The actual difference in pitch equals twelve harmonic degrees: '/if = 6 sharps, and g7 = 6 flats. Compare 290 b) Therefore the Enharmonic Chord-progressions must be regarded as still more unnatural and eccentric than the Chromatics. Ex. 206 exhibits the actual Enharmonic difference, at the Key-notes !' and O?; and the dotted lines indicate the manner in which it appears at other points in the modulatory circle also. See Appendix D. 302. The Enh. Change involves an inevitable change of Key, and therefore it is a modulatory factor. Thus: y is the Leading-tone of A and tends towards the "Sharp" Keys; but ab, which is practi- cally identical in sound with g, is the Dominant Leading-tone of c-Minor and tends towards the "Flat" Keys. 303. Enharmonic Chord -progressions, like the chromatic ones, are distinguished as Simple or Compound: Simple , when the Chord undergoes no other change than the Enh. inflection ; Com- pound, when a diatonic or chromatic progression is made simultaneously with the Enh. change. See 293. For example: a. SimpU. Ex. 228. i i i 1 ^ ^ n) Compound. r r yrr or: ^ 1) The enharm. change is divided between Tenor and Soprano: this is allowed. And the progression in Bass does not make the Chord-progression Compound, because it does not alter the sound of the Chord. *2, Here, on the contrary, there are diatonic progressions in Alto and Bass which produce an entirely new Chord-effect. At *3j all three species of melodic succession are simultaneously represented: diatonic in Bass, chromatic in Tenor, and enharmonic in Alto. See Ex. 226, note *8). Simple Enharmonic Changes. 167 804:. Simple Enharm. Chord-progressions are only possible when the first Chord is of such a con- struction that the exchange of Letter does not destroy the co-relation of the Intervals , 1. 1. the new Letter must still agree harmonically with the other Chord-Intervals, as well as the old. This is the case in Ex. 228 a; the Letters b-d-f-g(^ are as true a Chord-form as -rf-/-o([>). It is when this is not the case , that a simultaneous diatonic or chromatic progression (or both) is necessary, to restore a legitimate Chord-form. Thus: in Ex. 228 b, the Enharm. change of [? into rfJJ, alone, would entirely cancel its relations to the other tones, and therefore the progressions in Alto and Bass are necessary. Ex. 229. Simple Enharmonic Changes. SOS. The best Chord for Simple enharm. changes is the Chord of the Diminished Seventh (203 a), the properties of which, in this particular, are so remarkable and extensive that it is often called the "Enharmonic Chord**. Its susceptibility of enharm. transformation is owing to its peculiarity of structure, explained in 203 b, c, and d. As the Chord always sounds the same in every shape, and as there is, con- sequently, no distinction whatever in sound between the Intervals of the Chord, it follows that any (and each) of the four tones of which the Chord consists, may be regarded as a Leading- tone. This, of course, involves a successive change of Key , and, consequently, of notation ; and this change of notation is "Enharmonic". Applied to the Dim. Seventh on *, the result will be the four Minor Keys (and also the four Major Keys : see 205) of which the tones b, d, f, and op> (or y$) are respectively the Leading-tones. Thus: 2. .. 3cu 3b. 4^ * Leading-tone b : Leading-tone d : Leading-tone f or ft : Leading-tone g& : Keys: C, c. Keys: &?, >. Keys: (?>, JF#. /#. Keys: A, a. 1) All of these Examples in Enh. Modulation must be studied at the Piano! *2) These 4 Chords correspond exactly, in sound, to those in Ex. 146 (which see!) The modulatory distinctions obtained by making each one a separate and independent Chord of tie Seventh upon the separate tones of the original Chord, are apparent in the different Resolutions. While all 4 Chords of Ex. 14> resolve alike into the I of c-Minor, they each resolve, here, into a different Key, according to their notation. The Enh. changes are easily found, by simply comparing the Chords with each other. 806. It is evident, then, that wherever the Dim. Seventh occurs, in any of the above 8 Keys (in the notation corresponding to its Key) , it may enharmonically change its notation to that of any othtt of the 8 Keys, and so effect an Enharm. Modulation. For illustration. J. a. 2. f$A. 3. EbC. 4* GfrJp. Ex. 230. 168 Simple Enharmonic Changet. 1 This i? a change from Chord No. 1 to No. 4 of Example 229). It is not usual to make the enharm, chanjff , as here, upon one single beat fa> = g$ in Tenor). *2) Here, the change from 3b to 4 Ex. 229) is miulc upon two separate beats. This is much better than *1) , because the ear has more time to follow and apprehend the change. Comp. 3uS. *S) From Chord No. 2 to No. 1 Ex. 229;. It is admissible to make the enh. change from one part to another. Ex. 228, note 1). *4 From No. 3 a to No. 2 (Ex. 229). Tb* Bass-progression (c. to d$] is allowed, because it is Chord-repetition, in sound. Comp. Ex. 149, measure 4. Nos. 2 and 4 of th above Example sound best, because the Keys are Next-related. 507. There are only three Chords of the Diminished Seventh in Music which differ in sound ; for, as has just been seen, those which represent four of the 12 Minor Keys, though differing in Notation, sound exactly alike; in other words, one Chord of the Dim. Seventh answers (MI sound, though not in Notation) to eight different Keys, and therefore three different Chords of the Dim. Seventh cover all the 24 Keys. There are, of course, twelve of these Chords in different Rotations, and there would be 24, but for the fact that the notation is similar in Minor and Major. The j minant Seventh (for instance), on the contrary, actually occurs in 12 different sounds, as well as Notations, because in no two Keys (excepting each Opposite Mode) is it exactly alike. See, for illustration, the table made in Exercise 22, A. Besides the Dim. Seventh on the note b, treated in Ex. 229, there are two others, then, which lie respectively a half-step above and below the former. Their enharmonic ambiguity is determined in the same manner. Thus : Ex. 231. 232. A. i. Leading-tone a ft: ffa^ u Keys: B, b. Keyi: 5i,d. B. la. 16. 2. Ldt a: KeysrJ',/. Ldt g or/x: 808 When the Keys are Remote (and, in fact, in almost any case) the enh. Chord should be prolonged as far as the Rhythm will permit. The longer it is dwelt upon, the less perceptible will the changt of Key be. Comp. 282 c. For illustration: Simple Enharmonic 169 Beethoren. *1) The enharm. Chord hurts a whole measure. *2) These enhann. changes correspond to "Ex. 229, No. 3 b to No. 2. *3) Ex. 229, No. 1 to No. 3 b. *4) The moment a Dim. Seventh becomes a com- plete F(by the addition of the Hoot) its identity is fixed, and it ceases to be Enharmonic. *5) The enharm. Chord extends through 6 measures. *6 Ex. 231 A, No. 3 into No. 2. *7) The effect of this change can only be properly understood by first striking the Tonic Chord of c-minor. *8) First strike the I of /-minor. Exercise forty-three. ~ * +3 - i } 5 i + 3 , '. J . o * z d Tr i f x ^~~T"1 T i* f TV -? I -r L: ! ^-!-n rTJ irj 5 , L, 6. ^ li * f- J Jf* 1 1 i ~* k*~ * 1 1 ~-1 626 6 ft 6 - ft b7 4 b7 ^ 3^ 3 3~5 3 7 L^ -*)i ( >, ^ (--a 1 | - - -ijp - J * * -t--^ r j ^ & b? b7 55 57 8- ** 5 +8 T^ ft** 5 , . 3 t J ! -4 *-- t- L ~ *-t b7 7 I | * ft b7 UK 6 b8 S4 E?4 B B L c " * **<* x *^^ttELK''l LoLo* 7O R3 ff 60 o po F r r* r* - -^-^--^-f-Fzfc b7 , X4 it o 3 fi A 8T "i * o-*5 75 * o M 5 a x- 3 Jf- b5 S3 4# * ii s5 ^ *? is 1 S3 -^ Bfpa i^6 5 j? #3 8 1) The pupil may be at a loss to understand why, in several of the above changes of Key, the Modu- lation is not made chromatically instead of enharmonically, seeing that the former process is much more direct and simple than the latter. It will be observed that each Dim. Seventh (before its enharm. change) is introduced in its legitimate capacity as Dom.-9* h Inc. of the foregoing Key, and it may be justly assumed that this is the only absolutely correct way. If, as at *2), the Dun. Seventh does not belong to the foregoing Key, then, of course, the chromatic introduction is unavoidable. It is necessary to state however, that it is the common practice, even among classical composers, to ignore the confusing enharm. change, and progress, chromatically, directly into that form of the Dim. Seventh which is valid for the desired Key, especially when the Keys arc Next-related. Thus, in Ex. 230 1, no composer would write the a\r and g$ together on one beat, but would use g? alone. Similarly, in Ex. 23u 2, the e$ on the 3 rd beat (in Alto) would commonly be written fl at once, as chromatic alteration of the preceding /;?. The enhann. change in some of these' examples only serves to exhibit the actual nature of the Modulation ; in other examples, however, where the actual nature is most conspicuous, (as in Ex. 232 237 and 2a8) the en- harm, change is obligatory. Other Resolutions of the Chord of the Dim. Seventh. 309. The modulatory capacity and utility of the Chord of the Dim. Seventh are by no means exhausted in the above connections, because this most ambiguous and flexible of all Chords is not limited to its original signification as Incomplete Dom. Ninth, and to its original location upon the Leading- ton* These are its legitimate signification and location, but. as Altered Chord, it occur* m 22 170 Other Resolutions of the Chord of the Dim. Seventh. ttveral othtr location! in both the Major and Minor Modes! These may be found by referring to the tables of Altered Chords, and are as follows : ft, In Ex. 187 c. a Dim. Seventh is found, ae Altered II of the Major Mode, with raised 2 ttd and 4 th steps. Its characteristic features are, that it contains the Tonic-note of its Key, and resolves into the I. b. In Ex. 188 c. a Dim. Seventh appears, as Altered Tl of the Major Mode, with raised 1 st and 6 th steps. It contains the Dominant-note of its Key, and resolves into the V. C. In Ex. 192 a, a Dim. Seventh is found (Chord No. 5), as Altered iV of the Minor Mode, with raised 4 th and 6 th steps. It contains the Tonic-note of its Key, and resolves into the I. d. To these should be added , in order to complete the table, the two original locations of the Dim. Seventh, as they are given in the foregoing Examples. They are found, originally, in Ex. 146 (the legitimate V () of Minor , and in Ex. 185 (Chord No. 2; the Altered V of Major, with lowered _6*h step). They both con- tain the Leading-tone of their Key, and resolve into the I (or first into the V and then into the I). Applied to the Ch. of the Dim. Seventh upon d% (for example) the results, without enharmonic changes (in Notation), are as follows: At Y Q of Minor : At VQ of Major : At ifnf Major : As VI of Major: At IV of Mi > 4: fft nor: Ri. 233. E C .F*l) 1) F-Major, according to 309 b; but /-Minor may also be taken, in consequence of the v, which resolves into both Modes (283). 310. The principles of enh. transformation explained in 305 (which review) apply, self-evidently, to the Ch. of the Dim. Seventh in att of its possible significations. Therefore the Chord at Ex. 233 3 will be found not only as II in C-Major (whose Tenic-note it contains) but as II in all the four Major Keys of which its four tones are the Tonics, namely C, A, F$ (or ), and D% (or rather, E^}. Similarly, Ex. 233 4 will be found as VI in all the four Major Keys of which its tones are the Dominants (309 b). And Ex. 233 5 belongs as IV* to the four Minor Keys whose ToniCS it embraces (309 c). In each of these four Keys the Dim. Seventh has a different Notation : i. 9. is enharmonically changed, of course ; but it retains each time the same Chord-nam* throughout. 811. Summing up these possibilities, it appears, then, that any one single Chord of the Dim. Seventh will occur, in some Ts 7 otntion or other: o in the 4 Minor Keys (as V (1 ) \ T., . v $ . > of which it contains the Leading '-tone* ; and 4 Major Keys (as V ) / in the 4 Minor Keys (as IV h Jtf* } of which it contains the Tonics.- and 4 Major Keys (as II )/ 7 and in the 4 Major Ke> (as VI), of which it contains the Dominant*. Other Resolutions of the Chord of the Dim. Seventh. 171 > In this manner it is easy to determine the Keys to which the Chord will belong, and the Notation then simply agrees with the Key (and Chord in question. The Resolution of each Chord is also very simple- txcepting the Altered Six-seven, they all progress directly into their I. See 309 a d. The following table exhibits the Notations of the Dim. Seventh on 20 Keys. (or fa) in the abort Ex.234. * As y and 6 1? E y an ? \ , I Q Bb\ with the Leading-tone: Res. into the L with the Tonic: Res. into the I. " J *l ~ ' e? \ , II of A C Eb Qy ] . VI ofZ> F A\? d?(B) with the Dominant: Res. into the V. There are only four, of all the 24 Keys, which are not represented by this Dim. Seventh, namely: d,f, | and 6-Minor (those Minm- Keys whose Dominants occur in the Chord), and even these are ultimately obtain- able. See Ex. 2M3, note *l }. All the Major Keys are represented, not only by this Chord, but by each of the three Dim. Sevenths (307). It has already been seen that each Major Key contains all three of these C-Major. Chords, thus- which accounts for each tingle one occurring in all the Major II VI Keys (in four different Notations). 812. From this it is manifest that any Chord of the Dim. Seventh may serve as a modulatory medium between any of the 12 Major and 8 Minor (t. . 20) Keys in which it occurs. That is to say: the Dim. Seventh in Ex. 234 can be introduced (probably from a Tonic Chord) in any of the 20 given Keys, and then changed and resolved into any other of the 20. In modulating along any of the 4 vertical rows of Keys, no enharmonic change is necessary; but in modulating from any row into another row (to the right or left, in this table), the Notation must be altered. For illustration: /. AUegr* -_ Beethowo. ^ Mendelssohn. -^ --J- Ex. 235. 172 Other Resolutions of the Chord of the Dim. Seventh. Mendelssth*. timile ** ^R=F ^7** %F ? F I, etc. 1) By changing the b$ (of the first measure) into , the Chord loses its 7)-Major signification and W turned into .-Minor. See Ex.234. *2) ;w9a. *S) The same Chords as at *2), but in reversed order. 4) The same Chords at at *1); but in different Keys. *5 Strike first the Tonic Triad of the Key I 6, Like Ex. 220. 113. The ready and successful application of this complicated cluster of modulatory resources demands ^thorough acquaintance with the different Notations and Annies of the Chords of the Dim. Seventh, and with the In- troduction and Resolution of each, according to the Key it is in. It may be remarked, that there are two different ways of studying the modulatory facilities of the Ch. of the Dim." Seventh: l stlv , at the table, with strict regard to the Notation and actual harm, signification of the Chord; and 2 niU y, at the Piano, without regard to the Notation, but simply defining the location and progression of the Chord according to 31 1. The latter mode of treatment is the most practical: and, if preceded by a thorough solution of Exercise 44 A and B, is almost more recommendable than the former. Exercise forty-four. A. The Chords in Ex. 234 are to be written out separately , with their 20 corresponding Proyretiioni, always commencing with the Tonic Chord of the respective Key. Ex. 233 serves as a model. B. Define the Notation* of the other two Dim. Sevenths (the one with c> or d? t and the one with 4q or e-y in the 20 Keys in which they may occur (311), and add the Introductions and Progression! as at A. C. Basses, to be worked out and analyzed, as usual. The Positions may be ignored +3 -5 rp.. .t 1-| -* ^ B M i n r - 1 r ^ i j r 1 i i r~i ' Pi t~n ^'"i. ^ -r i T H J >H H- * \ I 3 E t -P-4J J i'^ft ] g> , 1 6 6 8?7 6 6 * 6 dtf be b7 b?be ^7 6 67 4 Pi K6S5 M >t 4 S Ml C3 C2 S3 5 4 a P* S +3 -7 [ rf ft ' -K*7 X4 4 65 *3 ^ S3 J r i r 35 4600 6 8t>7 ^3 5 b5 b4 So- 5 3 2 4 tf 5b7 565 3W S See Rubinstein, Prelude, Op. 24 No. 5, measures 92, 9397; 108, 109113, 124129. Robinstetn, "Le Bal" Op. 14, Mazurka (No. 8), measures 50, 51 ; 54, 55, 58, 59; 62. 63. Other Enharmonic Chord*. 173 Fundamental principles. A Chord of the Dim. Seventh occurs, as Legitimate Chord, in the 4 Minor Keys of which its four tones are the Leading-tones. These changes of Key involve changes of Notation, which, as they do not alter the sound of the Chord, are Enharmonic. A Chord of the Dim. Seventh occurs, as Altered Chord, in the four Major Keys of which its tones are the Leading-tones; also in the 4 Major and 4 Minor Keys of which its tones are the Tonics, and in the 4 Major Keys of which its tones are the Dominants. The Notation of the Chord agrees with its Key. Each of the three Dim.-Seventh-Chords is a modulatory medium between any of th 20 Keys in which it may occur. Other Enharmonic Chords. 314. Besides the Chord of the Diminished Seventh, there are a few other Chords which are susceptible of Simple enharm. transformation, namely: 1 . The Augmented Triad (composed , like the Dim. Sevenths , of equidistant intervals) . For example . Ei. 236. dm f\ni 21 9 a. ^t\ 248a, /> 247*, Cjf/ 245. 2 Certain Mixed Chord*: 3. The most common of these comparatively inferior enharm. changes is effected, how- ever, with the Ch. of the Dominant Seventh, which is similar in sound to a Mixed Second-class Chord of the Major and Minor Keys whose Tonics correspond to the Leading-tone of the original Key. Thus: 1> -> Resolution. -agjtg^-imd-jteg- r 1) Ex. 204, Chord No. 4. 2> Ex. 201 , Chord No. fi. Compare this treatment of the V, with 297 b. And observe that here the process indicated in 2bUc is exactly reversed! See Appendix F. The Enh. Modulations with this Chord, which w*>re much in vogue at one time, can be made equally well in either direction, between any tsvo of the four Keys represented. For example- 174 Compound Enharmonic Changes. Ti-tfeE b.237. Compound Enharmonic Changes. 815. The distinction between Simple and Compound enharm. progressions is explained in 303 and 304 (which review). Compound changes are the most gratifying and intelligible, because the diatonic or chrom. progressions which in that case accompany the enharm. change, assist the ear in appre- hending the latter, and in following the Modulation. This is impossible iu Simple enharm. Chord- progressions, because there is no change in Sound, and hence the intention of modulating is not perceptible until it has actually taken place. The pupil will become sensible of this important distinction, upon comparing the last 6 or 8 Examples with the following one, which contains only a few illustrations of the almost endless variety of Compound enharm. Chord-progressions: i i\ *!)- Ei. 238. Compound Enharmonic Change*. 