MAflUALOFHARMONY THE LIBRARY OF THE UNIVERSITY OF CALIFORNIA LOS ANGELES Gift Meredith Willson RIOHTER'S MANUAL OF HARMONY: PEACTICAL GUIDE TO ITS STUDY PREPARED K8PUCIAU.T fOB TH3 CONSERVATORY OF MUSIC AT LEIPSIC. BI ERNST FRIEDRICH \RICHTER, MUBIO-DIRECTOR, OEOANIST OP THE CHURCH OF ST. NICOLAI, AH7> BTEUCTOB IN THE CONSEBVATORY OP MDSIC. TRANSLATED JTEOM THE LATEST GERMAN EDITION fo BY JOHN P. ^OEGAN, OP THI LKJPSIO CONSERVATORY OF MUSIC, AND PUPIL OF THE ACTUOH SIXTEENTH EDITION. YORK: G. SCHIRMER, 35 UNIOX SQUARE (AYEST SIDE). 1891.. Entered, according to Act of Congress, in the year 1867, by G. SCHIRMER, In the Clerk's Office of the District Court of the United States for the Northern District of New York. 6100 Library .77 TRANSLATOR'S PREFACE IN offering to the American public this translation of RICHTER'S HAEMONIELEHEE we need have no hesitation in saying, that we offer a translation of the best feotf-book 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 a practical harmonist ; and no one has been more successful in leading pupils to real success. The Manual contains the outlines of the course which 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 full, to a more smoothly-rounded ono 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 duty to a 1900368 iv TRANSLATOR'S PREFACE. teacher to whom the translator owes all gratitude, and in behall 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, Kev. JOHN MORGAN, D. D., of Oberlin College, for his kind assistance in the work, 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. MORGAN. 3fnw YORK, June lit, 1867. FROM THE PREFACE TO THE FIRST EDITION. THE most immediate occasion for publishing this text book oi 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 believes to be these : It must contain the most essential, fundamental part of the musical theory 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 late* attempts at composition. The book contains no scientifically theoretic treatise on har- mony, but, although as far as is tho ^ase with any system ol 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 kno\* 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 tlie sort liave 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 accomplished in this regard, is 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 1n 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 .slced is not Wnj ? the inquiry of immediate application is, How? * It may here be permitted to call attention to a work which might be adapted to meet a palpable Trant : Die Natur der ffarmwik und Hfetrik by M. Hauptmann. PREFACE. Vli The thing to be done is, from experience, from the L^st models, to understand, not to calculate, the necessity of. certain principles; later, if education, acquirements, capability and calling require it, it will be time enough to investigate ihe^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, to 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 all 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 one, 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 itself 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 nil 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, with 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 already 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 capacity, certainly lead to the goal ALTHOUGH in the present edition also, the methodical order ol 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 : Generalbass- Uebungen nebst Kurzen Erlauterungen by BENEDICT "WiDMANN, and Uebungen zum Studium der Harmonie und des Contrapunktes, by FEED. HILLER. 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, still 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 worka above referred to, and, indeed, for exercises which, in part follow the course of mj text book, in part aim at other practice. The X PEEFACE. work of HILLER, however, besides the exercises which professedly follow the course 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 lias 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 uew edition may gain for itself new ones. EENST FKEEDR. RICHTER. LEIPSIC, December, 1863. TABLE OF CONTENTS. . Intermit, ' .18 PAKT I. THE FUNDAMENTAL HAKMONIES AND THE CHORDS DERIVED FROM THEM. CHAPTER I. THE TRIADS OF THE MAJOR SCALE, , 21 II. THE TRIADS OF THE MINOR SCALE, 40 III. THE INVERSION OF THE TRIADS, 47 IV. HARMONIES OF THE SEVENTH (VierTdange), .... 54 V. THE INVERSIONS OF THE CHORD OF THE SEVENTH, ... 59 VI. SECONDARY HARMONIES OF THE SEVENTH, VII.- -THE INVERSION OF THE SECONDARY CHORDS OF THE SEVENTH, . 7? VIII. THE CHORDS OF THE SEVENTH IN CONNECTION WITH CHORDS OF OTHER TONE-DEGREES, ^ IX. ON CHORDS OF THE NINTH, ELEVENTH AND THIRTEENTH, X. CHROMATIC ALTERATION OF THE FUNDAMENTAL HARMONIES. Ai^ 01 TERED CHORDS, XI. ON MODULATION OF A PASSAGE OF Music, .... 108 PAKT II. ACCIDENTAL CHORD FORMATIONS. TONES FOREIGN TO THE HARMONY. 105 XII. SUSPENSIONS, . - 1 0^1 XIII THE ORGAN-POINT STATIONARY VOICES, .... XI! CONTENTS. CHAPTER FAQT XIV. PASSING NOTES. CHANGING NOTES, ... 28 XV. PASSING CHOKDS, ....... . 138 XVI. ON THE MEANS FOR MODULATION, .... .143 PAKT III. PRACTICAL APPLICATION OF THE HARMONIES. THE EXERCISES US THEIR USE IN THE PURE HARMONIC STRUCTURE. XVn. THE SIMPLY HARMONIC ACCOMPANIMENT TO A GIVEN VOICE, . 157 XV ill. 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 OF A GIVEN VOICE IN MELODIC DEVEL- OPMENT, .... 195 XXIV. THE FIVE-VOICED MOVEMENT, .202 XXV. THE Six, SEVEN AND EIGHT-VOICED Movmoarr, - . 206 XXVI. ON THE Musi.'AL FORMS OF CLOSE, . . . . 218 INDEX OF SUBJECT*, ........, . Hfl JUST PUBLISHED! IN CONFECTION WITH THIS WORK: ADDITIONAL EXERCISES BY ALFRED RICHTER Price, 5O cents net. INTRODUCTION. 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. The relation in which one tone stands to another, in respect to difference 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. REMARK. By diatonic degrees is 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 degrtu . --*sr- is-- The numbers of the degrees produced thus, will be expressed in the following manner : :a - -^ * * T!Urd. Fourth. Fifth. Ste & 14 MANUAL OF HARMONY. As a rule, we reckon only to the octave, and begin the series aerain with the tones which lie above, and so on with each new octave, so .nat the ninth degree becomes a second, the tenth a third, the eleventh a, fourth, and so on ; just sc the fifteenth becomes the octave, the sixteenth the tecond again. Reasons, however, which find their explanation in the principles of harmony and theory in general, give now and then occasion for designat- ing tones which lie above the octave, according to the actual number of the degrees. The series of intervals from the octave upwards will, there- fore, receive the following double designation : Octant. Ninth. Tenth. Eleventh. Twelfth. Thirteenth. Fourteenth. Fifteenth. Second. Third. Fourth. Fifth. Sixth. Seventh. Octant. Greater distances between two tones, are simply reduced to their rel tion in the lower octave. More Particular Determination of the Intervals. It is easy to see that the above presentation of the intervals, is based upon the diatonic major scale of C, and that the relations of the tones which lie between are not affected thereby. In like manner, they are re- garded throughout, as based upon the first tone of the diatonic scale, whereas, it is conceivable that any tone of the scale can be taken at pleas- ure as lower tone, whereby the numbers of the degrees would be altered, and at the same time, small differences in the degrees themselves appear, In order to gain a clear view of the matter, in the midst of these mani fold variations, it will be well to note carefully the following principles : The series of intervals shoivn above, in which the lowest tone is first tone of the major scale, which forms the series itself, serves as foundation for all determinations of intervals. These intervals are called MAJORI some of them PERFECT. Every chromatic alteration of these tones, of the upper tone as well as of the lower, not changing the number of the degrees, consequently does not aVer their designation, but only renders a more particular determination of them necessary. Thus, for example, if to the fifth 3 C a sharp is in any way attached, it remains always & fifth, but requires, however, a more particular determina- MANUAL OF HARMONY. lt fcion, since it has evidently become a different fifth from what it was oi*- inally. Or, Since now such alterations of the intervals take place through chromati- cally raising or lowering them, the following various and more definitely determinative designations are made use of: 1. Seconds, thirds, sixths, sevenths and ninths, which result from the major scale, taking its first tone ior lower tone, are called MAJOR; primes, fourths, fifths and octaves PERFECT. 2. If the upper tone of the major intervals be lowered a small half-step, minor intervals result. 3. If the upper tone of [most] major and perfect intervals be raised, a small half-step, augmented intervals result. 4. If the lower tone of most perfect and minor intervals be raised a half-step, diminished intervals result. To 1. Perfect Major Major Perfect Perfect Major Major Perfect Major '-^'^^^ <-^~ r^~ -rr- T^~ T^ ^^- -^^ ^^ Prime. Second. Third. Fourth. Fifth. SiastA. Seventh. Octave. Ninth. To 2. Minor Minor Minor Minor \J c fe^ ? , |7^p v? v\y 1 J ' (fefr Second. To 3. A ugmented Third. Smth. Seventh. Ninih. Augmented * Augmented Augmented Augmented H) - Prime. To 4. Diminished Second. Fourth. Fifth. Sixth. Diminished Diminished Diminished Diminished f- jjfe- ^ Third. Fourth. Fifth. Sevenin. Octave. Augmented thirds, sevenths and ninths do r/>t occur in harmonic relation*. Aug mented octaves are to be regarded as augmented primes. 16 MANUAL OF HARMONY REMARK. Diminished primes, seconds, sixths and ninths, are harmonically inoon eeivable, although they can be conceived of in melodic relations, i. e^ in reference to progressing intervals, not to those which sound together. Remark on the Formation of the Diminished Intervals. The reason why, in the formation of the diminished intervals, the lower tont has beer raised, notwithstanding that a like interval would result, if the upper tone were low ered, lies in the peculiar relations of all the intervals in regard to their inversion, which will be spoken of farther on. General View and Classification of the Most Used Intervals, PKLMES. Perfect. Augmented. Major. SECONDS. Minor. A ugme nted. && TIIUIIW. FOURTHS. Major. Minor. Diminished. Perfect. Augmented. Diminished. i i~i : - -J-tt- ^=CT c:= en: ^* V if^a. V -** FIFTHS. SIXTHS. Perfect. Augmented. Diminished. Major. Minor. Augmented. in =m '=*m 3ii m SEVENTHS. OCTAVES. NINTHS. Major. Minor. Diminished. Perfect. Diminished. Major. Minor. Division of the Intervals into Consonances and Dissonances. If we speak in music of consonant and dissonant intervals, we un Jer- 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 etand 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 major and minor thirds and sixths. MANUAL OF HARMONY. n The first are called complete consonances, the 'ast incomplete Theduwtancn are the major and minor second, major and minor tfventh, and all augmented and diminished intervals. From this we derive the following general plan : I. CONSONANCES. a. Complete. The perfect prime, perfect fourth, perfect fifth and perfect octavt. 4 * b. Incomplete. The major and minor third, and the major and minor sixth. II. DISSONANCES. The augmented prime, the major, minor and augmented second, th diminished third, the augmented and diminished fourth, the augmented and diminished fifth, the augmented sixth, the major, minor and dim in iehed seventh, the diminished octave, and the major and minor ninth. Augmented J 3l4 c _ . u- : j_ -Z^c k^B. re Dimin. 5 ^u^. 6 r * y%k S-A^ *> Major. Minor. Dimin. ^ Dim in. 8 Major. Minor. 9 Later in the instruction in harmony, follows a farther explanation ?f ft* peculiar slations of ihe 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 determina the relation of two tones, taking the upper tone as tlie starting point, the intervals found are called intervals below. Thus, for examp'e, is d, the fifth from g ; g, however, from d the fifth below. It is easy to see that the interval cannot be al- tered by this. It becomes different, however, if the upper interval te 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 Intervals lelow : 8 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 : 1. All PERFECT intervals remain PERFECT in the inversion in th* octave. 2. All MAJOR intervals become MINOR, all MINOR MAJOR, the AUGMENTED DIMINISHED, and the DIMINISHED AUGMENTED. In the following table is exhibited a view of all the inversions : PRIMES. SECONDS. Perfect. Augmented. Major. Minor. Augmented. blTKETALS. _,_ ^~ '&. *~" OCTAVES. SEVENTHS. Perfect. Diminished. Minor. Major. Diminithed. I b 3 E z: * *- *^ == =J* MANUAL OF HARMONY. 