RICHTBR'S MANUAL OP HARMONY: PRACTICAL CTJIDE TO ITS STUDY PBEPABRD ESPECIAIJ.Y rOB THB CONSERVATORY OF MUSIC AT LEIPSIC. BY ERNST FRIEDRICHj^JMCHTER, UNIVERSITY MUSIC-DmECTOR, ORGANIST OP THE CHURCH OP ST. NICOLAI, AND Df- STRUCTOR IN THE CONSERVATORY OP KUSIC. TKANSLATED FROM THE LATEST GERMAN EDITION By JOHN P. MOKGAN, ALUMNUS OP THE LEIPSIC CONSERVATORY OP MUSIC, AND PUPIL OP THE AUTHOB, FIFTH jEDITION. NEW YOUK: Q. SCHIRMER, 701 BROADWAY. ^u%,€. VeT^TT Ent«recl> according to Act of Congress, in the year ISOT, by w, btiiililMEli t» the Clerk's Office of the District Conrt of the United States for the Northern District of New York stereotyped by Smrn & McDotra^T 82 & 8A Beekmsn St. ^^ ■ Mr so TEANSLATOR'S PREFACE, In offering to the American public this translation of Eichter*8 Harmonielehre we need have no hesitation in saying, that we offer a translation of the best text-hook of Harmony which has, as yet, been given to the world. No one knows better than its author the road which one must take to become 21. practical harmonist ; and no one has been more successful in leading pupils to real success. The Manual contains the outlines of the course w^hich has proved itself the best during his many years of efficient labor as Instructor in Harmony in the Conservatory of Leipsic ; and the im- mense sale the work has had in Europe, shows in what estimation it is held by the musical public. A few remarks as to the translation : — Every one who is at all acquainted with the matter, knows how exceedingly difficult it is to do justice to a German scientific work in an English translation ; and in no science is the poverty of exact and definite English terms greater than in that of music. The translator has striven to give, throughout, the exact sense of the original, without any embellishment for the sake of attrac- tiveness, and has always preferred a square-cut sentence containing the idea of the original in fuU, to a more smoothly-rounded one which would omit or add something. A few clauses or words which seemed necessary for clearness, have been enclosed in square brackets. The whole work has been performed as a pleasant dutv to a IV TBANSLATOR S PEEFACE. teaclier to whom the translator owes all gratitude, and in behalf of the many earnest students in this country, who are utterly with- out an adequate, 'practical Manual of Harmony and Introduction to Counterpoint. Thanks are especially due to his revered father, Eev. John Morgan, D. D., of Oberlin College, for his kind assistance in the vv ork, which, without the aid of his comprehensive knowledge of language in general, and of the German in particular, must have been done much less accurately. JOHN P. MOEGAN. New York, June 1«<, 1867. FROM THE PREFACE TO THE FIRST EDITION. The most immediate occasion for publishing this text book of harmony is indicated in the title. It was desirable, in connec- tion with the practical course of studies in the theory of music, to put into the hands of the pupils a help for the explanation of the doctrines brought forward, and for their repetition. The quali- ties of such a manual, the author beHeves to be these : It must contain the most essential, fundamental part of the musical t7i£ory ex- pressed in a manner brief but as complete as possible ; there must be these fundamental features always accompanied by reference and guidance to the practical application, in order to qualify for later attempts at composition. The book contains no scientifically theoretic treatise on har- mony, but, although as far as is the case with any system of harmony, it is supported upon a firm basis, is only dedicated to the practical object, which with the scanty means now accessible, would be very difficult to attain in an abstractly scientific way. There has, indeed, ever been a disposition to inquire after a mathematical definiteness in musical rules, and especially youth, opposed to the belief in authority, would like to have everything so clear that no doubt would be possible, much as it shrinks on the other side, from learning, by means of the anatomical knife, to know and understand the blooming life of art ; and it is not to be denied that in this respect a want is found in musical literature, which no one has as yet entirely succeeded in supplying. All attempts VI PREFACE. of the sort have as yet failed to create a really tenable scientifi- cally musical system, according to which, through one fundamental principle all phenomena in the musical realm are found exhibited as always necessary consequences, and what philosophers, mathe- maticians and physicists have accomphshed in this regard, ii^ indeed worthy of attention, but in part, too much divided into isolated portions to allow the easy discovery of the connecting links for the completion of the whole, in part, too abstract, serving music itself less than other objects, and with all the understanding of musical things shown in it, still having little reference to the properly musical, which is, after all, of the most immediate im- portance with the musician. "What is laid down in musical text books of a scientific basis, has not, however, hitherto verified itself, because it in part as application of single learned investiga- tions, was just as little able to create a system complete in itself, with indubitable conclusions, and in part, as a fanciful structure, was utterly without scientific basis. * Still, rightly regarded, this deficiency is perceptible only to the riper and educated musician, who likes to busy himself with theory, not, however, so disadvantageous to the advancing student of music that his immediate education must suffer in consequence of it ; and this scepticism, referred to above, might be compared in a certain measure, with that childish mode of procedure, which from over great curiosity, would get at the origin of all things through ques- tions which seldom can be answered comprehensibly enough for the questioner's stage of education. The advancing student of music has to apply his whole power to his technical education, because it will cost him time and trouble enough to attain the stand-point, starting from which he can with greater ease advance towards the position of a real artist. Here the question to be asked is not JVhy ? the inquiry of immediate application is, Hoto ? * It may here be permitted to call attention to a work which might be adapted to meet a palpable want: Die Natur dot ffarmonik und Metrik by M. Havptmann. I PBEFACE. m The thing to be done is, from experience, from the best models, to understand, not to calculate, the necessity of certain principles ; Idter, if education, acquirements, capability and calling require it, it will be time enough to investigate the why, and all knowl- edge obtained from experience will be an aid not to be despised, for discovering also the laws of nature pertaining to music. This practical aim in view, the author was at pains to give the exhibition of harmony, and of the propositions resulting from observation and experience, in a simple and clear manner, and since he destined the book for study, io let the truths, perhaps contained in it, work through themselves ; without wishing, through an espe- cially learned dress or an attractive form, to obtain for them an extended circle of readers. It contains the doctrine of harmony complete, with hints for a rational method of performing exercises, for the fixing of the whole, and for the ready carrying out of aU harmonic principles. These exercises extend to the beginning of contrapuntal studies ; the doctrine of counterpoint itself will fol- low, however, in a later volume after the same plan. In closing, still a word to the disciple of art ; an earnest onoj indeed, but well meant. It is our object to reach a distant goal ; this goal is the actual pro- duction of works of art. For this a vigorously exercised, enduring activity is necessary, to comprehend the musical principles, to form that which is won and recognized into structures capable of life. Those will bitterly deceive themselves, who, filled with the works of our great masters, gifted with a poetic mind, think to be able to pluck the blossoms, without learning thoroughly to know and prove the technical aids ; who are of the erroneous opinion that the consecration of beauty which extends itseK over the work of art suffers under the dissection of the material, or that the first natural formations of the latter could never develop themselves to that requisite beauty. No person of talent has ever, without thorough knowledge (to attain which was, to be sure, easier to him than to the less gifted), risen to that height, upon which alone TUl PREFACE. the achievements of art thrive. Exercise without consciousness is not artistic skill, it is only the working of the instinct, which will always make the want of a complete education sensible. The spiritual thought cannot do without the form, and it is this which must be recognized and learned. Even if it often comes with the conception of itself, still, \\ith music, more than with anything else, it is of importance, as it were, logically to dissect the thought, to remodel it into new forms, to transform it in the most manifold manner. The knowledge of these things and skill in them must be acquired by the person of talent also, and this can only be attained by taking pains to recognize the musical laws, and en- deavoring to imitate and extend what others have abeady long since discovered. Earnest, persevering activity, and above all, a rational method for the development of maturity, for the forma- tion of works of art capable of life, will, in connection with musical qapacity, certainly lead to the goal FROM THE PREFACE TO THE THIRD EDITION, Although in tlie present edition also, the methodical order of the former ones has been retained, still it has received material additions. The exercises for many subjects of instruction have been increased in number, where it seemed necessary. As concerns the last, some books have appeared lately which are in a measure related to the present manual, viz : Genercdhass- Uehtingen nebst Kurzen Erlauterungen by Benedict Widmann, and Uebungen zum Studium der Earmonie und des ConfrapunkfeSy by Fekd. Htller. Although this is not the place to speak more particularly of these works, still let me here be permitted to thank these authors for their friendly reference to my work, and to make the following additional remarks in respect to it. Although the study of the theory of music through the so-called thorough-bass doctrine has long since yielded to a more rational method, stiQ the thorough-bass figuring, as means to the end, has to me proved itself too excellent, to admit of my not using it for the first exercises in harmonic connections, as in general for the first applications of harmonic knowledge. A farther, more extended use of this has not been made in my text book itself, but in the first of the works above referred to, and, indeed, for exercises which, in part follow the course of my text book, in part aim at other practice. The X PEEFACE. work of HiLLEK, however, besides the exercises which professedly follow the xjourse of my text book, offers in general a rich material for elaborations of the most manifold kind, not alone for harmonic exercises, but for all branches of theoretic musical edu- cation. Since the exercises in my text book could not of course be exhaustive, and are, for the most part, given only in a suggestive way in order, when needed, to design others after them, both works may here be highly recommended for this object. - PREFACE TO THE FIFTH EDITION. It has been my endeavor in this fifth edition, also, which became necessary in a short time after the fourth, through addi- tions, in part through altered verbal expression, to attain that perspicuity, which a text book of this kind must possess, if it ful- fill its end completely. If I may also venture to hope that the book has been in many directions serviceable and of use, I am still conscious, that in order to reach the simple and luminous representation which is my ideal, many an improvement is still to be introduced. This edition, however, does not differ essentially from the preceding, and I wish, that beside the old friends, this new edition may gain for itself new ones. ERNST FEIEDE. EICHTER. Leipsic, DecemleTy 1863. TABLE OF CONTENTS. PAoa ISfTBODVCTioN.— Intervals, . 13 PART I. THE FUNDAMENTAL HARMONIES AND THE CHOEDS DERIVED FROM THEM. CHAPTER I.— -The Triads of the Major Scale, 21 II.— The Triads op the Minor Scale, 40 III. — The Inversion of the Triads, 47 IV. — Harmonies op the Seventh {Vierldange), .... 54 V. — The Inversions op the Chord op the Seventh, ... 59 VI.— Secondary Harmonies op the Se^t^nth, 64 VII.— The Inversion of the Secondary Chords op the Seventh, . 78 VIII.— The Chords op the Seventh in connection with Chords op Other Tone-degrees, 81 IX.— On Chords op the Ninth, Eleventh and Thirteenth, . 88 X. — Chromatic Alteration op the Fundamental Harmonies. Al- tered Chords, 91 XI.— On Modulation op a Passage op Music, . «... 103 PART II. ACCIDENTAL CHORD FORMATIONS. TONES FOREIGN TO THE HARMONY. XII.— Suspensions, 105 XHI.— The Okgan-Point. Stationary Voices, 123 XII CONTENTS. OHAPTEX TAOr XIV.— Passing Notes. CHANOiNa Notes, .128 XV.~Passing Chords, 138 XVI.— On the Means for Modulation, 141 . PAKT III. PEACTICAL APPLICATION OF THE HARMONIES. THE EXERCISES IN THEIR USE IN THE PURE HARMONIC STRUCTURE. XVII. — The Simply Harmonic Accompaniment to a Given Voice, . 157 XVIII.— Extension of the Harmonic Accompaniment, . . . 173 XIX.— On the Development of Melody, 176 XX. — On Development of the Accompanying Voices, ... 183 XXI. — The Exercises in the Three-voiced Movement, . . . 187 XXII.— On the Two-voiced Movement, . 193 XXIII. — Harmonic Elaboration op a Given Voice in Melodic Devel- opment, 195 XXrV.— The Five-voiced Movement, 203 XXV. — The Six, Seven and Eight-voiced Mo^tement, . - . . 206 XXVI.— On the Musical Forms of Close, 213 Index op Subjects, 216 A^ V -/.^ '" y. -^ s-/ INTRODUCTION. k Of the elementary knowledge for -which general instruction in music provides, and acquaintance with which must be presupposed at the beginning of the study of harmony, the portion which stands in the nearest relation to it, viz : The Theory of Intervals, will be treated of prelimina- rily in a brief and condensed manner. Intervals. I The relation in which one tone stands to another, in respect to differenc3 of pitch, is called Interval. The greatness of the difference is directly determined according to the number of the degrees of the staff, upon which the two tones stand, in respect to each other, and, as a rule, in such a manner that the lowest tone is reckoned as standing upon the first degree, and the higher is determined according to the number of diatonic degrees lying between. R EMAEK. — ^By diatonic degrees ia understood the series or progression of tones pre- sented by any major or minor scale. If we take, for example, g as lower tone, and situated upon the first degree, then the a, being the higher, will come upon the second, the e, higher still, upon the sixth degree : «^- &c. The numbers of the degrees produced thus, will be expressed in the following manner : 1 2345678 i •^»' ^ ^ ^ .^ ^ ^ .^ Unison or Prime. Seconiminished. -^•-^-|^r-^-E-:^: :#t m Fifths. Perfect. Augmented. Diminished. Major, Sixths. Minor. Augmented. $ mm izzzijzi ¥ 1=FF Sevenths. Octaves. Ninths. Major. Minor. Diminished. Perfect. Diminished. Major. Minor. fe=^=^-^'i^: m F r Division of the InteiwaJLs into Consonances and Dissonances, If we speak in music of consonant and dissonant intervals, we under- stand thereby, not well or ill sounding ones, which, to be sure, can be expressed by these two words, but by the first, we understand such as stand in a pure, satisfying relation to each other, which does not require a certain farther connection with other intervals ; by the last, such as defi- nitely indicate a farther progression, and without it would have no satisfying sense. The consonances comprise all those intervals called perfect^ and, in ad dition, the mayor and minor ihirds and sixths. MANUAL OF HARMONY. n % The first are called complete consonances, the ?ast incomplete. The dissonances are the major and minor second, major and minor seventh, and all augmented and diminished intervals. From this we derive the following general plan : I. CONSONANCES. a. Complete, The perfect prime, perfect fourth, perfect Jifth and perfect octave. 1 4*5 8 mmii ■^ ■» 19- h. Incomplete. The major and minor third, and the major and minor sixth. 5^fl II. DISSONANCES. The augmented prime^ the major, minor and augmented second, the •diminished third, the augmented and diminished fourth, the augmented and diminished fifth, the augmented sixth, the major, minor and dimin ished seventh, the diminished octave, and the major and minor ninth. Augmented 1 Major. Minor. Aug. 2 Dimin. 3 ^ -%; — ^^? |%r i Aug. Dimin. 4 ^wgr. Dimin. 5 -dli^r. 6 %^ ;6iE^E=i^:E^a^E^[^fe 1 I Major. Minor. Dimin. 7 Dimin. 8 Major. Minor. 9 b=1= "S* fe -^ ^ ;■ -r -F W •Later in the instruction in harmony, follows a farther explanation i>f the peculiar relations of ihQ fourth. 18 MANUAL OF HARMONY. Inversion ( Versetzung) of the Intervals, As was already indicated above, in determining the intervals we begin as a rule, with the lower tone. If, however, there is occasion to determine the relation of two tones, taking the upper tone as the starting point, the intervals found are called intervals below. Thus, for examp'Cj I is d, the fifth from g ; g, however, from dj the fifth helow. It is easy to see that the interval cannot be al- tered by this. It becomes different, however, if the upper interval be removed below the original lower tone. Since particular reference is had to this inversion in various kinds of composition, an explanation of it may follow here. The diatonic major scale will, by means of this inversion, assume the following form : Intervals above : 1 6 7 'Ji^^ -gg^ - J: j^9i 1 InUrvaUheloxD : 8 7 6 5 4 3 2 There result thus, the following series of numbers : that is, through inversion, the 'prime becomes an octave^ the second a seventh^ &c. The inversion of the major scale forming the basis, we must note the following in respect to all intermediate intervals : V 1. All PERFECT intervals remain perfect in the inversion in the Ipctave. \/ 2. All MAJOR intervals become minor, all minor major, the augmented ODIMINISHED, and the diminished augmented. In the following table is exhibited a view of all the inversions : Original Intkrvals. Imtersion. Primes. Perfect. Augmented. |Ei'gE^EgEEg^ ^^ Major. Seconds. Minor. Augmented. £ iz::zs:i m OCTAVBS. Perfect Diminished. 3finor. Sevenths. Major. Diminithed. ■^- .^_D hs MANUAL OF HARMONY. 19 FouETns. Augmented, Diminished . Major. Minor. DiminisTied, Perfect. Augmented. Diminished. Minor. Sixths. Major. Augmented. Perfect. Fifths. Diminished. Augmented. ■^^^^^^^^^^^l Fifths. Perfect. Augmented. Diminished. -t- f- Major. Sixths, Minor. it Augmented. Perfect. FOPETIIS. Dimiiiished. Augmented. Minor. Thirds, Major. Diminished. ^ ^^= ^1^= ^ ^^^^ ^^^:^^^^^ Major. Sevenths. Minor. Diminished. Octaves. Perfect. Diminislied. ipzzx i^ii m _<2- Minor. Seconds. Major, Augmented. Peimes. Perfect. Aicgmented. •=F= fe-^^^ An exact, certain knowledge of this essential inversion of the intervals is not alone important for the exercises in double counterpoint, but greatly facilitates comprehension and insight, in simple harmonic structure, for ■which reason their study is urgently to be recommended. A few more remarks may follow here : / The reason why, in the first table of intervals, (page 16), all diminished intervals were formed by raising the lower tone a small half step, and not by lowering the upper, is clearly to be seen from the above table of inver- N^ions. Since the diminished intervals result from the augmented through the inversion in the octave, this formation comes of itself; for example, if^nz must of necessity give the following dim- the augmented fourth mished fifth : /W— r,^ — jg — Just so the perfect fourth belongs originally to the consonances, since 20 MANUAL OF HARMONY. by inFersion it is converted into the perfect fifth, in the same manner aa the perfect fifth can only produce the perfect fourth, and never in any case does a dissonance result from the inversion of a consonance in the octave. Mention is made of this here because, in particular cases which are men- tioned farther on, the fourth requires a similar treatment with some dissonances, which induced some theorists in earlier times, to explain it simply as a dissonance. It will likewise be clear that the augmented octave, as also the ninth, cannot be inverted, since they never can become intervals below. Other kinds of inversions, such as those in the tenth and twelfth, which produce entirely different results, may be passed over here, since they ex- ercise no influence upon our next studies. Since a complete and certain knowledge of all intervals is indispensable for the following harmonic studies, the practice of them in writing, as als© an oral solution of given intervals, will facilitate much their correct com- prehension, — which exercises are to be repeatedly employed. HARMONY. Combinations of simultaneous tones, formed from different intervals, according to certain fundamental principles, are called in general, Harmo' nieSf Chords. The doctrine of harmony makes us acquainted with the different species and kinds of chords, and shows their natural treatment. This consists in the right and natural connection of the chords among themselves, that is, in the transition, the resolution, the commingling of one chord into and with the following. I PART I. THE FUNDAMENTAL HARMONIES AND THE CHORDS DERIVED FROM THEM. Among the various kinds of chords which can serve for the harmonic foundation of a composition, those which present themselves as indepen- dent, without a definite connection with others, can be easily distinguished from those which indicate plainly a connection with other chords, and are therefore not independent. To the first belong the most of the triads, to the last the chords of the seventh. These two kinds form the fundamental harmonies, from which all remaining chords are derived. CHAPTER I. Tlie Triads of the 3IaJor Scale, A triad is formed by a combination of three different tones. Of these, the lowest is called fundamental tone, to which its third and fifth are ^^dded, e. g. ;£ 22 MANUAL OF HARMONY. These triads, formed upon c, g and a, present, however, a difference as tc their intervals. While the triads of c and g are formed here hj majo7 thirds SLud 2>erfect fifths J the triad of a contains a minor third and perfect fifth. ^ A triad with major third and j) erf ect fifth is called a MAJOR TRIAD. A triad with minor third and perfect fifth a MIN^OR TRIAD. Remark. — The explanation of other kinds of triads cannot follow until farther on. As the diatonic scale makes up the content of a key, and forms the foundation of the melodic successions, so also the triads, which are founded upon the different steps of the scale, will form the essential part of the harmonic content. Natural Connection of the Triads of a Key, The triad which rests upon the first step of a key, is indeed the most important, the one which determines the key ; there stand, however, others in the nearest connQdiion with it, which make clear its position. In the natural presentation of the triad in thirds, the lowest tone shows itself as fundamental, the ffth as highest tone, and at the same time as its culmination. Fundamental. Each farther addition of a new interval would either alter the chord, or present tones already there, doubled. The next triad standing in connec- tion with this must, to be sure, as an independent chord, lie outside its tone- mass, still, however, support itself upon one of its tones. This tone can only be found in the outer limits of the chord, viz : in c and g. G, which is here the fifth, will thus form the fundamental of the one nearest standing triad, while c will in the same manner form the culmination, the ■fifth of the other, the fundamental of which would be F. The connection of these three chords can be most plainly presented in the following manner : «>i?=i^^ It is especially to be remarked of these three triads which stand in the closest connection, that their tones contain all the tones of the scale ; that they form the fundamental features of the key, and that they are, and must MANUAL OF HARMON?. 23 be those most frequently employed in practice, if the key is to present itself clear and distinct. On account of their importance also, especial names have been given to them. The one first found, standing upon the first degree of the scale, if called THE TONIC TRIAD. The second, upon the fifth degree, THE DOMINANT TRIAD. The third, upon the fourth degree, THE SUB-DOMINANT TRIAD. If we arrange these three chords according to their order in the scale, they present themselves to us thus : t ^ I IV V \ and they show themselves collectively, as major triads. Application of the Harmonies I>iscovered, In the application of these three, as well as of later chords, we avail ourselves of the four-voiced manner of writing. Remark. — The theoretical chord combinatioo can be well presented, to be sure, three- voiced in manifold relation. It would, however, detain us longer from our practical aim, and may, for this reason, be reserved for a special presentation. The four-voiced movement will always maintain its importance as the foimdation of all kinds of com- position. ■ We regard, however, each harmony not as a mere mass, as compositions for the piano-forte often present them, but divide its component parts into four different voices. The upper is called Soprano, the lowest Bass, these two together are called the outer voices : the voice next below the Soprano is called Alto, the one next above the Bass, Tenor; these two together are called middle-voices. The arrangement of these voices in the manner of a score is as follows, and the triad may be exhibited thus : 5. 