175 Andtnte. Chopin. *1) These two measures, hi both instances, are actually alike. The enharm. change in the first measure i* Cly rendered necessary by the transition from sharps into flats. *2) The Tonic becomes a Leading-tone (Jn Bass ; comp. Ex. 2214, especially the 2 nd measure, where there is a similar enharm. change. *3) Thii Chord may be not only in . J-Major, but also in 1), d, c, E, according to the manner of its Introduction. This principle, which greatly multiplies the modulatory possibilities, applies to a certain extent to every Chord in Music; especially to the Concords. *4) This Chord may progress into the Keys e, E, C, a, or F (see Ex. 2.s3). *5) Ex. 226, note *8>. *6) The Opposite Mode; comp. note *1). *7) See 289a. *8) Strike first the Tonic Chord of /-Minor. *9) This whole series of Chord-progression! closely retemblM Ex. 226. But see 297 o. *10) Comp. Ex. 227, note '8). Exercise forty-five. j^a^gs B X6 ft ft 5 tf b5 * 5 b 7 8t|7 S 6 5 4 77 X6 6 6 ft 6 u -5 5 86 beiy b6 b6 ft 55 4 tfX4 fijo H if b5 4 55 54 b 54 3 #- S 9 f2 ^3 33 4 73 #4 3 K6 94 2 B6155 ft bl ft ft ae b7 K5 q bb5 tf b zmt3 -5 65 '*f 6 H 5 S3 bs 5 85- I Here, at the close of Modulation, Short Original Phrases may be made, applying all the principles explained throughout this Division, in the most general and unconstrained manner. 176 Th* Harmonizing of Melodies, with Modulations. Fundamental principles. The Chord of the Dominant-Seventh may be enhanmonically changed, BO that its Leading- tone becomes a Tonic. Compound enharmonic Chord-progressions are the best. Section 5 th . The Harmonizing of Melodies, with Modulations. S16. B. Harmonizing a Melody with Modulations is, as far as each separate Key extends, precisely the same process as before. Therefore the scholar must first of all review the former rules, especially paragraphs 238, 239, and Ex. Is4. b. The only new thing that presents itself here is- to determine what changes of Key art necessary, awl where the changes take place. From the point where a Key begins, until it if exchanged for another, the Melody-notes are harmonized in the usual manner, according to the Srale-step of that Key! 317. The changes of Key, or, in other words, the points where Modulations are to occur in the Harmony, may be defined: !"', by Accidentals in the Melody itself; 2 nd1 ', by the general construction of the Melody, which affords more or less distinct evi- dence of intentional Modulations; and 3 rd1 *, by option, at any point in the Phrase where the Melody will admit of a change of Key l iUy . Melodies with Indicated Modulations. 818. Accidentals in the course of a Melody indicate either Altered Chords, or changes of Key. (The former are of comparatively little consequence, and will therefore be set aside for the present) . This is exhibited in the following Example, in which the Keys are indicated below the note* at the points where they begin: Ex.239. **} 1 *) III * 8 J 1 ') rff-S-g MI . i i ! i . J ill i * i u ' J i i . i . r rn"\ i J J J*J i T k j j ' if * ft ^s" ->^ -^ tl - -J-j 1 - 1 V J i -.r*. n J5 iT * ... 2 *1) These Accidentals, though apparently superfluous, are actually necessary, as contractions of the foregoing Keys. *2) A -Minor, not Major'. The Keys must maintain close relationship, as much a* possible. ^Jj D-Mojar, not Minor, for the same reason Applying the simple fundamental rules of Modulation to this Melody (namely : to leave each Key if possible at one of its Tonic Chords, and to enter the next one through its Dominant Chorda see 272; 274 b, c; and 276a), the result is as follows: Melodies with Indicated Modulations. 177 EL. 240. '"*.* 319. ft. In the above Example, the Accidentals proved to be the Lcadirg tones of the required Keys, with the single exception of cj* in the 6 th measure, which merely served to indicate that the preced- ing Key had been cancelled. Such Modulations as the latter may be called "Negative": and, as they afford no positive indication of what the coming Key is to be , almost invariably leave a choice between the two Relative Keys! For instance, the c* in the above Example indicates that the two-sharp Key (5-Minor) has been reduced to a one- sharp Key; but there is nothing in the cty, nor in the tones which immediately follow, to define which of the one-sharp Keys (G or ) it intended. Consequently, either (7-Maj. or -Min. may be taken. Thus. b o G Ex. 240b, b. This choice between the two Relative Keys (not to be confounded with the Opposite Model See Ex. 239, notes *2) *3),) is possible at other points also, and usually depends only upon the succeeding Melody-notes. For example, the f* in the 2 nd measure of Ex. 240 might also be regarded as an indication of e- Minor; but the two slurred notes which follow (gd) prove that (7-Major is intended. The same applies to cj* in the 4 th measure, which might also be b-Minor, but for the following d a. Compare 238, rule 1. This point is illustrated in the following Melody: Ex. 24L 1) o-Minor is not possible, on account of Ae next meagre. *2) J-Minor is impossible, because of the el which is slurred ^f" the 1,7. - *3 Must be C'- Major, on account of the Cadence. - For these - he two recedin te el wc s surre " e ,. - - , . reasons it is best to take J-Minor at 4). aad u-Minor at 5; ; at 6) (j-Mtfor, because of the two preceding Mtnor Key*. For illustration: Ex. 242. .n fi | , 1 n g ^\>9 r^ , J 9 4 f ' 7 1 ' ^ 9 9- g 9 * a | i iT f i t i I i ~~. | rr r -J - m r i L^- * : d J ^i i ' d * t \ Ft 01 f ^ 13 178 Melodies tcith Intimated Modulations. 2 Bdly . Melodies with Intimated Modulations. 820. There are certain features in the construction of a Melody which afford almost if not qniU as unmistakable signs of a necessary change of Key, as Accidentals do. The strongest in- timations of this kind are found : I*' 1 *, at the Cadences, and 2 ndl) , in the arrangement and treatment of certain Scale-teps, especially the Leading- tone. In the first of the following Melodies (Ex. 243. a) there are no Accidentals at all to indicate positively that the original Key (C\ is anywhere abandoned. But is is nevertheless probable that the Semi-cadence is made in G, and certain that the Perfect Cadence is in a-Minor. - Ex. 240 b also illustrates this principle; the Modulation from e-Minor back to G^Major is only intimated by the Cadence-note. If the latter were e instead of G, as it might easily be, it would continue e-Minor to the end. And it is also certain that the 3 rd measure (Ex. 243, a) does not continue in (7-Major, because the arrangement of tones does not conform to that Key; especially the/gj (3 rd beat) which indicates either a return to the original Key of C, or the point of transition into the ultimate a-Minor. Uj3m /UJJJM^ (O In the following Melody: . US ^N=n fet the Key of C-Maj evidently ceases at the end of the first measure, because the i in the next measure cannot be the Leading- tone of (?, and progress as it does, downward to e. It is therefore obvious that a-Minor indicated by g'} extends back to this 4. The Cadence must be made in C, of course. How far "back" auch intimated Modulations reach, or, in other words, at exactly what beat the new Key will tirgin, depends upon circumstances, and will generally be determined by experiment. Comp. 238, rule 4. The above Melodies will then be harmonized about as follows: G GI t Melodies witii Indicated and Intimated Modulation*. 179 Exercise forty-six. Melodies with Indicated and Intimated Modulations. Review, thoroughly, 238 and 239. . m 3= Ffr^EfTh^rp^c^ j i r rrj^ ) l i,i ==SB tj^> I LJJ or: 11) !) ^#=- $ *" L ) f . 19 ) -f f l * tPi ^ 1 eM f 2 - !B ife c F- -1 f p- r-t- '* * ^ 1^-1 i F 1 __^ __ 1) See 160. *2) Z)-Minor follows e-Minor directly, in this cage, because there is a melodic Sequence: Comp. Ex. 239, note *2). *3) E& or c; the former is better, because c-Minor is sufficiently represented, as original Key. *4) A.? or/. *5) G'-Minor begins at this 2nd beat, because the note a cannot, in thU case, be harmonized as Leading-tone of 2?!?-Major (Comp. Ex. 243, b). *6) Here the D- Major I should be used, as V of g- Minor. *1) II, of B?. *8) or e. - *9) ^1? I, as V of D;?. *10) Lowered 6th 8te p O f jpp. _ *n) It is evident, from the two slurred notes which follow, that this/x is only the raised 2nd s t e p of E, and not a Leading-tone of * * 1 1 1 i * * i ! fr*\ 1 j L VM> * * r~ 1 CI or i J-i 9 7 dV- GVl #o-* CVI I CVI FVI GVI FVI aVo I (dVT) eVI (F) (aV) *1) .E-Minor is not possible, because it has no /2l And o-Minor is a little doubtful on account of the g+ which follows ; from which it appears that, as usual, some consideration must be taken of the fo/ lowing tone, also. *2) In '/-Minor, the g in Soprano would be an ascending Seventh (of the V), and is therefore douutful. But see 18">a. ^4-Minor is impossible, as it has no gQ. *3) -Minor is doubtful, because of the d' f in the next measure, and also because it is too near the Cadence. C. This Melody may be harmonized, then, l 8 * 1 ^, in C-Major throughout; or, 2 B or 6. *4) ^-Major, but not c#-Min. *5) ^t-Major probably begins at this beat (as I) , because E- Major ends on the preceding beat *6) Bfy or g. *7j At each of these Accents either C or a may be taken: probably C first *8, Ay or/. *9) Db or b\>. - *10 Not e-Minor. *11) Not ^4b-Major. *12) Not Z>7-Major, unless the following slur is ignored (which is possible). *13) See 233. *14) ^P-Major. *15) Might be F-Major. *16) D-Major, I 2 . *17) From this point these Melodies contain indicated as well as optional Modulations. *18) The next notes b and d are so suggestive of the I of 6r-Major, that the preceding a$ mi^ht easily be a raised 2 nd step (V) of O t in- tead of 6-minor. *19) These slurred notes must be the Ij of F- Major, and therefore the preceding 6$ must be the raised 4*h step (probably 'li: see 247 b) of F, *20) The following tones prove that thii must be e-Minor, therefore the a % is a raited 4th 8tep ; the best Chord is the IV t . "21) See Ex. 249, note *5). C. To this Exercise may be added the Melodies given in Exercises 33 and 34, to be harmonized with Passing Modulations. Fundamental principles. Passing Modulations may be made, optionally, at almost any Accent Every accented Major and Minor Triad may become a I of the corresponding Key, if the preceding Melody-note belongs to the Dominant Chords of that Key; and if not too rudely contradicted by fo following tone. PART IV. The Inharmonic (Non-harmonic) Intervals. 825. a. When 3, 4, or 5 tones are combined in thirds, they mutually accord, and constitute a katmoft- ic body which affects the ear agreeably. Such tone-combinations are called Chords (see 31, 33), and the separate tones are Harmonic Intervals, or Chord-intervals. b. A body of tones, united in intervals which do not conform to this rule for the con- struction of Chords, is called an inharmonic Combination, and the tone or tones which disagree with the structure of thirds are Inharmonic Intervals. C. The Inharmonic tones are those which lie between the Chord-Intervals, and, conse- quently, do not belong to the Chord. For illustration, in the I of (7-Major, the tones c-e-g are Harmonic, but all the other (intermediate) tones, diatonic and chromatic, arc inharmonic, in connection with that Chord. Thus: Har. Inh Har. Inh. Har. Inh, . El. 25L ) 1 #- might be a Seventh, and d b or d^ a Ninth of this Chord, at Dominant Chord of F-Maj. 01 Minor. But they are inharmonic in the Chord as I of C-Major. S26. It is evident that the quality "Inharmonic" is merely relative, and depends zpaa 'it Therefore, before it can be decided whether a tone is Inharmonic or not, the identity of the Chord (in connection with which it appears^ must be established. This may be done by the accompany- ing parts, or it may he obviously deduced from the connection* with the preceding and (chiefly) with the following Chords. Thus : (the Inharmonic notes are marked o): Ei. 251 01 The Organ-point. 185 1) The weight (duration) of the tones in the Bass def, compared with the lightness and brevity of the upper tones, sufficiently defines both the Harmonic and Inharmonic notes. *2) The peculiar Baa figuring , 4 , shows at once that the tones are combined in an irregular, non-harmonic way. Whether the 4 ia a distortion of 4 , or 3 or 3, depends chiefly upon the Chord which follows. At *2) it is evidently the I| of 0; at *3), the V; and at *4), the IVj. *5) The d in Soprano cannot be a "Ninth*', because there k no Seventh with it See 192b, 2 d y. 327. Inharmonic notes are employed for the purpose of embellishing and animating the simple Chord*, and adding melodic significance and grace to the separate parts. Hence, the manner and extent of their use depends upon the degree of effect desired. There are four kinds of Inharmonic tones: the Organ-point, the Suspension, the Anticipation, and the Neighboring -Note; which are distinguished according to the manner in which they enter and progress. They may also be divided into three groups, as follows: The Organ -point is a heavy (long) embellishment, the Neighboring -Note a light (short) embellishment, and the Suspension and Anticipation result from partial mix- ture of a Chord with those which precede or follow it Section l rt . The Organ-point. 32S. ft. The Organ-point differs very materially from the other Inharmonic Elements , and constitute* therefore a distinct phase of "Inharmonics" by itself. As a general principle, Inharmonic notes are even more dependent, and demand resolution more urgently, than Sevenths, Ninths and other Active tones, which, though Dissonances, are at least Harmonic. The Organ-point on the contrary, as will be seen, is a heavy, impassive tone, which effects its "Resolution" by simply remaining until the other intervals return to mutual consonance. b. The Organ-point (also called "Pedal-point") conjists in sustaining a certain Scale-tone during a section of the Phrase or Period (or throughout) , almost or quite irrespective of the harmonic progressions in the other parts. As the latter progress from one Chord to another, and perhaps even modulate into other Keys, the sustained note must, necessarily, disagree from time to time with their Harmonies, and be- come Inharmonic. 829. The object of the Organ-point is then, obviously, to strengthen the impression of some important tone of the Scale, by prolongation ; and this is sometimes done in almost obstinate disregard of the other parts. For this reason, however, it must be a tone of such quality and importance as will endure prolongation without endangering the Harmony, namely: as a rule, either the Tonic or the Dominant note of the principal Key. The prolongation of the Tonic or Dominant note* as Organ-points is justifiable on the grounds that these are naturally the most prevalent, dominating tones of the Key, and whether they are merely retained in the mind, as ideal prolongation of those factors from which all the relations of the Key must be deter- mined, or are actually held and kept sounding in the ear, is not a matter of great difference; in fact, the latter seems the most rational course to pursue. 24 186 Tonic and Dominant (jigan-points. Ei. 254. The following is an example of the Tonic Organ-point, in BaSS: Legato. This, and the following Examples, are continuous, not single measures. *2 These asterisks indicate the points at which the sustained Tonic in Bass is Inharmwir. *3j Throughout this meas. the c in Bass might be regarded as a harmonic Seventh of the Chord; but it does not impart that impression. There will be many cases of a similar kind in this Part of the book, where the distinction between Harmonic and Inharmonic intervals will need to be defined according to other indications than the form or shape of the tone-combination. *4i Here, also, the c in Bass appears to be Harmonic (Fifth of the Chord ; but its identity as Organ-point is alreadv fully established. *5) The Pupil should, in studying this Example at the Piano, not hold but strike the Organ-point, at first at each beat. By this means a more correct impression of its effect and character will be obtained. The following is an example of the Dominant Organ-point in BaSS : Andante. Wagner* Hints and Direction!. 830. The Organ-point is a musical effect which is most naturally and effectively to be produced upon the Organ, by simply holding the corresponding pedal, while the hands continue the harmonic progression. Hence the terms "Organ-point", and, sometimes, "Pedal-point" or "Pedal-note". Still, it is by no means limited to the Organ, but can appear in any kind of Instrumental or Vocal music. The following peculiarities in the character and treatment of Organ-points must be borne in mind: ft. Being a tone which enrich* rather than embellithe* the Harmony; which aids in holding the Chords and Keys well together; and establishes a firm basis upon which the active harmonies in the other parts may move about with greater security the Organ-point is usually placed in the BaSS party '. . below the rest of the Harmony. Nevertheless, it may occasionally appear in Tenor or Alto, especially as duplication of the Bass Organ-point ; and is even possible in the Soprano, though very rarely, in the latter case it is sometimes called an Inverted Organ-point, a very significant and appropriate term. Tonic and Dominant Organ-points. 187 b. The Organ-point must, as a very general rule, begin and end as harmonic tone (i. e. M legitimate Chord-interval). And it should remain in the same register. C. As stated in 328 b, the Organ-point is sustained irrespective of the Chords in the other parts, but there is naturally a limit to this rule. If the sustained tone becomes harshly discordant for several successive beats, or if the modulations extend into remote Keys, it will be disagreeable and wrong. This limit will be most easily determined by the ttr. There is but little danger when the other parts move smoothly; when the harmonies are simple; and when care is taken to make the Organ-point harmonic from time to time, especially on the accented beats. Still, it b a tort of prerogative of the Organ-point to conflict sometimes almost fiercely with the other part*, and its persistency seems to be a sufficient justification. The following Example, however, is palpably wrong : J-* r etc. V J The length of Organ -points is optional; sometimes they extend through a whole Piece, or through large Sections, and sometimes, on the contrary, they are quite short. The difference be- tween ordinary (long) Organ-points and short ones is very great, and will be specially considered a little later on. Long Organ-points should, according to the law of Rhythm, commence on a cor- respondingly accented beat. Comp. 140, last clause. The Organ-point may be held, or it may be reiterated perhaps in alternation with the upper or lower Octave, or with the interposition of another harmonic Interval. This will depend largely upon the instrument for which the Composition is written, and upon the degree of effect desired. See Ex. 257 and 259 b, No. 3. It will be nf advantage to remember that the Tonic note becomes an Organ-point in connec- tion with Dominant (1 st Class) Chords: and the Dominant note in connection with Subdomi- nant (or 2 nd Class Chords. And both become Organ-points during Next-related Modulation*. Thus: Tonic: ^ i I i I i j * *i BE i* 3 \T ? fr\ >> % &* a - > J m TV/Z * :*" p * * S Jffl 3 9 J 9 Km J 7 9 GV V V II fi* o d \ T r a [&:. ~ & g. The accompanying parts must move as smoothly as possible! 