19 Perfect. FOUBTHI. Augmented. Minor. SIXTHS. Major. Augmented. Perfect. Frrnw. AuymtnUd. FotTETHS. THIRM. Perfect. Diminished. Augmented. Minor. Major. Diminished. pu 1 "I J [ -j .. -<9 Major. SEVENTHS. Minor. Diminished. OCTATM. Perfect. Dimlnithed. en E=3l Minor. SECONDS. Major. Augmented. PEIMCS. Perfect. Augmented. EE=S^S^E^^ , -=F=:&^ r-f =f=*= An exact, certain knowledge of this essential inversion of the intervals 18 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- sions. Since the diminished intervals result from the augmented through the inversion in the octave, this formation comes of itself; for example, the augmented fourth fe^te^ miist of necessity give the following dim- inished fifth : =**= Just so the perfetf fourth belongs origiDally to the consonMiees, n 20 MANUAL OF HARMONY by inversion 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 btadies, the practice of them in writing, as als an oral solution of given intervals, will facilitate much their correct com- which exer'>ms w U> be repeatedly employed. HARMONY. COMBINATIONS of simultaneous tones, formed from different interval^ according to certain fundamental principles, are called in geneial, Harmo- nies, 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. PART I. .HE FUNDAMENTAL HAKMONTE8 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 aa 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 harmonieg, from wbich 11 remaiing chords are derived. CHAPTER I. The Triads of tfie Major Scale. A triad is formed by a combination of three different tones. Of tbese, ?ie lowest is calkd fundamental tone, to which its third and fifth dded, e. g> 22 MANUAL OF HARMONY. These triads, formed upon c, g and a, present, however, a difference as U their intervals* While the triads of c and g are formed here by majoi thirds and perfect fifths, the triad of a contains a minor third and. perfeci fifth. A trad with major third and perfect fifth is called a MAJOR TRIAD. A triad with minor third and perfect fifth a MINOR TRIAD. REMAKE. 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 K.ey. The triad which rests upon the first step of a key, is indeed the moat important, the one which determines the key ; there stand, however, others in the nearest connection with it, which make clear its position. In the natural presentation of the triad in thirds, the lowest tone shows itself as fundamental, the fifth as highest tone, and at the same time as ts 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 P. The connection of these three chords can be most plainly presented in the following manner : 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 fornn tho fundamental features of the key, and that they are, and must MANUAL OF HARMONY. 23 be those most frequently employed in practice, if the key is to p: went itself clear and distinct. . On account of their importance also, especial names have been given to them. The one first found, standing upoil the first degree of the scale, u 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 they present themselves to us thus : i iv v and they show themselves collectively, as major triads Application of tlte Harmonies Discovered. In the application of these three, as well as of later chords, we trail ourselves of the four-voiced manner of writing. REMARK -The theoretical chord combination can be well presented to be sure,thr~ manifold relation. It would, however, detain us longer from ov position. . . We regard, however, each harmony not as a mere mass, as for the pfano-forte often present them, but dirid. . component par Mid the triad may be exhibited thus: 5. 8-DPEANO. ALTC. TKKOB. 24 MANUAL OF HARMONY. For the upper three voices especial clefs are used, which confoi m bettes to their compass than the above used violin [G-] clef, and which will b 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. BOPBANO. ALTO. TKJ.OE, BASS. 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 well-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 pur harmonic structure is the judgment sharpened, the sense for the tn and correct formed, and the taste purified. REMARK. Inasmuch as every composition should exhibit ieelt through a correc nse of all means at command and the purity resulting therefrom, (purity is here syuony nous "with natural expression), the term pure harmonic structure in a general sense would require no farther explanation, as being a matter of cuiii se. In a more narrow eense, hoverer, under pure harmonic structure we understand something farther, which is more nearly and better indicated by the expression of like meaning, strict harmonit structure, strict style, since this can be used in distinction to free style, whereas, properly speaking, no antithesis of the pure structure, such as, perljaps, impure structure, is to be assumed, since, as frequently as the latter in fact may occur, it were certainly to b* designated us false, while the free structure might be essentially founded upon the Ugiti mete of the pure structure. As was indicated above, bv rure \arionic structured understood in a narrower sens* MANUAL OF HARMONY. 24 *acu one as tit the natural development of all tone relati ont, allmei ihe fere* dijreuumt from the legitimate, and only tuch as do not touch that which it esuntia^ fundamental. If, in what precedes, the idea of pure harmonic structure is determined in geuers, way, still its boundaries are not yet drawn ; and just this is a point which gives r'se to th more difficulties for the beginner, as the boundaries are so very variously determined oj the theorists themselves. This difficulty has occasioned many of them, especially BOOM 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 iu inci dents. Whether this indulgence to youthful impatience, which does not willingly busy itself with the abstract, this inclination towards premature living creation, before th 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 basic conformed to nature. The real mastery has >ver 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-voifl. movement, will give occasion for remarks and observations, from whicl certain fundamental features and rules are to be established. Since the triads only contain three tones, one component part (interval) thereof, must be doubled, if they are to be used in four-voiced writing. Any Interval of the Triad can be Doubled. The fundamental, however, usually presents itself as the tone mo* adapted for doubling, more rarely the fifth and third, and, indeed, ** latter, in many cases which will be shown later, is not to be doubler In order to accomplish the connection of two triads, the following n is to be observed : If a tone occurs in loth of two chords which are to be conntdeJ, H u to be retained IN THE SAME VOICE, e. g. 26 MANUAL OF HARMON T. In the Example a f G occurs in both triads as common tone ; the Sopiano which gave the first C, retains it also as fifth of the next chord. Just se in Example b f in which the Gr of the Alto affects the connection. The remaining voices proceed to the tones which lie nearest to them, ae at a the Alto from G to A, the Tenor from E to F, &c. If in two chords no common tone appears, the voices are independently led in such a manner, that none appears with any other in PARALLEL riFTHS or OCTAVES. In order to explain this faulty progression more exactly, we must firs) make the necessary explanation of the movement of the voices in refer ence to each other. The Relation of tlie Movement of tlie Voices in Respect It. each otJier. 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. j They progress in contrary motion if the one rises and the other falls, e g I The oblique motion arises, if, of two voices one remains upon the same tone while the other moves on, e. g. MANUAL OF HARKON1. yj These three kinds of movement of the voices occur in chord connection in zmixed manner. Thus, in Example No. 7, b, the parallel motion show* 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 m parallel octavn and fifths, can only appear in parallel motion : if, for example, two voices progress by degrees or skips in the following manner : This fault is regarded as such for. all voices. The following connections of harmony contain both fault* ' 12. In Example a, are parallel octave skips between Soprano and Bass; in Example b, octave progressions between Alto and Bass, and in Example C f between Tenor and Bass. Parallel fifths are to be found in a, between Alto and Bass ; in b, 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 oblique movement of tht voices ; that is, the voice which already forms an octave or fifth with another, must either move with it in contrary mition, 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, a the oblique motion in respect to one voice, and at b and C 9 the contrary motion of all voices in respect to the Bass, u to b applied, . g. 13. 28 MANUAL OF HARMONY. REMARK. The reason for the prohibition of octaves, with whi>;h is con ected that a 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 unti now, much pains has been taken to express it clearly and definitely. On this point, let Me followiug 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. The sevenths, however, neither form, properly, new chords, nor do they lie, (according to the idea of a seventh), outaide of the circle of the original chord, and only serve to indi- eate the relations of two chords, and to make the connections of the harmonies mor 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 withcut con- nection, e. g. 15. As concerns ths diminished fifth, however, which in the dominant hord ol th eventh 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 p*rfecrf MANUAL OF HARMONY. 29 fifth, leaving cat 01 the account its farther laws of progression, the latter imm*rUly iteps 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 competition* ti the stricter style : 17. we may assume that the doubling of the diminished fifth (the/,) requires a double pr greasion of the same, and that the fifth-succession is thereby justified, because it lies in the middle voices ; that, however, the following progression could not be called paw, 18. partly because they come forward too prominently in the upper voice -partly bMM. the above condition of the necessary double progression is wanting, although such as No. 16. c. are often to be heard. Hereby it becomes clear, also, why such parallel fifths as arise from JJ* in many cases do not sound so unpleasant as those spoken of above, fo many theorists recognize them as faultless ; which, at any rate, eannd D ., 0. -. here, to b. mueh to M ; on mmy point, ; for "P'* <> exercises. 30 MANUAL OF ffAKMO\'f. If the sense of the foregoing representation should still be too obscure to the beghv ner, yet with more advanced knowledge, and exercises, and necessary frequent repetition! 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 a, fifth or octave, e. g. 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. REMARK. 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 01 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 : 1. 2. ao. fe C: I V 1 IV V I '8* 4. RF.MARK. These, 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 are to be added, will yet give us occasion for important remarks. * The fi-ruve over the Bass-note indicates the proper interval for the Soprano of MANUAL OF HARMONY. 31 We have 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 oosition 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. r & ~i g r g := F g := F = F 9^^ The first position of the chord (i is in 6 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 open (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. ~c~ i al&u with those found before, no new rule is at present necessary. Several things which are new will, however, appear in connection with it. The Bass can move either by skips or by 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 contrary mo'ion, 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 33. MANUAL OF HARMONY. a. The Bass progresses by skips. 3t> ft. NB. ItiUr. 30 1 ^^^o ' 1 *~^~~G~~ ii IV 1111=1111131111111 ii V As in this example, the skips in the Bass from the second degree hav been treated, the same can be treated beginning from all other degrees, so that tones common to the two 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. REMARK. The reason, however, why exactly this tone should be conceived as double, iiuce this cjuld also be the case with any tone at pleasure, is founded upon the fact that it is the 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 mori noticeable if it is contained in the outer voices, as in Example 32 at a* 32. 36 MANUAL OF HARMON7. By the contrary motion of the Bass at b, the leading of the voioei can be improved ; in like manner, by the contrary motion in Example c t although here also a covered fifth shows itself between Soprano and Tenor (See the Remark on Example 34). REMARK. In the cases brought forward above, we do not speak of absolute fault* I; 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 cantus firmus, of a motive, or on other grounds important for the composition, is unavoidable. Th improvement is here only presented from a theoretical stand-point. Concerning the covered fifth in No. 32 c, a farther explanation follows at No. 84. The unpleasantness of the covered octaves spoken of ceases at once if (fa upper voice progresses a HALF STEP, e g. 33. to. The Bass progresses by degrees. Here the contrary motion should always be applied, e. g. NB. i. better : 84. ui IV IV V V IV ii 1 MANUAL OF HARMONY. 87 Remarks on these Chord-connection8 In all progressions of voices such as that used at NB. 1, aud subsequen. similar places, it is better to double the third of the second chord, in ordef to avoid covered fifths. Their unpleasantness is more noticeable if the chords appear in open position, e. g. 35. The leading of the voices at 6 is to be preferred. If these covered fifths occur in the middle voices, they are moru allow* able, because they are less perceptible. 