80PKAN0. Alto. Tknor. Bass illpJllB 24 MANUAL OF HARMONY. For the upper three voices especial clefs are used, which conform better to their compass than the above used violin [G] clef, and which will be spoken of later. For our next exercises, we select for the sake of an easier view of the whole, not a separate staff for each voice, but will use the usual form of writing for the piano, (upon two staves). The distribution of voices in No. 5, may be exhibited thus : 6. Soprano, A LTO. Tksor. Uass. m: m^mimm ^^^^mm:^ A twofold consideration of these various voices will take place : first in relation to the progression of each voice for itself alone, then in its relation to the remaining voices, both of which must be pure and ivell-constructed. The result of the fulfillment of these two conditions is called pure lead- ing of the voices. This purity of the harmony and its progression is attained through •seeking out and practicing the natural and legitimate of harmonic com- bination. Hereby arises the so-called pure harmonic structure, also called strict style, which prescribes rules and laws which proceed from the nature of music itself, the observance of which will afford the safest foundation for a later free use of the materials for composition. By exercises in the pure harmonic structure is the judgment sharpened, the sense for the true and correct formed, and the taste purified. Remark. — Inasmuch as every composition should exhibit itself, through a correct use of all means at command and the purity resulting therefrom, (purity is here synony- mous ■with natural expression), the term pure harmonic structure in a general sense, ■would require no farther explanation, as being a matter of course. In a more narrow sense, Iwwever, under pure harmonic structure "we understand something farther, ■which is more nearly and better indicated by the expression of like meaning, strict harmonio structure, strict style, since this can be used in distinction to free style, whereas, properly Bpeaking, no antithesis of the pure structure, such as, perhaps, impure structure, is to be assumed, since, as frequently as the latter in fact may occur, it -were certainly to be designated as false, -while the free structure might be essentially founded upon the legiti- mate of the pure structure. As was indicated above, by pure harmonic structure h understood in a narro-wer senses MANUAL OF HARMONY. 25 inch a one as in the natural development of all tone relations, allows the fewest digressions from the legitimate, and only such as do not toicch that which is essential, fundamental. If, in what precedes, the idea of pure harmonic structure is determined in a general way, still its boundaries are not yet drawn ; and just this is a point which gives rise to tl e more difficulties for the beginner, as the boundaries are so very variously determined by the theorists themselves. This difficulty has occasioned many of them, especially some later ones, to omit entirely to speak of the pure construction, of the strict style ; indeed, to begin immediately with composition, and teach the laws of harmony from its inci- dents. Whether this indulgence to youthful impatience, which does not willingly busy itself with the abstract, this inclination towards premature living creation, before the organic has developed itself to the capability for creation, can produce anything really mature, need not be further investigated here. Let those who follow the views of this book and conform their studies to them, as also all who have to go through a strict school, be assured, that their freedom for future creation will by no means be lost by means of that which is forbidden to them, but will unfold itself so much the more fully, and with a more living power, upon a basis conformed to nature. The real mastery has ever been able to make itself apparent most genially within prescribed bounds, whereas the most lawless conceits frequently furnish proof of morbidity and weakness of mind. On the other hand, the pupil cannot be justified in making use of exceptions to given principles, which may perhaps be found in the works of the greatest masters, where the rule is concerned ; or, in any case, to wish to produce compositions, when the thing to be done is to work out exercises theoretically well. The three chords thus far known, being applied in the four-voiced movement, will give occasion for remarks and observations, from which certain fundamental features and rules are to be established. /\ Since the triads only contain three tones, one component part (interval) tjiereof, must be doubled, if they are to be used in four-voiced writing. A Any Interval of the Triad can be Doubled, The fundamental^ however, usually presents itself as the tone most adapted for doubling, more rarely the fifth and third, and, indeed, the latter, in many cases which will be shown later, is not to be doubled at all. In order to accomplish the connection of two triads, the following rule is to be observed : If a tone occurs in both of two chords which are to he connected^ it it to he retained in the same voice, e. g. V V y^- 26 MANUAL OF HARMONY, In the Example a, C occurs in both triads as common tone ; the Soprano, / which gave the first C, retains it also as fifth of the next chord. Just so / in Example &, in which the Gr of the Alto affects the connection. The remaining voices proceed to the tones which lie nearest to theniy as a the Alto from Gr to A, the Tenor from E to F, &c. 5k If in two chords no common tone appears^ the voices are independently \yj/Th Y^t a the Alto from G to A, the Tenor from E to F, &c. /^ If in two chords no common tone appears, the voices vuic, v (^ led in such a manner/that none appears with any other m PARALLEL FIFTHS or OCTAVES. In order to explain this faulty progression more exactly, we must first make the necessary explanation of the movement of the voices in refer- ence to each other. The Helation of tlie 3Iovement of the Voices in Mespect to each other. One voice can progress with another in Parallel [direct] motion (motus rectus), Contrary motion, [motus contrarius) and Oblique motion, (motus obliquus). The parallel motion arises, if two voices rise or fall at the same time, e. g. ict 1^1 i 2^zz=?: =:^i=izi:: :S ^: They progress in contrary motion if the one rises and the other falls, e. g. • "^ p •* I =>' -J I 7 The oblique motion arises, if, of two voices one remains upon the same^ tone yhile the other moves on, e. g. MANUAL OF HARMONY, 27 These three kinds of movement of the voices occur in chord connections niB,mixed manner. Thus, in Example No. 7, b, the parallel motion shows itself between Soprano and Tenor, the contrary motion between Soprano, Tenor and Bass, and the oblique motion between the Alto and the remain- ing voices. The above mentioned faulty movement of the voices in parallel octaves and fifths^ can only appear in parallel motion : if, for example, two voices progress by degrees or skips in the following manner : 11. This fault is regarded as such for all voices. The following connections of harmony contain both faults : 12. h. In Example a, are parallel octave skips between Soprano and Bass; in Example &_, octave progressions between Alto and Bass, and in Example c^ between Tenor and Bass. Parallel fifths are to be found in q^ between Alto and Bass ; in &, between Tenor and Bass, and in c^ between Soprano and Tenor, as also at the same time between Soprano and Bass. The best means, to avoid these and similar faulty progressions, is, for the above cases, the use of the contrary and ohlique movement of the voices ; that is, the voice which already forms an octave or fifth with another, must either move with it in contrary motion^ or, if the following chord contains the same tone, remain stationary. The other voices then move on to the tones of the new harmony which lie nearest to them. Thus in Example 12, d the oblique motion in respect to one voice, and at J) and Cf the contrary motion of all voices in respect to t.he Bass, is to be applied, e. g. 13. ^^^M\ "W lilii[^ 28 MANUAL OF HARMONY. Remark. — ^The reason for the prohibition of octaves^ with whi<5h is connected that oi the progression in unison, can be easily found in the necessary independence of the voices. It is more difficult to discover the ground for the prohibition of the progression in fifths, strong as the conviction may be of the necessity of it ; and from the earliest times until no-w, much pains has been taken to express it clearly and definitely. On this point, let tlie following view be examined. If each chord-formation presents for itself a separate whole, which, let it be formed as it may in other respects, is bounded mainly, as it were, by its fundamental and the fifth, as by a circle, (the seventh, as something additional cannot here be taken into account), and if the connections of harmony can only be produced by this : that one chord, so to speak, goes over into and resolves itself into the other ; then it is evident, that two chords with their boundaries, fifth after fifth, do not resolve themselves into each other, but, if they are placed side by side, will appear without relation to each other. This can be observed if we compare the following examples : 14. ©5S=i^.. . _^_^ M^^i^mw^i The sevenths, however, neither form, properly, new chords, nor do they lie, (according to the idea of a seventh), outside of the circle of the original chord, and only serve to indi- cate the relations of two chords, and to make the connections of the harmonies more intimate and firmer. Everywhere now, where the perfect fifth appears, it will carry in itself its character of boundary/ ; the remaining constituents of the chord, (as it were the content of the fifth), or anything additional, as the seventh, may lie above or below it ; the unpleasant- ness of the succession of two perfect fifths will always be discoverable in the deficiency in connection. Since we have spoken here of the fifths of the triads only, it may still be remarked, that in the case of perfect fifths which arise from added sevenths, the rule of their pre- paration, in part, to be sure, prevents parallel fifths, of itself; that, however, in the progression of one such seventh, which forms a perfect fifth with another voice, to a following perfect fifth, this last will cause the unpleasantness and deficiency of the connection to be heard, since this lies only in the second fifth, which enters without con- nection, €. g. 15. As eoncems the diminished fifth, however, which in the dominant chord of the seventh can enter free under certain conditions, its free entrance even in the case of par- allels, justifies completely the above expressed view, since, so soon as it appears after the perfect fifth, its connecting character makes itself felt, whereas, before the perfect MANUAL OF HARMONY. 29 fifth, leaving out of the account its farther laws of progression, the latter immediately gteps outside of the circle of connection of both harmonies. Compare the following examples, 16. If, however, instances of the following sort are frequently found in compositions of the stricter style : IT. we may assume that the doubling of the diminished fifth (the /,) requires a double pro- gression of the same, and that the fifth-succession is thereby justified, because it lies Id the middle voices ; that, however, the following progression could not be called pure, IS. --J- 2L^ I a^^^P^^^^^ s^ i i partly because they come forward too prominently in the upper voice ; partly because the above condition of the necessary double progression is wanting, although instances such as No. 16. c, are often to be heard. Hereby it becomes clear, also, why such parallel fifths as arise from passing notes, in many cases do not sound so unpleasant as those spoken of above, for which reason many theorists recognize them as faultless ; which, at any rate, cannot be unconditionally admitted, since many of them are based upon other false voice-progressions, (for exam- ple, upon covered fifths), and it is not to be denied, that with a very open position and sufficient duration of the same, the unpleasantness of their operation becomes per- ceptible. It is not the place here, to treat at greater length of these relations, and there would be much to say on many points ; as for example, concerning the progression of the fifth of the augmented chord of the sixth and fifth, which would here carry us too far. Individual casea will bring us back to this T^mi in connection with our practical exercises. so MANUAL OF HARMONY. If the sense of the foregoing representation should still be too obscure to the begin- ner, yet with more advanced knowledge, and exercises, and necessary frequent repetitions of the entire harmonic system, the comprehension of it will not long be wanting. The faulty progression, thus far mentioned, is called open fifth and octave progression. They are covered^ if, in parallel motion of two voices, the second interval forms 2i- fifth or octave^ e. g. 19. Open fifth and octave parallels remain, for harmonic combinations always inadmissible ; the worth of covered fifths and octaves will be dis- cussed farther on (in Chapter XVII.) ; for the present, this matter must be left to oral instruction, since, in general, with a correct comprehension of the exercises, not much opportunity will be offered for making unsuit- able fifths and octaves. Hemark. — The beginner will do well, in working out the first examples, to leave covered fifths and octaves entirely unnoticed, since, in a too anxious avoidance of them, frequently the first principles of chord-connection are violated, and other much worse faults easily arise. Much which follows will lead us back to this point, and with a more mature insight, the subject will be particularly discussed. Exercises, To bring musically into connection the three primary triads, with observance of the rules thus far established, will be the next exercise. We select for this purpose the following Bass progression : 20. §3 ;i^i IH^i C: I IV P i Remark. — ^Tliese, as well as all subsequent exercises, give an indication in what way and manner our practical exercises will proceed. They are always to be continued so long as the point under consideration makes it necessary. The situation of the upper three voices of the first chord, which arc to be added, will yet give us occasion for important remarks. * The figure over the Bass-note indicates the proper, interval for the Soprano of the first chord. — Ed. ZfANUAL OF HARMONY. 31 ¥ We Iiave already seen in Example 5, that the situation of the voices in a chord can be very different. This situation of the voices is called the 'position of the chord. Close and Open Position, A chord appears in close position, if the upper three voices lie so near to each other that neither the Soprano nor Tenor, if transposed an octave, can appear between the two other voices, even if the Bass is somewhat ^_ removed, e. g. 21. <7. The first position of the chord a is in & so altered, that the former E of the Tenor being placed an octave higher is given to the Soprano ; in c, the case is the same, with the two tones Gr and E ; on the' other hand, in d^ the C of the Soprano is placed an octave lower. In all these transpositions the situation is indeed altered, but not the close position. It is otherwise if the chord appears in o'pen (also called dispersed) posi- tion, which is the case if either the Soprano can be placed between the Alto and Tenor, or the Tenor between Alto and Soprano, so that thereby the close position results, e. g. 22. At cif the chord appears in open position ; by a transposition of the G between the Alto and Soprano in close position &/ just so at c and d. At /' the G of the Soprano of the chord e^ is placed an octave lower between the Alto and Tenor. In this sense, however, the following situation of the voices (No. 23), would not be open position, for by the transposition of the Tenor, the situation of the upper voices would not be altered, hf and only the 32 MANUAL OF HARMONY. transposition of the Soprano would produce the real open position of the chord, c» 23. ; 1 ^=&=\^^ l=^=\l Even if the open position allows the chord to appear fuller, still it ia not always to be applied, and, for our first exercises, is not clear enough to the view ; so that we will for the present, write them in close position. Remark. — It will always be better in the beginning to work out the examples in close position, and only to use the open position later, from the examples of the second and third part onward, in which last they necessarily present themselves. In the begin- ning, the pupil, in the use of the open position, stumbles now and then upon difficulties, to overcome which cannot be our immediate object, and which had therefore better be evaded. The various positions do not generally appear single, but occur com- bined, according as the leading of the voices requires. If the position of the first chord is determined, the following chords are no longer so free, as to their position, that each can be chosen at pleasure, but it is regulated according to the rules for the connection of chords already given, pages 25 and 26. This connection of chords and the leading of the voices of the first exercise, No. 20, may follow thus : 24. =^^i^§liiE g!=5E iz^: C:' I : :~ffl~: : IV The natural relation of these chords to one another becomes clear by the above simple example, if we observe accurately their connection ; especially, however, from the last two chords does the close connection, the mutual completing of one another, become plain. The feeling of return, of rest, of satisfaction, which lies in this connection of chords, adapts them for forming the close. This form of close through the domi- nant chord, which resolved itself into the tonic triad, is called, if the latter falls upon the rythmical accent, the authentic close. [Cadence]. MANUAL OF HARMONY. 3d 35. Another form of close, which is formed by the subdominant triad, aa above, No. 20, Example 4, is called the pJagal close. 36. 1 i^il^i IV I Of these and other kinds of close, we cannot speak more at length, until later. In order to become expert in writing the succession of chords which occurs if the Bass progresses by degrees, (as in Example 24, F — Gr), it will be to the purpose to write the successions IV-Y and Y-IY, in various positions and keys. Note. — The expression hy degrees is used here, as elsewhere in similar connection, to denote from one degree to the next, in distinction to hy ships, viz., from one degree t*. another at a greater distance. — Ed. The Triads of the Remaining Degrees of the Major Scale, All triads of the remaining degrees of a scale will, to be sure, belong to one and the same key, but will not indicate it so decisively as, for exam- ple, the combination of chords V-I. These triads are called, to distinguish them from the primary triads, SECONDARY TRIADS. They are situated upon the second, third, sixth, and seventh degrees of the scale. 27 ■I :r=^ A. _iLX vuo The triads of the second, third, and sixth degrees, appear as minot triads, since their thirds are minor and ihoii fifths perfect. The triad of the seventh degree is materially different from the others* 84 MANUAL OF HARMONY. because that, beside the minor third, it contains a diminished fifth ; for this reason it is called the DIMINISHED TRIAD. We select as an easy distinguishing sign, for the minor triad, a small numeral for the designation of the degree upon which it is situated, to which, in the case of the diminished triad, we add a 0, as above vii°, a manner of writing which the theorist, Gr. Weber, has introduced. All the triads of the major scale can now be exhibited thus : a ^-f-i— i— =-=^ — (R^n I n ni IV V VI viio ^ Remark. — The beginner must be very careful not to conceive of these chords, at their appearance, as all tonic triads, a misunderstanding -which renders insight into harmonic combinations much more difficult. As long as C major is the ruling key, the triads of G, F, D, etc., are nothing else than the chords of the various degrees of this Jcey of major, and belonging to it, and no mention will be made of G major, F major, d minor, so long as these keys do not appear as independent. Hereby arises an ambiguity of the chords, which should be particularly noticed Each triad can belong to various keys. The major triad of C can be : 29. HiEl^^ii C: I F: V G: IV If, therefore, in respect to this chord, C major is spoken of (expressing the key m the general use of language), this is true only in the first case, if the C major triad occu- pies the frst degree ; in all other cases, however, it is incorrect. Application, In the connection of these chords, as well among themselves as also with those found before, no new rule is at present necessary. Several things v^hich are new will, however, appear in connection with it. The Bass can move either by skips or hj/ degrees.* / In the first case there will always be connecting tones (like tones in two /consecutive chords) ; in the last the progression of the voices must be in j contrary motion, according to a rule mentioned above, (page 26), in order to bring out the inner connection of the chords. • See Translator's note on page 83. MANUAL OF HARMONY. a. The Bass progresses hy skips. b. NB. 35 better: 30. • — '^ f ^^ i — ^" 1 — g- - — g - — g— p u IV :gfF=S: gll 9^ i II VI &c. As in this example, the skips in the Bass from the second degree have been treated, the same can be treated beginning from all other degrees, so that tones common to the tico chords always remain in the same voice. To this rule there are, however, in many cases, exceptions. In Example 30, at NB., is found a progression of the voices formed according to the above rule, which contains an unpleasant covered octave between Tenor and Bass, and which is certainly improved by the following progression. Even if, in the last case, the local connection of the tones fails, still the inner connection is present, since the D of the Soprano in the first chord can easily be conceived as doubled through the lower octave, whereby the connection immediately becomes apparent, as in Example No. 31 : 31. ^m r^ Remaek. — The reason, however, why exactly this tone should be conceived as double, since this could also be the case with any tone at pleasure, is founded upon the fact that it is WxQ fundamental^ the tone which gives to the whole chord its determination. The unpleasantness of the covered octave mentioned, lies in the circum- stance, that the upper voice progresses a whole step, and is yet more noticeable if it is contained in the outer voices, as in Example 32 at a* 32. :miii 36 MANUAL OF HARMONY. By the contrary motion of the Bass at h, the leading of the voices can be improved ; in like manner, by the contrary motion in Example c, although here also a covered fifth shows itself between Soprano and Tenor. (See the Remark on Example 34). Remakk. — Id the cases brought forward above, we do not speak of absolute faults. If the leading of the voices is entirely given into our control, much can be avoided, which under other circumstances, for example, in the treatment of a cantu8 jirmus, of a motive, or on other grounds important for the composition, is unavoidable. The improvement is here only presented from a theoretical stand-point. Concerning the covered fifth in No. 32 c, a farther explanation follows at No. 34. /^^The unpleasantness of the covered octaves spoken of ceases at once if the njpper voice progresses a half step, e. g. -k^- 33. -JSrZ. M^^m^ll ^iilHl i h. The Bass progresses hy degrees. Here the contrary motion should always be applied, e. g. NB. 1. lititer : 31. lEig^i^lii^iiii g!^EE|EgE| -G l^gzi ^ -azj^gzzjzigzjng zzi^ titter : better : m^mm ^m= ^^ ^ m^- NB. :S^ gi^^Eg^ ^ ^l^i^^^-pg^^l^ ly IV |=E^ ^h= m=Mm m -.zi^zz 1 IV MANUAL OF HARMONY, 37 HemarJcs on these CJiord-contiections, In all progressions of voices such as that used at NB. 1, and subsequent similar places, it is better to double the third of the second chord, in order to avoid covered fifths. Their unpleasantness is more noticeable if the chords appear in open position, e. g. 35. ^i^i^^Ei^i; ifc i ^mMi^^m -^- i The leading of the voices at h is to be preferred. If these covered fifths occur in the middle voices, they are more allow- able, because they are less perceptible. 36. I^^fl zr ^^.a m^m^ At NB. 2, the doubling of the third of the second chord is not always to be applied, since in general, the doubling of the seventh degree (in Example 34, the B of the second chord), is to be avoided. Concerning the treatment of this tone, which is called leading ione^ a fuller discussion will be given in connection with the following exercises : Exercises to he Worked Out. 87. 9i i^zz:s^= ^g. EEEEi X m -« — fsiz:: ^?Et a §J=gn-= :e=£ \ ^E^JEx^i^=fZ -d <9- NB. 5.^ wMw^^m^^^^^ The fourth exercise gives occasion for a few remarks. The progression of the Bass takes place here in the first four measures, in a regular, consequent manner. Such a regular harmonic or melodic progression is called Sequence. 38 MANUAL OF HARMONY. This consequent progression of the Bass, occasions also a like regular leading of the remaining voices. The treatment of this example, according to principles of chord-con- Dection laid down above, by sustained tones, e. g.j 3§. -l-X --i=:|- wm i^ii^ii would not admit of the attainment of this end ; the progression must rather follow in such a manner, that the chord of the second measure is brought into the same position which that of the first measure occupied, whereby the connecting tone D, does not remain in the same voice. NB. Ill vii*^ , In the first example, on account of the sequence, the covered octaves ^ spoken of above will likewise be allowable, if they are not found in* outer voices. In the third measure of Exercise No. 4, we meet with a chord, which thus far we have not used. The Diminished THad. It rests upon the seventh degree of the major scale, and is more depen- dent than the triads found thus far, since it plainly indicates a progression, which indication is effected by the dissonance, the diminished fifth. The natural progression of the diminished intervals can in general be so conceived, that either both tones approach each other by a degree, (a), or the upper or lower tone progresses alone over against the other, (ft, c), a kind of progression which only becomes plain through actual chord-con- nection. 