188 Tonic and Dominant Organ-points. The following Example illustrates dirferent varieties of the Tonic and Dominant Organ-poinU; Beethoren. . *i * . Jjfl ' ' ' * Ei. 257. 1 Allegro. w -r +. etc. 2) Schamann. f 1 P r r Allegro. Schumann. Mendelssoha. ^r * . Moderate*. (D-maj.) * * * -& *- * * * Mendelssohn* -* '-0- 6) etc. 6* Allegro. Boethoyeu. * -^ 7 Larghetto. ryT2 r 9 -j 9 i 0rac ana Dominant Organ . . ^~^ --* 1 1 1 1 y -points. Jgc Schumann. > * # * * jj t; '^1 p n * - . C- * y W "^/ff * * * * ^ t? i R ? / > o / To !P -' c-rr 1 i fc 1 b f 1 PP 1 t^s z B^ ^ u p r c r ^ i Falsst 9. Mendelssohn* Allegretto.-* BeethoTen. *1) Dominant Organ-point in Bass. *2) Tonic Or^an-point in Bass. *8> This is the manner in which the Organ-point at *1) is reproduced later on in the Piece. *4) Tonic Organ-point in Bass, and doubled in Alto. *5) The Organ-point is transferred from Bass to Tenor. *6i Dominant Org.- point in Bass, and doubled in Sopiano. *7) The Tonic Organ-point which occurs at first in Bass is afterwards transferred to the Tenor by simply inverting the parts and repeating the Phrase. ^In no way could this unusual Tenor Organ-point be more ingeniously justified. *8) Double Org. -point in Bast am/ Alto like *4). *9, Double Org.-point in So/irano and Tenor; in the following measure, in Bass and Soprano as at *6). *10 This is an extraordinary example of an Organ-point in Soprano. Such un'ujue tone-combinations characterize Schumann's music. *11) Organ-points, especially when in are often interrupted, as here, by intervals of the accompanying Chords 190 The Pastoral Organ-point. The Scholar ia also refened to the following interesting Examples: Beet ho veil, Senate Op. 28, first movement, measures 1 24, din Bass; , .... .the last 24 measures, d in B*M; . . second movement measures i) 15, a in Bass; . . last movement, measures 1 16, din Bass; the same movement, measures 2534 /rm the end, a in Bass; and also the last 18 measure*, d in Bass. Beethoven, Senate Op. JS) No. I , the last 12 measures, g in Baas. Mendelssohn, Senate Op. H , flrat movement, measures 18 2>; last mov't, measures 44 2o/rorn the end. Mendelssohn, Overture "Meeres- tille", measures 29 36, d in Soprano. The Pastoral Organ-point. 831. Sometimes the Tonic and Dominant notes are sustained together, as Double Organ-point in the interval of a 5 th v Tonic below the Dominant), and almost invariably in the lowest parts. This beautiful effect is called the 'Pastoral" Org.-pt. , probably because the upper parts are necessarily limited to such simple and primitive Chords and Modulations as can be associated with either and both sustained tones, without producing too harsh a dissonance. See 330 c. e. f. g. For illustration : 1. Orazioso. * Moderate. JL Ex. 258. The Pastoral Organ-point. 191 9. Andante. Brahms. *1) Tonic- and-Dominant, or Pastoral Org.-pt *2) At this point the preceding Org.-points are inverted for a moment ; this is very unusual. *3) Here, the Pastoral Org.-pt. is produced by one part alone in alter- nating tones, and includes the upper Tonic also. Exercise forty-eight. Play the following Chord-progressions on the Piano, with the right hand, and hold at the same time the Tonic or Dominant notes (as specified) in the left hand, as Organ-points. When the Dominant is to be sustained, strike the Tonic note first, and begin the Dom. at the tecond Chord; and always end with the Tonic. The Organ-point may be held as octave, and should be re-struck at each accented beat. The Scholar is recommended to play the Chords not only in the given In- versions, but in as many other forms and Positions as possible; and they are to be played in several different Keys! A. With Tonic in the left hand: * 1 )I V I || la V 3 I t || I V (altered) . V f I Cn t V I o-min. V I -F-maj. I I a H, V 3 I t || I I t I CV, Ii V I <*V 7 7 9 C. With Tonic and Dominant together : 4 /4* 8)I -|- IVi n i V 2 -I } Vj V t IV, 1 1 ! V 1 2 Dom. Key V 2 | I, orig. Key V, I || . 1) The following will serve as a model for this one measure: ! || ijHj- 1 1| *2)C r -maj. I, 7 9b 7 7 V_I_CVo I C?V ^-CVj B. With Dominant Org.-pt.: I I IV I V I IV II IT, 1 2 V 1 1| CI V VI IV V I I V I Tonic Or'gan-point. etc. etc. ". 49- *& <* & *S) In transposing this Exercise into other Keys, the same Key-relations must be used. tinuous 4-measure Phrase. S) Aeon- Fundamental principles. Inharmonic tones are those which lie between the Intervals of a Chord. The Organ-point is generally a sustained Tonic or Dominant note, in Bass, held almost irrespective of the accompanying Chord-progressions. 192 The Mediant Organ-point. Irregular Organ-points. 332. Although the Tonic and Dominant notes are unquestionably the best adapted to prolongation as Organ -points , other steps of the Scale can also occasionally be used in the same way. But such Organ -points are only employed for unusual effects, and therefore but rarely appear, and only when carefully and sufficiently justified. 333. The commonest and best of these irregular occurrences is The Mediant Organ-point, obtained by sustaining the 3 rd Scale -step, which is so closely allied to the Tonic and Dominant (not only in its harmonic equality and relation to them as part of the Tonic Triad , but more par- ticularly in its similar quality as Inactive tone Ex. 10) that its prolongation as Organ-point is just fiable. The Mediant Organ -point is more common in Minor than in Major ; it is invariably in Bass ; is usually brief; and must be associated with very simple and smooth Harmonies. The following Chords are the best: Major or Minor. Major. Minor. , 1 J 1 r {7)5 4~ r H^J J, J 1 in L"t~^ 9~ . . y .. -^5 * -i ^Ms 1 ^ u : j v*J. JL i t, 7M 7 7 V* II JT r r Mediant Org.-pt. Illustrations of the Mediant Organ-point: ./. Allegro. Brahms. Sym. 77. . Andante. Schubert. & i 3 F in etc. ^^^ I FI J J =4^ ^^^r r ''Mediant Org.-pt. Med. Org.-pt. Med. Org.-pt. r?.J lJ>I.T^.f J^^.-P*. The Mediant Organ-point. 193 1) This example is taken from Schumann's 3 rd Symphony, 2 nd movement, commencing at the 4 th Dou- ble-bar. It ia no doubt the most remarkable illustration of the Mediant Org.-pt. that can be found. If at *7 it yields and proceeds into the Perf. Cadence. 534:. Other Irregular Organ-points will be found in the following works: Suhdominant Org.-pt., see Schnmann, Op. 2:<, f^Nachtstucke") No. 1, measure 24 1\ from the end, g in Bass. This, like the Mediant Org.-pt. of Schumann (cited above), does not remain a Subdominant 'of '/-Minor) constantly, but changes to a Dominant of C-Maj., then back to a Subdom., and ends as Tonic of G-Major. Also, Mendelssohn, Songs without Words, No. 27, measures 25 and 26, a in Soprano, in 3 35 3- 53 bS 80 787 07 55- 4 3- J The figures below the Bass notes merely indicate, as usual, which upper tones are required. It must be left to the pupil to find the Short Organ-points, and locate them properly. ' dd Original Basses, apply* ing all the pnnciples explained in this Section and introducing any variety of brg.-poiuts. Fundamental principles. . Any other than the Tonic and Dominant Organ-points are irregular The best Irregular Org.-pt. is that upon the Mediant. Short Org.-points are used to obviate unquiet or inconvenient part-progressions. ' Suspension. 195 Section 2 nd . The Suspension. 6. When, in any successi(-n of two Chords, an Interval of the first Chord is prolonged until after the second Chord has appeared, so that it sounds along with the Intervals of the latter, the result is a dissonance by Suspension. Such dissonances are subject to the three following conditions, strictly speaking: a. That tne prolonged note be one which, in the original Chord-progression, moves diatoni- cally (either downward or upward, but best downward} ; b. That it immediately make this diatonic progression, as Resolution; and, C. That it be a 'tone which does not legitimately belong to the Chord into which it is carried over. For example. 8. ) S. S. Ex. 261. p f> P 43 08 43 1) Here the "measures" are again separate, as in earlier Examples. *2) S. signifies "Suspension". *3 Measure 1 is the given harmonic succession. In No. 2 the Soprano note d of the first Chord (which has a diatonic progression is held over into the second Chord, to which it is foreign, and in which it therefore be- comes an inharmonic dissonance ; during the second Chord it is resolved by progressing to the note which should have appeared at once, and which was displaced (deferred, or "suspended") oy its prolongation. In No. > a Suspension is made in the Alto. In No. 4 there is a Double suspension in Soprano and Alto; hi No. 5, La Soprano and Bass. 337. It is obvious, from the above, that the dissonance by suspension does not alter or in any way affect the melodic progression of the part or parts involved , but simply alters the Rhythm of the latter, by causing them to make their original melodic progression a beat or so later than the other parts. The result might therefore aptly be termed "Oblique Rhythm", because one of the otherwise perpendicular lines of the original simultaneous tones is bent forward by the delayed progression in the part which contains the Suspension. Thus: the perpendicular tone-linei in measure 1 are bent, in the 2 nd measure, to / by the S. in Soprano Hints and Directions. 838. a. Suspensions may occur in any part, but are most common in the Soprano. They are also exeat- lent in either middle part, but somewhat indefinite and dangerous in Bass. b. The length of a Suspension is optional ; generally it is just half the value of the Chord into which it extends. It may be more, but very rarely lett than this. Thus: Kx. 262. 15 190 The Suspension C. The Suspension may be titd to its preparing tone ('. . the preceding tone) , as in Ex. 261 ; or it may be re-struck, as in Ex. 262, meas. 3. In the latter case it is more emphatic and effective. In Organ music it is usually tied. d. It is apparent that the Suspension must always appear on the full fraction of the beat, on the Accent; and that its Resolution is invariably less accented. It may stand on the 2 nd beat in Triple time, if resolved on the 3 rd beat, which is weaker. Ex 263a. 6. The Suspension and its resolving -tone 'called the "Suspended tone" or "Displaced tone") should not, as a rule, appear simultaneously, in different parts, of course. Especially not, when the Suspended tone is a sensitive Interval (Leading-tone, Mediant, etc.) which will not readily admit of duplication in any case : and under no circumstances in two cent parts. The Bats part is usually exempt from this rule. For example: r The Susp. / in Sopr.) and its resolving-tone e (in Alto appear together. This is palpably incorrect. *2 When the conflicting tunes are further apart, the error U less disagreeable, but still inadmissible when. M here, a note is involved (e. the Mediant, which should not be doubled hi any case. *3) The error which this rule aims to prevent is the inconsistency of deferring a note t'w one part , by means of a Suspension, and neglecting to do so with the same note in another. Therefore the blunder may easily be avoided, either by not don ill ni y the note which is to be suspended, or by suspending it in both parts. *4) This is good, firstly, because the Tonic note is involved (which may be doubled without hesitation), and secondly, because the duplication occurs in Bass. *6) Also good, as the Suspended note is the Tonic. *6 Suspended Dominant. Additional illustrations of the Suspension : X. Allegretto. & 6. 8. 8. 8. 8. Beethov FI h It -- r Harmonic Suspensions. 197 9. Allegro. Beethoven. 3. Lento S. S. S. J> 9 i - Schumann. 4* Allegro. S. 8. CJF *1) Again continuous Examples. *2) At each of these lines the role given in 338 e is intentionally Yiolated. Harmonic Suspensions. S39. It is not absolutely necessary that the tone which is prolonged in this manner from one Chord over into the next, should become an Inharmonic dissonance, as stated in 336 c. Very often the prolonged note agrees with the Intervals of the following Chord, so that they together assume the appearance, at least, of a Harmonic body. When this is the case the prolonged note is called a "Harmonic" Suspension; and it will nevertheless produce the effect of an ordinary Inharm. Susp. , if the apparent "Chord" does not conform to the har- monic progression which is expected or required. For illustration: Ex. 265. FI 7, 1) The 2 nd Soprano-note 6 appears to be a Fifth of the Triad III; but this Chord, besides being unusual in any connection, is out of the question here, where the I is required, as Resolution of the preceding V. This b must therefore, altlioui/li not inharmonic, be regarded as a Suspension; i.e., as a tone which is pro- longed beyond the first Chord for the sole purpose of deferring or suspending the next note, c. This is an- other proof that the underlying principle of Suspensions is that of lihijthm \ "Oblique Rhythm'', 337j, and not 198 Suspension- Chords . merdy of eelodic succession, or inharmonic combination. 2 This appears to be a III; but see Ex. 151, note ! . $) Appears to be a VI, and is therefore more plausible than *2). But it sounds more like * Double-susp. than like a Chord. *4) 5 Appear to be Chords of the 6 h . 6) All / 4 Chords, when used in this connection, partake very largely of the nature of Suspensions. *7) Looks like a 1 an im- possible "Chord". *) Looks like a IV; also impossible. *9) On the contrary, these Soprano note* (f and e) we not Suspensions, because they represent Chordi of undoubted identity. Suspension-Chords. $40. a. Analogously, a whole Chord may be prolonged from an unaccented beat to the following Accent, in such a manner that the expected (accented; Chord is obviously deferred for a beat or so. See Ex. 266. This occasions, of course, a Rhythmical Halt ;65 b, 221 No. 2); but an intm- tional one, which will be harmless if effected in such a manner that the intention is obvious! b It must be clearly understood that the 'Rhythmical Halt", which arises from a neglect to change (he Chord at the Accented beats, is simply a violation of the harmonical accentuation (4 a 1 , and has only been de- precated heretofore because this* mode of accentuation is probably the most natural and the strongest. But, as shown in 4 a , it is not the only means of defining the Accents, and, therefore, its violation does not inevitably result in complete confusion of the rhythm; it is only necessary to apply the other accen- tuations all the more emphatically, in order to define and re-establish the correct rhythm, in spite of the false harmonical accentuation. e. A misconception of the rhythm, which is apt to ensue in this case, must therefore b averted by such means as serve to denote, unmistakably, the location of the accented beats, namely: by strong Metrical or Dynamic accentuations; by close connection with measures in which the rhythm is correct; and by analogous and symmetrical arrangement of the Members of the Phrase, as in Sequences and the like. Such prolonged Chords may be termed "Suspension-Chords". For illustration. 1. Moderate. Mendelssohn. 2. Allegretto. Mendelssohn. m Ei. 266. 1) A ^Susp.-Chord", repeated from the preceding measure. The correct rhythm is defined by the symmet- rical agreement ^th the Metrical Accents 'heavier notes, on the l ft and 3" 1 beats of the meas. befcre. Suspensions. 199 *1) At these Susp.- Chords the rhythm is endangered more than usual, by the Ties, which completely stifle the Natural Accents. But the heavy metrical accentuations in Bass effectually re-establish the rhythm. *3) Here the fundamental rhythm is marked by the Dynamic accentuations (s/), and also by the Slurt, which indicate what notes constitute a brat together. See also, Ex. 2u3, No. 1; and Ex. 214, No. 8. Schumann, as a rule, takes but little pains to preserve the fundamental Rhythm, as the following extracts prove- Schumann. idem. op. 99, No. 12. -Vj -^ y See, to the contrary: Schumann, "Bunte Blatter" Op. 99, No. 11, Trio; and Op. 99, No. 12, measurM 57; 911; 16; 20 etc. Exercise fifty. A* Basses, to be worked out and analyzed as usual, marking each Susp., and defining the Chords accordingly. The Scholar is recommended to tie every Susp. to its preparing-tone (338 c). Fatsst. a. BjOEEE * f n p f H w -K ^ Bjj ff ' 4. 1 3 *V 6 ? 1\ 9 7- 6- 65 7 65 6 5- 2 1\ 6 6 7- ^ ,!_B 65 i 43 43 6 43 '" 5 43 - 21 23 * 8 7 , ,_ _ F 1 b P J 1* 1 C i T jtj ""FT J b s v j * fc * tr* J S* EE 6 6 5- '2 66 6- JT LA, 7 6 g- 7 w 4- 5 43 43 ^7 43 5 - 23 21 23 6 M 1 - , ft ^ -S **) 4 <* +8 ^)f|-B m > 08 65 5- 1) 9 7 6 5- 6- 656- 6- ^-6- 98 87 i' 8- 43 23 '5763 43 4- 44 16 43 45 76 65 gf. 11 23 3- 23 3- 3- 43 78 4o +3 +7 * 7-5 Baefc, f~ u i lr e -1 ^ 1 -1 r 1 - f P a --- t i I ii p 1 J, (3 m ' I i ! ^ I P J i ^ " A j = ft! u L 1 1 J a 1 1 | L * g 7ft 6 98 98 66 98 B7 78 6 7 - 5 J- S- 5 43 76 6 5- B43 6 5- 4 87 23 3- / 3 -*)-*- t 7 3 F 8- ft 5- 76 ^7- 5- ft- *78 6 6 5- 98 7ft 5-157 5 4 23 2 6 6B5 4S3 45 5 65 483 6- 4- 4235 S- 23 43 4# 4- 3- 3 3 63-6 -a 1 1 * ~p [ ~1 1 1 \ < 98 e 9H ^ 98 b4 78 ^ ' 8 - 4 3 5 7 5- 1! S3- ^3 43 3 . Jj 3 200 Suspension*. fy? jTg f -T~*l * s* - r i 1 z -P f 7 s *. 8 -- . f ' I 1- 1)^ a - * * ^~ -4 1 I. . r SU 6 6 S f 1 i Si 11 8 ^^ ' H 65 6 6 43 5 5 ^ 7 <*- 98 65 43 , ^ 98 6- 3- & b7 b?" 1?5 B "A X 5 67 7 6 t>? S3- S3 *1 These slur? before the Bas^ figures signify that the first Bas* note is a Susp., and therefore the upper parts are to take, at once, the Chord indicated bv the fodounmj tijnirea. *2) Rhjthm ,* f or f f; the Utter is the best After working out B and 0, add Short Original Basse*. B, The following plain Chord-progressions are to be furnished with Suspensions on the fint beat of each measure, as follows: 1. in Soprano alone; 2. in Tenor alone; 3. in Alto alone; 4. in any two parts together; 5. in all three upper parts; 6, 7 and 8, in alternating (tingle) parts, occasion- ally including the Bass. First review 336 a, b, and Ex. 261. This Exercise may be first written out and then played ; or it may be made at tight at the Piano. parts it is allowable. C Play the following Chord-progressions, at sight, with a variety of S>/j>nsiont, and in every Major and Minor Key: I V || I V 2 || V, I || \T, I, || I IV || IV I ||1 V, || V VI |J . Fundamental principles. Tke Suspension is a tone which does not belong, legitimately, to the momentary Chord, but to the preceding one. Suspensions are resolved diatonically, downward or upward. Suspensions chiefly affect the Rhythm. They always occupy full beats (or accented fractions). They must not necessarily be inharmonic. The Rhythmical Halt may easily be counteracted bj Metrical and Dynamic accen- tuations. Irregular Resolutions of the Suspension. 201 Irregular Resolutions of the Suspension. 