36. 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 tone, a fuller discussion will be given in connection with the following exercises ' Exercises to be Worked Out. 1. EEE^E^ffi^Si spz (Sirr T iz^zr .TT^I^J: rzm: ' xz^rs:i: t 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 meloiie p/ogression is called Sequence. 88 MANUAL OF HARMONY. This consequent progression of the Bass, occasions also a like regula. leading of the remaining voices. The treatment of this example, according to principles of chord-con noction laid down above, by sustained tones, e. g., 38. 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 ia brought into the same position which that of the first measure occupied, whereby the connecting tone D, does not remain in the same voice. 39. =g|E||E III VII In the first example, on accottnt 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 Nu 4, we meet with a chord, which thus far we have not used. The Diminished Triad 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), 01 the upper or lower tone progresses alone over against the other, (b, c), a kind of progression which only becomes plain through actual chord-con- ection. 40. if. --5 -- r-G I I ^F -- r -- "~FC s,-^ -.G..G) e^^G _f^cffl_ ;- O -^,& - It ~~ T" - - __ t __ t ___ *~~^-a_ nztj e. Inversion, MANUAL OF HAhMONT 39 The third following the diminished triad (d), exhibits the tiiad of the first degree (C) as incomplete, by omission of the fifth. Since, acjording 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 e. The fundamental tone upon which the diminished triad rests, is called LEADING TONE. Jt is found again as third in the dominant triad, and as fifth in the triad of the third degree. 41. rfF\ & 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 efiected, 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 he scale. This is noticeable particularly in the case of the dominant riad, if the leading tone is contained in tbj upper voice, as a in Example i2, operates more satisfyingly, than 6 and c. 42. This inclination upwards shows itself less in the middle voices, as at (?. Most intolerable in many oases, in such chord-connections, are skips in the 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 Formation 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 oer in the last examples. 40 MANUAL OF HARMONY. As the natural relation of the chord of the dominant to tne 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. ^a 1-4=;; r ' ^=1 ^ n v I n V I Besides the triad of the second degree, the triad of the sub-dominant is also adapted for this formation of the close, e. g. 44. F IV The dosing formulas (cadences) produced by this chord-connection, will assume more definite form through the application of the chords to be shown later. CHAPTER II. The Triads of the Minor Scale. a. Primary Triads. THE primary triads of the major scale were found upon the first, fourth and fifth degrees. Upon the same degrees we find also the primary triad* of the minor scale. The relation, however, in which the dominant triad stands to the touic 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 scale 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 acquires the character of a leading tone, e. g. MANUAL OF HARMONY. ^ 41 r >, e-S- 15. NB. i By this means the formation of the dominant triad in minor, becomci exactly like that in major, thus : "^1 minor. 46. ^L, A major. A: V A: V cr 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, 4?. 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. In A minor. 4. i p I ip I The three primary triads in minor can be thus exhilited in their natura relation according to previous explanation 49. := _ 42 MANUAL OF HARMONY. Hie minor scale, as it forms the basis for the formation of harmonta will therefore b * the following : 1 i 11 111 i R KM ARK. All other forms of the minor scale, such as : depend upon melodic conditions, which do not allow the step of an auginei. \t I setona from the sixth to the seventh degree, found in No. 50. These forms have no influence upon the harmonic formation in itself considered ; tb harmonic foundation, however, has a reflex influence upon the minor scale itself, as th following examples show t 53. -. h.- -. _ cc Tlie Inst case, in which the descending scale even exhibits the step of an augmented second B-A b, which in future, in chord-conneotions we shall carefully avoid, explains itself thereby, that B was necessary as component part of the chord, A|j, 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) it already perfectly secured through the minor third, Eb. I). The Triads of the Remaining Degrees of the Minor Scale. SECONDARY TRIADS. After the establishment of the minor scale, the secondary triads appe in the following form : 54. Ev VI vn 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. l>. c, it. e, f. _i _- 1-44 t-w -*, 1-44 t-ti ^ tu ft -59 & f-S5* I 59 I 39 & 1 $0 * 1 S<9 & II- -s e t- _ r_s _ t_z_g:_i:ia2_5:=3:_#g-- .,_: 55. --ja=: a: t a- t_a__t_a ^ 1 1 _ 1 11 iv V VI va<> 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. 56. __ _ * i ~ __ i _ ___ q * _'g~"g I g i?r~ 1 g~ I _ q g ~~ H ^^^" VI Its introduction is most tolerable, if the augmented fifth is 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, an well of the major as of the minor scale, so that this harmony, even when it appears imply 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, ^hich 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). MANUAL OF EARMONJ Application. The principles of the connection of harmonies an I leading of th voices, already developed, will also have application here, and particularl in the connection of the fundamental chords in minor, what was saic 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 57. V VI VI V Henoe, in the often recurring connection of the chords of the fifth and sixth degrees, the progression of the leading tone will be necessarily alwaya upwards, whereby, in the triad of the sixth degree the third appear doubled, e. g. fe 58. &c. VI VI VI VI VI Thus, it would not be possible to exhibit in a correct form the example given under No. 57 b, unless we make use of a mediating tone, such as, for example : 59. REMARK. The practice deviates, in certain and especial cases, from this ruJa. oe well, however w> 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 t/it vraeti?' is and should be only a will founded exception, whereas the observance of tb rule can DC instanced in numberless cases. MANUAL OP HARMONY 4b Exercises in connecting the Triads of the Minor Scale, 1. 2. 30. Memarfcs on these Exercises. A chromatic sign over a Bass note without a figure, as, for example, in the third muasure of the first exercise, refers always to the third of the Bass. This raiding 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 8 t by 3, 5, 8, or or in full, by 5 3 One reason fbv indicating it by 5, is fomnd in the third and sixth exer- cises. Here the introduction of the triad of the third degree in minor bas 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 feature hitherto developed. We select for this purpose the first exercise. NB. 61 The first principle of the connection of chords (by connection of tones ic the same voice), is here everywhere observed, and for this reason ilf MANUAL OF HARMONY. Alto, in the third measure (at NB.), makes the faulty step of an augmented second from F to GJJ. 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. (a connection of chords, which has already been explained in No. 81 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 tha G$, the Alto from F to E, whereby the close position is forsaken, and this and the following harmony appear in open position : 63. f\* 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 : Vieiv of all Triads of the Major and Minor Scales. Major. i n III' iv V VI in Major: -k Major triads are found in Minor: IV V 7 Ti MANUAL OF HARMONY. 47 In Major : in 3tin rr ; Minor triads Diminished triads Augmented triad II III Yl in Major : in Minor : Ill' CHAPTER III, The Inversions of the Triads. The Chord of the Sixth, the Chord of the Sixth and Fourth. The appplication of the triads, and indeed of all fundamental chords, it 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 third or fifth ol the fundamental chord. Hereby arise transformations of the fundamental chords, which are called INVERSIONS of the chord. REMARK. It should be well remarked, that only transpositions of the Bass to another interval are here spoken of, and that the before mentioned transpositions of the other "oices into close and open position, and to various intervals, by no means essentially altn the chord.* Two of the inversions are possible with the triad : a. If the Bass receives the third of the triad, there arises the cHOXt or THE SIXTH. Fundamental chwd. Chord of Vie sixth. C5. Third of the fundamental chord. * Tlte word is here used in ite general, not its technical sense, En. 48 MANUAL OF HARMONY, b. If the Bass receives the fifth of the triad, there arises the OHORB OF THE SIXTH AND FOURTH. fundamental Chord chord. of th sixth and fourth. " 9r Fifth of tht fundamental chord. The chord of the sixth is indicated by 6 over the Bass rote, that of the rt sixth and fourth, by 4 ; e. g. 67 o c o 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 chorda of the tsixth 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 first degree, since, in fact, these are no newly formed chords, but only chords brought into another position by the Bass, and therefore deri.ved chords. Every triad can appear in such inversions. Application. By the use of the inversions of the chords, not only does the leading of 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 chord, and the doubling of the Bass tone in the chord of tin 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. 48 The chord of the sixth can therefore occur in the following forms : 6. -* F ^ F P-g f & FF &C. i^|;E=illIllilliilli! \ The use of the chord of the sixth and fourth is more rare than wmt oi the chord of the sixth, and requires certain conditions which shall *, men- tioned later. We meet it oftenest in the formations of the close. Th Bass tone, the fifth of the original chord, is best adapted for doubling, and the chord will appear in the following and similar forms : 69. 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. :?~t=?=E=:^EE=: =t===t=i3 1 ___ __ 70. Exercises. __!_ 6_ 6 6 Y'ts. :=i ^ T ^ -T g = F1 |_i=z=^zii=- (i tf> si r f I (2 t I g h d >5l + 4 ^ 6 4 3 : ^ L__^ g _lt__" O 6 ^ G _4 4-36 50 6 6 MANUAL OF HARMON7. 6 6 9 9- 3 6 6_ ft 6 b f 10. 6 JET 41 -9- Remarks 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 th 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 tone, 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 * 6 66 v 1 ^r ^ r - s> a 1 e> ( f wid the progression of the remaining voices thus J^-fc ^d^r^-^=d=ir^=iipi=; ra. MANUAL OF HARMONY. 61 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, pag 88. We see, in the first example and others, B and F of the Soprano an Alto progress to C and G-. I "Jhe similarity of this chord, in sound, to the dominant chord of the snjith to be shown later, often induces beginners to lead the diminished fifth dwrnwards, even if it has converted itself by inversion into the aug- mented fourth ; this, as the above examples show, is necessary only in caoe i*. re&Jly lies above the fundamental as diminished fifth, and a progression * f thx following sort : 74. is faulty on account of the parallel fifths. REMARK. It may yet be remarked here, that parallel fifths, of which the one fifth ii diminished and the other perfect, are to be allowed if the diminished follmet the per fret fifth, but not vice versa, e. g. good. good. not good. ~^ E* p "S^G O jr- rp Oompei e 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 : not pure. 96. I = g F & F " ' ~ I 9 h & 52 MANUAL OF HARMONY. better : not : r " r ^- p r ~~^-' & r~ C a f- m-X 1- ts-"^ F ; ^jB-S__I. ^^ " i "* ^^ JQ JQ n ^ Q7 -Qf &* I i I ~ TIl II and uthen, 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 moving in contrary motion to the Bass, e. g. 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 iroies, e. y Covered octaves, as in the 2d and 3d measures between Tenor and re not to be avoided in such cases. It can be deduced from this, that io SINGLE progressions of the voices which are contrary to ride, that especial importance is not to be attached, IN OPPOSITION TO THE CONSEQUENCE OF THE WHOLE, which otherwise belongs to them, since the construction of th* MANUAL Of HARMONY. 