40. Inversion. :if MANUAL OF HARMONY. 39 The third following the diminished triad (rZ), exhibits the triad of the first degree (C) as incomplete, by omission of the fifth. Since, according to the relations of the intervals in respect to inversion before explained, (page 18, 19,) an augmented fourth results from the dimin- ished fifth, its progression must also appear in inverted order. See 40 €, The fundamental tone upon which the diminished triad rests, is called LEADING TOlN^E. It is found again as third in the dominant triad, and as fifth in the triad of the third degree. 41. fe— J E^^^^p zi-JJizif p VIlO Since the leading tone of itself comes out very distinctly , it is not DOUBLED in the simply harmonic four-voiced movement. Just so its progression one half step upwards can be effected, if the next following chord contains this tone. This tendency to progression lies in the melodic character of the leading tone, inasmuch as it stands as half-step before the fundamental tone of tie scale. This is noticeable particularly in the case of the dominant '-ftpad, if the leading tone is contained in the upper voice, as a in Example 42, operates more satisfyingly, than b and c, d.- e. §±e:s^^§^ ^ '^^^ m m^ This inclination upwards shows itself less in the middle voices, as at d* Most intolerable in many cases, in such chord-connections, are skips in tho upper voice (at c), whereas, on the contrary, skips in the middle voices (at e) are to be used, if the Bass is led in contrary motion. In Example 39, third measure, is found a doubling and progression of the leading tone, contrary to the above rule. Both took place on account of the sequence contained in the example, which allowed no alteration of the position or the progression of the chord. Concerning more Extended FormcUion of the Close. The formation of the close through the chord of the dominant, noticed on page 32, (the authentic close), shows itself in a still more definite man- ner in the last examples. 40 MANUAL OF HARMONY. As the natural relation of the chord of the dominant to the tonic triad, renders the two adapted to the formation of the close, so in these ex- amples a still farther preparation of it is noticeable, through the triad of the second degree, which stands in the same relation to the chord of the dominant, in which the latter stands to the tonic triad, e. g. 43. yii 1: h^-t-^ -I 1 — w Besides the triad of the second degree, the triad of the sub-dominant is also adapted for this formation of the close, e. g. ^iiiiHI 44. ^^mm^ IV The closing formulce {cadences) produced by this chord-connection, will assume more definite form through the application of the chords to be shown later. CHAPTER II Tlie Triads of the Minor Scale, a. Primary Triads. The primary triads of the major scale were found upon the Jirst, fourth Si-nd fifth degrees. Upon the same degrees we find also the primary triads of the minor scale. The relation, however, in which the dominant triad stands to the tonic chord, that is, as it becomes plain through the formation of the close pre- viously shown, renders the chromatic alteration of one tone of the minor Bcale necessary. Its seventh tone-degree, which, according to the signature of the minor scale, is always distant a whole step from the eighth degree, is chromati- cally raised a half-step, so that it acq^uires the character of a leading tone, e. g. manvaL of harmony. 41 -_s: i 45. By this means the formation of the dominant triad in minor, becomes exactly like that in major, thus : A minor. 46. a A major. *^ a: V A: V or briefly expressed : The dominant triad in major and minor is always a major triad. A comparison of the form of close of both modes shows this plainly : C major. C minor. 47. lElEmiEfedbl^l '- G_i E^^^ That, however, the sixth degree of the minor scale is not, in a harmonic sense, capable of any such chromatic alteration by elevation a half-step, as is often necessary melodically, the plagal close proves a (see page 33), which cannot be conceived of at all as at b» III A minor. h. 4§. fe^ii=yEbld=i=lEi^lEiEii^ $i=t=M2=t^g:— t=|-±z:_^:zzt=:fe._._^. -fi? l^m =11^1=11 The three primary triads in minor can be thus exhibited in their natural relation according to previous explanation : 49. ^== =iNi= IV I 42 MANUAL OF HARMONY. The minor scale, as it forms the basis for the formation of harmonies will therefore be the following : 50 .ii I?: Remark. — All other forms of the minor scale, such as : 51. or descending : 52. :M^ I -^g— ij^ depend upon melodic conditions, which do not allow the step of an augmented second from the sixth to the seventh degree, found in N"o. 50. These forms have no influence upon the harmonic formation in itself considered ; the harmonic foundation, however, has a reflex influence upon the minor scale itself, as the following examples show : 53. E^5^i*i "*" J I V &c. *_^f.^l,< US The last case, in which the descending scale even exhibits the step of an augmented second B-A b, which in future, in chord-connections we shall carefully avoid, explains itself thereby, that B was necessary as component part of the chord, A|y, however, in order not to destroy the minor character of the passage, which is done very perceptibly through A, while, in the ascending scale, (in the first example), this (minor character) is already perfectly secured through the minor third, Eb. b. The Triads of the Remaining Degrees of the Minor Scale. SECONDARY TRIADS. After the establishment of the minor scale, the secondary triads appear in the following form : 54. Pi iio ND. VI vuo MANUAL OF HARMONY, 43 The second degree gives a diminished triad, as before, the seventh degree of the major scale ; in like manner a diminished triad is found upon the seventh degree. The sixth degree forms here a major triad. ^ The third degree exhibits a new form of the triad. It contains a major third and an augmented fifth, and is therefore called THE AUGMENTED TRIAD. The constrained or forced character of the connection of this chord with other chords of the same key, allows it seldom to appear as fundamental harmony of the third degree of the minor scale. The following examples may serve to prove this : a. h. c. d. e. f. 55. %l-^^irS^r2^irF^^I=r^%-^E^ 77 6 ^ (^^E^^^^^^^^^^ iio IV V VI viio Of these examples, those under c and e will be best adapted for use. The introduction of this chord shows itself to be more difficult still. d. 56. 6 6 6 I nO IV ^ V YI Its introduction is most tolerable, if the augmented fifth ia prepared, that is, exists already in the same voice as constituent part of the preced- ing chord, (at d). Remark. — There is something peculiarly foreign in the chord of the third degree, aa well of the major as of the minor scale, so that this harmony, even when it appears simply as minor triad in the major scale, is very difficult to connect naturallr- and effec- tively with other chords, and therefore seldom occurs. Most of the practicable chord-connections exhibited above will occur in other relations, and not allow the augmented triad to be recognized as [triad of the] third degree of the minor scale. The augmented triad, »vhich is much used in the later music, belongs to the chromatically altered harmonies, which will be explained later under the name Altered Chords. (See Chap. X, Altered Chords). 44 MANUAL OF HARMONY. Application, The principles of the connection of harmonies and leading of the voices, already developed, will also have application here, and particularly in the connection of the fundamental chords in minor, what was said about the progression of the leading tone comes very distinctly into view since the step of an augmented second, occurring in the minor scale between the sixth and seventh degrees, as well as descending, between the seventh and sixth, is to be avoided as unmelodious, if both tones, which contain the step of an augmented second, belong to different harmonies, e. g. :=5|:zi=|=f±|:zi:S=FE ST. 1,^1^; VI VI Hence, in the often recurring connection of the chords of the fifth and sixth degrees, the progression of the leading tone will be necessarily always upwards, whereby, in the triad of the sixth degree the third appear doubled, e. g, \ 5S. Thus, it would not be possible to exhibit in a correct form the example given under No. 57 &, unless we make use of a mediating tone, such as, for example : 59. Remark. — The practice deviates, in certain and especial cases, from this rule. It will be well, however, to accustom ourselves to the leading of the voices above shown, and the more, as we must not overlook the fact, that every deviation from the rules in the practice is and should be only a well founded exception, whereas the observance of the rule can be instanced in numberless cases. <\K MANUAL OF HARMONY. Exercises in connecting the Triads of tlie Minor Scale. 45 60. ^ME^~?E^. ^^ l^el ef; i t 5$ 3 $ 5. 6. ^ 5 a -I _ -^ - t —I Q^ — I ri , Hetnarks on these Exercises, A chromatic sign over a Bass note without a figure^ as, for example, in the third measure of the first exercise, refers always to the third of the Bass. This raising of the third in the dominant triad, which occurs very often in minor, is the raising of the leading tone spoken of, (page 40). The triad is, as a rule, not marked in the thorough-bass notation, if the Bass contains the fundamental, unless especial reasons exist for indicating K 8 it by 3, 5, 8, or ^ or in full, by 5 3 One reason for indicating it by 5, is found in the third and sixth exer- cises. Here the introduction of the triad of the third degree in minor has been attempted, whereby it was necessary to indicate that the fifth is raised, since it likewise forms the seventh degree of the minor scale. The figure 3 or 5 over the first chord of some of the examples, indicates its position. See, in regard to this, the remarks to the next exercises, (page 50). The working out of an exercise will confirm the fundamental features hitherto developed. We select for this purpose the first exercise. NB. 61. i^^1ii:^iEL=iJi i^^: E :t J- i The first principle of the connection of chords (by connection of tonea in the same voice), is here everywhere observed, and for this reason the 46 MANUAL OF HARMONY. Alto, in the third measure (at NB.), makes the faulty step of an augmented second from F to Gjf. In order to avoid this fault (according to page 44), it will be necessary to let the Alto progress from F to E, and to lead the Soprano from B to G^, while the Tenor skips from D to B, in the following manner : 62. 5gi=EJ= l (a connection of chords, which has already been explained in No. 31, where the connection of tones does not take place in the same voice), or, the Soprano retains the B and the Tenor goes from D downward to the GJ(, the Alto from F to E, whereby the close position is forsaken, and this, and the following harmony appear in open position : 63. (I^g^ PMm^m Farther remarks, which the difficulties in the leading of the voices in reference to the chords of the fourth, fifth and sixth degrees of the minor scale render necessary, are in especial cases to be left to practical guidance. Before we proceed to the farther use of the triads, we will exhibit, in the following manner the chords hitherto discovered : View of all Triads of tlie Major and Minor Scales, Major. ;^f>^yf\'■'^ II III IV V TI VIlO r. 64. I Minor, -\^-%z^~mi-^%zz=m.- I nO IIP IV V VI viio in Major: Major triads are found in Minor: —m=.vi 1 IV v V VI MANUAL OF HARMONY. in Major : Minor triads Diminished triads Augmented triad in Minor : ^=ii^=sEEiri[| -^^ ^ II III VI in Major : in Minor : VIlO in Minor : iHIE III' CHAPTER III. TJie Inversions of tJie Triads, The Chord of the Sixth, the Chord of the Sixth and Fourth. The appplication of the triads, and indeed of all fundamental chords, is not limited to that use of them in which the fundamental lies in the Bass^ as in all previous examples; the Bass can also receive the thii'd ov fifth of the fundamental chord. Hereby arise transformations of the fundamental chords, which are called IN VERSIOIf S of the chord. ! Remark. — It should be well remarked, that only transpositions of the Bass to another intervttl are here spoken of, and that the before mentioned transpositions of the other voices into close and open position, and to various intervals, hy no means essentially alter the chord.* Two of the inversions are possible with the triad : a. If the Bass receives the third of the triad, there arises the chorii OP THE SIXTH. Funda'mental chord. Chord of Vie sixth. 65. i TTiird of the fundamental chord. The word P. o^.sposki'' n is here used in its general, not its technical sense. —Ed, 48 ' MANUAL OF HARMONY, ll. If the Bass receives the fifth of the triadj there arises the chord or THE SIXTH AND FOURTH. Fundamental CJiord chord. of the sixth and fourth. •^ ■* Fifth M /"■*"""" d The chord of the sixth is indicated by 6 over the Bass note, that of th^^^ 6 4' sixth and fourth, by . ; e. g 67. §i: 6 6 4 :~ gi: COG C: I I I The letter shall in future serve for indicating the fundamental tone, and, as before, the numeral to indicate the degree, whereby, as can be seen in Example 67, only the situation of the fundamental tone can be taken into consideration, not, however, the casual Bass. Remark. — As the fundamental tone of the chords of the sixth and of the sixth and fourth in Example 67, is always C, and not the Bass notes E and G, so the chord itself will not lie upon the third or fifth, but upon the^r*^ degree, since, in fact, these are no newly formed chords, but only chords brought into another position by the Bass, and therefore derived cliords. Every triad can appear in such inversions. Application, By the use of the inversions of the chords, not only does the leading ot the harmony receive more variety, but the movement of the voices, and particularly of the Bass, becomes thereby more flowing. According to the above noticed rules for the doubling of an interval of the triad (page 25), it will also be better in the case of the chord of the sixth, in the four-voiced movement, to double the fundamental of the original chords and the doubling of the Bass tone in the chord of the sixth (that is, the original third), can take place only if the natural leading of the voices requires it, or if thereby certain faults can be avoided. That the leading tone, even if it lies in the Bass, is to be excluded from this doubling, may be yet remarked after what was said on page 39. Just so, it needs merely to be mentioned, that the position of the upper three voices is conditioned only by the leading of the voices, and aside from this, has no essential influence upon the chord itself. MANUAL OF HARMONY. 49 The chord of the sixth can therefore occur in the following forms : 6§. t-g f — — r-5=rz:^^nrpzz— z= -g-F-|— F-§=-F-i— F- i; i &C. 9iEgEpEgE^E^=^=^Eg^gE^E^ The use of the chord of the sixth and fourth is more rare than that of the chord of the sixths and requires certain conditions which shall be men- tioned later. "We meet it oftenest in the formations of the close. The Bass tone, the fifth of the original chord, is best adapted for doubling, and tlie chord will appear in the following and similar forms : 69. mi=m^ lE^^m^^m In the connection of these chords with others, no farther mechanical rules are necessary beyond those already given ; we likewise omit the mere mechanical combination of two or three chords, and show the application of these derived chords in small pieces of music, which, however insignifi- cant, still contain the image of a whole, whereby individual cases can be better judged of in relation to the whole. Exercises. 70. ^JE^: la: ee; m mi i^?=?ii=E=!^ ^B=3i llalliP^J -si — s 6 6 cv=^_z=!==,2:zp:3ii:©-I=:^==^^==^=:s — ^ EtEEi i 9i^ ns: 6 6 -5, G- R 6 4—^ 6 6 3$; i^E^ ^ 50 MANUAL OF HARMONY. 6 6 n. 3 eS^ :e G 6 4 3 igEt 1 l^jEa= :^=± »• 6 6 t 6 4 3 6 6 ^eI^^Hf^^ c^ ^ E^EE^ z-P-EZgE JSr 6 ^ « tit 10. 1-^- 6 jsr 6 4$ s.^l^l=i-^li^l^l-sl=S 11. 9iiE$^:E?=^=E 1^-^- =1=^^ Ie \ Memarks on these Exercises, The indication of the fifth in the first measure of the second Example, as also all similar indications in the future, denote the situation of the Soprano, and therewith the position of the first chord. If no figure stands over the first Bass note, it is to be assumed, that the Soprano can best receive the octave of the Bass. The diminished triad appears in the second exercise as chord of the sixth. It occurs oftenest in this situation. It may here be called to mind that its fundamental tone is not doubled, because of its being the leading toncy whereas, in most cases, the third (in the chord of the sixth the Bass tone) is doubled. The leading of the voices occasions, sometimes, also a doubling of the fifth. The progression of the diminished triad is always conditioned by the leading of the Bass. The natural direction of the diminished triad in its fundamental position is already given, page 38. In the most usual cases the progression of the Bass is as follows * Tl ^^^^^ and the progression of the remaining voices thus : 72, Sr|r::g^:^=:ga:e=rgit:g=:giE:B:z::gJ: g-^- 3 -tf— «- EE gg^^JEgfJE^^g :=P=:4 :t:=t:: i^llE MANUAL OF HARMONY. 51 It is evident from the above Examples, that the inversion of the dimin- ished fifth, viz., the augmented fourth, will not necessarily, in four -voiced movement^ have the same progression as was given above, two-voiced, page 08. We see, in the first example and others, B and F of the Soprano an Alto progress to C and G. 73. ^ The similarity of this chord, in sound, to the dominant chord of the seventh to be shown later, often induces beginners to lead the diminished fifth downwards^ even if it has converted itself by inversion into the aug- mented fourth ; this, as the above examples show, is necessary only in caoe it really lies above the fundamental as diminished fifth, and a progression of the following sort : T4. flSMB S; HI is faulty on account of the parallel fifths. Remark. — It may yet be remarked here, that parallel fifths, of whidh the one fifth is diminished and the other perfect, are to be allowed if the diminished follows the per- fect ffth, but not vice versa, e. g. good. good. not good. T5, 9t 6 6 6 3 i; I Compare also the Remark, page 28. The progression of the voices takes another form in the diminished triad, if the Bass goes over to a chord, other than the tonic triad. A few chord-connections may follow here : 70. not pure. -Gh Q- fr^l |^^^E|^|EfE|^|E^ P VIlO TIl« IV M — G- vuo p 52 MANUAL OF HARMONY. H letter . not. «9- 6 m^pi^^ m ^^^-^ m ^mm -I o ^ — r — 'i^ ii i VIlO II and others. The diminished triad of the second degree in Minor allows another treatment, since its fundamental can be doubled. The succession of two or more chords of the sixth, with a progression of the Bass by degrees, as in Exercise 70, No. 3, and others, will render necessary one or more voices mV)ving in contrary motion to the Bass, e. g. f s=feisa=^^^'3=y The series of chords of the sixth of the 5th and 6th Exercises in No. 70 can, to be sure, be" carried out in various ways ; best, however, if the con- sequent succession of the Bass is retained also in the remaining voices, e. g 7§. m^m :i i=t:g s_^=:=:|; ^^=EE|E p -O (J»- 1 6 6 :E=t: &C. i Covered octaTes, as in the 2d and 3d measures between Tenor and Bass, are not to be avoided in such cases. It can be deduced from this, that to SINGLE progressions of the voices which are contrary to rule, that especial importance is not to hd attached, in opposmoN to the consequence of THE WHOLE, which otherwisB belongs to them^ since the construction of the MANUAL OF HARMONY. 53 details, although it must be as perfect as possible, will always be subordi- nate to that of the whole. Remark. — It is not to be ignored, that the principle laid down above can easily be misunderstood by the beginner ; however, the laying down of the principle was not to be evaded, and it may be added here, in order to avoid possible error, that a decision in these things, in the last instance, belongs only to a judgment fully matured by expe- rience and practice. Concerning the Signs of the Thorough-Mass Notation, The numbers and signs of the Thorough-Bass are called in general sig- natures^ [in German works Signaturen. — Ed.] Some of them have already been explained, as the chromatic sign occurring very often in minor. The notation of the chords of the sixth and of the sixth and fourth was given, page 48. A stroke through the figure is used, (for example, in the Exercises 8, 9, 10, of No. 70, a stroke through the 6 : 0), if a chromatic elevation of the interval a half-step becomes necessary ; instead of which, however, a }f or t] is often set after the figure [e. g.^ 6:j$ or 6t), 5t].) Other figures will find their explanation later in connection with the chords which they concern. Formation of the Close through tJ^ Chord of the Sixth and Fourth, In the Exercises of No. 70 we see, through the inversion of the triad, the formation of the close previously mentioned, extended and put into a much more definite shape. We discover, namely, that the chord of the sixth and fourth of the tonic triad, coming before the dominant triad, indi- cates decidedly the close. 79. The chord of the sixth and fourth is frequently preceded by the triad of the fourth or second degree. 80. 54 MANUAL OF HARMONY. As decidedly now as the chord of the sixth and fourth indicates the close, having also a decided influence in the modulation into foreign keys, just so weak is the effect of its entrance under other relations, so that its proper use is subject to certain conditions, which will be treated of later. CHAPTER ly. Harmonies of the Seventh ( Vierkldnge), The harmonies of the seventh are founded upon the triads. They result from the addition of a third to the fifth of the triad, which [third] forms a seventh from the fundamental. 81. Not only the various kinds of triads, but also the various kinds of sevenths will afford manifold harmonies of the seventh. The General Properties of the Chords of the Seventh, The chords of the seventh arfr not so independent as the most of the triads, but indicate definitely a progression, so that they never alone, but only in connection with triads, afford anything complete or finished. On the other hand, they will render the relations of the chords to each other closer and more intimate, and by means of this quality furnish in particular excellent means for the connection of chords and for the leading of the voices. The Dominant Chord of the Seventh in Major and Minor. The chord of the seventh which is most important, and occurs oftenest is the DOMINANT CHORD OF THE SEVENTH, also called primary chord of the seventh. It rests, like the dominant triad, upon the fifth degree, and is formed xactly alike in major and minor, that is, /row the major triad and minor Seventh. •^ C: V V c: V V^ I MANUAL OF HARMONY. 55 In the fundamental position it is marked by a 7 over the Basu note, and in our method of notation, indicated by V7 83. n C: V G: V. The relation in which the triad of the dominant stands to the tonio triad, has become clear principally through the formation of the close shown before, (see page 33). The close will come out still more clearly through the use of the dominant chord of the seventh. The following combination of chords will show the formation of the elose : 84. Remark. — It is to be remarked here, that the triad following the chord of the seyentb is ineomplete ; in both eases the fifth of the triad is wantiug. The reason of this will appear from what follows. The striving after a point of rest, inherent in these chords, and the resulting union with a triad, is called RESOLUTION OF THE CHORD OF THE SEVENTH, {Cadence). If the union of the dominant chord of the seventh with the tonic triad, follows in the manner exhibited in No. 84, or in a similar way, it is called CLOSING CADENCE. For the leading of the voices, the progression of the intervals of the chord of the seventh will furnish important observations. We observe first the closing cadence as the regular resolution of the dominant chord of the seventh especially. The seventh, as the essential interval of the chord, is, by its relation to the fundamental, confined to a definite progression. If the progression of 'tiie Bass, which contains the fundamental, is regarded as given, an upward jjrogression of the seventh will appear impossible : §5. ^ MANUAL OF HARMONY, «veii if, as at h^ a third voice is added ; whereas its downward progression F M4MM9FT. 121. VI IVt'TII^^ llliy VI17 Iliy V» The following rule may therefore apply for connections of harmony of this kind : If two or more chords of iJie seventh follow each other in the funda- mental rosiTioN, the fifth is omitted in each alternate chord. 4 3 6 Exercises, 6 6 5 yE^ik^:EEEl 1 7 3e; 2. 7 7 i^P^: EE 4- 5 S 7 77 77366 3=3 E 3 2 6 |3=i 6 2 6 7 7 -1- flil 4. 6 6 5 7 7 91^; E :a= ;^^ lom?'- 3E E^J3 1^^ Application of the Secondary Chords of the Seventh in Minor, The use of the secondary chords of the seventh in minor is more lim- ited. Many of them show themselves, to he incapable, or indefinite and ambiguous, for chord-connections as they were applied in major, others form, in their cadencing progressions, heavy, unmelodic steps of the voices. A chord of the seventh formed as the first degree gives it, can afford no progression analogous to the above, since the following chord connection is not conceivable. 123. m VANUAL OF HARMONY. 