141. In order to be absolutely strict and distinct, a Suspension should resolve itself at once, during the beat in which it occurs , and, consequently, before the Harmony can change (as was seen in the foregoing Examples). But this rigid treatment is by no means obligatory. Very beautiful and justifiable effects can be produced, by changing the Harmony at the tame moment that the Suspen- sion resolves itself. This simply involves a progression in one or more of the other parts, simulta- neously \\ith the progression of the'Susp. into its resolving-tone. 842. The rules of this very common irregularity (which may be termed the "Delayed Reso- lution", because the Resolution occurs in the 3 rd Chord, instead of in the 2 nd ), are aa follows : ft. The Suspension can not evade its Resolution, but must progress diatonically into ita original Resolving-tone Consequently, b. The other parts must progress into some Chord which contains this Resolving-tone. This will be, most naturally, some new Inversion or new form of the original Chord it- self; but it may also be a new Chord, of the same, or even of another Key. a. Same Chord.) s. b. (New Chord.) 8. c. (New Key.). S. 1.267. *1) The Bass and Alto make a progression at the lame time that the 8. in Soprano makes its Reso- lution, by which means the Chord changes its Inversion. *2j The Bass moves, and changes the Con- cord V into the Discord V, during the Rea. of the S. In the following meas. it is changed into a Vp. *3 Here, the arrangement of the Chord is simply altered, by exchanging Tenor and Soprano. *4) La this meas. the progressions in Bass and Tenor result in a change of the original Chord I into its Relative, the VI; but the Res. of the S. in Soprano is not interfered with. *5] The resolving-tone of the 8. in Alto becomes a Seventh.' This is unique, but perfectly justifiable. The Parallel fifths in the Middle parti are not wrong, because the first one embraces a Suspension, and is therefore not harmonic. The rule only applies to fifths which are Perfect and Harmonic. *6) The progressions in Tenor and Bass change the Key ; this is allowed if effected smoothly and without interfering with the Res. of the S. *7) Hera the change of Key is almost too great. See Appendix C. 843. Two other Licences muy be mentioned in connection with the above "Delayed" resolution, which they closely resemble, and of which they are in reality merely a more extended form, namely: a. The Prolonged Suspension. In this case the S., instead of resolving before any other progression takes place (as in Ex. 261], or during the progression of the other parts (as above, Ex. 267), is extended beyond its natural resolving-beat, so that the other parts move during it* prolongation: See Ex. 208 a. b. The Passive Resolution. Here, the Suspension is extended beyond its resolving-beat, exactly as at a., but the other parts progress in such a manner that the Susp. becomes Harmonic: See Ex. 26Sb. The term Passive Resolution is applied to this Licence, in analogy with Ex. 132, to which it is a parallel case. 26 202 Irregular Resolutions of the Suspension. N. B. In none of these cases can the ultimate diatonic Resolution of the Suspension be evade i 1) The Susp. * progressions, before the Suspensions are resolved. a. The Resolution of a Suspension may be Deferred, exactly like that of the Dominant Disso- nances (Ex. 131 a), by interposing any convenient Interval of the Resolving chord, between the Susp. end its Resolving-tone, or between the Susp. and its repetition: Ex. 269 a. b. It is also possible to interpose an Interval of the preceding Chord; but it is more dangerous, and more difficult to justify. In this case the interposed tone may be harmonized independently Ex. 269 b. C. finally, the Suspension may be Transferred to another part (like the Dissonance in Ex. 131 b) when the Chord remains the same. And Double or Triple Suspensions may exchange parts, fix. 269 c. d* In all of these Licences, the Suspension should be ultimately resolved, in the register (Octave) where it last appearedl O. (Deferred Resolution.) f Andante. )=-& Schumann. 1^ r to -. s.r=~?r - I/-1 el * Irregular Resolutions of the Suspension. 203 C, (Transferred Susp.) 8. Exceptional.*"*} same deferred Chord, is rehannonized, as independent beat. *5) The Susp. is transfe'rred to Tenor, and resolved there. *6; The Suspensions in Sopr. and Tenor change places. *7) These measures are both exceptional, becauM the Res. of the Susp., after being Deferred, is evaded altogether. Comp. 195 c. Exercise fifty-one. A* Basses, to be worked out and analyzed. 83 . ^ *V~ ro ' d 1 |-^ J F4 1 ] P~S FWP Hz^ f- * " i TV P * ~m 1 f * -\ f m GZ C * [ * j * f [ " Jxv * | 1 T LJ- xi -1 if 1 11 -^ F I 5 7 5""- 67776^776-567 9-7 t\ 4434 t 3 85 4 7- 33 4- 3 !*" 8 5 **^ 7 -I ' ' 9 : i~*~ JV^TJ i* M J* 1 J rtfe*-*r- ^M Hitf~ "75 667 ^5 4 =F^H^ *" 5 4543 2321 +5^) f-^^^^F -^_k t * 1 * JS r U 1 -^-H * 4 || ft 4H ^ * j 5 6-97 B65 U6 - 8b7 " 878 7 7^3 7 4543 73-6 5-65 5-6 * 4 3 2321 4 3- 42 ~. 7 As M JJ* I ' M 98- 7 78 5 ft 65 5-635- 45 4 43 3 37 3 4 -i 1 I 7 ft 6(5 5 36 5 7 !J7- ^ *8^5- 6 S- 6 t 8 958 6 57 65 7ft 3h7 798 b? 95108 4*5- '453 5 23 3 4 43 3- 5 5 4*3 423 +3 **) **) f +38 **) 6 -5+8 ^f^vpa- i JB | ( \ --a 1 i -j-^s ~'^r~ K * **~- * ^ 3 087 5 1H 754 ^6 5 S|7 9 10- 65 6 5fc7 6 $7 576 5 421 #3 #7 4 3- $43 6 59 8 4 3 243 487 85 5 * 498 3 243 -j I r -+$ | 1 * t* 56 87 5 6 K65 Hcwison. S _ -8 , | J J ; ^ ^~9-&\ 1 T- =f *~* J 1 J ''ftg^t *= - ~ ^ ^ J!' 1 L_J J -*3*- 5 6" 433 5- 98 5 6- 4*3 4 76 "fl 6- 2 96 K 43 M8 8 6- 85 6- 43 43 43 43 3- 23 *- c. = 466 a t 5- 6 5- 6 tt 5-98 71,6 43 4 43 4 b43 6- 4 4- 3 76 7fl 65 5- 4- - 43 30t 354 r 206 The Harmonizing of Melodies. igUHs Tfl 1 J J 1 1~~- ~~1 i 1 J 1 T~ & ^~* T' $r*~ir.-^ t- t * ;f-j 1 *_ 6 "-" *4 4 *Jt f 1 * / xe x - 1- 6- 85 43 23 75 ud ^~ %* j[l J - L ^ J-j 5 t -5 1 ' 1 076 7-44 65 93 43 * J J. 18 *- "t- 8 = 43 4- 43 7 34 * fi75 678 3- tiS- 5H 3C f (4 * 43 \ \ \ J I 1 56 5- 78 7- 5- 55 b43 4- 5- 43 #23 43 1) The Suroeniions may be introduced strictly, as before, or irregularly u thown in Ex. 270. The choice is left to the Scholar, but preference is to be given to the free introduction. *2j Suspensions strict 3) Suspensions all irregular, and chiefly in Soprano. *4) Exercise 50, note *1). *5 The Ch. of the " th falls on tbejirst beat. *6) It is not impossible for a Phrase to end thus in the Pos. of the Third. Such Perf. Cadences are called "Incomplete". *7) Melody-notes. The Harmonizing of Melodies. S47. The treatment of certain tones of a given Melody as Suspensions, mmy be obligatory or optional, according to circumstances The rules are as follows: a. Only an accented beat [or the accented fraction) may be regarded as a Suspension (338 d) ; and b. Only such tones as progress diatonically as Resolution of the Suspension). e. If the accented tone which progresses thus is tied to, or repeated from, the preceding tone, there is every reason to suppose it to be a Suspension with regular preparation; but, d. Even when such a tone enters with a skip, it may be a Suspension with irregular introduc- tion (as above). 6. The principal guides will be : the natural or necessary order of Chords; and the character of the Melody. Exercise fifty-three. Melodies, to be harmonized with occasional Suspensions in the given Soprano, or in any tfur part. t\ If The Harmonizing of Melodiet. 207 I) ! *\ ! fr^^JpU ^-^JJ^jqjz I tttsp. _^ S5 //I jm |-gj -ti - *=* tegnt. ^^E?S^r^g 4-1 ' -r'^'~ i> 1 Each of these tied notes may be a Suspension (347 a, b, e). In order to become such, it must be ignored (M Inharmonic tone) and the following tone mtut be harmonized in its place, as if the Melody were u.: etc. - and etc. The i- Minor. *5) It does not matter, of course, whether the tone is tied or re-struck, over the Accent. & | i i 6) 0-Major. 7) Modulations at option. *8) Melody originally: 9) At these (and other; points, the Suspensions may be irregularly introduced. See 347 d, and review 345b. The 2 d note of the slurred group is harmonized on the 1** beat, and the 1 st note must belong to the foregoing Chord, whose choice it therefore determines. The 1 st two measures of this (5th) Melody were then, originally: etc. 10) 5-Minor I. Ml) .F$-Min. IV. *12) Altered li of ^-Major. The I 2 follows. *13) Mixed IV of 6-Min. The I 2 follows. .*!*) ^>-Maj., ^I'-Maj., Off /-Minor. Harmonize also- Melody h of Exercige ;i3; and Melody y of Exercise 34. 208 The Anticipation. Fundamental principles. A Snsp. is a tone which must belong to the preceding Chord, whether it enters by pre- paration or with a skip. - Almost any accented Melody-note which progresses diatonically may be harmonized as * Suspension. Section 3 rd . The Anticipation. J48. The Anticipation is exactly the opposite of the Suspension, and consists, as the term im- plies, in a tone which does not belong (legitimately) to the momentary Chord, but to tht following one. It is much more uncommon and dangerous than the Suspension, because it is difficult and unnatural to accept a tone before it* time. Therefore it is limited in its uses It occurs most fre- quently I 1 * 1 *, at Cadences; and 2 nd1 *, in Sequences and the like, where one Anticipatiom appears to confirm and justify the other. For example : Ex. 273. . 1 | Ant. | ft. ^ 1 1 A A. A. Allegro. """^ A ' *~ ^M _ ! J ^ r ri j J^ ^- -*-*} &=-?- ! m * _iW** m ^^ i * s \\^) *rJi \ - 1 -' - y ffft=f> Ex.261 1. Ml 1 =^Ti J&- -& ?5*- r i r f- T- r- B *8] *4) J "T 1 _^ A_ m S> (^ O f<* * r i* i > ^V^* . J* 1 -r*r r ^, L| | | 1 M j > " rj ^ A. ^i. grf A A ienlo.-^"" n i ^ A. A. ^^*^ Bach. */ ^ ; ** t* ' f ^*'~ ^ -j j- i ; 4 ' F Bvll-lt h Wr* ft r. "9" C/ sr 2 tT & ^T. ^T ^1, A A A A. A. A. 9 r r --? ?i r ^^ -4 ,"! ^A *** -gJ ^ U- F > 1 -/r,-7, - A-F^I l r 1) Ant or A. signifies Anticipation. 2) This c does not belong to the Chord with which it appeal* bat to the Jnllnwiiiy one. A similar Ant may be made in Alto , as shown by the notes in parenthesis. 8 Any series of Chords may be embellished (in any part or parts) with Anticipations, as shown here, 4) Here the Anticipations (in Bass) are tied to the anticipated tone. This injures the rhythm very much, and U only comprehensible in rapid tempo. See also Bach, 48 Fugues and Preludes, Book I, Fugue No. 14, measures 8, 9; 16, 16; 19, 20; 2124 ; Beethorea, Op. 49, No. 2, 2nd movement, first measures. Harmonic Anticipations. 209 Hints and directions. S49. a. Anticipations are most intelligible im Soprano, but are possible in any part. b. The Ant. should never exceed in duration half the value of the Chord in which it occurs; the shorter it is, the more easily it will be recognizable as a foreign Element, and the less it will endanger the rhythm. A. A. Ex.274. C. Anticipations differ from Suspensions in their rhythmic location, being always found upon unaccented beats, or weak fractions of beats, whereas Suspensions occupy accent beats, or accented fractions (338 d). d. Anticipations are generally re-struck; seldom fc'edtothe Anticipated note. Ex. 273, compare c with I and d. 6* An Anticipation may be introduced from any lower or higher tone. As it pertains exclu- sively to the tone which follows, its introduction is of no consequence. Harmonic Anticipations. 350* Anticipations may be Harmonic as well as Suspensions. If a tone bears a closer and more legi- timate relation to the following Chord than to its own, and, especially, if it is comparatively thort, it will produce the impression of an Ant., whether it is inharmonic or not. And , on the same principle, the whole following Chord may be anticipated. Review 339, 340. Harmonic Anticipations are preferable to inharmonic ones, because they sound better, and disturb the harmonic sense less than the latter A. j* ^ .-N^i. b. Allegro. Mendelssohn. EX.27&, 210 Harmonic Anticipation*. r This f might represent the IV, and almost surely would, if it were not M> brief. *2) The/, M half- beat, is a legitimate Seventh; but ha relation to the following tone gives it the appearance of an Antici- pation. 3 Auticipating-chord. In these two Phrases, the 2d Chord of each beat is an Ant. of the follow- ing beat. S51. When, as here, a Chord is repeated over the bar (or Accent) in violation of the rule ot har- monical accentuation (4 a 1 , it may be difficult, or even impossible, to determine accurately whether the first Chord is an Anticipation of the second one. or the second a prolongation (as Suspension) of the first. The tied notes, in the right hand alone, in Ex. 266, No. 2, may be analyzed in either way). In cases where there is the least doubt, it doe* not matter how they are construed. The main and essential! requirement is: to define the fundamental beats so clearly that no misapprehension or confusion of Rhythm can possibly result. This matter is explained in 340 b and c, which review The following is an interesting and simple example of both cases in succession,: Allegro. BeethoTCD. Ex. 276. r r ui S. Ant. f 352. There is no doubt of the following examples being Anticipating-chords, principally on account of their brevity. They might aptly be termed ''Rhythmic Anticipations", as they do not affect tk* fundamental Harmony in the least : Beethore.. *..,. Jfci. (g~fj-ft 1 Allegro. It Ei. 277. 9. Adagio. Beethoven. QBE -?-^ r L rg FH - " Ant ^r 55 3 See Ex. 182, Mozart, measure 3. 3 Moderate. * ^ J- J9 J ^^.v j.,;1 != Ant? Anil c t>~ Wagner* 7 I/ Syncopation. 211 Syncopation. 853. Syncopation is the term applied to that kind of irregular Rhythm in which the linger tonea occupy comparatively weaker beats, or, more specifically, fall between the beats. It is simply a violation of the Metrical accentuation (see 4 a, b), and results from tying an unaccented beat, or fraction of a beat, to the following accented beat, or full beat. It is the most perspicuous example of "Oblique Rhythm" (337), because the syncopated part or parts are literally bent forward or backward so as to differ (by a beat, or fraction of a beat) from the other parts, which mark the regular Rhythm. 354. Whether the syncopated notes, when they fall exactly between the beats, are Suspensions or Anti- cipations, depends of course upon which way they were "bent"; that is, whether they belong to the following or preceding Chord. Sometimes, as stated in 351, they can be accounted for in either way, and, as a rule, it is quite unnecessary to consider this doubtful question at all. The notes can be produced, and defined, simply as "Oblique Rhythm", or "Syncopation". In the following Example the distinction is very plain at a and b : Beethoven.*^ Faisst. Ex.278. 8. S. S. S. s. & Ant. Ant. Ant. A., e JL , J | N *A) I J Jll IT ^*^ I I m\l ' ^* If J a""^-^-^ f- -f-^^ > Ti ^F~ " -^ * r f * f- 9 - r ill fi II r r ~^ i ti etc. 7 V I tf-maj. 8. S. 8. 8. S. 1) These syncopated Soprano notes, which fall exactly between the beats, belong to the Chord which precedes, and therefore become Suspensions. *2) Here the very same notes, owing to an alteration in the location of the Chords, are Anticipations of the following beat. The direction of the Oblique Rhythms is indicated by the slanting lines. *3) The syn. notes in the ' left hand", being struck after their beat, become Suspensions. *4) Piano-Sonata, Op. 2, No. 3, 1 st movement; see also, measures 11, 12 Bass ; also from the Double-bar, measures 26, 27; 30, ill; 3437; 58 65. 355. Upon this principle of Oblique Rhythm in one or more parts of the Harmony, very unique effects may be produced. For instance , any two parts of the Harmony (the two hands in Piano music and the like; or one voice against the other three; or the Melody against the Accom- paniment, etc. etc.) may appear successively, instead of simultaneously (Ex. 279 a, b, c). Or the Chords may be "broken" ("arpeggioed", as in Figuration) across two beats or rhythmic groups: . . partly in one and partly in the next. For illustration : a* Presto. Mendelssohn.* 2 ) C. Presto. Mendelssohn. Ex 279. 212 Syncopation. Allegro. Pretto. Scliumuuu. Op. *1) At a, h and r the Harmony is divided between the two hands, which strike alternately, instead of together. This doe not affect the Harmony at all, but simply the Kby'lnn, which it makes 'Oblique", M indicated by the slanting lines. *2; Variations serialises, Op. 54, Finale; see also Var. 5, 11, 15. 8) These Rests remove the appearance of Syncopation, but it is clear that they merely take the place of Tie* Thus- See also: Mendelssohn, Op. "2 No. :, measure 35, 11 13 etc. And Ex. 296, No. 3. *4) These Eighth- notes, with connected stems, should occupy a beat together, instead of lying across the bars (or beatlincs). The heavier Bass tones define the Rhythm. *5) The left hand here, is lie the right hand at *4). This example is from Schumann's Carneval" ; Paganini"). See also his "Fabel", Op. 12. *6 The connected stems define the "broken" Chord; the brackets define the half- measure groups. Their disagreement is somewhat similar to M). See further: Schumann, Phantasie Op. 17, 1** movement, measures !'5, 96; 105118 Bass ; 2 nd movement, measures -2o Soprano ; 62 65 Bass ; also the last 28 measures of the same movement; 3 rd movement, measures 27, 2b. Schumann, Op n, No. 4. XB. Theie nbliqiie rfiy'hini are only intelligible and effective in rapid tempi, where the conflicting har- monies are of but thort duration! S56. The Anticipation sometimes merely serves to prepare a Suspension. In such cases the Ant. is generally harmonic, but not necessarily so. For example: , , Beethoren. O. Allegretto. A. 8. -j A. 8, A, 8. Ex. 2*0. 270, measures 1, 2, (parenthesized notes). Syncopation. 213 Rx. 28L Exercise fifty- four. JL The following Chord series (in Period- form) : J J J i J J ; 1 ^ is to be elaborated with Anticipations in the following ways (at the Piano, at sight: or as \crittt* Exercise) CU Andante. 6. Lento. c. Allegro. etc. *; d. -4 6 9 "1 *1) It is by no means unusual to add supplementary notes here and there, as in these last two Chords, upon the upper staff, as here , wherever desirable. *7) Ex. 279 d. Melodies, with Anticipations, to be harmonized as usual, a. Andantino. hg-feiJ SL-r- 1 *** t ^5 &-3^r- ) i^ -f f ^jjr-f^* 4 - 1^" ' ~^M P--3 !) A. u ^ pg4-ri N r^. *jr~~ " & 1 ? 1 ^u-t >* =* ftp k & 4 ^ - ^- --? L^- -j 1 :^ ^--f- -1 m-^V-'- 1 ^^ f-^->r3rd -p i /\'. -^7-7*^ - T -n-^- r4 |^ 4-*-J^= ^ EC --# r ye^^s * r rj M j a ix =*-*-* *, **-*-* \ & a 214 The Anticipation. 1 All of these short notes altogether, because they do not or /-Min '3) Comp. Exercise two Melodies are to be harmonized in two ways: 1 st1 y, so that the syncopated notes will be Suspensions (on Mie heavy fraction of the beat]; and 2n d 'y. so that they will be Anticipations (on the weak fraction). The difference is explained in 354, and Ex. 278 a, b. *7) The weak fraction of almost every beat is to be n Anticipation. The 3 upper parts may be placed together on the upper staff, as at Ex. 281, c (note *6L Fundamental principles. The Anticipation is an Inharm. tone (or possibly Harmonic) which belongs to the follow* ing Chord. Anticipations are always unaccented; generally very short. Syncopation is a violation of the Metrical accentuation. Anticipations may merely serve to prepare Suspensions. The Irregular Anticipation. 