58 details, although it must be as perfect as possible, will always be st.. -)rdi- aate to that of the whole. REMARK. It is not to be ignored, that the principle laid down above can easily h misunderstood by the beginner; however, the laying down of the principle was not t 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 TJiorough-Bass 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 5 instead of which, however, a J or t is often set after the figure (e. g., 6# or 6J, 513.) Other figures will find their explanation later in connection with the chorda which they concern. Formation of the Close through the 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. C: I The chord of the sixth and fourth is frequently preceded by the triad fche fourth or second degree. C; IV 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, ju.st so weak is the effect of its entrance under other relations, so that iU proper use is subject to certain conditions, which will be treated of later. CHAPTER IV. Harmonies of the Seventh ( Vierklange), ' 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 o/ sevenths will afford manifold harmonies of the seventh. The General Properties of the Chords of the Seventh. The chords of the seventh are 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. TJie Dominant Chord of the Seventh in Major and Minor. The chord of the seventh which is most important, and occurs oftenesi 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, from ihe major triad and tvmth. MANUAL OF HARMONY. 55 In the fundamental position it is marked by a 7 over the Bass note, and in our method of notation, indicated by V? 83. L= z=^= a C 0: V G: V, The relation in which the triad of the dominant stands to the tonic 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 close : 84. C: V- A: V- REMARK. It is to be remarked here, that the triad following the chord of the seventh b incomplete ; in both cases the fifth of the triad is wanting. The reason of this will appear from what follows. The striving after a point of rest, inherent in these chords, and the resnltiug 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 reydar resolution of the iorninant chord of the seventh especially. The seventh, as the essential interval of the chord, is, by its relation to ihe fundamental, confined to a definite progression. If the progression of he Bass, which contains the fundamental, is regarded as given, an upward rogression of the seventh will appear impossible : 66 MANUAL OF HARMONY. tven if, as at b, a third voice is added ; whereas its downward affords full satisfaction : 86. feL_g_- Since tka progression of the fundamental by an upward step of a fourth or downward step of a fifth is already determined, the progression of the third and fifth of the caord of the seventh remains to be considered. The third of the dominant chord of the seventh is always the leading tone of the scale ; its natural direction is therefore determined by wliat has been said before concerning the leading tone, (page 39) ; its progression will follow a half-step upwards, and 6 will, therefore, not appear so nat- ural as ct '. 87. In the Example 87, &, the third, is given to the upper voice, which ren- der the unpleasantness of its progression quite perceptible. This leading becomes tolerable if the third is found in a middle voice, *. g. 88. ff /a ^. This downward leading of the third (leading tone) is therefore to b applied under the following conditions : St. If it does not lie in the upper, but in a middle voice, e. g. seldom practicable. 89. MANUAL OF HARMONY. 7 b. If the Bass progresses in contrary motion, e. g. b. not: 90. The reason of the second rule becomes evident, if we observe the cov- ered fifths in the last Example b, between Alto and Bass. The leading of the fifth of the chord of the seventh is free. While, for the most part, it is crowded a degree downwards by the seventh, reasons may exist connected with the leading of the voices, for allowing it to pro- gress a degree upwards, as Example 88 b shows, where the D of the So- prano is lead to the E. If we condense these remarks, we find the following rules for the regu- lar resolution of the chord of the seventh, and for the closing cadence in particular : The seventh progresses a diatonic degree downwards, while The fundamental makes a skip of a fourth upwards or a fifth down wards ; Just so the third is led a degree upwards toward the seventh, while The fifth can be led by degrees, upward or downward. REMARK. By the progression of the third towards the seventh, we are reminded of what was said of the fundamental and the diminished fifth in the diminished triad, (page 88). Both intervals are found again hi the dominant chord of the seventh. Applied tion. Except in the formation of the closes, the dominant chord of the seventh rs, in the middle of a piece, seldom employed in the usage thus far known to us, and, if it does take place, only in a position whereby the feeling of the complete close is not produced. , This takes place particularly in cases where the seventh of the chord lies in the upper voice, whereby the close becomes incomplete, or, if the dominant chord of the seventh falls upon the accented part of the measure (thesis), since in the complete close (cadence) the tonic triad must fal there. (See page 33). Besides this, the chord often appears incomplete through the miission of an interval. This interval, however, can only be the fifth, seldom tha third, while the omission of the fundamental or the seventh, would entirely alter the chord and reader it incapable of r cognition. 58 MANUAL OF HARMObY. b. e. rarely: d. 91. =Tz-=3ii?rrrz35=i=zgirc *z:3i^rzi-3 , a _ g_q z_s_l_ (S , -Z_5 g ' < T s g~ 3 g T < J g t g 1 t In (ff b, (If the fifth is omitted, in c, the third, and in each cas the fundamental doubled instead, which doubling affords, by means of the tone which is allowed to remain stationary, the closest connection with the following chord, and allows the tonic triad to appear again complete, which was not the case in the previous resolution. (See No. 84). We add the following remark upon the omission of an interval in the chord : Through the leading of the voices a chord can appear incomplete ; the omitted interval will, in most cases, be the fifth of the fundamental chord. Exercises. 92. gr-flp- T e-T P " T=P pT o __p-l g ^ 6 7 4 7 These exercises require no farther explanation. It has been already mentioned, that the chord of the seventh, in the position known to us now, MANUAL OF HARMONY. 59 is indicated by 7, also that the sharp found under it, or in general, all chromatic signs which occur without figures opposite to them, have refer ence to the third from the Bass tone. (See page 55.) CHAPTER V. The Inversions of tlie Chord of the Seventh. LIKE the triad, the chord of the seventh can be altered in such a man- ner, that the Bass receives an interval other than the fundamental. The first inversion arises, if the Bass receives the third of the funda- mental ; The second, if the fifth of the fundamental chord lies in the Ba, and The third, if the original seventh is given to the lower voice. In close position the inversions present themselves thus : A comparison of these inversions of the chord of the seventh, with those of the triad, shows plainly their analogous position : 94. 6 4/4P 6 4/4 (22) 33 ' ^1=1=^1=1=! ^7 G 7 G 7 < These derived chords receive their designation from the position ol theii intervals : The first inversion is called the chord of the sixth and fifth. The second : the chord of the sixth, fourth, and third, or briefly, '.hord of the fourth and third. The third : the chord of the sixth, fourth, and second, or briefly, chord of the second. Their designation in the Thorough-Bass notation is to be seen above, in Example 94. 50 MANUAL OF HARMOfrT It needs only to be remembered here, that in these inversi ns, just u before in the inversions of the triad, only the position of the Bass or of the lowest voice is essential, and that the remaining intervals can be vari ously distributed among the upper voices, e. g. 05. *y= ^^ - """& + & & (^ - ' ' T* ' J -I 4 3 3 &c. 2 2 The regular progression (resolution) of these derived chords is founded upon that of the fundamental chord. If, in its case, the dissonance, the seventh, conditioned the progression in cne direction, the tendency to the same progression (resolution), will also exvs* in the case of the derived chords, in which the two tones, the fundamental and the seventh, eithei appear again, or become seconds by nverson. 96. fc=, " T K, r F^gg 1=^ F-g t- fj 1 Progression of the Chord of the Sixth and Fifth. Since the original seventh shows itself likewise, over against the Base tone in the chord of the sixth and fifth, as dissonance, as diminished Jifth, the progression of which was discussed above, (page 38), 97. i the resolution of the chord of the sixth and fifth will naturally take place thus : 1 MANUAL OF HARMONY, 61 The progression of the fundamental, as before given, does not appeal here, since the G of the upper voice is sustained and transforms itself into the fifth. This is, however, only apparent, for that it forms the foundation of this connection of harmony, the marking below Gj C, of Example 98 proves. That however, the Soprano, or a middle voice, cannot in notes carry out the progression of the fundamental in such cases,, lies, beside other reasons, immediately in the character of these voices, which is to be foumj more in mediation and connection of the harmonies, than in laying theif foundation, which belongs to the Bass. REMARK. Deviating progressions of the fundamental in these cases, such as a freer leading of the voices in certain relations would give, are not hereby excluded, only there must be an inner connection of the chords. Progression of the Chord of the SixtJt, Fourth, and Third. We find again here, beside the seventh and its inversion, the diminished fifth or its inversion, the augmented fourth : . _ G 99. = The resolution of this chord follows thus : a. b. J2 -ZZ** a Z'' f + SI=^^2:=r:| feS^KZ 100. 2- * C 6 7 C The Bass, the original fifth, can progress in both of the given ways. Progression of the Chord of the Second. This chord has the peculiarity, that the original dissonant intervals, the seventh and the diminished fifth, can only occur in their inversions, as second below, and augmented fourth below. The progression of this chord is as follows : Thus the resolution of the chord of the second is effected here thiough the chord of the sixth. We can perceive in these resolutions, that they are all based upon the natural progression of the dominant chord of the seventh, which before 62 MANUAL OF HARMONY. was called cadence, for we find everywhere the same marking of the funda- mental &7 C or VY I. These resolutions will, therefore, themselves form cadences, only not o. BO complete a sort as those mentioned above, and as those are called perfect cadences, so these are designated by the name, imperfect cadences. View of the Natural Progression of all Inversions of the Dom- inant Chord of the Seventh in various positions, a. The Chord of the Sixth and Fifth. 102. : EEEEEEE^E; & -s-pg p zdFJEscz ^ -g jf & \ i-g-^ i^f? g-ji ^-3 F- g ^P :g b. The Chord of the Sixth, Fourth, and Third. MANUAL OF HARMONY. C. The Chord of the Second. - -- 1*1. -- .. - A* -- Lis^t_ (9 _ L^s=J -g I 8 6 6 2 6 2^6 \^&- 2 6 6^ C Exercises in tJie Use of these Chords. 6 6 5 66326 47 103. J-t dtt EEfESEfE^ =i=t-Mz:^= 4 6 2. 3 36 66 6 87 o^ ~T" T T c g T I I T i T IT 5 32 63 6 4 7 ,3 T & 4 6 26 36 43 6 J .22-- 6 81 -& = =g= j===ff 5. 3 87 6 6 26 67 4} f 3 6 67 41 6 f f 6 3 67 4J OBSERVATION. The marking 8 7 in the next to the last measure of the second, fourth, and fifth Examples, denotes that the seventh should nr.t appear with the chord itself, but follow after the octave. 54 MANUAL OF HARMONJ CHAPTER VI. Secondary Harmonies of the Seventh. WHILE in the case of the triads, three primary chords are requisite u> establish the key, (the relation to the tonic triad as central point), there is needed in the case of the chords of the seventh, only one primary chord, the dominant chord of the seventh, the content of which alone already enders the key certain, and the natural progression of which to the tunic triad represents the key. REMARK. The manifest fact, that the seventh of the dominant chord of the seventn is at the same time fundamental of the subdominant triad, renders the relation of the two tones G and F, (as fundamentals of the dominant triads), to their common centre, C, (as tonic triad), already entirely clear. (See above, page 22, 3). Beside this dominant chord of the seventh, also called primary* or essential chord of the seventh, harmonies of the seventh can be formed from the remaining triads in major and minor, the relation of which to a definite key is indeed undeniable, but by no means so decided as in the case of the primary chord. They are called SECONDARY CHORDS OF THE SEVENTH. They are to be formed, simply by the addition of a seventh of the fun- iamental to the triads : a. I* Major: *p * ^ * -K *p ^ ^ ^ ^J ^5 i^l .5 ^ s S /J) ^ ' "7 IH^ IV j T1 7 TUy 6. In Minor: NB. NB. ~^ ~ ~IT = =ig:=g:= =: =g=== ' ~ "We come here to chord formations, which, in part, without connection with other chords, sound very harsh, and, for this reason, foreign, because, as was already remarked above, their relation to a fundamental key is not so decided and clear as that of the dominant chord of the seventh. Their use will, therefore, be in part more rare, but not the less adapted for im- parting variety and especial coloring to the harmonic succession. Among these secondary chords of the seventh, the following kinds may be distinguished : MANUAL OF HARMONY. *n Major : in Minor'. a. Major triads with major -*. X~ ^ : % seventh. ' & c: fj iv 7 A: vi^ NB. Major triads with minor seventh always form dominant chordt of the seventh. b. Minor triad with in Minor: major seventh. SS^:! 