40 Remark. — Even if with the above combination of intervals, progressions can be formed, such as perhaps : 124. =g 1 i 11 6 still this -would hardly be admissible as proof that we have in this a progression of the chord of the seventh of the first degree in minor. The resolution of the chord of the second degree is into the dominant^ and is very frequently used. 125. i^i^l^i=l^^l =i=^: jsrz:. i^m. o iHII I. If IlO, A progression of the chord of the seventh of the third degree is not impossible, 136. il; I ^^m II a: IIIV VI it is ambiguous, however, and might be better adapted to C major than to A minor. (See Altered Chords). It may be remarked here, in addition, that the ffth in this chord, as augmented interval, will always go upward one degree. The chords of the fourth and sixth degrees are unusual, because the leading of the voices in their resolution becomes inconvenient and un- melodic. y^ ^ good : 1*7. a: IV ^ vii'^ >^- 7 lE^^l^^mm -p p-- s^- ■-P- :[[ 76 128. MANUAL OF HARMONY. g-f-i : VIjT- uo The forced character of most of the above progressions is unmistakable, and prevents their frequent use. The seventh degree in minor brings an important chord, which is gener- ally known under the name of \ THE «H#R1> OF THE DIMINISHED SEVENTH. A resolution of this chord in the manner of all the rest is impossible, since it would necessarily result in the triad of the third degree, which was already represented above as doubtful and ambiguous. Instead of this, its progression, as with the chord of the seventh of the seventh degree in major (see page 68), is based upon the natural progres- sion of the leading tone^ upon which this chord rests : V 129. Ei^?=l=!EE^:di c: vu°i. As the fundamental of this chord (leading tone), progresses a half-step^ so the seventh also moves a half -step downwards, while third and fifth are led just as regularly as with the other chords of the seventh ; especially, however, in many positions (No. 130 a) must the leading of the third be accurately attended to, because it easily produces faulty progression : not^ ^ ^ 130. Eil^^=fe iiill if^ •whereas- the position at h and c gives to the third greater freedom. Remark. — ^The natural progression of this chord, as well as of the chord of the seventh of the seventh degree in major, to the tonic, has occasioned the older teachers of har- mony to find the basis of it in the dominant harmony of the seventh. They conceived of thitf chord with a ninth (major or minor) added to it, and the fundamental omitted, whereby arose both chords of the seventh degree. While we refer to that which is said later (in Chapter IX.) of the chord of the ninth, MANUAL OF HARMONY. 77 fiQ can only bring forward here as reason for the view offered, that this assumption of the chQrd of the ninth is needless and far-fetched, and that for practical purposes, th€ Bimplicitj of the harmonic system has been preferred to the more excursive explanation of it. * For the application of the chord of the diminished seventh, observe in addition the following : The diminished seventh.^ as the mildest of all, needs no preparation (See page 72). 131. m& 3 6 ::r5t 6 7 Exercises, 7 % 6 ;if^ilililli 2. 3 7 5« 6 2 6 jar 6 7 4 « mm^ \=Si=f^Z±=^ZI^=^.. -^^^^ 1=1 7 T=1: JBT 6 *^?EiE^EEJEtEEH 7 6 ^ « 4 2 6 7 7 « C^- 1 r 9J.fe 7 If :F=t: -P—T- 6 7 4 Jf ^1 ■F ::1=' The foregoing and all previous exercises of this chapter, which, of course, only have the object to assist us in learning to use mechanically the chords thus far explained, and to test the rules and remarks laid down, have some- thing inflexible and stiff in their structure, because the great number of chords of the seventh could only appear here in the fundamental position^ and because the introduction of many of them upon our present stand point, which did not allow us the selection of other means, was difficult, and could only appear forced. "What follows may serve as explanation of them : The fundamental of these chords of the seventh makes everywhere the cadencing skip of a fourth or fifth, as is to be seen from the leading of the Bass, only, in the third exercise of Nos. 122 and 131, there is found, seem- ingly, an exception. In the fourth measure of the third exercise of No. 122, the Bass tone, to be sure, remains stationary, the progression of the funda- mental is, however, contained in a perfectly regular manner in the two chords: A7, D7. The Bass tone could here remain stationary, because we have already learned the inversions of the dominant chord of the seventh, and can therefore use them. The case is the same in the fifth 78 MANUAL OF HARMONY. measure of the third exercise of No. 131, where the progression of the fundamental A7-D takes place with a stationary Bass. In the second Exercise of No. !P81 the chord of the seventh of the third degree in minor is used, and, it may be assumed, that with this introduction it will not appear unnatural and harsh. CHAPTER VII The Inversions of the Secondary Chords of the Seventh. Through the inversions of the secondary chords of the seventh the same derived chords arise, which have already shown themselves before with the dominant seventh, viz., the chord of the sixth and fifth, of the sixth, fourth and third, and of the second. The variousness of the third, fifth and seventh of the fundamental har- mony occasions no alteration in the treatment of the inversions. For although the major seventh changes, through inversion, into a minor second, and the diminished into an augmented, still its progression will ensue in the same manner as has already been explained above. 132. There is need of no new rule for the progression of all these chords of the seventh. Only, that of the seventh degree in major and minor requires, as was before remarked, a little caution on account of the easily occurring open fifths. Somewhat more concerning their treatment may follow here. Progression of the Chord of the Seventh of the Seventh Degree in Major. 6 4 6 6_ 6 not: 3 6^ 2 4 All these inversions of the chord may be used, only the last, the chorrl of the second, will most seldom be in place, since the resolution into the MANUAL OF HARMONY. 79 chord of the sixth and fourth could only occur in rare cases, and at most as passing chord. We must not allow ourselves to be misled in respect to their usefulness, by the crowded position in which these chords are exhibited in No. 13S. It is only important, as was mentioned before, whether the seventh comes to lie above or helow the fundamental (see page 69), and positions of the chords of the sixth and fifth, and of the fourth and third of the following sort, 134. ^-=. 4 ^ * 3 6 appear more satisfying, because the seventh lies above the fundamental. The chord of the diminished seventh requires a manner of progression similar to the foregoing e. g. 135. 5 6 iE^i^E gi^i^g^tlii#i^i t=t^ 6 2 5 6 6 5 2 6 2 6 9Je$5^.= *§E^£ *EE^EEEtE:HEEEEfe 9=i^E^^^^SE 2 6 7 3 6 6 :qz:q=:p= 6 6 5 — (9 i Z5t?: 6 6 5 6 6 6. 3^2 6 2 6 4 2 6 5 7 7 -J^ZL^l 6 6 « 6 jar f 6 7 7 3 6 5 « ^^gfifei^i §iE!$; -S^/2- Ei f 8. 3 2 7 6 7 3 6 6 5 8 gfE^Egg^l^g^gE^ii :ip=t:i f 6 7 6 7 5 6 6 7 6 6'7 « 7 7 « 4 4S 9iiE^ -^ls-^|illliEL=|=|^= ^E; 10. ^ 4 66 73«2 6)8- 6 6 4 « ■?^ — (^ .-«.. SEE t=t iSPi^i: ^ \ MANUAL OF HARMONY. gl CHAPTER VIII. The Cliords of the Seventh in connection with Chords of the various tone-degrees other than those thus far used. Decep- tive Cadences. The known rule, that the seventh must, in the resolution, progress one degree downwards, verifies itself, to be sure, completely, in the connections of chords previously shown, but it has as little positive authority as any thing else which, under other conditions, and in the great variousness of chord connections, is subject to necessary alterations. In the movement of the seventh or of its inversion, the second, every- thing depends upon the progression of the fundamental. If this is of such sort, as in all the cases hitherto shown, that without the downward progression of the seventh no intelligible and satisfying result would be produced, then also the above rule will have full application. The progression of the fundamental, however, can entirely set aside this direction of the seventh ; it can either remain stationary or even pro- gress upwards, e. g. 13§. 7 f ^ L^ 3 ^Mm^mm This leads us to the possibility of connecting the chords of the seventh with chords of tone-degrees, other than those hitherto used. A few known kinds of chord-connections now follow with remarks, in order to be abley in attempts at new formations of the kind, to proceed according to critiedt principles. We begin with the dominant chord of the seventh. It has been mentioned before, that the resolution of the chords of the- seventh in the manner hitherto used is called cadence, and that of the* dominant chord of the seventh closing cadence. If any chord other than the tonic triad follows the dominant chord ol the seventh, the natural inclination to a close is either delayed or entirely set aside. The expectation of the natural succession experiences hereby a disap- pointment, and for this reason these connections of chords are called DECEPTIVE CADENCES. Deceptive cadences arise thus everywhere, where the progression of tha dominant chord of the seventh does not result in the tonic triad, but leads ♦:o other chords. 82 MANUAL OF HARMONY. Some varieties of them will next be explained. 1. The connection of the dominant chord of the seventh with triads^ other than that of the tonic, ivith a progression of the seventh hy de- grees downwards. y a* Connection with the sixth degree. In Major. Jn Minor. 3 ^ i^ 139. ^==|S^f z1==g£^£Ez^^E^3zg^r^g^^^ C: V^ Ti 0' ■2?!-^ "^L-^ x: V^^ TI This chord-connection (deceptive cadence) occurs very frequently. The effect of this progression is not so decided with the inversions of the chord of the seventh, and is. therefore more rare : 140. In Major. 6 6 In Minor. 6 5 6 ■G- "G^ ^^■^ '^'Z 1 1 ^ 1 ?5" r^: — &' rr r^^. VI y 1>. Connection with the third degree. 7 _ 6 letter position 7 6 141. Remark. — Tlie attempts with the inversions of the chord are omitted here and in what follows ; they are easily made. This progression becomes more decided under the application of modu- lation : 142. iL=i 6 g ? r =i^i=yi=z|= C: Vt a:V — j:. I ^ The connection with the triad of the third degree is also possible in minor, but this as dissonant chord (through the augmented fifth) will make A farther succession necessary. 7 6 t - 143. itz wimmM^ 325?: "m III' VI 2. The connection with triads, the seventh remaining stationary. MANUAL OF HARMONY. a« With the second degree, y 1 i4. ^'=\ 83 not: 6 impracticable in Minor, %=iH^M^i=^=h -t. I C: V a: V-y iio \ !>• TFii^^ the fourth degree. In Major : *^' ^=§=^^-]=g}:^^]=| /«. Minor : 6 u 6 C: V IV Tsr -^ A : V IT IV The connection of the dominant chord of the seventh with harmonies of the seventh of other degrees beside those before used, is likewise pos- sible. A few of them follow here : 146, I I, Gth Degree 2 Sd Degree , 6 5 5 J^ Minor : Sd Degree, C: Vh — 1^ ~g: V^ a:Vy a: V^ IIF-y VI we modulate into other keys, the possibility of new connections extends itself greatly, e. g. f. a* With a doivnward progression of the seventh. not. 14T, hett^r : C: V-yD:V. ^^^^^^mmt^m^ C: V^ Brvno*- a: Vo- F; V.y ArVo-Gtviio I*. The seventh remaining stationary. C: VyE|j:Y-j- C: Y,y^}:Y: vn^iy Remark. — The reason why the last exa-mple is not good, lies m the so-called cros»» relation therein found, the explanation of which follows later. C. The seventh remaining stationary. h. c. d. 6 6 C: iiy IV 11^ Yi 11^ I - ,-11^ I V The last chord-succession is often used. It forms a ^elay of the caden- cing progression of the second degree to the fifth, through the inserted chord of the sixth and fourth of the tonic triad. Its chord of the sixth also often appears between this chord and its resolution, as in Example €• The chord of the diminished seventh is often used in like manner : 160. G5 G 7'2 4 5i? 4 mmmmmiw^s^i r. vuo^ C: I TV 77 Here also the natural progression is only delayed through the chord of the sixth and fourth. The mechanical combination of such chord-successions may be left to personal practice and investigation. The advantage of it will lie in the insight gained into the relations of chords, and therefore is not to be esteemed so insignificant as it might at first appear ; this [practice] will, in fact, stand in about the same relation to composition, as the technical studies and preparatory exercises, to the practical bringing out and repre- sentation of musical works. Both produce aptness and skill, educate the powers, and render intellectual productions possible. It may here only be remarked in addition, that the relation of the seventh to the fundamental and its progression must always be regarded as the criterion of the above combination. If this is pure and the remain- ing voices form none of the before mentioned faults, then the chord- combination can be used for particular cases. Eijcercises, J}^ 5 C_ 101." 7 5 6 gil^E^i ^f Ez-EE^^^^S EEIgblr^-pI-l 88 MANUAL OF HARMONY. 6 5 6 7 6 §;eb; g T :F= eeefeE: 2 6 =t=::3: i^E 4 7 7 3 6 6 6 6 6 4 5 i&l^l^i=l^ m=^ iss 6 6 5 4 6 6 6 7 4 7 T-G- 6 6 7 7 6 5 4 S 5. 3 H=5-E ■« — trztis^ 6. 3 -Q- 7 5$ 6 js- 6 7 4$ Xg^E^EEE^ :=l: ?i£ ^SEgi^iEEE^^^Ii^Ji r 7. 6 s 6^^2« « 2 6 J9r 6 7 5 4 2 T-« — r-T-^ — *—» 87 6 5 lgi-lE^E=il^i f 6 4 6 3 5 6 7 4 # 9-p|E^_^|-^^^^^^3||3^1^_E:3i^ 1 Remark. — ^Many of the cases above adduced could not be taken up in these exercises, l>ecau8e they are based upon modulation, which is not particularly explained until latei-. (The sixth exercise makes a little application of modulation.) Many of the above Ex- amples would also have become smoother and less stiff and strange, by the application of modulation. CHAPTER IX. On Chords of the Ninth, Eleventh and TTiirteenth, In most text-books are found extended discussions respecting these cbord- formations. The views which can be plausibly maintained respecting them are vari- ous, and will lead to the same practical result. We can assume MANUAL OF HARMONY. Either, that this combination of intervals is to be regarded and treated fts real chords ; Or, that they, as unessential chord-formations, either belong to the sw£- pensions, or arise accidentally on account of a voice remaining stationary. In the first case, the explanation of their use, especially through their inversions, becomes very extended ; and also obscure, (since in the four- voiced movement one or more of their tones or intervals must be omitted) because they are then easily mistaken for other chords. In the second case their explanation becomes much more simple. Remark. — The ehoi'ds of the ninth, as -vrell as those afterwards named, are a relio of the old so-called thorough-bass doctrine, which was fond of conceiving of every combination of tones, however accidental it might be, as an especial chord and taught its treatment, without arranging the many chance chord-phenomena under a definite system, and thereby made the whole doctrine of harmony much more difficult and diffuse. ^ Without being able here to enter into the theoretic reasons which class this kind of formations with the accidental ones, the possible simplificatiofi of the harmonic system ^lihowi real practical disadvantages, determines us at once to the last view. (More respecting this in Part II.) In order to gain a clear view, the formation of these unessential chore's will be shown, and remarks added. If we add a ninth to the dominant chord of the seventh, a chord arises, which is known under the name of the dominant chord of the seventh and ninth. In Major : In Minor : 162. t^ In major we find the major, in minor the minor ninth. This chord is used in the pure harmonic structure, as in similar relations the dominant chord of the seventh itself, with preparation of the ninth or of the fundamental ; and cases of the following sort, where loth tones enter free 163. ^m ^ i are to be censured on account of their stiflFness and want of connection. This preparation can be effected thus : 90 MA^'UAL OF HARMONY. betUr: 164. 1^1 t=iE:Lzz:t:zidzit:=:bt:zz:liz:E -'g-H bg: :: pTE^E p ^E^E pEp;EE|; ;ee --=b: a mi How far the first examples are to be reckoned as belonging to the sus- pensions, and the last to other accidental chord -formations, cannot be explained until later, in Part II. Remark. — From the chord of the ninth in major thej derive the chord of the seventh of the seventh degree, -which we have treated of fully hefore ; likewise the chord of the diminished seventh from the chord of the ninth ia minor, in order to be able to form their cadeneing progression iu a manner analogous to that of the other chords of the seventh, since it is said, that these chords are themselves dominant chords of the seventh, to which the ninth is added, and the fundamental of which is omitted, e. g. 165. Through this arises, with the first, the complication that we must accept of two chords of the seventh of the seventh degree ia major ; one, the natural cadence of which is the following : 166. the other as derived from the dominant chord of the seventh, while it remains the sim- plest way to refer to the character of the leading tone upon which the above chords rest. That many musical text-books accept also of secondary chords of the seventh and ninths renders the explanation of many harmonic formations still more complicated, and is just as little necessary, since none of these tones are to be introduced without preparation, whereby, in their whole treatment and succession, they differ in no respect from the suspensions. That which, according to the practice, as well as according to a more simplified theory, applies to the chords of the ninth, will apply in still greater measure to the chords of the eleventh and those of the thirteenth. The strange and frightful form of these chords is the following : 167. MANUAL OF HARMONY. 91 In the pure four-voiced movement they can, of course, never be applied, since, through the necessary omission of many intervals, they will appear simply as suspensions, e. g.^ 16S. and even in the polyphonic movement they will not distinguish themselves at all, in their character, from the suspensions ; in the more free stylo, where they also appear without preparation, they can be regarded as changing notes. M--^^ ^,Zy CHAPTEK X. Chromatic Alteration of the Fundamental Harinonies, Altered Chords, The chromatic alteration of one or several intervals of the fundamental harmonies has a double effect : Either it produces a modulation, Or, it gives to the chord a new formation not hitherto used hy us. If, for example, the major triad is altered in this manner, there arise a. Modulations : 169. gH§j^ ^ Ep= | 5|^ | E^|H ^E^|=pg§^ Through Cjf, the diminished triad of the seventh degree in D major or D minor, or the second degree in B minor ; Through Et?, the C minor — triad ; Through El? and Gi?, the diminished triad of the seventh degree of D!? major and minor, or the second degree of Bj? minor. The last two alterations are mere transpositions of the same chord into other keys, viz., Cb major and CJj major. !>• New Formations: 1.0. mEm ^i='^ i^^= i ^mi^^ i Of these, the formations a^ &, C: m Ir »: V C: iii Q:V. These occasionally strange and rough sounding harmonic combinations acquire significance only through the situation which they occupy, and especially, if in a certain degree an inner necessity leads to them. If it is the province of a text-book to call attention to the possibility of such harmonic formations, it is also its duty to warn the beginner against over valuing the ivorth of such stimulants ; to advise him in general, not 94 MANUAL OF HARMONY, io occupy himself with such things and speculations, until he is fully versed in the treatment of the simplest harmonies of the simple pure harmonic structure. A too early occupation therewith, and intentional seeking out of especial effects will render difficult, and probably impossible the clear view, and the insight into the simple, fundamental features of harmony, and turn away the sense from the chief thing to secondary matters. Exercises, 1. 5 5$ 5 5$ 3 6 17H . ^E&EEE: -© I I 3 2 6 6jf 5 5S 6 2 6 4 7 ii^EETi^fe"El=E^rEl^«^^^l^l=i 6 6$ 5 4 2 6 7 m^=^. ::iipz 6 6 6 4 7 IE33EI^E^ 6 7 7 1 -^=^- i^i 3 5t 7 6 5 — ggE^l E^lE^ I 6 NB. 3 5t 6 6 :3= -si g- + G 5 T-T- lIZITZI iiy Remark. — In the fourth exercise the augmented fifth has been used, even with the minor triad of the second degree (at NB), which in this connection does not sound un- natural. This would correspond to the formation/ before in Example N"o. 170. It is seen from this, that with a natural leading of the voices, many new chord-formations can be gained. ■■=m-- — (which also occurs From the formation e of example 170 : under the name, double diminished triad) , arises a harmony which is much used, viz : THE AUGMEISTED CHORD OF THE SIXTH. The first inversion of the above chord gives it : 179. According to its progression, which is determined by the augmented sixths the original chord belongs here to Gr minor, the fourth degree of which, C minor, with a raising of the fundamental, goes to the fifth degree. Wherever this chord appears with its natural progression, shown above, MANUAL OF HARMONY. 95 Example No. 179, the last chord shows itself as dominant. The proof of this lies in a few harmonies formed like the augmented chord of the sixth, the augmented chord of the sixth, fourth and third, and the augmented chord of the sixth and ffth, the explanation of the basis ot" which follows farther on. Remark. — The relation, in which the augmented chord of the sixth stands to the just noticed chords, allows its origin to be referi'ed to the same source. See later. The augmented chord of the sixth has the peculiarity, that its third only (the fifth of the original chord) can be doubled in the four-voiced movement : I§0. Of the remaining positions of the original chord (the so-called double diminished triad), the first (fundamental position) can be used three- voiced, but very seldom, the third (second inversion), also four-voiced, only, however, in a very open position. a, b. not : not : 'better : Remark. — The chromatic alteration of an mterval of the minor triad is already con- tained in the formations of Nos. 169 and 170, and thus needs no farther investigation. Just so the chromatic alteration of an interval of the diminished triad will either pro- duce major, or minor triads, or formations which are already found above in the place referred to. Thus the formation of the triad in No. IVO, d will be like the following, which ig found in C major : letter in open position : ^.,.^m^E^^^^ C: vuo ^ This chord bears, in many text-books, the name : harsh diminished triad, (hart ver- minderter Dreiklang). The like chords, if they may be so called, appear generally only accidentally, in pass- ing, and their progression proceeds in accordance with their intervals, that is, augmented intervals progress one degree upwards, diminished intervals downwards. The chromatic alteration of an interval «f the chord of the seventh has 96 MANUAL OF HARMONY. been, in part, already mentioned, where to the chromatically altered triad; the seventh was also added (page 92). This occurred with the augmented triad. Among the remaining secondary chords of the seventh, the chromatic alteration of one receives an especial importance. This is the chord of the seventh of the second degree in minor, which, in the following form, produces chord-formations much used. The chromatic raising of its third a: iio.^ 7 gives the following inversions : a 4: ^ 5.3 2 Of these inversions, the second is the most important and is much used, the rest are unusual. The chord resulting from the second inversion is known under the name of THE AUGMENTED CHORD OF THE SIXTH, FOURTH AND THIRD. Its progression is based upon that of the fundamental chord, that is, as the chord of the seventh of the second degree leads most immediately to the dominant, so also will this. 185. 3F— ^« — ^ IlO, If the fundamental of this chord is omitted, the augmented chord of the sixth, already found, arises, the progression of which to the dominant is hereby explained, (see page 94) ; With omiHHion of the Fundamental : 1S6. ^mMmM or, for comparison with No. 179, in G minor : Cliro.raiHiug AuQ. chord of tl'f ftixth^ Aug. chord of Fundamental chord : of the third : fourth and third: the sixth : MANUAL OF HAR3I0NY. 9T Remark. — It may be mentioned here, that the formation of the augmented chortl of the sixth, fourth and third can be already reached through the harsh diminished triaa {hart verminderter Dreiklang) mentioned page 95, to which a seventh is added; that the resolution, however, must become a different one, since that was considered to be on the seventh degree, while this is found upon the second. Instead of the fundamental of this chord, the ninth of the fundamental chord can be added, whereby the AUGMENTED CHORD OF THE SIXTH AND FIFTH arises. Its origin is as follows : icWiout Fundamen tal : InverHon* : Fundamental with ninth : with elevation a. b. chord: of the third: 5 3 1§§. Of these chords, the one resulting from the first inversion a^ the aug' mented chord of the sixth and fifth^ is best adapted for use, the others are rare. Its natural progression is likewise to the dominant, but always produces varalhl fifths : 189. These progressing fifths, which do not belong to the most unpleasant ones, are avoided either through an earlier resolution of the fifth (the original, above-mentioned ninth as suspension), as in the following Example («), or through a skip of the same into the third, whereby the augmented chord of the sixth results (&)^ or most frequently, by the third and fifth remaining stationary while the sixth and the Bass tone progress, whereby the chord of the sixth and fourth is inserted before the resolution (c), which chord can be here regarded as a prolongation of the suspension. a. b. 190. mm not .— '^' better . =iirii[i^life S=F Remarb:. — ^The addition of the ninth does not justify explaining this harmony as a chord of the ninth ; the ninth has here, as everywhere, the same character as suspen- aion, as appears very plainly from the progression a/ just so the p'-ogression at b and 98 MANUAL OF HARMONY. C answers completely to the treatment of the suspensions, as it also (as fifth in the aboT« chord) requires a preparation. It would follow from this, that this harmony should be taken into consideration first in connection with the suspensions, it was however necessary to mention it here, be- cause the question of the origin was under discussion, and it was not the intention, by the above expressed view, to oppose a generally received appellation. Exercises, 6 6^ « 2 fmf^ 4. 