857. The Irregular Anticipation is the opposite of the Irregular Suspension, and is so called because it i>rogresse* with a skip, instead of justifying its inharmonic nature by remaining upon the note which it anticipates. The Anticipated note appears in some other part, or it is understood, as possible Seventh (or Ninth?) of the ensuing Chord, a. This licence is limited almost exclusively to the Soorano. The Irregular Anticipation 215 h. The Anticipation should skip downward, as a rule. Compare 345 a, For example: a. Ant ^ nt - * Andante. Ant Ant L Mozart. H 8 Ant. H it. Ant B E3: ^7-^-^-3-b imp. Ex. 273, b. r Schumann. <*. Mendelssohn. i K A.Ch. Mend. (IP I 1 ? 2 1 3-] ^11 *g ^, { 1 t^~^ ^ r 1 r i . i h- i i n Ji x ^^ \ "f" 3E r 3 V. 1 i p f~\ k 2 i P f -3 _J -t -9^ =a ^ 1.^ . -^ p 4. ' = E bk= T8 : -J 5 Htrit _^__,. W i IT /. Exceptional. -Jc -2 *** J ^ jf* 1 9* \ 45 Schubert. ^it^= 4^J < R: 2 * | Ant | rrr -^ F 3 ** zf-4- r r i -r V- | "^ En Ant. *1) This mode of treating the Anticipation, although a licence, is preferable to the strict treatment. The Aip is much more graceful than the repetition, as in Ex. 273. *2) The skip upward from th Irreg &nt is exceptional. *3j The Irreg. Ant. in Bass is vy unusual and difficult to justify. Exercise fifty-five. Melodies, with Irregular Anticipations. O* Molto mod. . 8. A. A. is Allegr etto. 1 Moderate. . - y=f=^=rt. w il f^-i * i J i j x ff 9-f-v * -0 , ^ 5 J f J i i* ! r c x Beethoven* - jj -&* ^ i L P*"! %. i n ^^ "j Q0 f 1 1 V*" \ 1 P 9 i ? f ' 1 or rr i > f V- I i i - J 4 *1) The descending Pass.- note, unaccented, is often identical with a Harmonic Seventh, nee Ex. 157, note *3 . *2 The accented Passing-note from below is usually subject to 362, rule b. In this case /g sounds better than /. *3 The descending accented Pass.- note is often identical with the Irreg. Sus- pension ; see Ex. 270, measures 4, 9. Also comp. note *1) above, and Ex. 253, note *3). 364. a. The term "Progreutve" embellishment may be applied to those forms in which Pass. -notes arc used, because a transition is thereby effected from one Prin.-tone into another. That is, two different harmonic Intervals are involved (connected) by the embellishing note or notes. b. It is obvious that the application of Neigh b. -notes (Local Embellishment, Ex. 285) is extremely simple and easy , and can be made at any single tone , in any part, without trouble. The use of Passing-notes, on the contrary, is not always so convenient, as all depends upon the tize of th interval which they are to fill out. In Ex. 286 they are invariably applied where the part has a progression of a third C, The difference between unaccented and accented Passing-notes is, as intimated above, that the latter, by reason of their rhythmic position, are more obtrusive and noticeable than unaccented Passing-notes. For this reason they are more effective when accented, but, at the same time, more dangerout than when unaccented, particularly in any other part than in the Soprano. 865. a. The space between two harmonic Intervals in the same part may be filled out in thia manner diatonically, even when two intermediate Passing-notes are required; that is, Passing-notes may occur in direct succession, in the same direction. b. Chromatic Passing-notes are possible, to the extent of 3 or even 4; but they should be limited as much as possible to ascending progressions. Descending chromatics, es- pecially in rapid succession (i. e. as Passing-notes are peculiar, and often ridiculously lugubrious. For example 287 CI Embellished Melody, and Running Parts. 219 1) The simultaneous occurrence of a harmonic Interval and its chromatic inflection is possible as here, but should be avoided, as a rule. Ex. 263 b (338 e) is a parallel case. *2) Descending chromatics. 8) In chromatic, and, as a rule, in diatonic progressions also, the larger intervals come first in the group. Compare the preceding measure. *4) The notation of chromatic tones must conform to the principles of next-relationship, and to the Altered steps, in general. Hence, not all descending tones are written with Flats, nor all ascending ones with Sharps. In this case gfr would be incorrect, as it is too foreign to the Key (probably C or F- Major). Embellished Melody, and Running Parts. 860. Neighboring and Passing-notes may be employed in embellishing any single Part, in uniform Rhythm. This device is perhaps most commonly applied to the Soprano Part (Melody proper). The following Melody, and its embellishments, appears in Op. 74 of Beethoven; Andante. Ex. 288. S. o o + S. o o + S. o o + S. fl _ [ .,.. . , . . F*^ Accompanied by the Bass, in 3 rd *. Beethoven, Sonata Op. 2, No. 2, last movement; compare measure 13 from the end, with measure 3. 867. Ampler forms of embellishment ('. . larger groups of notes, and in more rapid rhythm) almost always proceed from the simplest original figures, by adding Neighb.- notes. Thus: Ex. 289. 28 220 Embellished Melody, and Running Parts. Exercise fifty-six. The following Melodies are to be embellished alone (the indicated Harmony can be given to tk left hand) in a uniform Rhythm of 2, 3 and 4 notes to a beat, tuccessively : (see rules below) : Mm ^"* ^P* **^ rfr^T j J-j J ' J I I i J jJHl'i. j ^ J || J j ~~ i t / //i F ? -Jl k_J_ / F, ! * * / V ^__^_ 7, 7K 77 , / r / 3. -i-T^h?- J , -r-j n [_fa_*_L J z 3 <* =3^^- For example, (No. 1): 1 i 2 notes; Rules: 7. The running Rhythm must not be interrupted or altered until the Cadence-note is reached. The latter is not embellished. 2. The given Melody is not to be modified by adding any other Principal tones of the momentary Chord ; excepting an intermediate Interval, when the skip is large : and, in rare ca<5es, a Imoer Chord - interval 3. As a role, the original location of the given Melody-tones in the mm*" re should not be changed too often by preposing an accented Pass.-note, though the possibility and necessity of sometimes using the latter must not be overlooked. See Ex. 286b; Ex. 287, measure 1,2. 4. The Embellished part must run smoothly; repetitions, as in Ex. 288 c beginning of measures 3 to 6 should be avoided. 5 The running part, when finished, must be strictly analyzed, and each tone accounted for, aa Neighboring or Passing-note of the respective Melody tones. Review 362, and 365. B. The following Period is to be suppliid, successively, with a Banning Alto, Running TeilOF, and Running Bass, in a rhythm of 3, and then 4, notes to a beat [0 2 and 5). See rules below: MJJ For example : S3 02 4 ft b5 6 ft t) 06 7 ^L, Rules t /. The adopted Rhythm must not be interrupted at the Cadences. The embellished part generally nw* on for a beat or so past the final Cadence-note in Soprano. 2. In order to afford the running part the necessary "spaces", it should not, in its original condition, be too quiet. Compare the part-progressions in the next Exercise. The given Bass part mav be altered, at option. 3. The distances between the parts 'TEx. 36} is of no consequence in this case. Rule 2, above, is nt valid for any part but a given Melody (Soprano)! 4. The embellished part must run smoothly; but care must be taken to avoid formlessness and discursiveness. Hence, Sequences are very desirable. Comp. Ex. 288 c. See also: Mendelssohn. Op. 54, Vsi. I; Op. 82 Var. IL Beethoven, Op. 120, Var. 25. Cramer, Etudes 41, 80, 16, 32 Original Edition). C. Construct an Original Phrase with Running parts. Embellished Harmony 221 Fundamental principles. One, or more, of the 4 adjacent tones of any Harmonic Interval may be used in a variety of connections with the latter, as Local embellishment of that tone alone; or as accented OP unaccented Passing-note between that Principal tone and the next. The upper Neighb.-tone agrees with the Scale; the lower one is usually the half-step. Several Passing-notes may occur in succession, in the same direction. Chromatic Passing-notes are only recommendable in ascending progression. Embellished Harmony. 168. Instead of limiting the Neighboring and Passing-notes to the embellishment of one tingle part, u above, they may be employed in all of the parts, in alternation, (or in two or three simultaneously), for the purpose of filling out the spaces between the Harmonic Intervals. In such cases, not only the Harmony itself becomes smoother, and more graceful and agreeable in effect, but the impor- tance and melodic individuality of each single part is enhanced, in proportion to the extent and the manner in which Auxiliary notes are \ised. 369. Hints and Directions. a. All Embellishing notes progress diutouically. b. Passing-notes should not, as a rule, occur together with the Principal tone towards which they tend (in another part); comp. 338 e. Nor is it well to double a note which is being embellished, if avoidable; see Ex. 287, note *1). -- This rule must, however, be limited to sensitive tones, which are not likely to be doubled in plain Harmony. f. Accented Passing-notes should be used sparingly, especially in the middle parts, and must be handled with care and judgment, so that they may not disturb the harmonic sense, nor conflict toe sharply with the other parts. Comp. 364 b, c. Avoid chromatic Passing-notes, as far as possible. d. When Embellishing notes occur simultaneously in two different parts, they should generally harmonize with each oiler (i. e. should not differ from the Chord and from each other also . Therefore they must run parallel in 3' dt or 6 ths see 46, Rule III; and Ex. 305) ; or, if in contrary motion, they may meet (cross) upon the same tone. If Emb. -notes appear in three or four parts at once (which occasionally, though rarely, occurs) they must represent entire Passing-Chords or Neighb.-Chords. For illustration- 1. Lento. El, 290. 222 Embellished Harmony. BeethoTen. Brahms. 1) In such rapid tempo these are simply Neighb. and Passing-Chords. See also: Mendelssohn, Op. 81, Var. II. Bach, "Well tempered Clavichord", Book I, Prelude 2'1; "St. Matthe\v"-Passion, Introduction. 6. Parallel Fiftht, which are very liable to result from filling out the harmonic spaces with Unessen- tial-notes in this manner , are always to be judged according to the quality of the Second Fifth. If the latter is harmonic and perfect, the parallels are wrong; but if inharn.onic or imperfect, they need not be avoided. Ex. 267, note *5), and Ex. 125, note *4) are illustrations of this principle. See also Appendix A, c. Parallel Octaves, made in embellishing the Harmony, are, on the contrary, always wrong. These rules are also applicable to parallel Octaves and Fifths which are interrupted by a Passing- note. See also Ex. 106, note *l). For example: f. The Rhythm which is adopted for the Embellishment at the start, must be carried along from part to part throughout the Piece (or Section), with as few interruptions as possible. And when such interruptions are deemed necessary, they can only take place at the accen- ted beats, and must be but a slight change of motion. For illustration a. 1) These cessations of Rhythm are wrong, as they occur at the weak beats, and are too positive from 6 f ). *2) Here the Tenor part takes up the adopted Rhythm. *3) These interruptions are in the to f roper place, and are slight Embellished Harmony. 223 g. The Rhythm of the Soprano, as most conspicuous and important melodic part, should always be as regular as possible ('. e. the rapid notes should fall on the weaker beats 4b). Therefore the first measure of Ex. 292 b would be better thus: h. Regular Anticipation* should be avoided, as they disturb the flow of the part. Repetition are best when the second note is a Suspension, or in Sequences. See Ex. 288 c. For example: p '^ rrrf In other words, calculate the group of tones so that it will run into the next Harm. Interval at precisely the right moment; not before its time, as in Ex. 293. i. Short Rests constitute a very valuable resource of Harmonic Embellishment, and must not be overlooked. As a rule , a Rest may be substituted for the first stroke of any group, excepting immediately after an Inharmonic note. Ties, as seen in Ex. 292 b, answer exactly the same purpose, but are not always convenient. For instance : J, The Embellishment should not continue tn oy one part too long, but should be thrown from part to part; not in such regular intervals of time as to incur monotony, nor so irregularly as to destroy the melodic and rhythmic unity of the whole. It will usually be taken up in that part in which, 1 st1 *, the convenient "space" is found; and 2 ndly , where it conduces most to the melodic quality of the part. A glance at Bach, "Well tempered Clavichord", Book 1, Fugue 11 and Prelude 12; and Bookn, Fugues 2 and 4, etc. will suffice to show how the parts generally alter- nate and reciprocate, in keeping up the adopted Rhythm. k. That, from time to time, more than one part may be engaged with the Embellishment, has already been seen (Ex. 290) ; and particular attention is directed to the possibility of differ- ent parts embellishing simultaneously, in different rhythms (for instance, in ^ and j notes). 224 Embellished Harmony. Most of these rules must be applied with due allowance, for they are nothing more than general prin- ciples, which are subject to modification in multitudes of cases. If the Scholar has mastered the laws of fiarmony (and euphony) up to this point, and has made a careful and conscientious study of the Works to which reference has been made, he may now confidently trust to his ear in detecting and improving hank passages, after kmcing completed the Exercite* at the tokU. Exercise flfty-teven. AnchmU. las J -'^-4 : i r E^ -E =^f=f^A Allegretto. ft* rule notes to a beat. *5 The Embellishment does not include this short preliminary beat. Here, again, Exercise 56 A, rule 2, is not valid for any part but the Soprano! Review 369 a, d, f, g, i, k. Ex. 2a2b (and Ex. 302) will serve as models. Irregular Neighboring-notes. Appoggiaturas. 870. Either the upper or lower Neighb.-note may Replaced before its Principal-tone, without regard to what precedes (i. e. irrespective of the manner in which they are introduced, whether with a skip, or after a Rest, or at the very beginning of the Phrase, or in the strict diatonic manner shown in the former lessons). Because, similar to the Anticipation, a Neighb.-tone pertains exclusively to \t own Prin.-tona, mto which it must be resolved, but from which it is not obliged to enter. (Comp. 349 ). Irregular Neighboring-notes. 225 371* a. When the Neighb.-note enters with a ikip it is called an Appoggiatura, or, if very brief, an Acciaccatura. b. It may stand upon the strong fraction of its own beat, (like the accented Paw. -note), or upon tha weak fraction of the preceding beat. For illustration : fa. 295. Brahms. Sym. No. i. 3. Adagio. Mendelssohn. 4. Allegro *1 At each beat marked NB. the Neighb.-tone enters with a skip. This whole passage from Brahms u a curious (and intentional) exception to the rule in 369 b. The embellished Melody is doubled in the Tenor. See also Appendix A, d. - *2; The Organ-point is transferred to the middle part, contrary to 330 b. Sen also Beethoven, Sonata Op. 14, No. 2. first 4 measures; Chopin, Etude Op. 25, No. 5, first Part. 172. a. Analogously, both Neighb.-notes may be set before their Prin.-tone, in either order, and, as indicated in 371 b, so that both occur in the beat, or both before the beat, or one before and the other upon the beat. b* This is a Double- Appoggiatura, and the irregularity consists in the first Neighb.-tone progrestitif with a tUp (into the other one). Thtw 226 Irregular Neighboring-note*. BeethoreM. 4, Allegro. 1) Strike the I with the left hand, at each accent. - *2) 3i>2b must be respected in all case*. *) This order of tone* is not as smooth as the preceding figures. The choice of upper or lower Neighb.- tone, as defined in ;<62 a, refers to the last one in the group. *4 Whren the Neighb.-tones are shifted back in this manner, it is simply an example of "Oblique Rhythm", very similar to Ex. 279 d, e,f. *5) In rare cases, the first Neighb.-note returns, as here, before the Prin.-tone appears. See also: Webtir, "Rondo brillant" in E .-Major. 373. This is a species of "Deferred Resolution" very often applied to Suspensions (which are also ia reality "Neighb. -tones" of their Suspended note). This, and other interesting Deferred Reso- lutions, are exhibited in the following example (Comp. Ex. 269 a, b): 8. n S. 8. Ex.297. D-nO. - 8._ 8._ B._ 8._ 8.. inr ~f~~ JT Other Licences. 227 Other Licences. 874. a. The peculiar value and efficacy of Sequences, in producing and justifying irregularities, b illustrated in the following examples, in which the ultimate Resolution of t Deferred Neighb.- aote is evaded altogether. (Comp. Exercise 19, note *3), and 286): 1) 6. Prestf. A. 3-fcfc-w . -t- ... . "i - ' - *1) This first example does not consist of Sequences (like all the ret but illustrates how a Neighb.- tone which n-nembles an Anticipation, may evade its diatonic Resolution. *2) These unresolved Neighb.- notes are Sequences of the foregoing Irreg. Anticipation. *3) In each of these cases one Neiglib.-not progresses into the other (as Double-Appogg., 12), without being directly followed by their Prin.-tone. 4) Compare these Sequences with those in Ex. 288, from which they emanate. *5) These extraordinary Sequences like those in No. 4) are only imaginable in such very rapid tempo. See also: Beethoven, So- nata Op. 31, No. 3, first movement, measures 10,9 from the end. b. Daring the regular Local embellishment of a Neighb.-note, the other parts may make a progression into a new Chord, so that the Prin.-tone in the meantime changes its harmonic quality, or become* fatlf inharmonic (Comp. Ex.267, notes; Ex.271, meas. 1). Thus. 1. Andante. Beethoven. 2. Mod. Schubert. 3. ' ^ x 228 Other Licences. &L801 Si. 301. I IV IV V r During its embellishment, the tone c in Soprano changes its quality from Fifth to Root. *2 Th* Prin.-tone a? becomes an accented Pass.-note. The dotted line indicates that this is sometimes merely * diatonic exchange of Ant. and Susp. *3) These measures prove that this whole irregularity is but one W the many phases of "Oblique Rhythm". *4> Like note *2). Neighboring -notes are sometimes employed as Local Emh. of other Inharmonic tones, usually of an Organ- point or Suspension. Ex. 300, 1- ). IJQ very rare cases it is possible to embellish a Neiyhb.-tone itself in this manner, but only in very rapid succession, as "Appoggiatura- group". (Ex. 300, 56). 1. Allegro. Beethoren. lt 2. Allegro. I I Mendelssohn. Dom. Org.-pt. Mtzart, 6. Andante. Mend. See Beethren, Senate Op. 14 No. 2, 1 st movement, measures 1 5 and 17 ; Senate Op. 101, last 15 mea- sures. Mendelssohn, S. w. W. No. :<5, Introduction (Tenor) ; No. 45, last 12 measures. Schumann, Symphony No. '">, third movement, measures 1 1 5 from the end. Beethoven, Symphony No. 4, 3 rd moVt, Trio, measures ^O 59. d. It may be regarded as a species of Licence, to give greater prominence and weight (length) to an unessential Neighboring or Pass.-note, than to its Prin.-tone. Thus- Other Licences. 