51 -" :: not U8et * as fundamental harmony. in Major : in Minor: C. Minor triads with minor seventh. d. Diminished triads with minor seventh. C: vn 7 A: u 7 _ tn Minor : _O ^ C. Diminished triad with diminished seventh. at^Zugrz A: vn- The augmented triad with major seventh, f A: III is it is found upon the third degree in minor, is, to be sure, not useless, but from reasons before developed in the case of the augmented triad, is very seldom used, and ambiguous. REMARK. We find this chord again, with another foundation, in Chapter X. Application of the Secondary Chords of the Seventh in Major. The seventh or its inversion, tba second, may be major, minor, dimin- ished, or (which concerns the second only) augmented; it will always in its relation to the fundamental press as dissonance to a progression. This natural progression is, with the secondary chords of the seventh, no other than that already found in case of the dominant chord of th seventh, viz., one degree downwards toward the fundamental, if the latter moves by fifths or fourths, downward or upward. If accordingly the progression of the principal intervals of the chord It ound, 106. tte====ZE~C===L -& [ i"*"- Tr 6. q/ 1 to second dt F 5 p 9 F I-* 1 "* -^ ~ ISHS r >"g= T^ g- J 9t __rzBe___j. .. Q=t-- f6> __g 1 O: n 7 V ^ not: without fifth : I ~~ ^| g -P gg=| I^ElUggl^^i 11 o<: rv~ T o r~ "izii^zzii: j^ g 9- 6> 4 = F -g-f t-^F =z===: _i ti= zi^z- e. of the third degree : without fifth : g - <5-f-6> n d. of the fourth degree (seldom with this resolution). *+ ^w. -- - .-g, -jzzgiiij gi i :=:: F~ '] g: r ?o< good: - not ; without fifth : =E^z =f 6H-T ==tz 68 MANUAL OF HARMONY. e. of tkt tint.' dtgree. pzigiscia :=3sc : =53_: r g p-g r e | -p-g>- J tr riza~^;' ^n : a ^L~^ii REMARK. The above found progressions of all chords of the seventh are neither in their positions exhaustive, nor have they been exhibited as the only possible ones. The difficulty of forming such progressions lies only in the frequently occurring covered fifths and octaves. All the remarks also, -which are added above, such as " not" " not good" which, for the most part, refer to the leading of the Bass, (inasmuch as this, with other necessary voice-progressions, produces these faults,) are, in many cases, only to be understood from a theoretical stand point, while such cases and similar ones in the practice, even in the so-called pure harmonic structure, must often be judged according to the principle before expressed, (pages 52 and 53). Since the theory has not yet succeeded in furnishing positive rules for all cases of th kind, the true and false, the admissible and inadmissible in this respect, can only be dis- tinguished by means of complete harmonic education and a really musically educated ear. More about this follows later. Concerning the especial Progression of the Chord of the Seventh of the seventh Degree. In the above found collection of the progressions of all chords of the eventh in major, under No. 110, that of the seventh degree, analogous with the others, has been led to the third degree, that is, the progression of the fundamental takes place, as with the other chords of the seventh, through a step of a fourth uy ward or a fifth downward. This progression is th MANUAL OF HARMONY 69 more unusual one, and is, for the most part, only used in a leading of the harmony according to a certain formula (sequence). That progression occurs oftenei, upon which the diminished triad, to which here the seventh is added, is based, (see page 38 and 50), viz., that to the tonic triad. . 111. C: vn vn The above Example shows plainly, that the relation of the diminished triad to the tonic triad is not altered by the addition of the seventh, but on the contrary, becomes more decided. It is likewise to be remarked, that, if the chord appears in the above position, the third of the following triad must be doubled, (see No. Ill 6), because otherwise, perfect fifths would arise ; (See No. 112 a), 112. j==g: =*= or a skip must be used, as at l) 9 a leading of the Tenor which is often found, and which, in spite of the covered octave, is very effective. It is peculiar to this chord, that only that position of it in which the seventh lies in the upper voice produces a satisfactory effect, while the other positions, if not impracticable, still appear less clear. 113. REMARK. Whether the reason of this is, that in the se\>enth with its above used progression, the character of the ninth lies, (as some theorists assert, that the dominan chord of thv seventh, with added ninth, is the basis of this chord -with its resolution), which, th ugh similar to that of the seventh, is still much mr re comprehensive, and does not I jar the situation in the middle, cannot here bs further .avestigated. 70 MANUAL OF HARMONY. The JFreer Treatment of the Third and Fifth in the Chord oj tlie Seventh. Various progressions of these intervals have already been used in tht previous connections of chords. The fifth goes upwards and downwards, the third likewise, sometimes goes a degree upwards, and sometimes makea a skip of a third downwards. This all took place principally in reference to, and in avoidance of, covered fifths and octaves. Where these faulty progressions do not interfere, the third especially, can make still other steps, by means of which the leading of the voices often becomes more independent and freer, e. g. 114. That this leading is also possible in the middle voices, if the position admits of it, is shown at C The leading of the Soprano at & is not good, because a skip of an augmented fourth occurs in consequence. The skip from the fourth to the seventh degree, (F-B), is called the Triton US, because it contains three whole steps. More of this sub- sequently. A different leading of the fifth is possible only if the Bass at the same time deviates from the above progression, which is that of a fundamental ; as in general, still other leading of the voices will present itself, if we search out other than the chord-connections hitherto used. The Preparation of the Seventh. Thus far the progression of the chords of the seventh has been spoken of, but nothing has been said of their introduction The harsh effect of the entrance of many dissonances, and particularly wf most of the sevenths in the secondary chords of the seventh, renders necessary a careful introduction of them, which consists in their pre- paration. A tone is prepared, if it exists already in the foregoing chord IN ONB AND THE SAME VOICE, and as harmonic tone, so that it can be connected bj a tie. MANUAL OF HARMONY. 71 SucL preparation of a tone is contained already in the fivs< connections of chords pre7iously shown, e. g. 115. It can be said here, that C of the Soprano in the second chord is pre- pared hy the C of the first chord ; likewise the Gr of the Alto in the Example following. The necessity of the preparation of the sevenths, however, does not result alone from the harsh effect of their entrance if they are struck free, [enter unprepared], but particularly from the character of harmonic con- nection and binding of two consecutive chords, which is especially characteristic of the sevenths, and which, without the preparation, would not appear. The preparation of the seventh can now take place in the following manner : 116. In all these Examples, the tone which is connected by a tie with the fol- lowing like tone, forms the preparation of the seventh. In the formation of such preparation, the following rules are to bn bserved : a. The preparation takes place upon the unaccented part of iht measure (arsis) and must l>. at least, e of as Jong duration as the succeeeding seventh ; it can indeed be longer but not shorter . g. MANUAL OF HARMONY not: 117. REMARK. TTic preparation of the sevenths forms one of the most important parts oi the doctrine of harmony, and is to be carried through and practiced with much care, because upon it rests the most essential part of the inner and most intimate connection of harmony. If here also exceptions in the practice can be adduced, we may still again be re- minded, that they are even nothing else than exceptions, which prove nothing against the importance of the principle of harmonic connection, but can only be intended and judged of as called for in a concrete case by the position and relations. (Page 44 Remark). These exceptions occur mostly with the minor sevenths, as the less harsh, as those o* the second and seventh degree, and are then always softened by good leading of the An especial exception, howeTer, to the necessary preparation is formed oy the seventh of the dominant thord, also called the essential seventh This is the one, which, through its relation to the tonic triad, enters [wit an effect] the least harsh and foreign to the fundamental key, and does not require preparation in all cases. Of its farther use the following may be remarked The dominant seventh does not, to be sure, require preparation, yet its free entrance demands the presence of the fundamental, if the lead ing oi the voices is to be wre aad without harshness. C: I REMARK. The so-called passing sevenths, which of course, as such, cannot be pre- pared, conform to the rules of the passing notes, which are explained later Concerning the passing sevenths, see Chapter XVIII. The seventh also of the seventh degree in major and minor (in the last case, the chord of the diminished seventh), by reason of their especial character do not by any means always require a preparation. MANUAL OF HARMONY. 1 3 Exercises. 76 119. 2i "sue g p q 1 TVie Connection of the CJiords of the Seventh among themselves. The progression or resolution of the chords of the seventh, took place in the former Examples, always through the triad of the fourth degree above, or, which is equivalent, of the fifth degree below. Instead of the triad, a chord of the seventh of the same degree can also follow. The progression of the voices suffers hereby no alteration, only, in this case the third of the first chord of the seventh will serve, as the necessary preparation of the following seventh, and will therefore not progress, bu* remain stationary, e. g. 1 2O. i - i -- tt _ __ _ ^: =! a -i -v^& r F 2i~ ~ 1 -=g -iz=z=it E - 1_ --- -- Lt C: ii IV Here the third of tbe dominant chord, the B, forms the preparation of the following seventh. The peculiarity in this connection of harmony is, that in one of th chords of the seventh, the fifth will always be wanting. In Example 120, the fifth of the first chord has been left out. If several chords of the seventh succeed each other, thf fifth will always be wanting in each alter naff chord. 74 121 MANUAL L=rg._ ,9 c=g:=gz=i:ir g_=:i r It 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 CHORD 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 th seventh degree in major (see page 68), is based upon the natural progres- sion of the leading tone, upon which this chord rests : 129. v-cr f,. g- o j- -- ^=yp 'A: Til - o: vu As the fundamental of this chord (leading tone), progresses a half stef. 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 : 130. whereas the position at 6 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 peveiith degree in major, to the tonic, has occasioned the older teachers of bar- Tnouy to find the basis of it in the dominant harmony ^f the seventh. They conceived of this chord with a ninth (major or minor) added to it, and the fundamental omitted whereby arose both chords of the seventh degree. Whi e we refer to that whict is said later (in Chapter IX.) of the chord of th ninth MANUAL OF HARMONY. 77 *e can only bring forward here as reason for the view offered, that this assumptit i of the ehc rd of the ninth is needless and far-fetched, and that for practical purposes, th iinplicity 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). Exercises. 1-36 6 7 * 131. The foregoing and al. 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 uadeneing 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 tw chords: A7, D?. 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 A.-JD takes place with a stationary Bass. In the second Exercise of No. 131 the chord of the setenth of the thira degree in minor is used, and, it may be assumed, that with this introduction >t 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 thesanu 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. 6 4 63 132. IV There is need of no new rule for the progression of all these chords if 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. 1*3 Al- these inversions of the chord may be used, only the last, the chor< : of the second, will most seldom be in place, since the resolution into iht 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 133. It is only important, as was mentioned before, whether the seventh comes to lie above or below the fundamental (see page 69), and position? of the chords of the sixth and fifth, and of the fourth .and third of th* following sort, 134. 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. 6 8 9S 5 6 or: 5 6 36 4 6 25 4 135. r rri F- E E!EE^[ That here likewise the third inversion, the chord of the second, will be that least adapted for use, is shown by the unsatisfying resolution into the chord of the sixth and fourth, a chord which always requires a careful treatment, concerning which chord, what is necessary follows later. That successions of fifths, which arise through resolution of the chords of the sixth and fifth, and of the fourth and third, in this manner : 136. are to be regarded as faulty, has been already mentioned above, (page 70). Concerning the succession of this sort of fifths, compare also page 29, Nos, 16, 17, and 18. With this exceedingly pliant chord, the position of the fundamental aa respects the seventh produces no such material difference, as with the chord of the seventh degree in major ; the seventh can lie abovi or below the fundamental, the similarity of sound of the augmented second to the minor third, will always impart much mildness to the chord and cause ihi former only to be felt as such in reference to the key. 80 MANUAL OF HARMONY Exercises, 1. 