3 3 - mm: At the close of this chapter we survey once more the broad field which was opened in it for harmonic formations. We have found much which is generally known and adapted for use. Much appeared to us unadapted for use and worthless. Nothing however showed itself in its original condi- tion, everything had received an addition, experienced an alteration, in a certain sense, adornment. This forsaking of the original gives us occasion to refer once more to that which was remarked on page 93. A long time indeed elapsed, before these harmonic transformations were discovered, and a still longer, before they became common property ; much, which until now is unadapted for use, may with time be developed, but, in order that the healthy inner germ may not be lost, we cannot ad- vise the direction of the whole effort, out of desire for originality, to the discovery of new harmonic forms, or the immoderate use of them and devia- tion from the primitive. Since all these transformations serve more for adornment, and It might be said, for the more elegant carrying out of the simple fundamental idea, we may venture to use them only with discrimination if wc do not wish to overload the work of art, and thereby ourselves be reckoned as without taste. MANUAL OF HARMONY. 99 At the close of the exhibition of all essential harmonies and their most immediate use, may still follow a brief view of them, their varieties and derivatives. View of all Chords belonging to a Major or Minor Key, I. FUNDAMENTAL HARMONIES. a, Tlie Triad. b. The chord of the uventh. i A« The varieties of the Triad : Major, Minor, Diminished, Augmented. Major Triads, Of the Major Scale : Of the Minor Scale : ^5 O^ C: r IV V a: V VI Minor Triads. Of the Major Scale : Of the Minor Scale : C: II m VI a: 1 IV Diminished Triads. Of the Major Scale : Of the Minor Scale : C: viio a: 11° vno Augmented Triad of the Minor Scale. A : IIP N. B. — The remaining augmented triads see mider II. : Altered Chordi, Inversions (Versetzungen) of the Triads : a, Tlie chord of the sixth. 6 6. The chord of the sixth and fourth. 6 ^ 4 o «-- 100 MANUAL OF HARMONY, B. The Varieties of the Chord of the Seventh. a. Tlie dominant chord of the seventh or primary chord of the seventh b. Secondary chords of the seventh. a» Dominant chord of the seventh (major triad with minor seyentb). Formed alike in Major and Minor : 7 7 7 I C: T, c: Yxf a: V» b. Secondary chords of the seventh 1. Major triad with major seventh In Major. C: IV' 2. Minor triad with minor seventh In Major. C: 11^ In Minor. : Ylj In Miner, =^= 3. Diminished triad with minor seventh In Major : Jn Minor : C: vu«>. I a: xi^f 4. Diminished triad with diminished seventh (chord of the diminished seventh) In Minor : a: yiV>, $. Augmented triad with major seventh In Minor: %=\ MANUAL OF HARMONY, 101 Inversions (Versetzungen) of the Chords of the Seventh, a. The chord of b. The chord of the c Th^ chord of the %ixth and fifth : sixth, fourth and third : the second : m ^ «s«: --^-- 3^ II. ALTERED (cheomaticallt changed) CHORDS. a. The augmented triads formed from the major triad : In Major : C: T IV V ll« The augmented chord of the sixth, formed 1. From the minor triad with raised fundamental (so-called double diminished triad) : I rfc: 2. From the chord of the seventh of the second degree in minor. (See the following chords) : C» The augmented chord of the sixth, fourth and third; d. The augmented chord of the sixth and fifth, — both formed from the chord of the seventh of the second degree in minor : With the ninth from liaising of Second Without Fundamental, the Fundumental ilte third : Inversion : aug. chord of the sixth : and without the latter. fe — J §g o: no» ^ 102 MANUAL OF HARMONY. CHAPTER XI. On Jlodiilation of a JPassage of Music (eines Tonsatzesj. The term modulation has a various signification. , Formerly was under* ?tood thereby the way and manner in which the succession of harmonies is arranged to a vocal part. In the later sense is understood the digres-f sionfrom one key into another. The name, digressive modulation^ which is sometimes found, would be no pleonasm according to the original signi- fication of the word. According to the import of the term, it will next be important, to learn rightly to recognize and determine each occurring modulation (digression into a foreign key) ; farther on, in Chapter XYI., the means for modula- tion will be discussed) whereby the capability of recognizing the latter is more fully supplied. , : ,.- : ' A modulation arises^ if a harmony foreign to the previous hey ap- •pears. The previous key is then wholly forsaken, and the harmonies must be reckoned to the new key, so long as no harmony, again foreign to it, appears, which effects a new modulation. Thus in the following Example : , 193. is a modulation to D minor in the third measure, because Cjj-E-G-Bjz, belongs no longer to C major, but undeniably to D minor, whereas in the fourth measure it is doubtful whether the C triad, which is foreign to the previous key (D minor), is to be reckoned to C major, or to the Gr major fol- lowing, while the modulation to A minor in the fifth measure is unmis- takable. The dominant chord of the seventh^ as also the chord of the diminished' seventh^ are, as the chief means of modulation, never to be mistaken ; all the remaining chords are amhiguous^ that is, they can belong to several keys. MANUAL OF HARMONY, 103 Thus the Gr major triad belongs not exclusively to G major, but is also sub-dominant to D major and sixth degree to B minor. This ambiguity often allows the modulation to bo recognized first from the succeeding chords, as in fact, the decided motlulation itself can be formed first through the dominant harmony of the seventh with its derivatives. The musical ear itself proceeds very simply in the apprehension of a modulation : it always apprehends the foreign haru^vW as belonging to that key, which is nearest related to the ruling one. Thus, for example, in 193. the major triad of D in itself considered, would belong to tl^o key of D major ; in connection, however, with C major, it will be most imxir^d lately recognized as dominant to G major, and the following chords first can de- termine which key becomes the ruling one. There follow here some more exercises for practice in searching out tV > modulations; for the farther discussion of this subject see Chapter XY/ 194. Exercises, G 6Q 5 C: I G: V,. 1 C: IV Vi Tb 6_ 5 izid: I d: vii°» I C: I liny V wm 5 2 6 6 EEIEE^ 3. 3 . fs ■ ■ 6 7b b 6 6fe 2 f 6 7 3 6 9-ir =::zz^= \-f4- (&- Et=: tili 1 -^—i =M 6 7 4« 4. 7b - :i^iPL: lE^^^l^i^g^ 6-7 4-$ ^6 ^ 2 6 4-$ 5. 5 6 jar 104 MANUAL OF HARMONY. t 2 iy^^3^.li=Jife%^E^li^llPii '7_ 6 4 7 I 6. 3 6 ff -=i^33^ 4 JB^ 68 313 5t5 4 3 6 8 7 ZICL -O +->B 4 3b 4b 4 3 3 6b 6 4 5 6 6 5 6 C ± ii^=i=^i^i^^=gEi3^fS^f§Ei 9Jp=j=l 6b 6 4 7 3 2 6 ii^lil^^li^l^l I 6 3 6b 4 6 2 6 C ^ 52 « — I — « — it-j Ja — 1 ^ 6 7 ::^~3=::3: #^ iSz::®: 1 The modulation can be indicated in the same manner as in the first exercises, according to which the letters indicate the key and the Roman numbers, as we know, the degrees upon which the chords in ques- tion rest. / MANUAL OF HARMONY. 105 PAET II. ACCIDENTAL CHORD-FORMATIONS.— TONES FOREIGN TO THE HARMONY. CHAPTER XII. Suspensions. The simultaneous progression of all voices to the following chord, par- ticularly if, as in our previous examples, it takes place through no metrical variety of the movement, produces a certain measured character and monotony of the musical sentences. A new chaining together and binding of the chords, and a thereby more interesting change of harmonic connections arises, if the voices do not everywhere progress simultaneously ; if one or several of them linger in their places, while others already form the component parts of the next harmony. The most important manner of thus linking harmonies together, and the one to be preferred is the SUSPENSION". This arises through the delaying of a progression of a voice, which is ex- pected at a definite time, or even necessary, and in such a manner, that the voice, which has to progress one degree downwards j in order to occupy its position in the following chord, lingers still upon the tone of the Jirst chord, while the others progress to the second, and this voice does not pass over into the harmony until later. In the toUowing connection of harmony : 195. ^^^^ ii^i^i^^fi 106 MANUAL OF HARMONY, the Soprano can linger upon the C during the entrance of the second chord^ and pass over later to the B in the following manner : 196. Just so a suspension can be formed from Example No. 195, through the delaying of the Tenor : , ^ 197. ;?^=^=Ie^[| jiii i^[E That which is characteristic of the suspensions is, that they form a dis- sonance against the harmony with which they appear, and that they thereby act as a means for harmonic connection, since they render the necessary relations of two chords more intimate through the resolution expected. In this respect they have a similarity with the sevenths, in common with which, as connecting intervals, they require preparation as well as resolution. The dissonant character of the suspension is, to be sure, not always con- tained in the interval of it which disagrees harmonically with any particular voice ; cases can occur, where the suspension disagrees as interval with no one of the other voices, but where the character of the suspension appears only through situation, position [in the chord] and progression ; as in Ex- ample No. 197, where the tone of suspension forms a chord of the sixth, and where only the unusual appearance, as well as the entire situation of the triad of the third degree, combined with the progression of the Tenor, produces the character of the suspension. The above examples give the rules necessary in the formation of the suspensions : A suspension can he formed with a descending progression of a voice hy degrees, under the following conditions ; it must 1. Be prepared, and . i » 2. Resolve itself. There will, therefore, be three things to observe in connection witli t!ifc suspension : its preparation, the suspension itself and its position, and its resolution (progression). MANUAL OF HARMONlc, a. The Preparation. The preparation of a suspension can take place througli either compo- nent part of a triad. The sevenths also are used for preparation, although more rarely ; most often the dominant seventh. fc Preparation through the octave of the Fundamental: Through the third: 19S. Through the ffth m^^^^m^m^m 9 8 6 -6^ 7 - 4 3J C: I G: V C: I I e: viiO- Through the dominant seventh . I i =§-r-^=^ 4 3 9 8 $ 9i: C: V^ -siz: a:V /^he preparation takes place upon the arsis, the suspension itself enters at the thesis. Besides this, the rule mentioned before (page 71) ap- plies, viz., that the preparation may be of a duration equal with or longer than the suspension, but not shorter. ' hm The Suspension. The entrance of the suspension at the thesis has just been mentlo'aci' ; its position in other respects should be still more particularly explalncf*.. The suspension can appear in any voice, before an^ interval of tM triad, — before the seventh, only in rare cases. 108 MANUAL OF HARMONY, Suspensiont before the Octave of the Fundamental: 199, 5 — 4 3 9:=« 6 — 4 3 — gzz: • ^9- ^X cl C; IV I I V Before the Jt/th rarely, only in certain positions: IV I ^ p^^ r gi =EE|E^ 6 6 r- I ^ 2 — .bfij*! if^i^ 6 5 5" ^4 P^liiM ^siE C: I F:I C: I Concerning the suspensions in case of the fifth, reference may be made to that which was remarked in connection with Example No. 197. Thus the first and third examples will be entirely in the character of the suspension, while the fourth is not to be called a suspension at all. If a seventh is added to the chord, as in the second example, the dissonant character of the suspension immediately shows itself. /^ That the seventh can but seldom have a suspension, appears -from the fact, that it [the suspension] would necessarily be formed in most cases by the perfect octave, which in and for itself is only an interval of reduplica- tion, and can never come into a dissonant position (a), except as in the fol- lowing Example bf where the octave is diminished. 200. MANUAL OF HARMONY. 109 In the first case the seventh will always be a parsing one. C. The Resolution. The resolution of the suspension ensues, as was remarked before, in tht same voice, by a step downwards. Remark. — Ways of resolution which deviate from this will be shown later. Here it is further to be observed that The tone of resolution (the tone which is delayed by a suspension) can he contained in^ no ^ther voice ; only the Bass or the lowest voice can receive it without disadvantage to the harmony. a, not: h. letter: c. not : d. NB. 201. lEfe^EE^ X ^ ^ In Example a the Tenor steps from A to C, which last, in the Soprano^ is suspended by D; in Example c the Tenor receives the G, which, in the Alto, has the suspension A. Both reduplications are faulty, especially be- cause they concern the third and ffth of the chord. In Example d at NB., the reduplication takes place with the fundamental. In this casa the effect is better, especially if the consistency of the leading of the voices necessitates it as in the following movement : /""^^ Fundamental : Third. I I Fifth: I \ ^ — ' I -ft" -rt^ 202. ZSlT. <^^-^_ i Remark. — It may still be remarked here, that the doubling of the fundamental always assumes the distance of at least an octave, and that the doubling in unison is faulty, e. g., The suspension can indeed appear in such proximity, only between Bass and Tenor, or with the voice which lies next to the lowest. The lowest voice, commonly the Bass, has, however, as the one which determines the chord, the power of counterweight against the dissonance 110 MANUAL OF HARMONY. of the suspension ; reduplications are therefore admissible, if they are based upon a good leading of the voices, e. g, favZty : 203. The faulty progression of the Soprano and Bass in the last example be- comes clear, if the suspension as mere delay of the progression of the voice, is taken away, through which means the open octaves appear : 204. :_.g= =m a!=gpE^B The relation is the same with the fifth-successions, which are covered through the suspension : 205. I^g^i PIE^ S Here, however, the considerations will rule, which are to be had in view in the case of the covered fifths in general, since position, situation, pro- gression can permit such leading of the voices, without the unpleasantness of the fifths appearing. We condense these remarks into the following rule : The suspension does not remove parallel octaves and fifths ; the follow- ing progression will, therefore, be faulty : 206. Parallel fifths of this kind are not, however, to be unconditionally rejected, if through the movement of the other voices a compensation is made for the unpleasant succession, so that they do not appear too plainly. To give positive directions regarding them is impossible ; to reject them always would confine us too much. MAIS'UAL OF HARMONY. Ill The suspeiisions in the Bass, wliich occur oftenest before the third of the chord (or, which is the same thing, before the chords of the sixth and of the sixth and fifth), allow of no reduplication in the other voices. 207. :g.-=zir The suspensions before the fundamental and the fifth rarely show them- selves practicable. 20§. iiiiiiliillE The indication of the suspensions in the Thorough-Bass notation is, in A)art, contained in the previous examples. If the suspension lies in one of the three upper voices, its interval from the Bass is given at the same time with the resolution, ^« i7-> 4 3", 9 g 7^ [the remaining figures determine the chord where it becomes necessary, g.j the chord of the sixth | ^ the chord of the sixth and fourth t T :or 7 6 4-. If the suspension lies in the lower voice, the chance intervals of the remaining voices are like wis© /indicated by numbers, e. g., gZj or in case of the chord of the seventh W- ; the dashes which follow denote that the voices retain their tones during the resolution of the suspension. The suspension in the Bass is also marked by a diagonal stroke above it, and the corresponding chord set over the tone of resolution, which ia plainer as concerns the latter, e. g. r—a 209. In the succeeding examples the first manner is chosen, as the most common. llti MANUAL OF HARMONY, Exercises, K 6 4 3 7 6** _5F^-js- ■ The most common compass of the voices exhibits itself in these clef* thus : -f-^-^-^Tlllll lill r i I I I I I I I ! lA Soprano-clef. TT"— i~;~ j~i^~f ~f~r~i 1 ' M?^=^-r^^, AUo-clef I I 0-ft- :ir3=:i='=tipiit-E=Ez£: I I \_\ _\ I ! I _ ^^^^^ ^=^=f3=t=t=i=t=:^==^«:: 114 MANUAL OF HARMONY. Remark. — The origin of these various clefs from the most simple foundation, from the 80-called Tablature (commonly a system of ten lines, upon -which all the voices were written, with especial designation of the lines upon which the principal tones, F, C, G, came to stand) is interesting, its farther explanation would here, however, lead us too far. The easiest method of impressing these clefs upon the memory, is probably, to observe accurately the position of the 0- triad in the various voices, whereby the tones which lie between and on each side are easily found out. Thus the position of the complete C- triad, with doubling of the funda- mental, will be : Jn Vie, Soprano : ff5=' In the Alto . I^E? C :So-- Jn the Tenor, best in the position 5]^. — *— c • of the chord of the sixth and fourth : "^ — m — g The carrying out of the first exercise of No. 210 in these clefs follows here : 211. 80PBAN0. 1 Al.TO. iBKOR. Hmk. ¥ ^: 53; i^ m^=^ t^B -G- i^[f ii^; lis: 7 © - 7 6 5 — 1 ^1 F IV ^7 II •v The working out of these examples requires, with all observance of tho rules thus far given, a skillful and a freer leading of the voices in relation to their position, since the necessity of a better position of the suspension often renders necessary even an alteration of the position of the voices, which we have hitherto always endeavored to make as uniform as possible. In this manner the open position of the voices will come, of itself, and again be necessarily exchanged for the close position where necessity and conformity with the end in view require it. MANUAL OF HARMONY. 115 In tliia exchange of the position of the voices, the following rules must be observed : The voices can never ^ simultaneously, move-hy^degrees or skip out of their nectsscm/ position from one chord to another (foreign one), except in indi- vidual cases in the transposition of one and the same chord into other positions. . Ani/ voice ca7i forsake its position, if one or more remain stationary iipou one ton\ The following carrying out of Exercise 8 of No. 210, will make this plainer . ¥ 213. 150PRAN» Altu. Tbnoe. Bas'j. 5 NB ;iE=T^§ © — ^T—- (2 s>- o — G : I — _ 7 aO^ d r*- Bb El, Bb C7 F 7 IV — 7 iiO-rBkiii yI 1 IV ir:v4 I Bk V -(2-« 1 NB. 8 7 10 11 7 1 Jsp: V Y 12 rEgEEE^EEgEggE=| JEtJEEJEEg= r: -<2— •" : i m^ ^^^^m %m. r.y Bb C 00 BbrV^ 1 11 o: I IV The following may serve as explanation of this treatment. The close position in which this example begins, is forsaken in the fifth measure, in which the open begins, and remains until in the eleventh measure the close position again appears. 116 MANUAL OF HARMONY. This was effected through a freer leading of the Soprano and Tenor. The first makes a skip, in the fifth measure, out of its position into the seventh^ El^ (at NB.), a skip which can take place if the fundamental is already present and remains stationary (as here the F in the Bass) ; in like manner it forsakes the position in the seventh measure, by a skip into the fifth, G, the chord remaining stationary, whereby the suspension cornea into a better position. At last the close position is attained again through the better and free leading of the Tenor in the tenth measure. Suspensions from JBelotv Upward, Suspensions from below are only in a few isolated cases to be regarded as such ; most progressions of this kind arise out of the suspensions from above, before treated of, through contraction (abbreviation) of the same with a farther succession in a upward direction, e. g, , 313. i - -#- -i2- ^^f=f-r^:^===-^fSFf-T=f^TT^ ^^ l 3Iore rapid figures allow this approximation more readily, e. g. 260. ~i— I — I — F-# -j L • •- "Sij faulty Progressions in Connection with Passing and Changing Notes, Since it is the province of the passing notes to fill out the movement in skips of the harmonic progression, we must take care in connection with the change of the harmony, that no false progressions arise, as in the fol- lowing examples, from covered fifths opeji ones arise : a. , 261. giSii: --^ — j- •*W I -rr-r^ I r I Open octaves formed with passing tones cannot occur, because the first of them will be harmonic as much as the second. 262. -J-^ ^rrrr i On the other hand, in the following instances, the passing notes will not cover the open octaves, and consequently will be considered as faulty * 263. Remark. — The last tind of octaves would find application in instrumental movements, •aoder the condition of intended strengthening and reduplication. 134 MANUAL OF HARMONY. In like manner the entrance or progression of the changing note in parallel movement is to be called faulty if it takes place in the following manner : 261. letter : I ^^= I J _j — ©=>=^— ©— , -; T- -f2- mm^t I I ii; :i^^ -(2-^=^ .-- i^ The last example is better because the octave progression appears covered. Passing and Changing Notes in more than one Voice at the^ same time, r fl The movement of the passing notes in more than one voice at the same time is best adapted, in parallel motion, to the successions of thirds and^^^ sixths, e, g. fl 265. t=^— l=^fIE]^^E^=lh= J^fr^^^ 1 ^ The free movement of the voices with the use of the passing notes can also produce parallel seconds, fourths, fifths, and sevenths, of all kinds, which require great caution in their treatment, and on account of their disagreeable effect are only to be allowed singly , and in a very favorable position. Progressions in fourths are good if a third voice is added as third below : 266. jgl3r4mliB Single fifth-successions arising from passing notes are occasionally met with in good compositions, which, however, is no reason for recommendicg I MANUAL OF HARMONY. 135 them as faultless. (See that "which is said concerning fifth-successions page 27 and what follows). Just so the harshness of the seventh-successions can only be alleviated through favorable position and good leading of the voices throughout ; indeed, through tempo, movement, etc. In contrary movement the various intervals of the passing notes often give to the passage an especial, peculiar coloring, and contribute much to the independence of the voices, but they must not appear too numerously and in too many voices at the same time. I •H — iji — ^-G T-* — I— ^F^ — 1^*^— — r r ^ -rzi ^ I ^^ Here also it will be found, that those passing notes, which, outside of the simply harmonic structure lying at the basis, form with others, as it were, a most intimate, new (passing) harmonic leading, are more natural and milder than those whose collocation cannot be harmonically ac- counted for. A judgment concerning the worth of such movements can, however, b€ arrived at only by taking into consideration their character and tempo. In case of regular harmonic progressions, several voices can receive pass- ing tones at the same time, e. g. 30§. In all such places everything depends upon the question, whether at the hange of the harmony the voices are in a position which allows them form their progression regularly. Changing notes can occur in various voices : a. In tivo voices : 136 MANUAL OF HARMO.¥T. in pa -allel motion : 869. gz!»;p^=E3t=PE:^r|S=?=K^^^L=: I in contrary motion: ( aro. 9: [^ b. In /Are^ voices : 271 1 I t In/( our voices : I I ^,^ Remark. — ^The most of the above examples can also have the force of harmonic pro gressions with the organ-point. It becomes evident from these examples, that also in the parallel move- ment of two voices in changing notes, the progression in thirds and sixths appears most natural, while the parallel seconds, fourths, fifths and sevenths always produce a very disagreeable effect. Thus no one ^-ould be likely to pronounce changing notes of the following sort, good : good 273. Changing notes can also be of longer duration, than the harmonic note io which they are joined, e. g. 274. i£ilp!i^4%iij| mmm I> MANUAL OF HARMONY. 137 The significance, in composition, of the subjects explained in Chapters XII., XIII. and XIY., is great enough to subject them to a careful inves* tigation ; as a thorough knowledge of them contributes materially to the understanding of the inner harmonic structure. We have still to speak concerning their relation to the pure harmonic structure — the object of our immediate studies. Since on page 24 the term " pure harmonic structure " was only spoken of in a general way, it becomes necessary to consider the question more narrowly, and to present it something in this manner : What application of these meayis for composition does our immediate purpose, {the exercises in the pure harmonic strudure)^ allow ? It is undeniable that these means are particularly adapted for develop- ing and adorning the voices. If, however, our most immediate work is the recognition and carrying out of simple harmonic formations, then, to be sure, everything which is adapted to develop the voices will be appropriately used ; but anything else, serving only for embellishment, will be excluded ; in brief, the essential must be separate from the unessential. As belonging to the unessential will always be reckoned, firstly : ' All harmonic artificialities (Kunsteleien) in general^ in so far as they are founded upon no inner necessity ; unnatural introduction of little- used harmo7iies. They easily produce over-fullness, swollen over-loading of the passage, and bear witness rather to a morbid or mentally weak condi- tion, than to originality and fresh, free, powerfully secure movement ; Then: Irregular introduction of the suspensions ; the use of stationary voicesj and of the anticipated and after-struck tones ; Especially, however : The changing notes which are struck free and the figures formed there- from ; in shorty everything which appears inappropriate to a simple, good four-voiced song. If, in fact, vocal composition is received as the basis upon which all music is founded, then much in connection with it will of itself remain excluded, which is appropriate to instrumental compositions. If also for practice in the use of the harmonies, and for the learning of a good and pure leading of the voices, the elaboration of chorals or simple movements in the manner of chorals is directly suggested as most to the purpose, this also will not exclude the use of those means in so far as they serve not merely for embellishment but for the development of the lead- ing of the voices. 