229 A* Allegro. Schumatm, Op. 8, A'o. 1. *1) These Neighb.-notes are accented, and much heavier than their Prin.-tones. *2) The Dim.-Seventk of Jv^-Major ('/-/-a7-e7), with proportionately heavier Appoegiatura on each '-beat. *3) Along, heavy Pasiing-note between/^ and d, *4;> A similar heavy Neighb.-note of a. See Beethoven, Op. 12U, Variation No. 1 (Bass . Quartett Op. ^ No. 2, last 8 measure* of the "Trio' 3^ mov't;, in the Bas. Also, Op. 120, Variations 12, 28 (Neighboring Chords), 8, 9, 27. Exercise fifty-eight. Moderate. A. 2 i 1 ^ fe 1) The Melody alone of this Phrase is to be embellished, firstly, in $-notes, as in Ex. 295 1, and ia Ex. 299 8 ; secondly, with 3 votes to a beat, as in Ex. 296 1 ; and thirdly, with 4 nntes fy as in Ex. 2961, and Ex. 2'J5 4. The Harmony is placed in the left hand, for convenience. Besides this, the Pupil may take any thort Melodies of former Exercises, and elaborate them in the same three ways. OX Ox tegue 1 D-m*j. TJ) ( f *2) This Melody is to he harmonized according to Ex.299 3, with 4 Chords in each measure. The second note of each group is a Neighboring-note; the third note may be harmonic, or may be a Passing- note; but in either case the Chord must be different from that upon the accented beat Simple form- etc. C. The following Period (an excerpt from the Pianoforte Works of C ), is to be embellished in alternating partt, as in the preceding Exercise: firstly, with 4 notes to one of the given beat*; and secondly, in 9 / 8 time, with 3 note* to a beat. Any necessary or suitable Licences (chiefly those given in Ex. 295, and 296 2) may be applied. Review 369 d, f, i. k: 230 ' Polyphonic" Embellishment of Harmony. "" ^^-=f * v 4 lB/ 8 tme: D. To this Exercise may be added a similar elaboration of some of the former simple Phrases and Periods, either Original, or given in Parts n and III. "Polyphonic" Embellishment of Harmony. t76. As stated in paragraph 5, 'Melody" u the most important factor of Music. It is the continuous, coherent thread or line" of tones _which the ear grasps and follows (as the eye traces the outlines of a picture), and from which the mind receives its most distinct impression of the Form of a Composition. In ordinary "Har- mony"', as distinguished from "Counterpoint", the principal melodic line, the '"Melody" proper, is placed in the Soprano part, for reasons given in 41 a; and the other parts, though also melodic-lines, are of an inferior order, and only serve to accompany and support the primeMelody, without assuming sufficient individuality to draw attention to themselves and away from the real Melody. This singleness of Melody is the charac- teristic of the Homophonic style of Composition (e.p., Mendelssohn's "Songs without Words") in distinction to the Polyphonic style (e.g., the Fugues of Bach), in which each part is a separalr. and independent Melody- line, of eyual importance with its fettowt, or which is, in other words, a combination of Melodies. 176. When simple Harmonies are embellished to such a degree that the attention is diverted from the fundamental succession of Chords, by the melodic individuality which each separate part acquires, the result is a species of Counterpoint. (Comp. 368 and 327). But absolute individuality of the parts can only be obtained when the Embellishment is based upon some adopted melodic Figure or Motive, which, appearing in alternation, first in one part and then imitated in another and another, institutes that melodic uniformity and equality of the parts, which is an indispensable requisite of pure Counterpoint or Polyphony. The Pupil will be sufficiently convinced of the fact that the simple Embellishment of a given Harmony can never quite reach the high standard of strict Polyphony, upon comparing his most elaborate Embellish- ments of the above Exercises, with the simplest 4-part Fugue of Bach. For while, in the former, the part- progressions emanate passively from a predefined Harmony, in the latter case the Harmony itself is created by the independent active progression 01 the separate parts. 177. Polyphony is the highest grade ot Music , and demands the greatest skill in the treatment of mu- sical Material. Hence iU practice by beginners is out of the question. Nevertheless , Harmony 'Polyphonic* Embellishment of Harmony. 231 which ii embellished according to an adopted melodic Motive (376), approaches the idea ami resembles the effect of the polyphonic style, and is well worth being thoroughly exercised. 878. Thus, any given succession of Chords, for example Ex, 302 4/ 4 i__ n v yi|n v may be embellished in many ways, with a variety of Motives, as follows : J. Motive: /J J_ . Motive: ff r. Allegretto. B ' ET ^ 232 'Polyphonic" Embellithment of Harmony. C l> .' j Jut-f IIIUT rn. "j p^J bd r-J J n ^. > T ^ fcf fl JT i i ft etc. _ ftJ ^ ^TIT -7V- r V 4, JLL-^-U r 5 ^J ' *1) "Pr^grftsiTf" Embellishment (364 a) is more appropriate ID this style of Music than "Loral" Em- bellishment (360) as at note *2 , because it is of a superior order, and more essentially melodious. *8 The direction of the intervals may be reversed, as here, at any point This is called an imitation im Contrary Motion. *4) A slight modification of the given Harmony, like this Passive Res., mav be made without scruple, for the sake of the adopted Motive. *5 Harmonic Motives of this kind afford the most natural and convenient basis for more rapid and ample Motives, as in No 6. It has already been seen that larger Motives and Figures proceed generally out of simple small ones. See Ex. 289. *6) Motive. *7> Motive. -- *8) Op. "4. See Ex. 288. For further examples of Embellished Harmony, or Free Polyphony, see Beethoven, Op. 120, Variations 11, 14. Mendelssohn , Op. 54 , Variation 2; Op. 83 Var. 2. Bach, Well-tempered Clavichord, Book t Preludes 12, 22, 23; Book II, Preludes 5, 11, 1. Exercise fifty-nine. The following Melodies are to be harmonized with moderately simple Chords (and Modulations) and the Harmony thus obtained is then to be embellished in a continuous Rhythm of J**- notes (2 notes to a beat) in alternating parts, as in the two preceding Exercises, but with respect to the principles above enunciated. That is : the main object should be to increase the melodic effect of each separate part, especially of the three 10W6F parts. The Embellishment may simply tend to promote the melodic flow of each part, in a general way, r it may be based partly or entirely upon simple Imitations (with small Motives) as in Ex. 302. Rules: /. Review 369 a, d, t nd 370. 2. The given melody is not to be changed, '. e. does not take any part in the Embellishment 3. The Embellishment may be added after the Chords have been found; or the Harmony mav be determined at once in its embellished form. 4 The use of regular Suspension! (with Ties;, and of ties generally, is very advantageous! 1. Moderate. ~T~ it / v r F r * ^3. Adagio. - f ^ P f ? F.J - - i-l Ntg ^-TV-* i 1-^-^ m m f :SE*~*3 f ' ' s -^ 2 i i Mr* f f -^c^ i ~5= * y | | 1 1 ' **) ) Choral. 3. Adagio. 7^ r^ ->. /TV y J H-f -* J 1 J^i iii^- P n - i I f : tJ4^ U4-*- ~* * UJ ~**-^4* 1 ^J. tj 1 f ff -g, V V/ * * j" 1 " **) // Choral. . -^ <^r _*^, t-rV- = *!- \ -m ^ -f 1 f m . . J ) 4* Aimgi%. zEnck, J-^rj r-t-i i- r H"-H r i i -t tfa ,. f . ,_ f ! 1_ _i y. ^ j w j j j 4 -i ^ J 11---* f j .==3= |=3 The Harmonizing of Embellished Melodies , and unfigwed Basses. 233 ^JJJUJlTfete^^Ee Choral. 8. Allegretto. mm *1) Besides this Melody, add the similar manipulation of Exercise 32, Melodies b, a, and d; and Exercise 46, Melody d *2) The end of each line (marked -*^) must be a strong Triad, and the Rhythm is interrupted. These Choral-Melodies are to be harmonized and elaborated in a more serious (strict) manner than Melo- pupil should work with the utmost freedom, and depend somewhat upon hia car. *7) This last Melody may be elaborated in several different wayt (but only in The Harmonizing of Embellished Melodies, and unflgured Basses. 579. When a florid (embellished) Melody is to be harmonized, it is first necessary to reduce it to itt original simple Harmonic tones, by setting aside all such brief ornamental tones as are certainly, or apparently, Unessential notes. The melodic outline thus obtained may then be harmonized more or less simply, according to the character and tempo of the Melody 381). The mor animated and ornate the Melody is, the more smooth and guiet should its harmonic accompani- ment be. 580. La reducing a florid Melody to its simplest elements, the following points must be born* in mind : ft. Every note which progresses with a skip is almost certain to be Harmonic. (See 369 a; and comp. 357 and 372 b). b. Notes with Accidentals will be Inharmonic, excepting when they are unmistakable indi- cations of a legitimate and natural Modulation. C. The longer notes are likely to be Harmonic. d. The natural order (and rhythm) of the Chords, and the fundamental principles of Modu- lation, define the nature of most of the notes, especially those which occupy accented beats. 341 334 The Harmonizing of Embellished Melodies, and unfigured Boise* 801 b.804. The following Melody : reduced according to these principles, becomes as in Ex. 304. 381. The tempo of the Melody is a consideration of such moment, that it will usually pre- cede all others, in defining the order and rhythm of the accompanying Chords. For the more rapidly a Melody moves, the more Emb.- tones it is naturally likely to embrace, and etc* versi\. Comp. 232 a. The foregoing Melody would be harmonized about as follows, im different grades of tempo : r rr^ a _m ,i .J^l * * J ,- i . J"1 , 1 , _JL 3 : i V * 4 9 - ^-j J- --W a. f 7 r- rx r 7 1 L_ 7 f 7 1 V 1 T V ' 7 7 ft. / /, . / 7 2 /i / J 2 r F P7/F, v i r^i 1,0 nj- 0,1 P^- 1> i 4~ rV . i f^l > n R| 2 ^ 1 H , * = w*^? +- r 1 ^ iTi ui [^ ^ ^_ r ^r- - -f- CKy / ^ ^-*-l It JIT ^ n 3- : rt- -* 1 *" s?< * Tt 1 IfH-. Two-part Harmony. 241 890. Rules for fractions of beats. a. Upon fractions accented or unaccented) of beats, any interval may be used, either M harmonic combination, or as Suspension, Neighb.-note or Passing-note. b. All exceptional intervals (7 th , 2 nd , 9 th , 4 th , 5 tk ,) must appear as modification of the unobjectionable 3 rd , 6 th or 8 th . Thus: Sevenths and Seconds: Fourths mnd Fifths. Ex. 810. uci'cjiHus unc* accujius.- j: OUT in* mna j: tjtru. ^ < i-jrJBess^o.'ij MI J iijuij_iJ tt*n\G\\ j. 1 891. a. Intervals of the Third or Sixth should not occur too often in direct succession ; as a rule, not more than three (or four) times ; otherwise, the necessary harmonic variety, aud independence of the parts, would be altogether wanting. b. It is objectionable to use weak or harsh intervals in succession. C The part-progressions must be as melodiout as possible (385 b). d. The rules of Rhythm must be strictly regarded. Ex. 308, note *4). For example: Ex. 3k , Monotonous. Good. f r f f (b,) (d.) Rhythm: 1 fl II r.f) J ' j Exercise 19, note *3\. The rules of Tiro-part Harmony, M here enunciated, are the essence of the lawa of two-part CaunUr- point ; the Scholar will do wisely to itudy theim with great attention, for thi reason. Ex. 312. Exercise sixty-two. A* Exercise 33, Melodies a, e, g, and Exercise 46, Melodies b, c, i: to be supplied with an accom- panying Alto part, according to the above rules. It is not necessary to construct the Alto part in exactly similar Rhythm to the given Melody ; on the contrary , diversity of Rhythm ii very desirable. But see 39 Id, and be careful that the heavitr notes occupy accented beata. Th* utmost freedom in modulating is allowed. B. Exercise 32, Melodies a, b, and Exercise 47, Melodies a, b, d, f, g, h: to be transferred an Octave lower, at Alto (or Tenor] part, and supplied with an accompanying Soprano. For example a. (Exercise 34, g.) j. $ r Eg r rr f Given Melody) rrf r 'r^tr'rrcmr r 5 8-part Harmony. (ExercUe 33, e). $~? ] 1 nn 3 1 j j j i ' J j ; j ; Jj nif~ _. ( 3Z^ rf s>^ -f ^T fj* r r * * * * ' P. ,j/cll .'. *si b f r L; r N W=P= J (Given Melody) 5 8-part Harmony. 892. When Five, Six, Seven or Eight parts are employed, it IB important to keep the parts weB balanced, in regard to their distances from each other, and in regard to the duplication of the Chord -intervals. It is particularly unfavorable in copious Harmony when the lower parti It* toe clost together; but even the upper parts should avoid too great proximity. For instance: Sparta. 6 parts. Ex, 813. r 393. J lints and directions. a. In serving to prevent unevenness in the disposition of the parts, and as an efficient mean* of avoiding parallel 5 th " and 8, the inner parts may be crossed without scruple. But aa inner part should never cross either the Soprano or Bass. b. Sensitive notes of the scale , and sensitive Chord -intervals (t. e. the Leading-tone , Fifthi, Sevenths, Suspensions etc.) may be doubled. e. Interrupted 8 Te and 5**, and Unequal 8, are allowed between any but the two outermost parts. d. The two or three lowermost parts must be kept wider apart than the higher ones (excepting when any two adjacent parts have the same tone m uniton) , as small intervals sound dense and disa- greeable in the low register. Ex. 313, measure 3. . Wide skips are often unavoidable, particularly where the parts cross and re -cross; but car* should be taken not to write such progressions as are difficult to sing; such as skips of the seventh, and augmented or diminished intervals. f. When a larger number of parts are employed, Chords of the Seventh should be freely used, a* they are more copious and afford more tone-material than simple three-tone Chorda. See also Ex. 142, measures 3 and 4. g. The harmonic progressions should be very simple. The difficulty of connecting certain Chords in Four-part Harmony is greatly increased with each additional part. This appliei 5 8-part Harmony. 243 particularly to Foreign Chord-progressions (Appendix B.^ and Chromatic successions. Tht combinations of related Chords, and especially Repetitions, gire but little trouble. 194. The above-mentioned licences are to be applied more or less freely, in exact proportion to the number of parts ; for the greater the volttme of Harmony, the let* perceptible are all irregularitie* m the treatment of the separate inner part*, and, at the same time, the more difficult are they to prevent. Compare 385 b. 896. a. In Fi ?e -part Harmony (the usual four voices with an additional Soprano or Mezzo Soprano, or Tenor) , sensitive notes and Intervals need not be doubled. The Principal notes of the Scale and Chord are generally tripled. See Mendelssohn; "St Paul 1 , Chorugeg Not. 23 and 36. Bach; -B-Minor Mags, Choruses Nog. 1, 4, 11, 12, 15 etc. b. In Six -part Harmony (doubled Soprano and Tenor) the Principal notes of the Scale are tripled, as a rule, and the next best Interval of the Chord doubled. But, as strict observance of this rule would needlessly enhance the difficulties wbich attend the manipulation of a large number of distinct parts, it must only be applied as a general principle. See Bach; .B-minor Mags, Chorus No. 20. Seven-part Harmony is comparatively rare in vocal music, owing to the inequality of the parts. The original four parts are usually doubled, as in eight -part Harmony, with the exception of the Alto, or Bass. See Handel; "Alexander feast", ChorugNo. 6. Beethoven; "Fidelio", Act I, Finale, Chorus of pri- soners (also eight-part). d. In Eight -part Harmony (each of the four original parts doubled) every licence, in reference to the duplication of sensitive Intervals and irregular part-progressions, may be freely employed. See Bach; 7)'-rninor Mass, Chorus No. 21. And the following illustration- Sopr. 1. Adagio. b. 814. Bast 11. Other examples of Six, Seven and Eight-part Choruses may be found in Handel's "Israel in Egypt", (*.. Nog. 12, 13, 16, 19, 23, 25 etc.j. 244 Instrumental Harmony. Exercise sixty-thre*. . Adagio. Fot 5 parts. ) I I I German ChoraL 6. Adagio. 6 parti.*** s= v_ ^ >- J r ' _ ^. .->*- flTF"^ _ff- -t- J-*-'- <^- 1-*- - ,y-l ^s EgE F** f i I p: ,& ^N ^ s === A ) ^N I I r' /^ ^ 1 .fa p: -*- -*&- t ] .1 J-l t 5 ^-- J f i E Grerman Choral (\VaIther). c. Adagio. 1 and 8 parts.* 6 ) "Old Hundredth." 1) To be harmonised twice; at fint with two Tenors, and then with two Sopranos. Three stares are to he used similar to Ex. 308). *2) The end of each line, marked *^, will be a substantial Triad. *3) These heavy Choral -melodies must all be harmonized, naturally, with very strong Chords. On full beats 1^), A Chords, and Inversions of Chords of the Seventh, should be avoided, only excepting the I& Vj. V : , and It,. Third-class Discords are only permissible oujractirms of beats t.j- notes , and Passing-notes should be -ised with caution. Suspensions are good. *4) In this Choral four staves must be used, as in Ex. :. 2 -part. 6. 1-pan. ^F^^^-y-t 1 j-rr.Tf-Trjt J or r i 1) The given harmonic progression (a Melody, with necessary Chord-basis). *2) The notes of the original Alto and Tenor are taken successively, constituting the single Figural part *3) Here in At- tending succession, the Tenor note first *4) The open fifth is somewhat too meagre. Comp. .'589 c. 5j The notes of the original Bass and Tenor in ascending succession. *6) In descending succession, the Tenor note first This is a little objectionable, as it seriously interferes with the Bass to displace its tones iu this manner. *7) Soprano and Alto merged in one Figural part *8j This is still more ques- tionable than note *6), because the Melody is more important than the Bass. *9) The three lower parts merged in one Figural part. *10) All lour parts merged in a Figural part 402. All larger, (. e. longer or more copious) Figures (or Figural Motives) grow directly out of the simple Motives which are derived in this way from the original four-part Harmony , by the following means: a. by Rests; b. by Repetitions (. e. returning to a former Chord-tone); c. by Extensions into a higher or lower octave (equivalent to more copioui Harmony); and d. by adding Inharmonic tones (Melodic Figuration, gee -J09). Thuar Ex. 316. b. ) *) ) ) * 8 ) = = M ^ TO m r r r r *1) The ghen simple Motive is from Ex. 315, No. 2. *2) A Rest is substituted for the first stroke. 8) The first tone recurs as third stroke. *4) The lower octave, of the original Alto note is proposed. Th Bass is lowered, to make room for the extension. *5) The "Extension" of the original Motives upward and downward is perfectly natural, and subject to no other limitations than those set by the Outer parts, which must not, as at *6), be passed (crossed) by the Figural part 403. It will be seen from these examples, that when one part is made to fulfil the object of two o? more parts, by taking their respective Intervals in succession, it separates itself from the rest of the parts in the diversity of its rhythm, and btcomes a distinct Accompanying part (399 e). And, by this means, the number of parts is reduced to three, or perhaps less, if the Fif unl part includes either the Melody, or the Bass, or both. Harmonic Figuration. 