66 6 6 6 5 6 I d:-yt 2-=tf7 ff-j-g J5 1 & r=r =M= :5J4* 35 -|- & ^ ft =M=p-=t===4 6 2 5 6 6 6 2 6 6 26 5 SQE Lit:: '-& e-^ e> f 5 p-g^g f E^zEESzztES^EE^EiE 26 7366 2 6 2 6 6 6 5 7 7 32626 42 65 36 76 755 6 7667 I 77 * 4 4 ft } yfc i-ia=i)-j:ijg~TT-grr"q-iTq ,_i_q 1 1 1 . MANUAL OF HARMONY. gl CHAPTER VIII. The Chords of the Seventh in connection with Chords of th various tone-degrees other than those thus far used. Deceit 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 thia direction of the seventh; it can either remain stationary or even pro- gress upwards, e. g. 138. 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 able, in attempts at new formations of the kind, to proceed according to critical 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 of 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 th dominant chord of the seventh does not result in the tonic triad, but lead, to 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, triad* other than that of the tonic, with a progression of the seventh by de yrees downwards. a. Connection with the sixth degree. In Major. In Minor. - J g^^io t-S-v q -l-cgIZZ!fc 1 O _ ffl 0: V This chord-connection (deceptive cadence) occurs very frequently. The effect of this progression is not so decided with the inversions the chord of the seventh, and is therefore more rare : 0: Viy vi b. Connection with the third degree. 7 6 141. better position : 76 r & 9 V (9- \ & F -5 ; C: V* m v REMARK. The attempts with the inversions of the chord are omitted here and in wont follows ; they are easily made. This progression becomes more decided under the application of modu- lation : 112. _ __ A: V The connection with the triad of the third degree is also possible in minor, but this as dissonant chord (through the augmented fifth) will mak< & farther succession necessary. 7 6 143. III' VI 2. The connection with triads, the seventh remaining stalionary. MANUAL OF HARMONY. ft. With the second degree. 83 not: impracticable in Minor. 145 144. 0: V 7 n b. With the fourth degree. In Major : & % IT-"- C: V 7 IV A: V 7 IT In Minor : 6 ,. 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 : 6th Degree : 2 Minor : 8d Degree. 146. C: V 7 Tl If we modulate into other keys, the possibility of new connections extends itself greatly, e. g. a. With a downward progression of the seventh. not: 147. C: V 7 B:yii 7 A: V 7 F: V 7 AtVpyGirn D: V 1). !7%e seventh remaining stationary. 148. C: V 7 Efc:V 7 C:V 7 Bb:V 7 A; BS=E=giizj}2 C: V 7 A: V 7 G: V 7 3. T% connection cf the chords through an upward progression oftkt teventh. This case can occur with the common cadence (V I). il. With an exchange of the progression of various 'joic 64 149. MANUAL OF RARMON7. not: ^ "- ' r Of ^^ ' r --- r~~" __.._^._ <] _ , _^ 1^3 _ _ rfy ,.*n _ L _ ffSn _ &^, L _ jrjQ _ ^5 ^i _ t_jzr? -- t_ S t-^L*- 76 76 76 7 6 Through the step of a third, of the Bass, the downward progression of the seventh becomes impossible, since the covered octave occurring thereby 150. is in any case faulty. In the remaining voices this progression of the fundamental cannot btf introduced. 151. ~-^^-t5r- r ~ ~^-&i r ^ ^ rr \ ~7~~^- fi \ _. _^- n \ Either that this combination of intervals is to be regarded and treated aa real chords ; Or, that they, as unessential chord-formations, eiflier belong to the sus pensions, or arise accidentally on account of a voice remaining stationary. In the first case, the explanation of their use, especially through theii inversions, becomes very extended ; and also obscure, (since in the fou r 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 chords of the ninth, as well 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 simplification of the harmonic system without 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 chord 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 : ** :=c fz: 162. mil 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 01 of the fundamental ; and cases cf the followiiig sort, where both tonei enter free 163. 1 tre to be censured on account of their stiffness and want of connection TV 1 '* prftparation can be effected thus : 90 MANUAL OF HARMONJ. letUr: 164. 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 ui.til later, in Part II. REMARK. From the chord of the ninth in major they derive the chord of the seventh of the seventh degree, wliich we have treated of fully before ; likewise the chord of th diminished seventh from the chord of the ninth in minor, in order to be able to form their cadencing progression in 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 chorda f the seventh of the seventh degree in major ; one, the natural cadence of which is the following : jQ I 3 a 166. fe== the other as derived from the dominant chord of the seventh, while it remains the sim- plest \vay to refer to the character of the leading tone upon which the above chorda rest That many musical text-books accept also of secondary chords of th* seventh and ninth, 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 : 13 11 11 7 7 167. MANUAL OF HARMONY. 91 In tho pure four-voiced movement they can, of course, never be applied, eince, through the necessary omission of many intervals, they will appear simply as suspensions, e. 5F~ G *i &. 15 & ftG i C: in D: V C: m These occasionally strange and rough sounding harmonic combinations icquire 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 atso its duty to warn the beginner against orer valuing the worth of such stimulants; to advise him in general, net MANUAL OF HARMON1 to occupy himself with such things and speculations, until he is fully versed in the treatment of the simplest harmonies of the simple purg 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 o'. harmony, and turn away the sense from the chief thing to secondary matters. Exercises. 1- 6 65 6 51 3 6 7 6 6 NB. 6 6 REMARK. In the fourth exercise the augmented fifth has been used, even with tha 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 No. 170. It is seen from this, that with a natural leading of the voices, many new chord-formations can be gained. From the formation e of example 170 : (which also occurs under the name, double diminished triad), arises a harmony which is much used, viz : THE AUGMENTED CHORD OF THE SIXTH. The first inversion of the above chord gives it : 179. According to its progression, which is determined by the augmented tixth, 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 abcra MANUAL OF HARMONY. 95 Bxajaple 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 end third, and the augmented chord of the sixth and fifth, the explanation of the basis of 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 referred 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 : 10. ~ fc> G _t=|g=gg F : g ~ fe r & Q rr m 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. * 6. not : better: REMARK. The chromatic alteration of an interval 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 plac referred to. Thus the formation of the triad in No. 170, ll will be like the following, whJch M found in C major : better in open poxitton: 182. C: VH" This chord bears, in many text-books, the name : harsh diminished triad, (hart rt- minderter Dreiklang). The like chords, if they may be so culled, appear generally only accidentally, in pats- tng, and their progression proceeds in accordance with their intervals, that is, augm&nttd intervals progress one degree upwards, diminished intervals downwards. The chromatic alteration of an interval of the chord of the seventh ha* 96 if A NUAL OF HA RMONT. 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 chrtvnatio alteration of one receives an especial importance. This is the thord 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 13. 1 gives tho following inversions : 6 I 5 ; :===J=-=|=^-ig=FF II^ULI 2: ^ z=EE * 2 1*1. Of these inversions, the second is the most important and is much asod, 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, aa the chord of the seventh of the second degree leads most immediately to the dominant, so also will this. If the fundamental of this chord is omitted, the augmented chord of tht sixth, already found, arises, the progression of which to the dominant if hereby explained, (see page 94) ; With omi/non of the Fundamental: 16. 3trzz n". or, for comparisor with No. 179, in G minor : (Jliro. miring Aug. chord of the sixth, fundarrtfjtal chord : of the third: fourth and third : Aug. chord of the sixth : 1ST. MANUAL OF HARMONY, 97 REMARK. It may be mentioned here, that the formation of the augmented chord 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 resolu ion, however, must become a different one, since that was considered to be oil 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 : without Fundam ental: Inversion* : Fundamental with ninth : with elevation a. JB" b. c. 2 1 chord: of the third: 5 3 188. Of these chords, the one resulting from the first inversion a f 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 varali 'el fifths : u __ __ _ H z __ :S"-v, igiz^juzrfflrv: :B~~"~i: ISO. 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 (5 I f \ 102 MANUAL OF HARMONY. CHAPTER XI. On Modulation of a Passage of Music (einet THE term modulation has a various signification. Formerly was under stood 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- sion from 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 XVI., 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 key 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 : 192. C: is a modulation to D minor in the third measure, because C$-E-G-Bi?, 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 G 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 dimvnished seventh, are, as the chief means of modulation, never to be mistaken; all the remaining chords are ambiguous, that is, they can belong to severaJ keys. MANUAL OF HARMONY. 103 Thus the Gr major triad belongs not exclusively to G major, but is also Bub-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 modulation 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 harn>vy 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 *.ho key of D major ; in connection, however, with C major, it will be most incv^diately recognized as dominant to Gr 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 tl modulations ; for the farther discussion of this subject see Chapter XV/ Exercises. 194. , I 6 6Q 5 7!> 6 6 5 x"^v * | ~1 l r ! ^ r 3 ' ~JP^J=] =t=l f^ f lEgeE C: I tt: V 7 T 6 6 {L 1, C: IV V 7 ^6 4 I D: 6 5 vn 7 2 ~^ iff 6 7 n 7 V I 7 :z:szir ztr_ 6 j9- 9 :: i^^"rf-~q z: =T==q=l ::: = = ==f-g^-ff : ^--r : -- gt== f- ffl - 104 MANUAL OF HARMONY. {2 6 65 7 47 36 g 6 3fl 5fl 43687 I >.i ft a I ,H 6b 4 46 3 25 667 The modulation can be indicated in the same manner as in the fi^t exercises, accwding to which the letters indicate the key and the Koman numbens, && *\j know, the degrees upon which the chords in que tioc *et MANJAL OF HARMON* 106 PAKT 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, in order to occupy its? position in the following chord, lingers still upon the tone of the first chord, while the others progress to the second, and this voice does not pasi over into the harmony until later. In the following connection of harmony: 106 MANUAL OF HARMONY the Soprano can linger upon the C during the entrance of the secotd 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 th delaying of the Tenor : 197. 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 o. 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 be formed with a descending progression of < voiet by degrees, under the following conditions ; it must 1. Be prepared, and 2. fiesolve itself. There will, therefore, be three things to observe in connection with tha suspension : its preparation :he suspension itself and its position, and its resolution (progression). MANUAL OF HARMON*. 107 a. The Preparation. The preparation of a suspension can take place through either compo. nent part of a triad. The sevenths also are used for preparation although more rarely ; most often the dominant seventh. Preparation through tbe octave of the Fundamental: Through the third: 108. C: I G: V n C: I Through the dominant seventh : C: V The preparation takes place upon the arsis, the suspension itpelf enters at ihe 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. I). The Suspension. The entrance of the suspension at the thesis has just been mentouc I- Js t-g 7 6 598 ?=ElS= 7 6 4 4 - 3 2 -- EE^3==SF C: V. Before the third: C: IV Before the,^^ rarely, only in certain positions: IV I ^ ^ ^,_l& g J I ^ t I 6 5 I = - 6 5 ^4 ci 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 jf 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 iu the fol- lowing Example b f where the octave is diminished. 000. o '"p &fy-^}- FF MANUAL OF HARMONY. 