138 MANUAL OF HARMONY. Among these is especially to be reckoned the use of the suspensions and of the regular passing and changing notes. In accordance with the foregoing, the strictness of the pure harmonic struc ture in connection with the first study of harmony, and later contrapuntal labors may now be judged, which forbids many things the practice likes to use in appropriate places, as not to the purpose, immaterial, and as causing deviation from the chief object. The thorough study of good compositions will serve for the complete understanding of all subjects thus far discussed. Chapter XIX. in Part III of this book, in which we return to this subject, will afford opportu- nity for attempts of our own. CHAPTER XV. JPassing Chords, Those are called passing chords, which in smaller parts of measures, after the manner of the passing notes in several voices, appear as actual chord-formations, in the entrance and treatment of which, however, a manner is sometimes found deviating from the general rules of chord- connection. Of these, one kind has appeared already in such passing and changing notes in three voices, as take on the chord form, e. g.^ in Nos. 271 and 272. Just so, the most of the chords which are formed over an organ-point can in a certain sense be called passing chords. There are, however, still other phenomena of the kind, which are to be here explained. As, in general, passing and changing notes depend principally upon the relations of measure, it becomes necessary for the explanation of the passing chords to cast a glance at the various division of measure. It is known, that in the simple, even varieties of measure^ the natural accent rests upon the first measural-division, while the second receives a less weight. If now the harmonic progression be based simply upon the two measural- divisions, then the harmonies, which come upon the accented division (Thesis) will always appear as the more weighty, and must alwaj;.. be conceived of as the goal to which the chords of the second divison (Arsis; lead: MANUAL OF HARMONY, 275. In this sense, the chords of the second measural-division can be called passing chords, although in the regular movement this character of theirs does not appear so plainly. That this has been so understood in the theory, even if seldom plainly sxpressed, is shown by the fact that, at their entrance, more care has ever been bestowed upon the chords upon the thesis ; and in case of those upon the arsis, much has been allowed which was not conceded to the former. The character of the passing chords appears, however, more plainly with such harmonies as are assigned to smaller divisions of the measure, as in the following examples : ^ 2T6. 6 6 4 7b 2 7b m^^=\'^m=^^^^=l :F=tzt i^: _j__...^ 1 8 4 np^ngn 277. :J=d: mmn rr^- i §! mmm^ :f=!r- The peculiar manner of appearance of the chord of the sixth and fourth in Example No. 276 ci and c^ as well as of the chord of the seventh in c, is only to be explained through the ensuing progression [in the character 140 MANUAL OF HARMONY. of the passing notes) of all voices^ hy degrees ^ to their nearest goal — the chord of the thesis in the following measure. These voices can be still more easily recognized in their character as passing, if one voice is allowed to remain stationary, for example, the Bass of No. 277 a^ or the upper voices h, (See above, No. 277). The leading of the voices in No. 276 a^ has arisen from the application of both modes. If this condition (the progression of the voices by degrees) is fulfilled, then all chords can enter free ; they will find explanation in the principal chord which immediately succeeds them. NB NB. 37§. ii^fi^il ii 111' — <5- F=t liii: Remark, — In this explanation of the passing chords, the free treatment of the seventh, mentioned before, finds also its justification. (See NB.) In the simple uneven varieties of measure the accent likewise falls upon the first measural-division, whereas they contain two measural-divisions of less weight. Passing chords will show themselves in the following manner : 279. ¥: ^ ■^Hkl 64 2 6 7 6(2 987 24j8^756 ^m Smaller measural-divisions can also contain passing chords, and after the above, no example is needed for it, and just as little for the compound varieties of measure. Here also the study of good compositions will be explanatory, and lead to advancement. For personal attempts the following remarks may still find place : All chords designated as passing will either progress according to the known rules of the connection of harmony, or deviate from them. In the first case, which is more frequent, no farther remark is necessary ; in the last, it will depend upon a flowing melodic leading of the voices, as well in them- MANUAL OF HARMONY, 141 selves, as also in relation to each other, whether formations of this kind arc to be called correct. It can only be remarked in general, that the progression of the voices hy degrees will also here determine the character of the passing chords, and that all such passages are to be judged after taking into account the rythm, tempo and character of the composition. CHAPTER XVI. On the Means for 3Iodulation, The term modulation has already been explained in Chapter XI. There the object was to determine each modulation correctly ; now we are to treat of the best means for effecting a modulation. The art of modulation consists in finding out those harmonies which stand in connection with two or more keys, in order, by means of these to pass from one key into the other. Every modulation can be effected in various ways, and will serve various purposes. It can, Firstly : begin abruptly, be quicMy completed and pass by, or Secondly : be more gradually prepared for, seek out the new key as a goal, and take it for a length of time as basis. In the first case it will avail itself of the simplest means, make its ap- pearance with decision, but soon leave the new key, and perhaps, indeed, not allow it to attain to a definite development of itself; in the second case it is commonly prepared and worked out gradually by various means, and, endeavoring to impress the new key upon the ear, will probably also lead to a close. Thus, in the following example : I 280. ! 1— ^-^ — !_J — |_J _J_-I— I_J_ 1 I t 6 4 ♦ U*: 6 4 5 6 2 6 F: V, G: V. 0: I the modulation will be transient and frequently changing, without forsak- ing materially the principal key, C-major. 142 MANUAL OF HARMOjs r. Tliis kind of modulation is only adapted for the nearest related keys, and although more distant ones can be reached by especial and decided means^ still in their development very natural and organic combinations must prevail, if they are not to appear unintelligible. In the next example, however, the more distant key becomes the goal, which is gradually reached ; the original key is entirely forsaken, and the new one takes its place : 291. pi^^^ii=i C: I b|): vu^iy This example shows plainly, how the extended modulation, whicb sets for itself the new key as goal, makes use of the passing modulation, in order to reach it, and this the rather, as it was not the object to reach El? major quickly. Unless we wish to use such short passages as interlude between two compositions of different keys, or as exercises, they must be made use of in composition in a special manner, since upon the formation of the modula- tions themselves rests, in part, at the same time, the formation of the periods and their divisions. This, however, is an important part of the doctrine of Form, and belongs to the arrangement of the modulation of a composition, and is thus foreign to our immediate purpose. Remark. — An elucidation of this may be found in the author's work — " Die Grund- zuge der musikalischen Formen und ihre Analyse!!^ — (Leipsic, G. Wigand.) We make use at present of the formation of such modulations as exer- cises, in order thereby to promote skill in the use of the harmonies and their appropriate connection. While the means for modulation are being searched out, no immediate attention will be paid to the hind of modulation used, since the same can serve for both the above designated kinds. The first and simplest means will be THE TONIC TRIAD OF THE NEW KEY itself. If, however, this triad is already a component part of the first key, then what succeeds only, and particularly the subsequent dominant harmony of the new key, will really determine the intended modulation. Thus, in the JJU.I't J^ ■'^ """^ MAX UAL OF HARMONY. 143 following example at a^ no modulation will be felt, while at h we hear the key of G-major plainly only when we come to the third harmony : a. ^ *• In ease of more distant keys the minor triad can, to be sure, as tonic triad, hare a more decided effect, still for the sake of definiteness the dom- inant harmony will succeed it (at a) / the major triad, however, will incline to make itself understood as dominant (&)• 2§3. :i=Hg: 'l^i~: M A — O i._g i^l^ii^l^f^l^g C: I C: I 111 e: I feHl^=^I^E^I!i=l As tinsatisfying as the tonic triad shows itself to be, for modulation, in the way used above, in as great degree has one of its inversions (the chord of the sixth and fourth) the quality of rendering such modulation particularly decided. For just as it naturally takes part in the closing cadence (see pages 49 and 53), so it produces at its entrance the feeling of a modulation, if it is not used in the manner of the passing chords, but enters at the thesis. However, in this case also, it is naturally followed by the dominant, which first completes the modulation. 284. 6 4 t ^^mmi 144 MANUAL OF HARMONY. Upon the arsis it will not indicate the key so definitely : 2§5. 6 G 7 r. 4 71? ^ 4 I 4 Jf All examples given above, however, point to a still more potent means of modulation, viz., THE DOMINANT HARMONY. The triad, as well as the chord of the seventh of the dominant, shows itself as the most natural and best means of digression, since, through it, (which applies especially to the dominant harmony of the seventh) the key is most unmistakably determined : The modulation through the chord of the seventh of the dominant can be effected without intermediate chord in the following manner. According to the principle that that connection of harmony will be most easily comprehended, which is effected through like or stationary tones (preparation), modulations can be effected through the dominant chord of the seventh, from the tonic major triad into all remaining keys, except the keys of the minor and major third, and that of the augmented fourth. From C-major we can reach all keys, except El?, E and Fjf, (it can remain undetermined for the present whether major or minor) thus : From C to d: F: F ^^^=bf Everywhere in these examples the like tones, which are connected with each other by a tie, mediate the transition to the dominant of the next key; thus, from C major to D minor, the tones G and E, which become fifth and seventh of the dominant harmony, &c. MANUAL OF HARMONY. 145 Remark. — It only need be mentioned, that these modulation? ^t. also be reached through other positions of the chords, e. g. C — d: or: ^^ 287. ' ^ ^ - ' ^ - ^ I If. we wish to modulate in the same manner into the three keys which are wanting above, it can be done by means of an inserted chord (in the simplest manner, by a triad), which then supplies the missing connec- tion, e. g. From C to E^: C — E: C — Fjf: t2SS. pi^^-bSg^EE^^^l^ ■*■—•■*• Sir tf" - ||,r|* The modulation from the minor can be formed thus : From AtoB: A — d: a — e: a— F: G: Si^ ^ "*^^Zi -w- -r^- -f.^ -— oUr „^: fc._t_«._5ea_-^g — It *|- - ■^if-Ti- To the remaining keys C, Dj?, Ej?, Fj( and A|?, by means of a connecting chord : From A to C: a — D^: a — E{y; -»«• feg&lif^3=l^^^=QEt^#EE FJ: A A\}'. 5 ^^ ^^^m^^mm. ^ I- It is self evident that this manner of modulation is only exhibited as the simplest principle, and that it is by no means necessary that a modu- lation should always take place in this way ; likewise, that as simple con- nections of harmony can be produced without a stationary tone, so also can modulations ; as, for example, the following modulations can be accomplished without intermediate chord : 146 MANUAL OF HARMONY. From C to Eij: .».. $=mt~^^^^g^H^^^^ For the connection of harmonies and especially of the keys, it will, how- ever, always be of great use to make ourselves thoroughly acquainted with this principle, and to this end to write down modulations from all keys, and therewith to bring the chords into the most various positions, as also to make these connections evident to us by performance upon the piano-forte. This mechanical proceeding will greatly further dexterity in the use of all means of composition. Another chord shares with the dominant chord of the seventh the capa- bility for modulation, viz., THE CHORD OF THE DIMINISHED SEVENTH. This chord, which in most cases takes the place of the dominant har- mony, will frequently be more adapted for modulation than the latter, Hince its entrance is much milder, particularly in those cases in which seventh and fundamental of the dominant harmony would be obliged to enter free at the same time. The following examples present the use of this chord : From C to Bfe: C — B: C — d: a — b: 29i2. -mw^^^^^m^m^" Beside this application, this chord shows, by means of its enhannoniG nature, a farther, peculiar capability. The following chords, entirely like as to sound, but variously written : 293. i^gi^te^i^ belong to four different keys, viz. : in the first form to F minor, m the second to D minor, in the third to B minor, in the fourth to A{? minor. Through this circumstance a fourfold modulation is possible : From to r: C — d: C — b: C — a^: - |l^i^^li|pifi|^|lf Since now all the chords of the diminished seventh can appear in the following three positions, as the piano-forte shows most plainly, MANUAL OF HARMONY. U7 295. _ and each of them, through enharmonic interchange, will belong to four keys, modulations present themselves for all twelve keys in minor, to which in many cases we can add the twelve in major, since this chord can often be used instead of the dominant harmony in major. Here also the industrious writing down of this manner of modulation will tend greatly to advancement in the comprehension of the inner connection of all keys, as well as of the multiplicity of harmonic con- nection. Although this manner of modulation shows itself to be adapted to mani- fold uses in actual composition, still it must be remarked that it should not be used too often, since, being applied lightly, its artistic worth becomes less. A similar application, though not in so comprehensive a manner, is exhibited by THE AUGMENTED CHORD OF THE SIXTH AND FIFTH. Its similarity as regards sound, to the dominant chord of the seventh with enharmonic change, adapts it, in connection with the latter, for mod- ulation into certain keys, e. g. From C to b: E{y — - d: 297. pms^ m ^^m^^m m 77 C: V^ b: iio^ i V i K2: V^ d: 11°^ i V Although, in the above, the means were sought out with which to pass quickly from one key into the other, still (since it will not always be the intention to carry out a modulation quickly and decidedly), for the fur- therance of skill the exercises can be extended and given out in the following manner : From one key into the other hy means of the triads of various d£gre€s . From C to D through the i^riad of the third degree : 298. -^^m^¥- From C to D through the triad 148 MANUAL OF HARMONY. Of the fourth degree : Of the fifth degree : Of the sixth degret : \ 299. =f id=z|: =s=^g^^^^ ny- ->,- — iri cy 6 41) 71) :^^==l f? EE=^^ig=lE^ d2. 11 The following modulation from C to a in No. 286, would require a cadence in this position : From C to A : Cadence . 305. =!::f=:i: Hiiiiliiilli^l f 3 •*^ Si- 4 « -^- ^^^^^^^^^ 'TJie modulation from C to B with use of the cadence under No. 303 b •* From C to B: Cadence: 306. Si^i^i§|i:Wi«^^ or from to 307. Cadence : Impi^pi^M^fE 4b 6 3ir 5ir B^^^^^^^M^^ To close, we present an example of a more extended problem : From G through e minor, C major, and BJ^ minor to Ajy major. Cadence: ^ ^-,_J 1-_, 1 l-^—J -J - 5— fc^-Th-d— rH— f — 30§. ;^iEfe^ifeliiii^fe^EMpglE ife; i^ 3^s==g ^3= These indications will be sufl&cient to enable us to form for ourse^ manifold problems. MANUAL OF HARMONY, 161 PART III. PRACTICAL APPLICATION OF THE HARMONIES.— THE EXERCISER IN THEIR USE IN THE PURE HARMONIC STRUCTURE. Through the following hints respecting the manner most to the purpose in the use of the harmonies, the principles until now developed will be, at the^ same time, still more exactly explained, extended, and made complete. To this end, individual cases will furnish opportunity for farther remarks. CHAPTER XYII. The Simply Har^nonic Accofnpanhnent to a Given Voice. It may first be remarked, that here, only simply melodic progression ol a voice will be discussed ; all other elements of a melody, as, for exam- ple, its metrical and rythmical development, will be for the present excluded. 1. Harmonic accompaniment to a Soprano. We select the following simple exercise : 30». ^:^EgEE |^|gE|^|^|^lP To facilitate the work, those fundamental tones, which can serve as the harmonic foundation, will be added in the manner used before. c G c i> G c With every harmonic progression^ the leading of the Bass is the most important point. We turn our attention therefore first to this, and write its progression, perhaps, in tne following manner : V 162 311. SOPKANO. Babs. MANUAL OF HARMONY C G C n G C n P-^ ^11=1=1^^1111 9iE^^;:: im^f^ er in the following way : 312. 9iEI$Eis: The addition of the middle voices will now present no difficulties 313. /[J G c D G c — pif^^l=l^l^lll[| Alto. Tknob. Bass. ,_^__«_-__«. ., . - g^ — -r — » — |— ey — J — — -, — jy — Y'^ — rr Siillifliillililii Let this working out of the exercise serve, for the present, for the expla- nation of the exercises themselves. The next exercises will give opportunity for becoming acquainted with the principles of a good leading of the Bass, as well as of melodic voices in general so far as the simplest harmonic progression requires. Examples worked out in a faulty manner can best serve this end. Exercise with indication of the fundamentals : 314. •^m^lii=l^iilll[^ Remaek. — la the treatment of this and the following examples we use the vioHo «lef for the sake of saving room, and write the voices together on two staves ; for the personal work of the pupil, however, we recommend, mest earnestly, the manner of no tatioQ used in No. 813. The working out of this exercise may be as follows MANUAL OF HARMONY. 163 315. m^^l^l^^mim zis: fiispj=j=ipgigE(| There appears nowhere in this example a transgression of any rule of progression and chord-connection thus far known, and still, on account oi the stiff, uncertain, and powerless Bass, it is to be rejected entirely. Except in the case of the organ-point^ a good harmonic leading of the Bass allows it to remain stationary only if its continuity is conditioned by necessary preparation of a tone, or compensated for by a decided pro- gression of the other voices. The previous example also contains the chord of the sixth and fourth twice, which may give us opportunity to add what is farther necessary con- cerning the use of this peculiar and difficult chord. / ff v^y/* • 'X^ Of the Use of the Chord of the Sixth and Fourth^n^y/ The rare use of the second inversion of the triad, the chord of th C( sixth and fourth, has its reason in this, that its appearance depends upon^^-^ certain conditions. First, we find it oftenest in connection with the cadence formations, as ^ former examples show. Then, it appears in a like character in connection tvith modulation. "* (See page 143). It can probably also enter free in both cases, it must then, however, be regarded not as a passing chord, but always appear upon the thesis.-^.^ Except in these cases, it appears most naturally as tonic, dominant, or sub-dominant triad, under the following conditions : a. If the fourth is prepared ; ,s. X |>, J/ the Bass progresses by degrees to the following new chord, or remains stationary . The following examples show the application : 316. 6 6 4 6 154 MANUAL OF HARMONY, fr=.x='- 6 6 4 6 mmmim^^^ In the Examples at a^ it appears most naturally, because it rests upon tonic, dominant and sub-dominant, while upon other degrees (&) it easily produces the feeling of a modulation. Used upon the arsis (beside appearing under the above conditions), it can also appear with preparation of the Bass. |i_lli:-i=i 317. The chord of the sixth and fourth shows itself in all these examples, either as passing chord (upon the arsis), or, as above, in the character of the suspension upon the thesis ; with preparation of the Bass upon the thesis, it appears much weaker. "Ipilii^iiippl^ 31S. Not unfrequently it will appear as itself a suspension, whereby the preparation of the fourth i^ perfectly justified, v 319. MANUAL OF HARMONY. 155 Iq the second case still more decidedly, because it arises with a rarely occurring chord (that of the third degree). That the chord of the sixth and fourth, however, can also enter free in connection with a leading, by degrees, of the voices of smaller measural- divisions, in passing, as : 320. s^^^ 6 4- P=E^g^=[E will require no farther explanation after what was said in Chapter XV., of the passing chords, and after the examples, Nos. 276, 279. Remark. — The often necessary preparation of the perfect fourth in the chord of tlie sixth and fourth, has led many theorists to reckon it among the dissonances. In the introduction to this system of harmony, in the division of the intervals (page 16), it is introduced among the consonances; and also (page 20) the reason of this view is given. ■>, ■ ,A^ ^ ■ f'' ■;, . y/ I , The doubtful relation of the perfect fourth, and the necessity of its preparation occurs only over against the JBass, or the lowest voice, and, in fact, in the chord of the sixth and fourth only, since in the chord of the sixth, fourth and third, itself, this necessity of preparation is not always found ; between the other voices the perfect fourth is to be treated just as any other consonance. With the real dissonances this is not the case, for these retain their character every- where, whether they appear above, below, or in the middle. The chord of the sixth and fourth of the diminished triad will seldom be appropriate for use four-voiced, because it appears too incomplete. 321. On the other hand, it will occur in three-voiced composition, where it often takes the place of the chord of the second. (See later, the three- voiced movement). Besides the condition of a good harmonic progression, viz., that the Baw itself should form a good and intelligible foundation for it, the second requirement is, THAT THE PROGRESSION SHOULD ALSO BV, MELODIC. ir,6 MANUAL OF HARMONY. Among the unmelodio progressions have always been rightly reckoned certain skips. The succession of two fourths and fifths in the same direction, e. a. 322. p: lUPlll These skips are improved thus : g-" J :3_« C — f^-. — I _I»i2 L — s- -C?^ i i Even skips of a sixth, if the situation and compass of the voices admita of it, are better carried out by skips of a third in a contrary movement : tetter : tetter : »S84. ^j=.- ;^iif; m Augmented interval-steps and skips are to he avoided as unmelodic ; diminished are, however, good. not : better : 325. g^ not : tetter : not : i^li^^^^i^ not: ^= fI- tetter: not: better: 11 fi- i #= r|=: :i^ --^ Deviations from this rule are often found ; they find their explanation in A formation of melody, or in the especial character of the composition as a whole. The observance of the rule in theoretical labors will always be very improving. The skip into the major seventh is to he entirely avoided; that into the minor seventh can he used, hut only in case of an inversion of the same chord. not: not: .(5- »*«• ii=^^E§==PE=iE i i?^ If The last, perhaps, with the following progression of harmony : 327, not very good ' not: not: m^ —G>— G- EE^ :^:=:(fe ^-^ -^ ^W- ~^w- -If mi ~a:z .^.. 6 — r-©~ i^^ l\^. ba- -^^- or- ill MANUAL OF HARMONY. 15: These few observations contain the principal features of a good melodic leading of the voices, and especially for the next (simply harmonic) exercises, prove themselves sufficient. It should still be remarked, that these rules apply, not alone for the leading of the Bass, but in general for all voices. The exercise given under No. 814 can, -with an improved progression of the Bass, be worked out something in this manner : 32§. iPpppiiigiipipB -2 8 7 giE^E^lEg^l ^1 32§d. 'M. "^ a -■ ^ Exercises, -r-O- £EE^ C — m F C G 3. S^l= l^ |3=^ m C Qt c ©Y 15: illimi^^ii The next example will give occasion for the explanation of an impor* tant and difficult part of harmonic connection and leading of voices. 329. Exercise, bO C A Diy Gy 3 ^=^ f =s=:|-g=|-g=|=^ i The following faulty work may serve for illustration : "T o? 330. ■-w=^ iiE^i -^■ C_<5 (2- 6 7 5 158 MANUAL OF HARMONY. The faults of this treatment of the exercise consist, firstly, in the doubling of the third of the second chord through the Bass, which, with- out occasion, gives to this and the following harmony an awkward position ; secondly, in the indicated covered fifth (from the fourth to the fifth measure), and lastly, in the introduction of the seventh by a skip, in the next to the last measure. As concerns the last, this can take place with the dominant seventh only — the fundamental being already present (prepared). (See page 70). 