247 The Registers of the Fignral pan. 404. The Figural part perhaps most commonly occupies the Middle Register (Ex. 3151), embracing a part, or, if necessary, all of the possible harmonic Interval* lying betwtem the original (given) Melody, and its Bass. Thus- Melody. Mendelssohn. S. w.W. No. 1. Ei. 817. Figural part Motive Basa Bee also: Mendelssohn, Songs without Words, No. 15*1! figural Motive of 6 notes '; No. 19 ( 5 notes preceded by a Rest) , No. 21 ., ,,l(i notes and a Rest: peculiar rhythm); No. .HH ( it tt tt 3 or 4 notes: arpeggioed Chords . Becthoren, Sonata Op. 1H, Adagio, measures 1 S (figural Motive of two notes, repeated). *1) Where the Melody proper begins (meas. 7); and the same in every other Example. 405. a. But the Figural part may also occupy the Lower Register Ex. 315 3), embracing the Bass, and accompanying the given Melody and, if three-part Harmony, one middle part (Alto). b. Or it may occupy the Upper Register (Ex. 315 4), embracing the original Melody, and accompanying the Bass and one middle part (Tenor). e. Or it may occupy the Uppermost Register as Accompaniment, independent of the Melody. The latter, in this case, will appear in either middle part, or, more rarely, in Bass. See 41 a, note *1). For illustration: Andante Mendelssohn. No. 2. Attegro, &L 318. 248 The Registers of t/ie Figured part. 4f* Allegro. 8" Mendelssohn. No. 5. ) M *NH^ 77 ^ / m Si 1) 4<>f>. *8) 405 b. The added downward stems merely serve to mark the original Melody, and Ic not constitute a separate part. The Figural part embraces the Melody. *3) 405 c. The Melody lies ia Tenor, and, in playing, must be made prominent by accentuation. See also : Mendelssohn , 8. w. W. No. 18, measures 69; 1417 etc.; No. 5. measures 1922, 5S64. Cramer, fitudes, Nog. 3, 9, 12, 74, 5\ 51. /JV. 7?. Original complete Edition). Beethoven, Sonata Op. 53, I 8t mov't. measures 42 4. Chopin, Preludes Op. 28, No. 3; Nocturne. Op. 72, No. 1. 406. The Figuration may, furthermore, be transferred from one Register to another. Thi* usually takes place at the beginning of a new Phrase or Section ; but is also possible from one Melodic Member to another, or from Measure to Measure (or even from Beat to Beat). See Mendelssohn, S. w. W. Nos. 2, 5, 40; Prelude Op. 35, No. 1. Cramer, Etudes, Nos. 15, 38, 79, 52, 53. Beethoren, Var. Op. 120, Nos. ti, (26, 27). Hints and Directions. 407. The general requirements of a Figural part may be defined as follows : it should flow smoothly and naturally, and in regular, uninterrupted Rhythm (408 g) ; it should be sym- metrical (408 b); ii must produce a complete harmonic impression, at prominent point* (401 b), and must sound well. In detail, the following rules must be observed: 408. a. The figural Motive is defined by the direction and rhythm in which the Intervals succeed each other; not by the size of the intervals. The following figures all represent the same Motive: Ex. 819. 1) Any characteristic feature which the adopted Motive may contain should, however, be retained, for instance, Inharmonic notes , or Repetitions. Hence, this last figure will not impress the ear as a parallel of the first one, to the degree in which the rest do, as they all contain the Repetition on the 2 nd and 4 th 5j- note, and consist entirely of harmonic notes. The Motive adopted for the Figuration at the outset, should be retained throughout the whole, or during a complete Section, of the piece, as strictly as the Harmony and Melody will permit. The following exceptions are allowed, and are very common : 1. The contrary motion of the Motive (Ex. 302, note *3) may be substituted; 2. Fragments of the Motive may be used, instead of the whole; or the direction of certain ingle intervals may be changed, in case the original Motive cannot conveniently be made to express the required Harmony. This is usually necessary at thorttr Melody notes, or at mot* rapid change* in the Harmonv : Figuration. Hints and Directions. 249 Ex. 620. 8. The motive may be entirely changed during melodic Cadences (and also at the Semicadences and Perfect Cadences) ; for the uniformity of the Figure is liable to become too conspicuous and monotonous at longer notes, or at pauses in the Melody ; 4. A Best may be substituted for thejirtt note of the Motive, at any point, even if not a feature of the original Figure. Thus 1 ELjLT etc. Comp. 369 i; 6. The Motive may be changed upon altering the Register (406). N. B. These changes should not affect the rhythm of the Motire: or, at most, but exceptionally (see g). For example . 1. 2. 8. Bx. ttL C* It is next to impossible to define the qualifications of a "good Motive", experience is the only teacher. Long Motives, especially when of copious range, are naturally more difficult to handle (entire) than shorter and narrower Motives. Harmonic Motives are generally more convenient than Melodic ones (409), especially when "Progressive Embellishment" is employed in the latter. "Local Embellishment", t. e. merely intro- ducing Neighboring-notes , is very simple, and easy to treat. i* According to 40 Ib, an open 5 th or 8 Te should not be used at prominent rhythmic points, except- ing in rare cases where the 3 rd immediately (and rapidly) follows. Ex. 321 a. 6* It is forbidden to double sensitive tones and Chord-intervals (Leading-tone, Seventh etc.) at the Accents or on accented fractions of beats, although this may be done anywhere else, especially in rapid tempo. Still, it is wise to avoid the duplication of the Leading-tone, wherever convenient. Ex. 321 b. For illustration : a. 250 Figuration. Hints and Directions. Parallel fifths or octaves must not occur between the Figural part and the other parts, m direct succession. When intercepted by at least two figoiral notes, they are generally unnoticeable. But much depends upon the rhythmic position of the intervals: if both occupy the accented (i. . the first] fraction of the beat , the parallels will be observed , even when more than two notes inter- vene. - - Parallel 5 tbi and 8 in oblique rhythm, between the different Intervals of the Figural part itself, are never wrong, unless the harmonic progression is very irregular. And intentional Octave-parallels are often extremely effective (See Appendix A, d) . For illustration . Mendelssohn, Op. 54, Var. 1 1. g. The Rhythm of the Figural part mtw< no/ 4 interrupted or changed at Rests, at the Cadenctt, nor in the course of the Period. See 369, f. h. The progression of the Leading-tone, Sevenths and Suspensions in the Figural part, is the same as in the Deferred Resolutions; that is, they are resolved where they_/ir/ appeared. In exceptional cases (usually in the Middle Register) they are transferred to another octave, and resolved there. This is of the greatest importance in the Bass Register, where evaded Resolutions, and the like, lead to awkward inequalities. As a rule, the Group* or Figures should succeed each other with the same uniformity of register as the unbroken Chords themselves would. (See Ex. 323 b). For example : 5 V I L The Registers. When the Figuration is in the Middle Register, the Outer parts may, if neces- sary, be transferred to a higher and lower octave, so as to avoid embarrassing the Figural part. This may be done during any Member of either Melody or Bass, but always so as not to injure the connection. Comp. Ex. 316, measure 5 (Bass), measure 9 (Melody). When the Figuration is in the Lower Register, embracing the original Bass part, care mut be taken to preserve the effect of the latter, by using the separate Baas tones as lowest note of each Figural group, and generally, though not necessarily as /?/ note also. When the Figuration is in the Upper Register, embracing the original Melody, the same consideration is still more important than in the foregoing case , *. e. the separate tones of the Melody must be distinctly heard as uppermost (and almost always as first] note of each Fig- ural group , and their continuous connection with each other as "Melody", in distinction to the Figuration. Hints and directions. 251 Ex, 524 accompanying lower tones of the "Harmony", must be made conspicuous by violating them much as convenient from the other (lower) tones of the Figural Motive ; thus : not: If, on the contrary, the Figuration in the upper Register does not embrace the Melody (405 o), care must be taken to keep it so subordinate in its melodic character, that it does not detract from the necessary superiority and prominence of the Melody proper. J. It is important to recollect that whatever movements take place within the Motive, probably being only "CllOrd-repetition" (47), are not subject to any other regulations than that of 408 b, and of smooth progression in general. The critical moment id, always, where the Chord change*, i. t generally from the last tone of one group to the first tone of the next. At this moment the same rules apply, and the same care must be taken, as in ordinary progressions, especially in Bass ;Comp. Ex. 323, b). Exercise sixty-four. Melodies, with given Bass, to be elaborated with Harmonic Figuration as indicated below No. 1. Andante. o \ v B. Z -9 _ !^ ir - FV.2 - IL rr-9-i-T,-K-f?. i- *MV, *1) This first Melody-note is not to be accompanied. *2) The Seventh may be added to almost any Dominant Chord, in order to gain an Interval, or to avoid an open STB O r 5* h , if necessary. In general, the given Bass (Harmony) is not strenuously insisted upon. The pupil may make whatever alterations in the Chords, or even in the Key, his fancy suggests, or his adopted Motive mav demand. *3j In- dicates the Semicadence. *4) F^ in Bass. *5) The Figural part runs on to the 4 th beat. This Melody is to be supplied with a Figural part (3-part Harmony) in the Middle, Lower and Upper Register in succession, in a rhythm of 1, 2, 3 and 4 notes to a beat ( ^, ^, *^*3> S 8UC ~ s cessively, according to 404, 405 a and 405 b, and with the following Motives, (each model to b worked out complete] : A. 1. 9. A, 4. ^-^~ i ifc ^ 3* 32 252 Harmonic Figuration. B. 1. *1) Contrary Motion of the adopted 3-tone Motive. *2) The Motive may embrace any number tf notes , in the adopted rhythm. (See 408 c). *8) The object of the Middle part is, principally, to aatijt in completing the Harmony. Its progressions are quite optional, but should be as quiet as possible. 4) The original Melody notes as highest but aa second note of the Figural groups. *5j Compare thi Motive with C. 2, and see 402 and 367. Ho. 2* Andante cantabiU. ilEfEEE? a ^ ^- s - s L_,_B_ J j J_ j J 4 ' - */ i, 11 . CV5 b3 and fc). For instance o 254 Harmonic Figuration. -Lj3-^= z^zrf^Frl* -!3= -t ^LLULLLJ^^ nr ^_i '*>-* - -f-4-^g He, . Moderat9. , 64-5 H 1 J ... - -.-< -^^ 1--J l-J- , -14- ^ f A -i*- ! *~3 d f W-4-: J- ^ * Hn 8 2 I i / VI /t /F Fi Fj / F F 8 /i /Ft IV V F, / I ' III y i Bach (adapted). gy ? 7 777 7 77 I>F 8 /, / IF Pi I FFi J 1 1 f* t^ 1 -14= 4>-s J J i J J i ^1 1 / i i_ r r 9 fi 5 3 2 C C ^ ^ .1 ' ks E ^f T -.7 r P 2 6 C C 4 3 ' 1) Continue in the simple manner indicated in the first half of the measure. *2) The 2 nJ half of the Motive, twice. Tliia Exercise may also be made at the Piano, with other (original) Motives. No. 3. The 6 th Melody of Exercise 64 is to be elaborated at the PiailO, in the following wayt: 1. 2* 3. tt TT 418. On the other hand, the Figural part may be accompanied by three or even more harmonic p*rt; in this case he Motive i likely to be shorter and more narrow than it. three-part Figuration. See Cramer: Etudes 10, Is, 25, 28, 36, 4<, 56, 80, 62. Mendelssohn: S. w. W. No. 11. second Part (i. e. after the 2 nd Double-bar); No. 21. Irregular or Indefinite Part-writing. 259 Irregular or Indefinite Part-writing. 413. a. In music of this kind the number of parts may be increased or decreased at option during certain sections of the piece, or at single points. b. Casual or momentary additions may thus be made to the fundamental body of Harmony (2, 3 or 4-part as the case may be) for the purpose of avoiding meagre combinations, or in order to em- phasize certain tones or Chords, or to heighten the effect of crescendo or forte passages. And, on the other hand, the number of original parts may be reduced for the sake of diminuendo or piano, or for any other desired variety of expression and effect. C. But these alterations in the volume of Harmony should always be accomplished in such a manner as not to disturb the flow of th,e original (fundamental) parts, or entirely destroy the impression of individual part-progression or voice-lines) , so indispensable in good Harmony. Hence, when a fundamental part is temporarily omitted, it is advisable, though not necessary , to introduce Rests in its stead , as a means of keeping its trace. And addi- tions should create the impression of a single fundamental part separating into two or more tone-lines for the time being, and ultimately converging again to the original single part For illustration- 1. Allegro vivace. 881. Beethoven. Beethofen. 4. Allegretto. ten Mendelssoha. 260 Figured Motives trith Supplementary tones. 1) An example of 3- part Harmony, reduced at first by partial Rests to 1 part. *2) Here all 3 part* appear, bu . the '2 upper parts are stroked fat/ether on one stem. - *3) Reduced to 2 parts, but without Rest*. In the next measure again 3 parts. *4) Four parts. *5! Here a momentary addition which equals 5 part*. *6 Again 4 parts, the 3 upper ones stroked together. *7; Fundamentally 4 part*; increased here to o. ) Decreased to 3 parts for one beat. --- '9 Intentional Octaves in the upper parts. - *10j The Rests only suffice for two parts. The Harmonv is here reduced to 3 parts. *11) Here (and in the next 2-3 measures) again 4 parts. *12) Fundamentally 4 ports, increased by intentional octaves in Tenor to 5 parts. 3) On the first beat of this measure the Harmony is reduced to 3 parts, immediately afterwards increased to tixt 14) Here increased to eight for a moment, on account of the crescendo and forte. *15) Here again 4. ^ 16) Four parts. *lf) Increased in Alto to 5, and immediately afterwards reduced to 2, and then 1 , with partial Rests. *18) At this single point 6 parts, and then 3. 414. Such tupplemenfary nntet or part* can onlv be employed in music for Manual instruments (Piano-forte, Or- gan, etc.). In Vocal music, or in music for Wind instruments, where it is impossible to produce simultaneous tones, the only change that can be effected in the volume of tone, is a decrease in the number of parts, either by the introduction of Rests, or by intentional Octaves or Unisons (see Appendix A, d). See also : Bach, Well-tempered Clavichord, Book 1, Prelude 22 (J97-minor). Mendelssohn, S. w. W. No. 2, measures 2, 3 ; No. 11, measures 8, 9, 11, 12(!) ; 16(1); 17; 20(1). On the contrary, in Beethoven , Sonata Op. 14, No. 2, 2 nd movement (Andante) the fundamental 4 parti tre retained throughout the Theme, with but very few addition! and reductions. Figural Motives with Supplementary tones. 415. a. Upon this same principle , Figural Motives may be made, in which certain Intervals are furnished with one or more harmonic supplementary tones (or twin notes, as they might be called). b. The twin -notes should occur as a rule at the corresponding place in each Group comp. Ex. 319, note * 1 ). Still, quite unique effects are sometimes produced by an irregular disposition of ths supplementary tones. For illustration : El. 332, ri* B Mead. ' (-S-- I *-. 1) .1) Mend. r r -^ f | ~cl ~?t* '> L , I \^^ ' r rJX 1) The twin-notes occupy different place* in the groups. In Nos. 1 and 2 they are regular. See Mendelssohn, 8. w. W. Nos. 6, 12, 13, 29. Cramer, Etudes 17, 58, fiO, 76, 78. Chopin, Ballade Op. 38, 2* part; Nocturnes On. 9 No. 2, Op. 15 Nos. 2 and 3, Op. 32 No. 2 and Op, 41 No. 1 ; Etudes Op. 25 Nos. 3, 4. 5 'especially the middle Section), 9. Beethoven, Sonate Op 2 No. 3, last movement, measures 29 etc. Henselt, Etudes Op. 5 No. 2, No. lo (middle Section). Rhythmic Figuration. 261 Exercise sixty- eight. A* Melody No. 3 of Exercise 64, to be elaborated with the following Motive* 1 . 1* 9. 8. r B. Melody No. 5 of Exercise 64, to be elaborated with the following Motives: 1. 2. S , t I ^ H 1- -4 3 J * .0 \ f. | ff- f 25'iipid tempo . _^, _ , Xo. 4 i2 a Act). In moderate tempo: Beethoven, 8 th Sym., Allegretto Kftenando. Exercise sixty- nine, A* Melody No. 4 of Exercise 64, to be elaborated as follows: B. Elaborate the following models at the Piano: Exercise 64, No. 1. Exercise 64, No. 6. Exercise 67, No. 1. ' c. i T5*- Pei Ped. Double, Compound and Complex Figuration. 418. In Double Figuration there are two Figural parts (usually representing adjacent roicet, but sometimes separated by one or more harmonic parts), which operate in concert through- out the whole, or certain Sections of the piece, and employ the t,ame Motive, or different Motives. This mode of employing simultaneous Figural parts must not be confounded with alternating Registers, which it may sometimes resemble in effect, but from which it alwayi essentially differs. See 406; and compare Exercise 66, A, No. 3. and D, No. 3. Also Mendelssohn, Prelude Op. 35, No. 1. Double, Triple and Quadruple Figuration. 263 419* The distinction between Double, Compound and Complex Figuration is as follows: Double, when the Melody and Rhythm of the figural motives are alike, the Figural parts generally running parallel, as timple duplication in 3 rd * or 6 thi (on au average) ; Compound, when the Rhythm of the Motives is the same, but the Melody (direction different; Complex, when the Rhythms are different. For example : TV...*;. M.i i J* - .JA i *. tee Ex. 334. 5 r ^f^ M. M. !ljj _? jj Of these three varieties of duplicated Figuration, the 'Complex" is no doubt the most common and favor- able. Compare 369 k. There is no rule as to which Register should assume the more active of the two different rhythms, although possibly the quieter Figures are more appropriate in the lower Register*. See also : Double Figuration: Mendelssohn, 8. w. W. Nos. 7, 32, 42; Cramer, Etudes V, 19, 20, 22, 35 (at times compound) 48, 50, 54, 61, 63, 73, 81, 8J Chopin, Prelude Op. 28, No. 14 (!); Etude Op. 25 No. 12; Beethoven, Sonata Op. 7, third mov't, "Minore". Compound Figuration: Cramer, Etudes 42, 59, 65; Chopin, Preludes Op. 28, Nos. 2, 5, 11, 19, 21 ; Etude Op. 25 No. 1. Complex Figuration: Mendelssohn, S. w. W. No. 13, (24); Cramer, Etudes 5, 8, 21, M, 36, 38, 46, 79; Chopin, Prelude No. 8 ; Etudes Op. K Nos. 2, 9. Etudes for the "Moscheles-Method", No*, 1 and 2. Fantasie- impromptu Op. 66. Triple and Quadruple Figuration. 420. Triple or (Quadruple Figuration is of comparatively rare occurrence in Piano-forte music, but not uncommon in Orchestral or Chamber music. For illustration : 11.535. Cramer. Beethoreft. 1) Melodic Fig. in the upper part, Harmonic Fig. in the middle and lower parts. See Chopin: Etudes Op. 25 Nos. 3, 6, and 8. Etudes for the "Moscheles-Method", No. 3. Cramer, Etude 29, 70. Double, Triple and Quadruple Figuration. Exercise seventy. A* Melody No. 2 of Exercise 64, as follows: B. Melody No. 6 of Exercise $4, in */t l i me (instead of C), a* follows : Lari i ~ HE ?