109 In the first case the seventh will always be a passing one. C. The Resolution. The resolution of the suspension ensues, as was remarked lefore, in tht tame voice, by a step dotonwards. REMARK. "Ways of resolution which deviate from tliis 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 be contained in no other voice ; only the Bass or the lowest voice can ~eceiv* it without disadvantage to the harmony. d. NB. U r =p:gg-pz= r I o j- 201. 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 fifth of the chord. In Example (I at NB., the reduplication takes place with the fundamental. In this case the effect is better, especially if the consistency of the leading of the oice necessitates it as in the following movement : fundamental : Third: 2. REMARK. It may still he remarked here, that the doubling of the fundamental always assumes the distance of at least an octave, and that the doubl'Mf in unison u faulty, . y^ The suspension can indeed appear in such proximity, only between Basa *od 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 art based upon a good leading of the voices, e. g. 03. faulty: E 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 : 201. The relation is the same with the fifth-successions, which are covered through the suspension : 2O5. 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. __ __ _ . __ __ I ~ ___ 3 "^ T i? __ t 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 giv positive directions regarding them is impossible; to reject them always would confine us too much. MANUAL OF HARMONY. r I" ~ I" 6 * ^ o IF L~gizi~._i!n l-i. '.g TL g and reading of scores, since many voices and instruments are exclusively or partially written in these clefs, and the Soprano clef itself, which occurs more rarely, affoms with various instruments, which are tuned in a particular way, an especial facility ID reading. The clef which is used for the upper three voices, Soprano, Ait.o, and Tenor, is called the C-clef. For the lowest vocal part, the Bass, the F-clef or Bass clef used before is still applied. The situation of the C-clef always indicates the place of the onc marked [middle] C, and in such a manner, that for the Soprano this C i* found upon the lowest, for the Alto upon the third, and for the Tenor upon t\ie fourfh line, e. g. Soprano-clefs. Alto-clef #, Tenor-clefs. The most common compass of the voices exhibits itself in these clefs thus -*- Soprano-clef. _' I ' f ^ ^ 114 MANUAL OF HARMONY. REHA tit. The origvi of these various clefs from the most simple foundatio.i, from Lh Bo-called Tablature (commonly a system of ten lines, upon which all the voices wen written, with especial designation of the lines upon which the principal tones, F, C, Q, o*me to stand) is interesting, its farther explanation would here, however, lead ua too far. The easiest method of impressing these clefs upon the memory, is probably, to observe accurately the position of the C- triad in the various voice?*, 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 : _ In the Soprano ; In the Alto: 4fT _ < ^?T? r n the Tenor, best in the position Jjjj- 0C- \he chord of the sixth and fourth : " f- g~ Ii of the cho The carrying out of the first exercise of No. 210 in these olefs follows here : 211. SOPRANO. ALTO. TEKOR. BASS. 13 ^ f^~~ f^E f^E : f^ _ T _ 1 __ ___ _ Lt it? _ -- 1 | i -- 1 -H -- (S--HP - 31 i-p: F-Ff Ft- s -e IE If 5 - 4 3 657 - 4 3 &E[EEf:^3F + | f tp- it C C: 1 F IV G~ C yl i The working out of these examples requires, with all observance of the 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 bo necessarily exchanged for the close position where necessity anH aouformity with the end in view require it. MANUAL OF HARMON J In tins exchange of the position of the voices, the following rules mut De observed : The voices can never, SIMULTANEOUSLY, move by degrees or skip tut of their necessary position from one chord to another (foreign one), except <.n Indi- vidual cases in the transposition, of ONE and THE SAME chord into tthcr positions. Any voice can forsake its position, if one or more remain stationary upon one ton*. The following carrying out of Exercise 8 of No. 210, will make this plainer 212. &OVBANI Ai/ru 5 NB BABC " 69875 6 _ E ^ J- -^ - J 1 -sEffli^g^ 1 ! Q _ _ 7 A o D F 7 Bfc EH B(, C 7 F 7 : i iv 7 H 7 Bb:m V 7 I IV I F: V 7 IB1,:V 7 6 7 NB. 8 9 10 11 12 70 4-6 6 6 5-3 7 J^ - 3 2 6 434 765 557 . V Fy BK GO Btr:V 7 I H s: i iv B A 7 D 7 VI H<> 7 V 7 Tho 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 Eb (at NB.), a skip which can take place if the fundamental is already present and remains stationary (as here the F in the Bah; ; 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 corned 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, Below 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 sam with a farther succession in a upward direction, e. g. from : 213. The suspension from below can take place in connection with the pro gression of the leading tone : 214. 3t= also with several intervals, which progress a half-step upwards, especially with those altered chords, which receive augmented intervals througb elevation, e. g. W _j_^'j_g- I _. "1 ,JC~ ' ( 1 r~ | i j^"^~p | ^_ *9-^ ' ^ a -3 J e/9 tit-SHH ~Lla C .. , !_,_ Observe here, that as before, the tone of resolution (harmonic tone) jiust be in no other voice with the exception of the Bass. REMARK The last of the above examples brings us the same tone-combination which presented itself before (page 64) as chord of the seventh of the first degree in minor, and which was explained as unfit for use as fundamental haimony. (See pag 74). That, in the above application, it is to be considered as suspension of the leading tune, requires no farther explanation. MANUAL OF HARMONY. 117 Of other suspensions, especially those which progress a whole step upwards: 216. some show, of themselves, the unnaturalness of their progression ; and some the theory must pronounce not genuine, and unfit for use for the pure harmonic structure, however often they may find place in the practice. If these false suspensions should be carried out after the manner pre- viously shown (No. 213), faulty progressions would show themselves, upon which they are based : 217. ' .11 I * _ i ^XT^J I _ ,^'^P' m ~!~P r '^i fr r^Jt Suspensions in more than one Voice. Suspensions can occur in more than one voice at the same time * Suspensions in two voices : In three voices: == g : _^_ = -^---g --.,--.-y- g ^ g'^-^g p ~z: ^ E 218. The chord of the sixth and fourth frequently shows itself as double suspension, e. gr. 219. Freer Movement of the Voices in the Resolution of the Sus- pensions. Preparation, entrance, and resolution of the suspension took place in the previous examples by means of two chords, since the voices which did not take part in it remained stationary during its resolution. The same can als. take place with three chords, whereby the interchange of chords and the leading of the voices becomes still richer and more manifold. This takes place, if, during the resolution of the suspension, several of the remaining voices, or one, usually the Bans, progress at the same time and } 7 this mear form a new harmony 118 MANUAL OF HAKMON1 For example, by progression of the Bass : 920. C: V By progression of more than one voice : 2-21. C: I In all these examples the resolution of the suspension ensues regularly during the progression of the remaining voices to a new harmony, of which the resolution-tone is, itself, a component part. REMARK. It may here be remarked, in explanation of the view conceruiag chords ol the ninth expressed in Chapter IX, that many places in which the ninth occurs, and which are recognized by many as chords of the ninth, can be explained 111 the above manner-, as in Example 221 b, where the cadencing Bass progression F-B could be easily explained as the progression of a secondary chord of the seventh and ninth, il the above explanation of a suspension of a ninth vnth the use of three chwds were not much more simple and did not lead to the same result, and, as with all subsequent ex amples, present itself in the same manner : Suspension of a ninth with two chords : with three chords: better: 222. "gm-^^Szrr i~q f-S-Jgl^-E 13 !--! t~ ^JffS Zltl _tl 1 f r ~eni -o j ^ H! -f-- 1 * Concerning the ninth whicn enters free, we will speak later in connection with the Or^an-point. It may still be added as completion of what was said in Chapter IX, that as a reason against independent chords of the ninth, the impossibility may apply, of biinging them Into such inversion with the fundamental that the latter is brought iato immediate oroxiuiity with tb 3 ninth, as can always take plpce with the cHorrU of tK aavonth, e. g MANUAL OF HARM ONI 223. In tue same manner four chords can be applied with the suspension, U it ftands before a harmonic tone, which is not contained in the remaining voices, e. g. 22f. 1 _2 3 4 ;_o f~ . ~ BS Without auspenxion : 1 234 --jL-eJl 956 4 cv^-Si- ni_ri \~&~ I ~J_ ?5\- & rr ^,=j a _. -&- -F-p g-r a t I. T t 1 czzz;zi_i tt C: I IV ii \u vi Exercises. 56 5 825. 677 67665 2. 82 2 6 4 5-5 46- 6 747 t^ tit A* \J f2 ^^^=r^zr^^Q^c^^^^S^^^E;^P^^^^^^3^3 z ^- F-F-| | p-i^^ -ffp-j-^-4- 1 - 1 -P- i f f Y -t 5 67- 467 4-3 36 97 47 6 94- o Jo 4 4 2 3 9 6 7 5 6 4 7 - 6 7 _ __ _ _ ^ __ _ _ _ _ _ __ _ 5 6 465 6 7 6 - 4 6 iP^l^iliiP^^liI^llliPI^E?P 6 t 7 6 6 547 7 4 6 824 6- 5 120 MANUAL OF HARMONl 9 6 =:= 7 5 6 432 736746 2747 BLfe :&*= ^=* 9- 5 4 7 7. 8 6 4 7 2 ^'-f> Q -i -| f~ "^~~" ~~f "a~~ff8ii~rfc'-^ ^"F-r WT T-J- ""*-*- : ^-FFr^l ^=^=l-^^-g=p f=-l ^E=E^p t:=tr: 6 5 9 326 643 3 6 767- 4-6 5 326 7 - 5- 4.3 96 7 9 6 4 38 + - -- - -i --i-* - E Between suspension and resolution, other tones can be inserted in ttu same voice. These can be : \. Tones which belong to the chord, e. g. 226. 5fc~=i*=r4rjBtr ti=t^=: 2. Tones foreign to the harmony, changing notes, e. g. ^ i ^ i fj i 227. g L -O- The explanation of these and similar instances is completed through th> exhibition of the passing and changing notes found farther on. Instances also occur, in which the suspension receives no resolutioi at al^ e. g. Usually in this manner : l-G>~- t ** -9- ' ~-~ -r pr f * TLoy have arisen from the following passages, by omission : MANUAL OF HARMONY. 121 229. Anticipation. ( Vorausnahme.) The anticipation of a tone, which is more rarely used than the saspen sion, is the opposite of the latter, and consists in this, that one or mote voices allow some tones of the next following chord to be heard earlier than others-, and before the metrical division allows us to expect them. With notes of long duration, and in a slow movement, this manner of leading the voices occurs seldom or not at all, since the harshness of the dissonances which appear here would amount to unintelligibleness; it is mostly shorter parts of measures which are anticipated, e. g. 23O. it -*-_< Anticipation in the Bass : In the Soprano : ._ J 4 r-| - J i-j J -h ri 4-d 5 1 * ri d /n several voicet: I &9 a 4-9 1 & ~ra* I- m-* +-r& rr ft & J. & -0 I_X| _^ ASCI ,5 L _ 0-\-s> Lt T-& r.^.* *-*?*&&& i* 75- The similarity of this movement of the voices in its metrical form, with that which general musical instruction comprehends under the name syncopated notes, is not to be mistaken; the latter, however, are formed not by anticipation of the chords, but by after-striking (Nachschlagen) of them, or they have merely rythinical significance. The movement of the voices can here also be freer under some circum- stances ; for example, a harmonic tone can be anticipated, other than that which is intended at the entrance of the chord, as in the known closing formula : 231. As antithesis to anticipation may yet be adduced the after-striking of harmonic tones, which has a similarity with the suspensions, in so far, as also he 'e preparation and resolution take place, but differs again, mate- 122 MANUAL OF HARMONY. rially as its character expresses itself more in the metrical and rythiuica: movement, for which reason it also always appears in more extended suc- cessions ; the suspensions, however, appear under entirely other conditions, singly or in greater numbers. The following Bass would be a succession of such after-struck tones : AUegro. ^^~0^=^ri=^,4=fJ=: 232. I Here would also belong that unison passage from the overture to ' Leonore " (No. 3) of Beethoven : 233. & *- *-k, .tc. MANUAL OF HARMONY 128 CHAPTER XIII. TJie Organ Point. Stationary Voices. AN especial manifold character of the harmonies, and a mingling of them, arises by means of one or even more than one of the voices remaining stationary upon one tone, and by means of the chords thereby accidentally formed. We frequently meet (particularly in the Bass) as well at the beginning of a composition, as in the middle and at the conclusion, at the point where the cadence should begin, with a long sustained tone, during the continuance of which the remaining voices, apparently without reference to it, continue their harmonic movement. If this tone lies in the Bass, it is called ORGAN-POINT [Pedal Point] ; f such prolonged tones occur in the other voices, the lattei are called STATIONARY VOICES oa STATIONARY TONES. REMARK. Many give these last also the name Organ-Point, but incorrectly. The tones, which are adapted for remaining stationary are the tonic and dominant ; they also occur together. REMARK. Attempts with the third of the triad, which in later times have been instituted by many composers, betray too plainly to the ear the unnatural and far sought. The harmonic connection, as well as the progression of the remaining voices takes place, always, during the organ-point, according to the known rules, so that the next lower voice assumes the conduct of the harmony, and in general without regard to the stationary tone. Before we enter more particularly into the manner of treating the organ- \ oint, some examples may follow. a. Organpoint upon the tonic: * I 1 -. J ! * * I *- T -* * wf I I i |-i-* * i rr ;SE,^EE^|-i=5E^^3E^g=| -f 1 -*-| F | - 1 F * m >- ' '^ g - 1 f 9; 124 MANUAL OF HARM NT. b. Dj>< i the dominant: * zr;j jjiate* ' zz^rJrTijzrj jri Pr T T f t2 _ T~ Upon both at the same time: * # # * ******* vTjVj T^ ^ -3 J -rf--J-H -n 1 1 J j J ^ _ I__^_^I *-J_^_J_ 1 r i7 rr r r fTi ' r r ' In these examples, those chords to which the Bass tone does not har- monically belong, are marked by a cross. The following remarks may serve for the treatment of the organ-point : 1. The entrance of the organ-point takes place at a rythmically definite 'ime ; 2. By means of a chord to ivhich the Bass tone harmonically belongs ; 3. The last chord of the organ-point must likewise be in harmony .vith it. Tho first takes place at the beginning or close of a period or division of one, and upon the thesis ; the second and third commonly by means of the fundamental of a triad, as in Example No. 234 a, C 9 d^ or at l) 9 through the chord of the sixth and fourth. Care should be taken, further, that the chords foreign to the Bass tone Jo not succeed each other too frequently, but are often interchanged with chords to which the organ-point harmonically belongs. This is necessary, in orier to avoid d \gressiois violating the character of the organ-point which is only to be Lund in the holding firmly together of various chord-combinations. MANUAL OF HARMONY. Thas the following organ-point would be faulty in this regard . 