331. More tolerable and less harsh is the free entrance of the seventh, and of the fundamental in contrary motion ; -g o — FF 332. m parallel motion^hovf e\er^\t is either to be rejected entirely, or only applied in connection with especially favorable progressions, if, perhaps, as in the first example of No. 333, the fundamental (G) is already present in the previous chord, although in another voice. 333. feziz i czzis: l=li The first of the faults instanced above will be corrected in what follows. The second is more important, and will give us occasion to speak in general OF COVERED FIFTH AND OCTAVE PROGRESSIONS. The nature of these progressions has already been spoken of, page 29. Covered fifths and octaves arise, if two voices^ starting with different intervals, progress in parallel motion to an octave or fifth, e. g. 334. Covered fifths ; -s- f=::r^z2zi:=-:Sirszrp; 1= i :i:: Covered octavet MANUAL OF HARMONY, 159 These fifths and octaves become open, if the skip which one or both voices make, be filled out by the tones which lie between, as is indicated above by the points. Since in every four-voiced movement certain covered fifths and octaves can occur, without which the choice of chords, as well as the leading of the voices, would be very much limited, and also, since others are to be avoided, it becomes necessary to take a somewhat nearer view of the manner of their appearance. An attempt to give positive rules for their use, which would be sufficient for all cases, has not yet been success- ful, and would probably with great difficulty succeed ; there are, therefore, only general observations to be made, which, however, will furnish a stan- dard of criticism for especial cases. Covered fifths and octaves between two voices can occur : 1. If one voice moves hy a step and the other skips ; 2. If hoth voices skip. In the first case : a. By a step in the upper, and a skip in the lower voice; h. By a skip in the upper, and a step in the lower voice. In regard to both cases as concerns the kind of voices : a* Between the outer voices, h. Between the middle voices, and C. Between an outer and a middle voice. Covered Fifths and Octaves in the Outer Voices,* They are to be allowed, if the upper voice progresses hy a step. Fifths: h. c. Octaves: d. e. 335. Here it is well, if one voice be at the same time led in the contrary movement or remain stationary, as in Example No. 335 a^ 1)^ C, It is not so well, if all voices go in parallel motion {d). Remark. — Although the above rule will suffice in so many cases, still it cannot always apply, as the above Example, No. 335 rZ, shows, which is not to be reckoned among those which exhibit a first rate leading of the voices, since the progression from the chord of the sixth, c, is a very forced one. We must remember also, what has been said before concerning the cadencing pro- gi-ession of the Bass, pages 35 and 36, viz., that covered octaves which pass over the leading tone, or in general, over the half-step, are always more tolerable than those rhich pass over the whole-step. 160 MANUAL OF HARMONY. In the exercises exhibited above, the octave always shows itself aa fundamental of the chord ; cases in which it forms the third of the chord are much more questionable, and therefore to be used more cautiously. not. not: 336. pp=«3:-|=i Even as fifth of the chord it is not to be called good. 337. :^ -G- •77 / Remark. — With the covered fifth, the lower voice will always be the fundamental of tiie chord. fiovered fifths in the outer voices are to he rejected if the upper voice skips, h. e. d. e. 33§. iwim^^^^^^i ^^!^| fiifji; I XWherever a seventh makes the connection of the harmony firmer, as /at Of df Cf the progression of fifths appears more covered and less harsh. Covered octaves in the outer voices are not to he unconditionally rejected if the upper voice skips. 339. b, not .' d. not : m^^MM^^i^^^^^t^^l 6 •^>v«^ i^HE^-MliTMHiMflllMi Here also those cases in which the Bass progresses a half-step (a) show themselves to be most tolerable. What was said in connection with Nos 336 and 337 applies for d and e» Covered fifths and octaves in the outer voices are to he rejected ifhoth voices skip. MANUAL OF HARMONY ;:.io. y If, however, they only form inversions of the same chord, they are not to be considered as faults, since in that case they are not progressing fiftha and octaves at all. 341. 11131^ — -s w iiiHilii^lim^lE Covered Fifths and Octaves in the Middle Voices, Although the leading of the middle voices must be just as pure aa that of the outer, still their situation, which is much covered by the latter, allows them occasionally a greater freedom ; this particularly applies to tlic covered fifths. Covered octaves are, here, if only for the sake of the good relation of the voices, not to be called good ; with respect to the covered fifths, aside from the above observations, all will immediately depend upon an otherwise good connection of harmony. A few cases may have place here : not : Slt2. i^iP^3ilil3ii^^^l^^ ■-t^ li^il^^l^^^^j^j^l 1 \ — o - i: te--?ps: Covered Fifths and Octaves between the Outer and 3Iiddle Voices, The considerations which are to be taken into account in connection with these progressions of the voices, are to be sought in a good and natural 162 MANUAL OF HARMONY, connection of harmony, rather than established through merely mechani- cal rules. Here are some examples : 34S. I '^l^i^l I i?=i=:gziiz^$ii=T-^ f^ ^^i^m^mm^^m not good: not: S;_ ^s^ni^f m= — "~ ■» <5 ^ ;i^r=^^^l^lii[| f An especial kind of covered octaves is still to be mentioned, viz., such as pass over the seventh ; these, in all voices, are to be avoided as faulty. 344. '^m i^-^iaiiiiiiMf (See page 84.) That which was remarked of the octaves, applies also to covered unisons. Between Soprano, Alto and Tenor, the latter are to be avoided entirely, between Tenor and Bass, however, they are to be regarded as covered octaves — according to the postion of the chord and of the voices themselves. The cases, in which covered fifths and octaves can appear, are so man- ifold; that it would be superfluous, if it were, in fact, possible, to adduce them all. The above observations may suffice, if we add the following maxim, which, to be sure, is not written for those beginners who . still have to do with the technical, or the properly mechanically-harmonic structure, without regarding the higher requirements of art : Avoid, indeed, covered fifths and octaves as much as j^ossihle ; consider ihem^ however, as safe if on the one hand, an otherwise natural, good con- Election of harmony takes 2^lctce, or on the other, considerations of a higher aort prevail; such as melodic voice-movement, application of defimite motives, etc. " MANVAL OF HARMONY. lC?i After this digression, we return to No. 330, in order to correct the before- mentioned fault. A correction of the covered fifth found there, which belongs in that category where both voices skip, will be hardly possible in this case, because, even if the Bass-progression proceed in the contrary movement, the evil presents itself again in another place, e. g. 345. / l-ilil iiliMa Thus it only remains to alter, in this case, the harmony itself, and select another marking of the fundamental tones. The following alteration can take place : 346. or ; 347. bO Dij- G^ s^^^^ -^ i 6 5 8 7 i::^: EEE ^^l bO P7 ^ '-W ^^^^ its: I 347 ft. =rk(pps= 2. — — -^— yfc- Exercises, ZZSZZ ZZ^^I T, Hil^ F Bb kO F D G^ C^ F 164 MANUAL OF HARMONY, 348 The following exercise : G c o I m Dy G C G il we will work out in this manner : 1. 2. S4i). I 3. 4. 5. ^^^H^^i^l^ "#■" ■.«ar- g.-^:^^ 6 6 4 5 §ife t I ^ 8 7 i lis: l^PiE The faults of this work are indicated by figures. The movement of all the upper three Toices, by skips in parallel motion, at No. 1, is not good, since it ofiends against the first principles of all har- monic connection and is by no means necessary. A leading of one or two voices^ hy skipsj can take place only if through a third voice (by a tone remaining stationary or by a contrary motion), the harmonic connection is preserved. No. 2 also contains the same fault, which here becomes still harsher because seventh and fundamental enter free and come thereby into an awkward position, so that one is crowded by the other. It has already been mentioned (pages 72 and 158), that the free entrance of the seventh can take only place without harshness, if the fundamental is already present, and can remain stationary in the same voice. Thus, none of the following examples exhibit a superior leading of the voices. 350. i^ssiisgggi^^gsi __^,j§-_.j^ _^__j^r^^_^_^^|2a__j?L.^:^__^ @eiysiii[i§uimiifitiiE I MANUAL OF HARMONY. 165 Probably few of these and similajr instances would be excusable for more important melodic reasons. The following examples may still serve as completion of the free intro- duction of the fundamental and the seventh in contrary motion, mentioned on page 158. 351. ._fi_,_-^_,_-^_,-l2g-:r-_^_,-j*^2-^fc ^^mm-^\^^\mi The instance No. 2, of Example No. 349, contains besides this, another fault, contrary to the rule laid down above (page 153), in connection with the chord of the sixth and fourth, viz., that the Bass should not skip from the chord of the sixth and fourth. The third fault of Example No. 349 consists in the covered fifth, which is the more prominent in connection with the skip of the Soprano in the same direction, as well as in the general scattered leading of the voices. The covered fifth in No. 4 is to be condemned, on the ground that it was tot necessary ; that at No. 5 is better ; it can take place in connection with the leading of the Alto, as well as of the Bass in contrary motion. The following will be a better working out of Exercise No. 348. I, ( 352. ifElEi 5: EE: im^ ^Me^^ ^ ^ ±r .sj ^ 6 6 2 4 8 7 «— r-^ Eocercises, 352. •^•ii&=l ^ «— r-«- T^P Ttsu::. i GC — G — D aDGD, T— ©— T E?EI^5^ r=iPJ^i^i^i^Ei C D. ^7 166 MANUAL OF HARMONY. 4. P t^- ^_ C— -42— T-©. ^i==1 _«_, ^; The next exercise^ FttO 353. ■*"7 i with the followiDg treatment : 354. i •' 4>^g — - - 1 1~" ^^11 iQz::: iGiii ^.^..p. ^[fi •rv^^ gives us opportunity to speak of a fault which bears the name, UNHARMONIC CROSS-RELATIO]!^. The unharmonic cross-relation (relatio non harmonica) belongs to the unmelodic progressions, and consists in general in this ; ihat upon one tone immediately follows the same tone in another voice, chromatically raised or depressed^ as here upon the Gr of the Alto the GJ( of the Bass. In order to avoid this fault, note the following rule : Immediate chromatic alterations of a tone are to be applied in that voice^ alone in which the tone unaltered immediately before occurs. Notwithstanding this rule answers, in so great degree, to all theoretical principles of harmonic connection and progression, there is hardly any one, to which so many exceptions in the practice can be shown. For this reason, in the books of instruction of later methods, great sus- picion has been cast upon the doctrine of the cross- relation, and instances brought forward in which the unharmonic cross relations occur in a per- fectly natural manner, without examining the reason why they do not sound faulty. Some of them will be here adduced : 355. i^p^^-^^ipipi ^: Mk ■la.*/ ''= W ^^ilill^ MANUAL OF HARMONY. 167 ) It ^' ' H ' .J I I S §_^ ^;r _ _ In all these cases the cross relation appears, not formed through the simply -harmonic leading forward of the voices, but either In the character of changing notes at a^ b^ g^ or through contraction (drawing together) of natural^ hut for the metrical construction, too cir- cumstantial harmonic connections, at c^ cl^ €^ f^ 7l, The first needs no proof, and there is only the observation to be added, tbat this kind of cross-relations would probably occur mostly with smaller divisions of the measure, and the above notation in half notes is rare and therefore unsuitable, because through it the simple harmonic foundation ig expressed, and not those tonic elements, which serve for embellishment. The original progression of the voices with the above cross-relations, which are the result of contraction, is the following :' 356. I d. , 5i ii ill ^E^=^ ; ^ =r- zis: Let these examples be compared with those under No. 355, at C^ it^ e, lu 168 MANUAL OF HARMONY. All these conditions, through which cross-relations are most endurable are wanting in the following and similar cases, which are therefore faulty. 35T. m^^^wm. In all the above instances, which are taken from practice, but sep- arated from their connection, is still to be added the consideration of the temjio, of the consistency of a whole brought out by means of ryth- mical divisions, which will make all these formations not unpleasant, but rather, precise. Among the cross-relations is reckoned also a progression which is known under the name Tritonus, and the explanation of which follows here : Of the Tritomis, The tritonus is contained in the diatonic major scale, and embraces the distance from the fourth to the seventh degree (in the C major scale the augmented fourth FjtJB.) This step from F to B embraces three whole tone-steps ^ whence its name is derived : 35S. V — gy— #— «- -o — It is held to be unmelodic and unvocal because each of its tones requires an especial progression, which tones properly appear assigned to two dif- ferent voices : 359. of which the one must remain disregarded in its progression, if the step is transferred to one voice : 360. ll^l^E^^jH , _ unless the melodic succession be formed thus : »«»• §^^^'^^11 MANUAL OF HARMONY. IGO That this, however, is not the only reason of the unpleasant effect of this interval-step, is shown by the very often used inversion of the same, which would likewise require a two voiced progression. 363. f^l^llE ^F=c ': and is just as intelligible and easy of performance, as the tritonus appears difficult and refractory. Remark. — It may still be remarked, in this connection, that the tritonus depends upon the diminished triad and its progression, as becomes plain from Example No. 362 alx)ve. (See page 38). That this step was formerly especially held up as faulty, lay in the circumstance, that, in connection with the otherwise customary simple harmonic formation of tone-compositions, it formed the only augmented progression which diatonically exhibited itself. At this day, with the extended use of all artistic means, it is simply reckoned among the aug- mented progressions, which, in a pure harmonic leading of the voices, are to be avoided as unmelodic, or at least, used with caution. The things to which reference is to be had in the use of the tritonus, are its situation and its manner of appearance. It can occur, based either Upon one chord (a) or Upon two chords (&), e. g. 363. a. h. nil if. q . J±=. fa M^- b fc.^b*^ t^-d h" It 1^ — _t>a i_s — L._^ — O-i-o — L_g-d_jj — L_5ijdL L_(5-J 5^ .t 9'E^~i I -=i- E-ri^^i^ M ~t If it occurs upon one chord, its entrance is not unexpected, and the ear is prepared; in connection with two chords, however, the feeling of a forced progression is easily produced. Formerly the prohibition of the tritonus was extended to the two major thirds, which follow each other at the distance of a whole step, e. g., not however : 364. ;^2^i^l=i^fe=^=ii=i tnd it is not to be denied, that this progression produces, two-voiced, the 170 MANUAL OF HARMONY. same unpleasant effect, whereas the same three and fonr-i oiced, especially if it does not appear in the outer voices, is rendered much milder. S65. That formerly the step from the fourth to the seventh degree of the minor scale, e. g.^ D to Gr+(, was not reckoned as tri tonus, is founded upon the former usual representation of the minor scale itself, and its harmo- nies. The effect of this step, since it is augmented, remains the same. We return again to our Exercise No. 353, and attempt a better treat- ment. 366. S66&. m & 1— (S? — &c. jiigE^p^g^i rJ!^i=?=:T 1 Exercises. m ^: ^i ;^ S"^: 4. fj: :^ ii; bO fI^ ^ ^^felEgE izo- DjO l\ *? 2. Harmonic accompaniment to a given oniddle voice. This exercise, wliich belongs properly to the contrapuntal labors, cannot begin too early. It is introduced, for the present, with the addition of tho fundamentals. MANUAL OF HARMONY. Ill ALxa C 367. t 1^: Exercise, F G A D-r G C i In the treatment of this exercise, the first and most important thing will, again, be the sketching of the Bass. At the same time, however, the Soprano, as the most prominent voice, can be added, e. g. 368. i-i^E: o — ■ ^i^i: d: Dy G C m& I:E^eeIe^Ie^e^I= ii^i T 5 The foregoing can answer as a three-voiced movement ; through the addi- tion of the Tenor it will assume this form : S69. 1^ —\—^ — T^^^"=^s^ — ^d— F-^ ;i^ -© — I I 1^1 §f^E£ -G — c:=i:=:^ii=izz5i=i±_^ e_Ez=i:tE Exercises with given Alto, 369 A. |16^: : :.-« : ;i^i :5Z fe T-fi'-- D Giy F F Bb Bb C nziisz i^^; F G Cy F 4. F C D w. ^^m\^=m m^ m C F p:E^: -» r— & is: "^ ^ ei Bb B^ A 172 MANUAL OF HARMONY. wmm^ \ ^^= ^\^^ ^^ ^m a D —.J- o Bj? A Tenor voice would be treated in like manner. Exercise, Tenob. C 370. _(© I_fi <9 111 <2 c nszui Sketch of the Bass and Soprano : »T1. Four-voiced 372. ;^e=;;e£^ :3i :G, 373. m The Bass can be sketched in this manner : 3T4. In the second and fourth measures, sevenths of secondary chords of the seventh show themselves without preparation. 174 MANUAL OF HARMONY. This kind are called passing sevenths. They start from the fundamental of the chord, and always appear upon the arsis. In such a manner they can occur in all voices. The addition of the middle voices to the above sketch of a Bass, gives the following four-voiced movement : 375. |iii!iEi=l^= \ — tdfe^fegEElE^g i: i 6 7 8 7 The same exercise with a richer change of harmony can be given in this manner : C FfJo^ GgJOy AC-yb dD G— y C 376. " 36e?:e m 377. Treatment : ;i^ :~CL t--5?:^ 'S* ?r3 -G I I gEE Egp.^^= i fEfeife& ;i m 7b 4 6 3b The next exercise will exhibit the use of the suspensions. 378. F Bb C D o 379. ^/•(Wfmeni; |fc^: ■4=H=^ -s--='- ■ P^i 6> g) 9 8 6 - MANUAL OF HAUMONY, §il _(2- mm We pass over the exercises in the middle voices. The using of the simply melodic progression in whole notes, as exercises, (cantus firmus) took place for this purpose, viz., in order to exhibit the simple harmonic content of a measure, or, as takes place in Alla-breve measure, to exhibit- it in its principal divisions (half-notes). If the exer- cise is given in half-notes, then chorals can be selected for the purpose. For personal practice the fundamental tones of existing good har- monic treatments of chorals can be very easily drawn off, and the treatment attempted. In the next exercise the process will be be shown. Choral: Haupt voll Blut und Wunden. D7 A — E — , 3§0. ;^i 1333 'ssL il=ii^g^ GO FbO CF CC '7b A AFjfO 1 — -^- -^ilj— ^:^=±-5^-ii? — I (9- .5^-L_-^ C G ^7\ .7 D GO G-y C D-y 5:: z^ 3Eb=d=ElE==[| The treatment of this choral can, according to the above exercise, be t.he f blowing : 3§:/ 176 MANUAL OF HARMONY. rs\ i=7^1zf:r:±t=5;:=:i=-=::«-L-e=--p-f_-:5=.Taiz±rs=::f= iff ', s I ', '> ' ' ' 'i I I I J J <=( t I I i '^mw^^mM^mmi ^^^^B: I 'l —-fg— i/— ,e- -J: ^j i r— r I ■F ^£^I^E^I II 1 I u I I u ^"^Ie^^I^ After sufficient practice and certainty in the management of tlie simple harmony, we can proceed to a farther development of the leading of the voices, by means of the passing and changing notes. For this purpose will follow in the next chapter the farther discussion of melody and melodic progression. CHAPTER XIX. On the JDevelopnient of Melody/, "We are not to treat bore of the invention of a melody, but of its devel- opment, and, what is most important for our harmonic exercises, to treat of it in order to learn, by the elaboration and farfhioning of melodies, to know and use what in them is essentially harmonic. AH will here depend upon the recognition and comprehension of the following principles : MANUAL OF HARMONY. 17. Every melody^ however extended and developed it may be, has a founda iio7ijust as simple as those ive have used, as exercises, in our last examples. Every harmonic leading of the voices, however complicated, admits t therefore, of reduction to a simple connection of harmony. In order to recognize this, it is necessary to learn to distinguish the essential notes from the subordinate and accessory work. We select to this end the analytic method, and endeavor to develop the following melody, which we will write down in the simplest manner according to the above mode with indication of the fundamental tones. - Bj F c^ F ~ :^^:2eI= -dZi mm M\ Both melody and harmony are, as selected, simple, and the latter may be carried out, four-voiced, in the following manner : 3§3. i^i^i g^ajjjg r- iiiiiiia: =;rJ <9 'r \t * %■ T «jr i liililll^B X> 6,.^^ Xrr^ --^ • Before we proceed to a farther development of this movement, it becomes necesary to premise what is to be mentioned concerning the rythmical for- mation of a melody. A melody can be either a musical movement without definite boundary, containing more or less measures, as it is often found as theme (motive of a composition), or it can be a whole, separated and bounded by means of Antitheses. In the last case it is called a Period, and it contains then, as a rule eight measures, which, in two divisions, each of four measures, form antitheses. These antitheses or divisions are often called " thesis and anti thesis" (Vordersatz und Nachsatz)/ 178 MANUAL OF HARMONY. ■ The more complete treatment of this subject belongs to the doctrine of Form.* That the above movement will form a period, is seen in the close of the whole, and it will be necessary, above all, to seek out the separating point of the divisions. This point of separation is very often discovered in the cadences, whicli either as imperfect whole or as half-cadences, show themselves as plagal in the middle of the movement. Such a half-cadence (in general, a close in the dominant) is found in our exercise in the sixth and seventh measures, and the separating point of the divisions of the periods may be assumed to be at the place where the sign t stands. The first division, the thesis, would accordingly receive seven, the antithesis six measures, each of which can be rythmically altered so as to contain four measures. This may take place in the following manner : 3S4. If we add the harmonic accompaniment selected above, we obtain a com plete musical period. It needs, also, only a glance, to enable us to see that all farthei transformations into various kinds of measure, e. ^., into 4y 9 > o or ^ measure, admit of easy accomplishment, e. g. 3§5. pr%=f^:E^ EEE^ -6(-i- I^ M¥^l &|H'"nE^ESE?E|E^EE?E 3^ ^E^^^ "^^^^^m. &c. •fcc. . We proceed now to the tonic , variations of the melody, and add to it •passing and changing notes, e. g. ^86. Spjtm^JM^ * See the work of this author — " Die Grundzuge der musik xlnchen Formeny — (Leipsi<^ 4J^ > ^ '^^ ^^^ ^^ ffe -^~0-^ -0 f-*-«-*-i I j I 1.1^ j I k.^ &c. The accompaniment at ci is harmonically figurated. The figures arising therefrom are called also broken chords. That at b is metrically figurated^ and that at c is melodically figurated. The figures which have arisen from the last are formed from changing and passing notes. Any accompanying voice can be used for such figuration, either alone or IQ connection with other voices. We select the beginning of Example No. 382, in order to attempt some kinds of accompaniment. i^ This may be preceded by the following remarks : f' If the figures repeat themselves uniformly {e. g. in broken cliords), then I 184 MANUAL OF HAR3fONT, all the rules of the harmonic leading of the voices are to be observed at the CHANGE OF THE CHORDS, as ivell as in the reduplication. "We must not write : 396. '^^^m^^0^ 9— a -J^ m ■-f^^-- ~^r. but somewhat in this manner : -^ _,_«_,. _•, — __# — 307. { " ^:^™i, — j^'^^A— i — 1 y-* —0-1 — '■■ — f — -^-#-1 #-j — #-- FF At the change of the harmony, the last note of one figure and the first note of the next must not form a false progression with any other voice, e. g. not: ietUr : twt: «0§. ' im i^i^^fi "^ -rr not letter: ^^^m^ ,=%. 1 The harmonic figuration also affords the means for forming one-voiced movements in greater perfection. The examples will begin with this : 309. One iwiced : MANUAL OF HARMONY. 185 That these movements are calculated for an instrument, probably such as a violin or clarionet, is easy to be seen. 400. Two voiced ': m :t:zz:=it±it:: 1-: ^iizzziiz: 'M Tliree voiced: in the niicldla voices: in the lower voice: ife M^m^^ 3 ^3 3 d": in the upper voice: -9 •-H In two voices: T^t.—-=X, i ip|E&=^^^E^^^ The figuration in the four-voiced movement, after these attempts witl the above example, will be equally easy of acoomplishmer t. Oty^r^rM^^ -^^r^fCP^y-^-^ - 186 MANUAL OF HARMONY. Instead of this we prefer to select, as an example of manifold figuration, the following passage from the above quoted quartette movement of Beethoven. 101. ±^=:^ :^=3 9—^- :q-— . fc^^::£:i^i::&i:£i=T=tj£,,jfe._f_-^^^f^ ;b: ptzz. m^^ l=^E^^E $= \ ^-^^^^-E$E^=i * fci^ * — i- i=:|: '■w^ feE -<<— I— «!— I 1 — J- 9Ji^ *• Slr=g^i=fei^?^^^Ef=^=fe^=lE:| liEE=S^.^=2^^-=lEf=^=^,%.i^,^I=§ I MANUAL OF HARMONY. 187 #— ^ in il6l^?=^^=i=i=s^EElE5=^=!^_^i^i This whole rich development rests upon the foundation given in Nos. 390, 391 and 392, and wherever the harmonic change enters, the leading of the voices is carefully observed. If we wish to obtain a clear insight into such elaborated compositions, and arrive at an understanding of their inner harmonic structure, it will be very useful to reduce compositions of this kind back to their simple foundation ; industry in this will reward itself by enrichment of knowl- edge of many kinds, and by our being rendered capable of formations of our own. CHAPTER XXI. Tlie Exercised in the Three-voiced 3Iovenient, With few exceptions, the four-voiced form of writing has been used for our exercises hitherto, and although it affords greater completeness, and appears most adapted for the harmonic connections, the three-voiced movements are also of much advantage, since they are especially calcu- lated to make the leading of the voices more skillful and many-sided. AVe begin, as before, with the problems with figured Basses. 