=? 67 5 4 Jf SOS 9 7 3 BcethOTen, g: i f"irvTi ^ 2X6 4 46 4 5 4 S S 05 41 To be elaborated a follows (in 3 / 4 time) : . u U * *'- ^^=1= ^^ f ^5 And in a number of othi ways, with original Motiret Double, Trivle and Quadruple Figuration. 265 D. Melody No. 1 of Exercise 67 (inC-time instead of f) as follows : E. Melody No. 6 of Exercise 64, at the Piano, as follows : 1. Allegro. 2. \3. Allt. 4. Appendix A, d. In conclusion, the scholar is to apply each of the different varieties of Figuration, independently. For this purpose, any Original Phrases or Periods made during the course of Parts II and III, or any familiar sacred or secular Air, may be utilized. Or, best of all, he is urged to make thorough use of the following section upon Paraphrasing (421). Paraphrasing, or simple Variation. 421. By " paraphrasing" is meant, the elaboration of a given theme (8-16 measures) after the manner of very simple variations, without altering any essential feature of the theme, but only the style. The best illustrations will be found in Mozart, Pianoforte Sonata XII (Cotta edition, Book I, p. 155, 2 nd movement) ; in the Chaconnes of Haendel ; and in the simpler variations of Beethoven (e. g. : 13 Variations in A, Peters edition, p. 120 ; 9 Var. in C-minor ; 6 Var. in F-major ; 9 Var. in A ; 8 Var. in C ; etc.) These very themes may be utilized, before being analysed. Leading points and suggestions : 1. The Rhythm ; (elaboration in a rhythm of 2, 3 or 4 notes to an original beat). 2. Location of the rhythmic figure; (figural 8opr., or Bass, or inner part; alternating parts ; running voice). 3. The Melody preserved intact and the Harmony changed, or vice versa. 4. The register of the Melody ; (melody transferred to a higher or lower octave, or to another voice ; trans- ferred entire, or in sections). 5. "Change of mode (major to minor, or vice versa). 6. Change of rhythm or Time, from duple to triple, or vice versd; (this should be done rarely and with caution, as it is apt to alter essential traits of the theme). Appendix A. Parallel 5 tn " and 8'". The unpleasant effect produced by a succession of perfect fifths in parallel direction may be accounted fw in the following two ways: Firstly, the perfect fifth, being the most perfect harmonic relationship of two tones to each other (23), represents a harmonic body of such absolute completeness and distinct individuality, that it can not connect and interlink with another body of corres^ onding distinctness. Hence, when perfect fifths appear in direct succession , the necessary intermediation is lacking. Secondly, the weak, unsatisfactory quality of the Fifth as Chord-Interval (defined in 49 c and corroborated in numberless subsequent examples) is in a very great measure to be regarded as the cause. If one Fifth alone is unsatisfying, the effect of two or more in immediate succession must naturally be sensibly disappointing. The degree in which this disagreeable effect is produced is proportionate to the prominence of the Fifths. Therefore they are most painful when they progress parallel with their Roots, as actual and most palpable "Fifths" (hence the common designation, parallel Fifths : or when the succession of Fifths lies in the Soprano (successive Positions of the 5 th , 59 b), or in Bass (successive 6 / 4 Chords, 142 b'. But they ar> also qualified according to the relationship of the Chords in which they occur, Fifths between foreign Chorda sounding worst; and they uiay be ameliorated by many circumstances: as, for instance, when the second Chord is an Inversion, in which case the Fifth in an upper part sounds more like a Third or Octave (Ex. 93, *2) ; and when in contrary motion. For example: N 206 Appendix A. Parallel 5 lhs und 8 V ". C Other devices may be resorted to, for the amelioration of their unpleasant effect, as follows : When a Dissonance is added to the second Chord, the attention is partly distracted from the consecutive Fifths I 5 5 g od - r m 43 When one of the 5* ht represents some other Interred of the Chord than the Fifth itself (e.g. the Seventh or Ninth), the disagreeable effect is in a measure removed, because the Seventh or Ninth, although weak, U not nearly as vapid and "flat" as the Fifth (49 c). This is also true of the diminithed 5 th * 79. 5. 9. IE ^' -*^^ ^w- 232 A 9^9 J * i I * ^ * *^+- 1^1 i ' 1 - 1 \ 8.1 7 f y 1 j good. , f ! J J J J j* P i ^ ^ s r * 9 z r H 1 See Ex. 125, fy J T L L. ' noteM).- IX H Ex. 267-6. Finally, the evil is entirely removed when the second 5i U not Harmonic (369 e)- Ex. 291. In regard to parallel Octaves, and their occasional admissibflity, the following explanation will suffice. Should the succession of Octaves or Unisons be extended d'iriny a distinct $i'ctwn of the harmonic or melodic progression, for the obvious purpose of strengthening and supporting a part by duplication, it would be justi- fiable, and might he very appropriate and effective; but the 4-part narmony would thereby be reduced to J or lesi parts. Mendelssohn. etc Bee Ex. 164 No. 1 ; Ex.J75b; Ex.277 3 ; Ex.'-^Sc; Ex. 2.i 2. Handel, Six petites Fugues, No. 4, measures :i 9, 40; 4:<, 4-1; 4", *; il.5'2. Bach, Well-tempered Clavichord, Book I, Fugue ID, measure* 19. 20; 38, 39. Mendelssohn, S. w. W. No. 1 1, meas. 18; No. 5, mea. 23 27; No. 18. meas. 20 13/rom the end; No. 23, throughout the principal Parts. Appendix B. The Grades of Harmonic Progression 267 Appendix B. The Grades of Harmonic Progression. Harmonic progression is simply an exchange of harmonic impressions. The force of the sensations pro- duced upon the ear and mind by the different varieties and degrees of change, is proportionate to the difference in construction, and consequent difference in effect, between immediately succeeding Harmonic bodies; there- fore, practically considered, Harmonic Progressions may be classified' according to the degree of similarity between the Chords (in reference to their component tones). * The First Grade of harmonic progression is the simple Repetition of a Chord (all the tones common . No new tones are acquired, and the impression conveyed is rather that of Repose than of Advancement ; the only Element engaged is Rhythm. Ex. 44. b In the Second Grade, one or two new tones are acquired, and two or three are common. The Root of the first Chord changes its location by a 8 rd , upward or downward. Exs. 76, S2, 65, 861, 2. C. In the_ Third Grade there is one common tone. The Root of the first Chord generally changes its location by a 5 th , upward or downward. This Grade includes the Normal Progression and its reverse, and is the most natural and gratifying succession in music, as comparison \\ ith the other Grades clearly shows. In this stage, harmonic progression reaches the highest degree of vigor and perfection; the change is striking and sufficient, but the darners of disconnectedness, etc., which attend the progressions of the Fourth Grade, (d) are averted by the one common tone, which serves as a connecting-link. If the First Grade be excluded from the actual progressions (as is a correct assumption), the Third Grade represents the mean between the Second and Fourth Grades, in which the changes are respectively too inconsiderable, and too great. Exs. 47 etc.; Exs. 62 etc. d. In the Fourth Grade of harmonic progression there is no common tone, and consequently the Chords are entirely foreign to each other. Ex. 67 . The Root is transferred to the next higher or lower step; or, more nronerlv a 9 th (= two 5 ths , or four 3 rds ). For illustration: properly, a. (Repetition One common note) d* (Foreign chords). NB. The difficulties and dangers of harmonic progressions or "exchanges" increase in proportion to fhe number of new to'ii-s acquired: i. e. according to the Grades of progression, a* here defined. "While it is almost im- possible to make an error in the Fir^t Grade (Repetition : see 47), the greatest care must be exercised in the treatment of the Fourth Grade (Foreign Progression: see 79, Ex. T4 etc.). Appendix C. Condensed or Compound) Chord- progressions. The great majority of Irregular harmonic progressions may be easily accounted for, and sufficiently justi- fied , upon the grounds of simultnnenus part-progression, where successive movements were expected, and demanded, according to the natural laws of harmonic succession. For instance, the following irregular single Chord-progression : ^L is obviously only a condensed form of the following double-progression: An investigation of the wide range of possibilities which this peculiar mode of treatment opens, would xtend far beyond the limits of this book , and it is therefore simply brought to the Scholar's notice at this point, and left to his own research, with a warning reference to footnote *10 of Appendix E, and to Appen- dix G. The justification of such condensed Chord-progressions is often a very difficult matter, and must 34 268 Appendix C. Condensed (or Compound) Chord-progressions. generally be referred to the tar alone, which, irhen well trained, is a sufficient guide. Usually, but not regularly, the Chord which follows a condensed Chord - progression will be one which either of the com- ponent Chords could reach atone: see the VI, with which the above example terminates. Furthermore , th condensed progression should not embrace more than two or, at most, three ordinary succession*. Further illustrations . Ex. 158. Ex. I87t). Paragraph 296 a, b. ' 1 \ . i VI V V1\JT\VQV CV GV (QCVCVidVt (CD FVtyV (FI) Ex.226. Appendix E, L 3 r^-^-p i T s ^ 8. Ex. 2G7b. r rrr Ex.270. ftL i ^ r d^U .Kg faa m y r I gV E?V dV Jl (dl FT) *1) All examples of Compound chromatic or enharmonic Chord -progression belong to this class. *2 All these irregular "Deferred" Resolutions of the Suspension are also Condensed Chord-cuccessiona. Appendix D. The Enharmonic Change. The dotted tinea in Ex. 206, which indicate the actual successive arrangement of Key-notes (or Tones in general; in the Harmonic System, can be prolonged in both directions parallel with the other lines, completely around the Circle, again and again. The ultimate result will be a scroll, commencing at the centre and running on outward into infinite space. The modern Tone-svstem obviates the infinitely repeated Enharmonic discrepancy, by limiting itself to one single circuit of 12 fiarmonic Degrees, which is rendered complete ft. e. perfectly nn>d, instead of spiral by the Enharmonic adjustment at Ft and G ', directly opposite the adopted starting-point C. This adjustment is not effected by simply substituting F for t\c<> infinitesimal }>arts ichicli are indiscernible by the ear, amswers perfectly well for both. For illustration: if the corresponding black key of the Piano-forte were tuned exactly G?, it would only be applicable in those Chords and Keys which con- i Q . i i L ~ Uin thit tone and not because in such Chords and Keys M r- On the other hand, if uin F$ it would sound out of tune. Thus Appendix D. The Enharmonic Change. 269 this tame black key were to be tuned exactly F%, it T*mld suit the leeond set of Chords given abort- be disagreeably anomalous to the first get. The intermediate tone obtained by the present mode of "Equal temperament" agrees, however, sufficiently well with both sets. - formerly, before the Equal temperament was recognized and adopted, the instruments weit tuned in absolutely perfect fifths, so that at the end of 12 such fifths the enharmonic discrepancy (tech- nically known as the "wolf") was fully developed. In the Equal temperament this discrepancy is dis- tributed in equal parts among the 12 Key-notes, so that each fifth is a trijie smaller than if perfect '/Jt being a little lower than //?, about in the proportion 167: 171;, and the Circle of tones, as demonstrated above, becomes perfectly round. The difference, though inconceivably small near the starting-point (say C), becomes greater with each succeeding fifth; consequently the'Composers in olden times were obliged to limit themselves to Keys in the vicinity of C-Major. 'These, being perfectly true, were purer than the modern Keys, but this slight advantage Is more than counterbalanced by the present possibility of using all the Keys, in unlimited conjunction and alternation. This also explains the quaint title of J. Sebastian Bach's 48 Fugues and Preludes for the "Well-tempered Clavichord": Being a strong ad- vocate of the new system of Equal temperament, he wrote both volumes of this work in all of the '24 Major and Minor Key, which, as above shown, could only be obtained upon a "Well- (or equally) tuned" instrument. Appendix E. Exceptional Progressions. Allegro. Raff. 6. Larghetto. , Mozart. 270 Appendix F. G. . "Flying Dutchman." n. Admgw. n j\amy\o. &J#.b , ~,-^UgU "Walkflw/ Ld-t Fifth. Ill ,fcL ? ^ etc. O. Allegretto. 'Xohengrin." -ir - -^~ J ^- X 0: 2 X -&- X X etc. m U 2 .^ ' X ' _^.. X 1) Ascending 6* h step. *2 Descending Leading-tone. *3! Ascending 6 h step. *4) Descending Leading-tone. *S Ascending Dominant-Seventh. *6) Six-four Chord entering with a skip. *7) Suc- eesaive ",4 Chords. *8) Skip from a 6 /4 Chord. *9) Peculiar resolution of a \ into a foreign I. 10 The scholar is strenuously warned against imitating such fantastical and adventurous harmonic suc- cessions as these last two Examples of Wagner. They are noted down here as interesting illustrations of what a highly imaginative mind has succeeded in extorting from the natural resources of tone-combination and progression, with a tolerable show of plausibility. Iheir influence upon the beginner U undeniably pernicious. Compare Appendix O. Appendix P. Summary of the progressions which the Chord of the Dominant-Seventh can make. C-major. Appendix E,L Appendix G. Concluding remark. The chiei and deplorably common error in modern Composition is the inclination to employ eccentric and complex harmonies, in endless succession, without relaxation or rest, and with studied evasion of vulgar "Resolutions"; partly in obedience to the Spirit of the Age, and partly in the ambition of producing something "Original". The Composer who leads his auditor through a perfect labyrinth of harmonic by-ways, adding Suspensions (Irregular, of course) to every single succession, and fitting out the whole with an Organ-point, dare not wonder when his work is pronounced incomprehensible and unenjoyable. This truth cannot be too early and deeply impressed upon the scholar's mind; and he is warmly recommended to adopt Haydn, Mozart and Beethoven as his models, in preference to such adventurous explorer* as Schumann, Chopin etc. etc., at least until he has Jinislmd his sturiii'x, and is prepared to assume an individuality of his own. Not that the Author wishes to be understood as depreciating the real value of these more modern Masters' works. Thei significance in the progress and history of music, and their agency in unfolding a new world of tone-beauty, U unquestioned; but they are not the proper source from which the Sc/iular is to expect natural and healthy development. * THE END. * TABLE OF CONTENTS. PART I. DEFINITIONS AND RULES. Rhythm 1 Modes of Accentuation. ... 2 Melody The Scale 3 Rules of Melody i Harmony. Interval! ............. 8 Tone-relatiom 11 Chord* . . 13 The Voices or Parti Duplication of Chord-Interrali The Positions of a Chord . . The Rules of Part-writing . . ....... 16 ....... 18 19 20 The general Exception .....' 21 The Qualification of the Tone*, Interval! and Chord* 22 PART H. THE COMBINATION OR CONNECTION OF CHORDS. Division A. Concords. Section I rt : Triads. The Tonic Triad, I. The Dominant Triad, V . 24 The connection I V 25 The reversed succession, V I 26 The Perfect Cadence 27 The Phrase 28 The Subdominant Triad, IV 32 Combination of the Subdominant and Dominant Triads 35 The Principal Triads in the Minor Mode .... 37 The Subordinate Triads 39 The Changing-dominant Triad, II 40 The Submediant Triad, VI 43 The Mediant Triad, III 45 The Subordinate Triad* in the Minor mode ... 47 The Period 48 The Inversions of the Triad! 49 Section 2 nd : The Chords of the Sixth. The Principal Chords of the Sixth 51 The Subordinate Chords of the Sixth 54 Consecutive Chords of the Sixth 57 Triad and Ch. of the r.th O n the same Bass-tone . 57 Section 3 rd . The Six-four Chords. The Combinations of Six-four Chords. 1'* Connection 62 Second Connection 63 Third Connection 64 The Plagal Cadence 67 Six-four Chords as Passing-chords 68 Division B. Discords. The Classification of the Discord! 72 The Resolution of a Dissonance 73 Section !*: The First Class of Discords. A. Th* Chord of the Seventh upon the Dominant 73 The Ii troduction of the V . .... 74 The Inversions of the Dominant-Seventh-Chord . 77 Irregular Resolutions of the Dominant-70-Chords 80 The Passive Resolution 81 B. The Incomplete Chord of the Dominant-seventh 84 (The II in Minor) 86 C. The Chord of the Ninth upon the Dominant . 86 272 Table of Contents. Introduction and Resolution of the V 89 The Inversions of the Five-nine ........ 91 D. The Incomplete Chord of the Dominant-ninth 92 The V in the Major Mode 92 The . V in the Minor Mode 95 Section 2 nd : The Discords of the Second Class. A. The II and it* Inversions 99 B. The IV and Inversions 100 The Digression into the next higher Class ... 101 Section 3 rd : The 3' d and 4** Discord-Classes. A. The Discords of the Third Class .104 Irregular Passive Resolution 105 B. The Discords of the 4 Class 106 The ill in Major. The HI, ill and l!l in Minor 107 Table of the Harmonic System of a Key .... 109 Synopsis of the fundamental principles of Rhythm. Melody and Harmony 109 Rhythm. Melody (Soprano part). Harmony. 110 Movements of Chords . . . Ill Division C. The Harmonizing of Melodies. With Principal Chords 112 With Subordinate Chords . . . 115 Harmonizing successive tones together . . , . . 117 With Dominant Discords . . lit Division D. The Altered and Mixed Chords. Section I*: The Altered Chords. A. In Major 125 B. In Minor . . 128 Section 2 d : The Mixed Chords. A. In Major . 152 B. In Minor .134 PART HI. MODULATION. Section I" 1 : Key-relations. Relationships between the Keys ........ 138 First Rule of Modulation 140 aection 2* d : The process of Modulation. 141 Harmonization of Unfigured Basses 144 Altered Chords, as Modulatory Mediums 146 Extraneous Modulations (1. Through Next-related Keys.) 147 Extraneous Modulations. (2. Direct.) The Stride . 149 The Opposite Mode 150 Modulation in Sequences, and at Cadences .... 154 The Mediant-Modulations 155 Other Cadence-Modulations . 156 Section 3**: Chromatic Progression, as a special modulatory agent. Rules of Chromatic progression 159 Chromatic Chord-progressions 160 Section 4 th : Enharmonic Modulation. Simple Enharmonic Changes with the Dim. Seventh 167 Other Resolutions of the Chord of the Dim. Seventh 169 Other Enharmonic Chords 173 Compound Enharmonic Changes 174 Section 5 tk : The Harmonizing of Melodies, with Modulations. l*ly. Melodies with Indicated Modulations . . . 17i 2ndly. Melodies with Intimated Modulations ... 178 3*