8 7 6 6 5 4 6 2 *•»• i^3=^^^:^Ei^= d=I=: :rq: zzst 188 MANUAL OF HARMONY. 4 6 3 -^ m^^ 3^ 1 The three-voiced movement is sufficient, indeed, for the triad, but the leading of the voices will often result in the omission of one of its inter- vals ; in the case of the chords of the seventh one interval must naturally always be wanting ; this, however, can never be the seventh itself. As a rule, the fifth can be omitted, as has already occurred in the four-voiced move- ment, and the fundamental also in many cases ; the third, as the interval which determines the mode, can only be omitted in a few cases, without producing an especial emptiness. The treatment of the exercise is the following, to which a few remarks will be added : p^^i^l ¥=^ »Eg=|g^g^E|^g^Ep »-n— P G-^-&- pE^gE^E gr^TE l^^g^^ 4 6 3 6 6 5 ii^^^i3^i^^i^= In the fourth measure is found, at NB., the chord of the sixth and fourth of the diminished triad, E-G-B]?. It stands instead of the chord of the Becond, Bb-C-E-G, of which the fundamental C is here omitted. For four- voices, this place would stand thus : MANUAL OF HARMONY. 180 404. Concerning this chord, compare what is mentioned page 155. In the fifth measure a fourth represents the chord. Now, although a fourth can neither in the three-voiced nor in the two-voiced movement, have the worth of a complete chord, as can the third and sixth, yet, in cases where the chord of the sixth and fourth as passing chord can be used upon the arsis in the four-voiced movement, probably the sixth or third of the fundamental chord can (for the sake of a better lead- ing of the voices) be omitted in the three-voiced, so that the fourth alone remains, marking, here, fundamental and fifth of the original chord. In the two-voiced movement, the fourth will occasionally take the place of the chord of the second, especially in the case of the passing seventh, e. g. I I 405. Four-voiced, the above place in Example No. 403 would, complete, stand thus: I— ^- 406. IS fi)_I-lJ5l ^ IC In the eighth measure of Example No. 403, the chord of the sixth, fourth and third is, by the skip of the Alto, formed complete. The tenth measure exhibits apparently a chord of the sixth and fifth. Fundamentally, the fifth here is nothing else than the suspension of the fourth, which here, however, through the progression of the Bass, becomes a third. Four-voiced this becomes plainer : 190 407. MANUAL OF HARMONY, 9- -r- ^ •*• — ' r iiiEEEiE^I -^---.- :1=d=I=: 'zst=:^ ;P3= I The closing measure of Example No. 403 shows, through the octave F, that the triad can appear, in such cases, even without third and fifth. That the omission of the third is often conditioned by the leading of the voices, is shown by the first and second measures of the next example. i08. |igzzzp:zz£i^zgz=g^.£^; m^ ^^^^^^^^^^: 6 7 4 « - 3 65 ^fr>-3— ^— 1—74 :pt &^ fJN: ^^li^^il 5 - 4 3 ^ 7 6 3 6 6 4 - $ gfil^EE rzq: ;iii: The omission of the third takes place best upon the arsis, as here in the last measural- division ; upon the thesis, (accordingly at the beginning of the measure), the third should not be wanting. Farther exercises are to be left to the especial guidance [of the teacher]. Exercises in the Three-voiced Movement to a given Upper Voice, The following exercise, with indication of the fundamental tones, is to be worked out three-voiced : ■ *o».pe; MANUAL OF HARMONY C G C — F AD 101 c \mm=m Treatment. r 410. sj^ii^i^i: '\{ r—G—^—G ^^Mmm^^mm^mi i^^fMiiii^i-^ilii izTs: ^\ tcithout fundameiititl. This treatment needs no explanation. The choice of the middle and lower voices will depend upon the position of the chords in general. Thus, in a low position, the Tenor as middle voice, will be more suitable than the Alto, just so the Tenor can be selected as lower voice instead of the Bass. For the following example the Tenor is selected as middle voice, since its movement attaches itself more to the Bass, while on the other hand, the simple song of the Soprano appears, of itself, isolated. The previous Exercise in more extended harmonic treatment ; ,411. p^! E A G C D GJfO.^ 1) D G — S> — T ^1=1 413. T/'eatMcni: IF ^. mmEmmmm s iSHgll 6 G 9^^Bil|gg|Bggp6g£i^; KB. In the fifth measure at NB. appears the real ninth-suspension (through the position of the voices), as second, which occurs very seldom, and only between Tenor and Bass. In this connection it is to be remarked, that a second-suspension cannot exist, because the second depends upon the inver- sion of the seventh, and governs itself according to the progression of tho latter, e. g. 192 3fANUAL OF HARMONY. Inversion - &^* - ^g - 413. -■ f^^ ^^ A D 4H. gH^g^l^ -©— - i^ie^ff As upper voice, the selection of the Alto is here most to the purpose. 415. ^T3=F ee: i^lilSlll !!S-=S=:l^iE=i E}l BES=ll: 3 6 ii^i^l^j^l^^^l-^^H^feME The same Exercise with the following determination of chords D o A— ^ Bb Q- C F Bb Co- » Bb F o rO » A 416 gJ£gEgpjg|g|;|gE|?i;E|^|=:|g^E|^;||^p| 7)'eatment: 417. -T— (2J-!S> (2 |BlEilg^i|=^tE|EgElEgg| ^gg^"5 | ?!iiiHliiH^"lFJ ::-siizzz::— 7 « - ©jFEEE:i=i :|_^g. G G 4 =^ 3- =.3^E^I |J|^^|EE=| P-T— «- ?:=^ ;E^iEt=E iiii[E^: 13] ^ii^ll^i^ii; 6 4 6 7 6 « 6 i^^i-^^^i^lPi^^^^lf MANUAL OF HA HMO NY. m The next to the last measure affords the proof, that even the sixth can be suspension. For farther practice, former exercises, which were given for the four- voiced movement, may be used. CHAPTER XXII. On the Ttvo-voiced Movement, The great meagreness of the two-voiced movement, in a purely harmonic )oint of view, allows it rarely to appear adapted for other than contra- rantal labors, in which it first receives actual significance and comqs to be applied even in polyphonic movements, e. g., in fugues. If, indeed, for simply harmonic use, the metrically and rhythmically various formation of the voices makes the two-voiced movement toler- able, still the contrapuntal development of two voices can alone free them from the monotony of many successions of thirds and sixths, and give this movement that individual completeness, which every other polyphcraic move- ment must possess. The omission of one or more intervals will, In every case, necessarily take place in connection witli this movement. With the triads, it will' generally be the fifth or the fundamental. If chords of the seventh are to be applied^, then, of course, the seventh cannot be omitted. Octaves and fifths are seldsDm to be introduced, since they appear too empty ; the fourth could ©oly be admitted in a few cases where the chord of the sixth and fourth can regularly stand, or if it occurs instead of the chord of the second. (See page 188). Example: 418 bO p ^nii^^^: F Ilia: ;[f 419. Treatment : A ^ ^ ^i mf^mmm^ m: 5 3 6 7a: 6 3 6 6 3 3 1 I^l^l^ i 194 MANUAL OF HARMONY. The omission of intervals is plain through a comparison of the fun- damental tones of Example No. 418. Want of clearness of the harmony •will be rare in connection with this, since each chord explains itself through its situation, i. e., through the preceding and following harmony. The same exercise with the following marking : F— . 4*0. p^; ;i^i; G ^--fi- m^ 421. Treatments / —is>—^ — ©- ■ "O - 1 ■ T 2 6 — t . 6 ^ 5 ^2 — s -a— ■ V5115=:p'-[:=: ;-t=E- -X =E-: -=^ ^ — o- -5-j — ©- w- — ©- i 4 - 3 - 6 w^mmmmmm Most of the exercises exhibited in the third part trespass upon the domain of counterpoint. The difference consists only in this, viz. ; that here, the succession of the chords is prescribed, and it only remains to form the leading of the voices, while in the contrapuntal exercises the knowledge of harmony, as well as certainty in its use, is assumed, so that the suc- cession of the harmonies can be left to our own choice. We may, therefore, regard these labors as a useful preparatory exercise for those, as they also afford at the same time an insight into the relation of harmony to counterpoint. The exercises in the next chapter are also to be considered in this light, since they drop the above limitation of a prescribed succession of chords. MANUAL OF HARMONY. m CHAPTER XXIII. Harmonic Elaboration of a given Voice in Melodic Develoj)- tnent. By melodic development of a voice is not here to be understood that richer ornamentation, such as Chapter XIX. exhibited. Through met- rical variety of their measural-divisions alone the simple, choral-like pro- gression of oui* earlier exercises will be avoided, and thereby opportunity be given to learn to develop better the voices of the harmonic accompani- ment also. The following exercise will make this plainer : 422. _e_._iz ¥^ ^ — .(2- f2— S(- r^^9,T-^~.- |gE.^E| ^EEEf^EEE£|-z^-E|-:EE-|^ The choice of the chord- succession is left to the treatment itself. Even if the kind of measure selected will, of itself, produce a like melodic leading of the voices to be elaborated, still especial attention must be given to a good leading of them, according to the principles developed in the previous chapters, if a free, skillful treatment of them is to be attained. This exercise will follow, first in three-voiced treatment. 423. zzc: -^ ::zgsi It TV- ^9- E^ _fi-*:o. P^^ ^ -f=i^ i^HUill -=e: 9 8 7 6 7 6 6 G 7 6 4 5 i This treatment, after what has been remarked in connection with the three-voiced movement, needs no farther explanation. The harmonic treatment of this melody as middle voice will show its many-sidedness, and may be recommended as a useful exercise. In order to be able to retain the Alto voice, we transpose the melody, foi the sake of the better position, to F major. 196 ■ MANUAL OF EARMONY. 424. mm-^mm^mm^m cantus Jlrmitt. iilE^I-^EE: ■^'1^^4^1"^E|ii[^ iillElliii 7 683984 5 9 8 7 -F gE^lllgi^i The explanation of the chord of the sixth and fourth which enters free in the fourth measure, is found in what was remarked in Chapter XV. concerning the passing chords. It arose accidentally, through the progression of the Bass by degrees, and stands, here, in the place of the chord of the second. The treatment of the same cantus firmus transferred to the Bass: 425. Lfi^gl^^^l^i ¥■ ?G (S. •» • mf m^^i=^i^=^mi .(2-«_ e c./. K -^-©-.— 4 ^ 5 - 6j8r 6 36 3b2-4 5-G ■ ■ ' ' VS^^^ »- - & — ^ — H'-rH' — » — 1-^ H- — &-( — jKTv — r ^ . r This treatment exhibits a weakness in the third and fourth measures, in the harmonizing of the sustained A of the Bass. In like manner the bare fourth in the sixth measure is a very imperfect representative of a chord, unless we wish to explain it as a passing note. If we wish to develop the leading of the voices still farther, we can mtroduce passing and changing notes interchangeably, into the two voices to be added, e. g, cf. ., — . ^ — - 15 426. ^ : S^Ef^E l!S= -#-•- E 7J91 EEgB-r-r-T±± pitztzp^F 7 6 t^KEHE^i ==E^F=E MANUAL OF HARMONY, U e; 19; m ig3_^^t^f=rf=^-:z4^: EE|^E3_^-c if^ 6 5 3 3 7 i!=3E^^EiEg^ricE»E_E: Of the remaining treatments, that of the cantus Jirmus in the middle voices will here be given : 427. £ S^Egg #-==u-#-, c./. HIe^^^"^ llElil^il^m: 6 7 6 9 6 G S^^iti^. ^-# ^E?EHEEEEEEt'~^" f3= Si 0-^-0-^. li^^^iysii^iE ■^ ^ ^ :E=t^^ -r— S" T- J^-il 9 8 6 5 ^ m m gl^ ^ g EgEE^ l EEEEEEE p^ 5 6 i=3=iE«E I^IE As examples of four- voiced treatment, the following may stand here : 4 2 S • Given toice : , _ . ^ JsStE {^HsBg^gg^gggg^ 198 MANUAL OF HABMONY. 439. Four-voiced treatment : c.f. . . ^^Em^^^^^^mmw^m^ ^ "^ ^ a ^ ^m^m^^k m^^ 4 3 9 8 6 6 6-6 7 6 7_4 3 51] 543 867 za- SES?E^ff?E?£jE I In the fifth measure, at NB., the skip of the Tenor into the seventh ia not good, because the Soprano, at the same time, makes a long skip in the same direction, into the fundamental G ; only the position of the Alto can excuse this case. In the same measure is found the chord of the sixth and fourth of the augmented triad, the original fifth of which is prepared (pages 91 and 92). It stands here in the character of a suspension from below. (See Suspen- sions, Chap. XII., page 116). The same cantus firmus in the Alto, transposed to D major : 430. -& — ^- c./. isipj -.« — ^ £EEc"£EE NB. :iCi fi, — ,o_. ^_0- X- 3EEEEaEEF£5 ;i i*l^ 5 — 4 3 ■H :i~?' .X ^ ? i ^ 4 7 ~Q~,vzzzz: I0~== MANUAL OF HARMONY, 199 ^ tt ^ ^ — -H— -r— (2- NB. -f^- Q-r-n- 11^111== 7 6 6 3 6 7 iLipr^-^ iZTis: In the fourth measure are found suspensions in three voices (see page 117). In the fifth and sixth measures the position of the Alto and Tenor 5 is not good, because the distance from one to the other is more than ait octave. Of the remaining treatments, that of the canius Jirmus in the Bass will here follow : 4S1. Si: I* E ^TE^^j -G-f-o — ?5-T-S'-T— ri -(5L«_^_(2. =iz^°—Y—^-^k^-¥(^'^-^--^-'- ^l^l^l^ggl =f-^ ^=&=^^- iig^iiiif ^sSPii e./ 4 3 6 6 4 6 _2 6 3 6^356 6 6 4 5^ ^t^- 4 6 3 NB. The introduction of the chord of the seventh of the seventh degree, in the fourth measure, is not clear, because the fundamental lies imm©- liately above the seventh. (See page 69). Besides this, its progression does not ensue here according to the leading of the leading tone, but in the same cadenciug manner as with the other chords of the seventh : Cj{ "7 Fjf. (See pages 68 and 69). The treatments of this canius firmus with a leading of the voices in which there is more movement, can be carried out in this manner : 200 MANUAL OF HARMONY. II, *i ^ •, 432. O T-® / t 5>- E3; 1 B-^il==r=*' i-#-«-#- ^r^iSii^; ,^^^^:^ :3:zFt: G 4 5 F*= iill^g^^iN^iEi=sii^p •^ w- ;l^5E^^EE:E=ii i-«--^E^_^i^ i fclf^gi^li^^E^llli?^gE|^iEi J1>=e; NB. l=E^^i^E=?=li^e 6 5 6 4 7 4 3 6 7 liE^^E^Eiig^i^^lfe^lliili The upward progression of the seventh ia the next to the last measure (at NB.), is conditioned by the movement of the Soprano. . (See page 84), The treatment of the cantus firmus in the Tenor follows: ^^^^ — u-3— f-^-f-r-r-f- i^m^^=i E^gE gggEE^ -* J4-^3I-0._g,. 433. ?ES£ IzcdiiB -| -2— g-^— 9 T-« , P— (9 _tiiiz: — ^ ^^ — ^ ^m :4=. gi!bigfei^sa5=M=i :q= MANUAL OF HARMONY. 201 ©i^Ei £= m ;i^i ^^^s; ^*-f cEB3 Pil The third measure gives opportunity to speak of octave and fifth-succes- sion in contrary motion. According to the principle developed on page 27 and the following pages, they are just as faulty as those of the parallel motion, and it is to be especially remarked in connection with octave-successions, that they confine the free movement of the voices ; with the fifth-succcessions, how- ever, the character of separation is rendered much milder by contrary motion; this is particularly true of those which approach each other while those which progress from each other, make the separation or want of connection more perceptible. (See also Example No. 430 in the 6th and 7th measures, between Tenor and Bass). Compare the following examples : 434. ^m^ m ^ t=€m^Mm^ If we glance at the treatments found in this chapter, we cannot fail to recognize the melodic development of the voices, and herein lies the ground for regarding them as contrapuntal labors ; for exactly in this consists the essence of counterpoint, in distinction from the purely rhythmical-har- monic form, viz., that it conditions the freer melodic leading of the voices, but with observance of the harmonic laws, which latter form, as it were, its innermost substance. Everywhere now in these examples, even in those where the voices move in quarter notes, the simply harmonic structure can be demonstrated, and thus they may serve the purpose, for the present, of making us under- stand the difference between simply harmonic and contrapuntal treatment of a given voice. The more particular discussion of this can only be taken up in connection with counterpoint itself. 202 MANUAL OF HARMONY. CHAPTER XXIV. The Five-voiced Movement As the doubling of the intervals of a triad is necessary even in the four-voiced movement, so in five and more than five-voiced movements it becomes a necessity in a still greater degree, and this even in the case of the chords of the seventh. Since in the pure harmonic movement, each voice must maintain its independence, those intervals especially which admit of a double progres- sion, will, for the sake of attaining this independence, be capable of a reduplication. This, to be sure, can take place with each interval of a chord under certain circumstances ; the seventh will be least adapted for doubling, except where a melodic leading, as, for example, in passing, ren- ders this reduplication necessary. Farther remarks follow in connection with the examples given. Exercise* 6 6 5 4 2 3 435. ii^^S :t:: 31=^ 1 In the treatment, we can select, according to the position of the voiceSi either two Sopranos, two Altos or two Tenors. 436. BOPBAKO. Alto I. Alto II. Tknob. m^^m B E^E^I^^ l Eg^ i^[| S p T I r-^ o o p f p f 443. #--; I I :p- I \-r' r I I I iPi G G In the repetition, the following succession of harmony can be applied 206 MANUAL OF HARMONY. 444. 2 CHAPTER XXV. The Six, Seven ami Eight-voiced Movement* The necessity of doubling or trebling increases with the number of the voices which are added ; it will also often occur in connection with an independent leading of the voices, that the voices cross each other. The simplest harmonic progressions become here, in a still greater degree^ fundamental condition of the possibility of such polyphonic movements, and it must be remarked, that many chords are not adapted at all for this manner of writing, because their intervals, in as much as they are subject to a definite progression, do not allow of multiplication, as, for example, the altered chords and the diminished chord of the seventh. A few progressions of the triad may follow here. Progression to the second degree : 4-toiced : -- I I I -7 VIS z:lzx=rt:^l:±xi=it:ziiz:tizz:t-l :fz=F=lzT=r[:^; :=t: -#=S T r- » — -I — 35 m—^ — X >= — r — c^ o —I-, I I ip|i#i^iii^g^i 6 6 5 Pl^^^^^^^l^=^ MANUAL OF HARMONY. --:i=::5': S r— 5,- .l_p 1 — I. :«—- s< (g — \ IjfeEEr^ EE T^X 5^: I J- rpntrip— p-l iii3: 2 6 ■=1^ w^^^mm A — 4- r ^ ri=^EEpp^g ;e^e: -© Q — =s:=3: Si-i — s, — ^^-f-g — ^jp-K^ — g— F -g— (g-f— ^-g — T-d — g — 3 6 « -^7 r f 6 :ij-Tiz: 7 4 3 ifi^ii^ # p f^>^M:^C K^M=E^ P^E^:^pi^pii^i :^- r^ll^l^ -S»- EEE :«s: — 1=- H^i J. t:^—: J—J— I J ■Jis=: tip: EE i 7 4 - 6 7 3 - fl 6fl i^pE3EJ= g Fa- i.^^l^^i ^ i ^ MANVJ.L OF UARMONY. I 20$ tT:d: ■— ©5>- ^ :?siT ?^^: i I J 7 — 4 3 e^^H^i^l^ll^i^ Since in polyphonic chorus-movements, all the voices do not always work at the same time, as in a choral-treatment, the movement often appears only three and four-voiced, and receives an increase of intensity through the accession of a numher of voices. The following examples will explain this kind of chorus-movement and especially serve to show, that in polyphonic work also, suspensions and passing notes can very well be introduced, without detriment to the clear /ess and intelligibility. 447. ~ SOPRAXO I&ll. Alto. Tkkof. l&il. Ba.39. |^ = \ — r z=::za: is:: :::^z: ::j==lz[ its: isi^^lz ZSi- '.'srj. ff-3^^ J — I i-;-' I ^=: J*L_^ ^H^iH -5>~t— ilg^l^B^I^ ■T-S T-«^5!n ffJ 13: .-U L r—v -6€h g_^ Ig^g^l^^l^fe^l^^ S^ 4r-^ =^t^--i ■■i— 4-,__j ,1— J— I- FT^~ 1^1 i^-^?^^I^L^I?^lEEl^^ 210 44§. fiOPBANO I. 8OPBANO II. MANUAL OF HARMONY. 4S. • Alto. I. Alto II, Texok. Bass. ^—m -1 w >5 r— ?^^E; t^-^ t3: i^EE^'EEEi^ #=^-: ^leoi ;ee^s fp^^ ^^^^^=^^^^ ^-# ^iHi^ii^ B 4a ^-0 ^m^sm ¥ X-- li^^=^l^ :^e; fri^^ H ::s: Ec-^-r — 3 ^^P^gj^ i! szx: S: -#— MANUAL OF BARMONY. 211 't- n T~s: a i lfe=ife=iS^^[^E^ m JE^ f— ^ i^^^^^^^^l P^,^i|^ Hiii^^fi; E5: :E3^ i In eight-voiced chorus-movements, for which, as a rule, the customary four voices are used twice, the latter are not always found employed as eight independent voices, which would easily cause too great fullness, but frequently two voices of like kind are employed in unison (for example, two Sopranos, two Altos, or two Tenors and two Basses in unison), so that the movement often appears four, five and six-voiced. We find also the eight voices divided into two different choirs, which work each for itself, and only in single passages together. As an example of the particular progression which many of these voices must make, the beginning of the choral given above may follow here for eight voices : 449. SOPBASO I. & II. Alto I. & II. Tkkob I. & II. Ba68 I. & II. 6&=4|3iS^: =t:=t=i=P !=:?=; E3 |5 lit: ZIZ&ZZ] ^gn^n 212 MANUAL OF HARMONY. — TT-g— ^-f-F"^ :^p -G&- 1 m=. ^^^^^^E^^^E^\ :t=.^ p=i^; i^i The difficulty of this manner of writing is, in the case of polyphonic movements which are divided into two diflferent choirs, met by this, that where two or more choirs work together, it is not altogether the ionicdl difference, but often the metrical^ which separates the voices ; it is always to be presumed, however, that the harmonic succession takes place in the simplest manner, and never in rapid changes. The above is generally to be understood when we speak of twelve or six- teen-voiced choruses, movements, etc., and single pieces of Bach only, are found, where eight and more voices (among which, however, instru mental voices are to be reckoned), are treated obligato. These hints concerning the polyphonic movement may here suffice, since the rest, with thorough knowledge of harmony, can be left to per- sonal study and the inclination for polyphonic movements. Concerning its application, however, we may farther remark that the use of the polyphonic form and its manner of treatment above shown, will have appli- cation mostly in compositions for choirs ; in instrumental music, however, e. g., in orchestral works, will not find place (as the taking part of so many instruments of various kinds allows us to suppose) in the compass adduced ; for this last, in the majority of cases, the four-voiced movement will bo sufficient, concerning the farther treatment of which only the actual instruction in instrumentation can give information, since here the rela- tions of reduplication (even if often approaching the manner shown above), mast still be subject to other principles. MANUAL OF HARMONY. 213 CHAPTER XXVI. On the Musical Forms of Close, Several kinds of close have already been mentioned (pages 32 and 33) , in relation to the authentic close, farther remarks followed on pages 40 and 53 ; in the course of the whole treatise, however, no farther opportu- nity has been given to take up the subject, so that a fuller explanation of these and other kinds of close may here follow : The forms of close are immediately divided into The authentic close and The plugalic or plagal close. The authentic close has the formula V-I, the plagal close IV-I (or in minor : V-i, iv-i), as was before remarked. Both kinds are used not only at the conclusions of whole compositions, but also at the close of the principal parts, of the periods, and their divisions. The more particular discussion of this point belongs to the doctrine of Form. (See the book referred to, page 142). If the plagal close concludes a piece, it seldom stands alone, but suc- ceeds the authentic close ; in a composition in minor it also frequently leads to major, e. g. I 1 . auth. plagal I close 450. ii i In the last case, as in the above example, it is introduced by means of a modulation. The closes (cadences) are also divided into ivhole and half closes (cadences). By the first is understood the same which is comprehended under the authentic cadences. In the case of the whole cadences a farther distinction is again made between perfect and imperfect ones. The perfect whole cadences are those in which the Bass receives the 214 MANUAL OF HARMONY. fundamentals of the dominant and tonic, and the Soprano the fundamental of the tonic, e. g. not: 451. gsfii j=j^ =p=i If this is not the case, they are called imperfect^ e. g. 452. ^i^igEg^i^i^rB ^ ^ &c. f^^^^^^^^i i If the Bass progresses from the dominant to another degree, they are called deceptive cadences. 453. ^^iHiUF^i ;i^^i: i See the examples, pages 82 to 85. The half-cadences have the formula I-V, e. g. 454. ;ee 1^1 V They consist therefore in this ; that the dominant triad completes the movement. Besides the tonic triad, other chords of other degrees can precede the dominant in the formaction of a half-close, e. g. 455. ^Ef,|E^Epi : i^iE |^ Er^ *.. IV G^ <^ -ST TI V Among the half-cadences are also counted those closes in the key of the MANUAL OF HARMONY. 215 dominant which are formed by a modulation into the same; with which, however, the modulation itself is not, in a definite manner, effected through the fundamental position of the dominant harmony of the seventh, but fcither through its inversions or through the chord of the seventh of the seventh degree, e. g. G: viio^ I g: vii«»y C: V c: ii^^ V This is, however, the case only in relation to the ruling key, which has immediately before been made use of. For the farther understanding of these kinds of cadences, compare those which are found in the examples of this book. In No. 388 is found in the third and fourth measures a half cadence formed through ii-V, which effects the close of the first division of the whole period ; in the seventh and eighth measures, however, we find a perfect ivhole or authentic cadence. In Example No. 392 is found a half cadence, in the third and fourth measures, formed through I-V, and a perfect whole or authentic cadence in the key of the dominant at the conclusion. (Thus this is no half cadence, since the dominant harmony of the seventh renders the modular tion decided). In the choral treated under No. 446, the first strophe ends with an imperfect whole cadence, the second with 2, perfect whole cadence, the third with a AaZ/"-cadence to e minor (iv-V), the fourth with a perfect whole cadence in G major, the fifth with Vkperfect whole cadence in a minor, the sixth with a half cadence in e minor (iv-V), and the seventh with a perfect whole cadence in Gr major. The application of the various cadences is easily found in chorals ; for more extended pieces they form the means of boundary and connection of the smallest, as well as of the more extended movements, and are therefore to be used with much care, because upon them depends a great part of the Form-construction of a piece. INDEX OF SUBJECTS. Ae€