125 235. The voice lying next to the Bass, in a four-voiced movement, the Tenor, becomes, in case of the organ-point, the fundamental voice of the harmonic leading. Therefore, all necessary harmonic progressions will be condi- tioned by this voice, even if the organ-point should also, accidentally, belong to the harmony. Thus, in Example No. 234 ,-the progression of the Bb in the Alto (in the first measure) is determined by the leading of the remaining voices, and not by the circumstance that it is seventh to the Bass. If the organ-point stands upon the dominant, as is often the case at the close, no plagal close can be formed upon it, as appears already from the third of the above adduced rules, e. g. 236. i I I i NB - i j I -9- 4 ill i - I m-j-0 * J r I- 1 i 1 1 T r r i i r r T r * * & I _ The plagal close can, however, ensue with the organ-point of the tonic : ^f r~r i f-f ~r~ if"!*?**?^* 237. ITT The end of the organ-point is indeed to be just as carefully treated as its entrance. In the examples brought forward above, this always takes place through a cadence. In this case it presents no difficulty, except in instances such as at No. 236. The organ-point can, however, also pass over earlier to the harmonic leading, and then the third rule is to be carsfullj tbserved, e. g. 126 MANUAL OF HARMONY. 938. - . The notes marked by a cross x form the pass, those marked wkh a are harmonic by-tones, that is, in so far as with the first note a C or A.-triad can be conceived, e g. MANUAL OF HARMONY. o 129 fcfS. fl r F The passing notes found under a, of Example No. 245 are called dia tonic, those under & chromatic passes. The passing notes go from one harmonic note over to another har- monic note; they appear, therefore, not with the entrance of the chord> but after it, upon smaller divisions of the measure, and can be introduced only in progression by degrees. Changing notes, on the contrary, are those tones foreign to the har- mony, which either appear in the character of a suspension or appog- giatura at the time of the entrance of the harmony (thus in this sense upon the accented part of the measure), and attach themselves to the harmonic note (No. 247 a), or, after the manner of the passing notes upon the unac- cented part, serve for the melodic adornment of two like notes. (No. 247 ft). _i_4_ g;_*^_;_j^ ^_j_ _i_ d _4_ r-j-jL, -- Fff s* -* j--*- 3L f-^-3 g P .o IL ' il '__^o t~g: zz:^ t_g 1 - ^ * _ * The changing note can therefore appear IN SKIPS, it must however b joined closely to the harmonic note, as the examples in No. 247 show. It is further to be seen from the above examples, that the changing notes can be formed by the note which lies immediately below the har- monic note, as well as by the one which lies immediately above. The changing note below the harmonic note, especially if it enter after the manner of an appoggiatura, upon the accented part of the measure, haa the peculiarity that it inclines to -form a minor second to the principal note, whereby chromatic tones arise, as is to be seen from No. 247, hence the formation of movements like the following would not be admissible : 130 MANUAL OF HARMONY 24. J7JJJ J* ' This applies particularly to the changing notes introduced by skips. It is otherwise if they appear in a progressing series, whereby they take on the character of the passing notes. Thus the following series of chang- ing notes at a would not, of necessity, be so formed as at b. 249. Those changing notes below, which fall upon the unaccented part, requiis only partially the minor second. Thus, in the Example No. 250 tt y the formation will not necessarily be like b, while c is not so good as d. Definite rules on this head cannot be given ; it is also unnecessary, in a .\flch as every musical ear will certainly find that which is right. REH \RK. The third of the triad bears the changing note as whole step better than lU fifth and octave. Since -with the latter the changing note can appear at the sanw hiv.s as seventh, so that the succession only can determine in respect to it. Chxiging notes above the harmonic note, whether they enter free (uy skips), or in the manner of No. 250, can form major or minor seconds to the ch2. -j^. M A :' UAL OF HARM: NJ . 131 Upon this is founded also the following often occurrkg manner of bellishment : 253. Passing and changing notes can occur in all voices. If this takes place, by preference, in one voice alone, this one will become prominent in com- parison with the others, and receive a concerting character, while the remaining voices serve for accompaniment. If this should not be the case, all the voices can be made prominent, interchangeably, by such by- tones, and gain thereby in significance. Wherever the position and progression of a voice adapts it for the introduction of such by-tones, it will by this means admit of more significant melodic development ; but here also the proper mean must be found, since, otherwise, over fullness and a lack of clearness can easily arise. The following simply harmonic movement, -^=J=q^=H-rj 4=g=r 254. might, by the use of the above by-tones, assume the following form 255. *"" ""* I ~ ~ * 132 MANUAL OF HARMONY. - * ^ _^ * * The passing and changing notes are here marked by crosses X That through such copious use of tones foreign to the harmony, the pas- sage can easily suffer from overloading, is to be seen in the above example if it is executed in a somewhat rapid tempo ; a slow movement is better adapted to this manner of writing. In the introduction of the changing notes, care is to be taken, as wa& before remarked in connection with the suspensions, that no voice receives, the harmonic tone which in another is introduced through a changing note, e. g. 256. This can only occur if the distance of the harmonic tone from the ton oreign to the harmony is at least one octave, e, g. 257. This reduplication, according to the principles of reduplication in gen- eral, will take place better with the fundamental or fifth, than with the third of the fundamental chord. In a rapid movement, however, and more extended carrying out of such figures formed through changing notes, other considerations arise, as the following passage shows; this to be sure, cannot be conceived of as a four- voiced vocal movement : 25. In the case of the regular passing notes, like regard is to be had to theii approximation to harmonic tones, and figures such as No. 259 tt f ft, d not appear so pure as c f <1 9 MANUAL OF HARMONY. 133 259. i i More rapid figures allow this approximation more readily, e. g. J, i - J JSL_. , 260. il 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 open ones arise : 261. Open octaves formed with passing tones cannot occur, because the first of them will be harmonic as much as the second. 262. On the other hand, in the following instances, the passing notes will not oover the open octaves, and consequently will be considered as faulty 263. mf====== REMARK. The last kind of octaves would find application m instrumental under the condition of intended strengthening and reduplication. 134 MANUAL OF HARMONY. In like manner the entrance or progression of the changing not in parallel movement is to be called faulty if it takes place in the following manner better : i 1 264. i ^rgg p^^-5~c^zr=ec=zii-_ gczzrrp =P^==b=^=b'=E=t==tf = r-i =8 The last example is better because the octave progression appears covered. Passing and Changing Notes in more than one Voice at th same time. 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 ixths, e. g. 265. 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 : Single fifth-successions arising from passing notes are occasionally mei with in good compositions, which, however, is no reason for recommending MANUAL OF HARMONY. 135 them as faultless. (See that which is said concerning fifth-suv cessions 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 f 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. 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, be 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. 26. In all such places everything depends upon the question, wretlier at the kange of the harmony the voices are in a position which allows them o form their progression regularly. Changing notes can occur in various voices : a. In tivo voices : l86 MANUAL OF HARMONY. in pa -fillfl motion : 209. fcfct in contrary motion 7O. p= EEEE: 1 b. In three voices : C In four voices : 272. HE. ~J2f< 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 third and sixths appears most natural, while the parallel seconds, fourths, fifths and sevenths always produce a very disagreeable effect. Thus no one yould be likely to pronounce changing notes of the following sort, good : good ~l l~l * j u J #J -* S*- -^- 1 1 -fl -S-fcT-ft ft. M\ * -TL-' *-* '-T ~ II " ^ *- - * 'Jhauging notes can also be of longer duration, than the harmonic not fce which they are joined, e. g. 274. 3t*:dit -^>1, MANUAL OF HARMONY. 137 The significance, in composition, of the subjects explained in Chapters XII., XIII. and XIV., is great enough to subject them to a careful inves- tigation ; as a thorough knowledge of them contributes materially to th understanding of the inner harmonic structure. We have stilji 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 spokon f in a general way, it becomes necessary to consider the question mor<3 narrowly, and to present it something in this manner : What application of these means for composition does our immediate purpose, (the exercises in the pure harmonic structure), 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 (Kiinsteleien) in general, in so far as they are founded upon no inner necessity ; unnatural introduction of little- used harmonies. 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 voices, and of the anticipated and after-struck tones ; Especially, however : The changing notes which are struck free and the figures formed theri- from ; in short, 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 IL 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 tbe 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 rag of the vobefe. 188 MAX UAL OF HAliM^ NT. 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. Passing 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 always be conceived of as the goal to which the chords of the second divison (Arsis) lead MANUAL OF HARMONY. 975 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 expressed, 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 : 276. t.. ,) j ,_ rr ^ * ! i <= - t HC J . u 8 ' ^ ^ '6 ' -47 ~V i~S" t~(2 1 1 J ^ - ^ ? II ^ i- r-F"T-; EH *=F* : \ =1 -^ -- f= -- 9 - f 5-4- - J - 9 --- \-9 - - O -- _ -- L -^ -- - & -- -t - -ty - 277. The peculiar manner of appearance of the chord of the sixth and fourth in Exan;] le No. 276 a and c, as well as of the chord of the seventh in C 9 u only to be explained through the ensuing progression (in the chat actt* 140 MANUAL OF HARMONY. of the passing notes] of all voices, by degrees^ to theii nearest goal th chord of the thesis in the following measure. These voices can be still more easily recognized in the'" character as passing, if one voice is allowed to remain stationary, for example, the Bass of No. 277 a, or the upper voices 6. (See above, No. 277). The leading of the voices in No. 276 a f 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. 27. KEMAUK. 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 ol less weight. Passing chords will show themselves in the following manner : : 3=' = J~-| Z *EJ&ES& 279. 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 w 11 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 are to be called correct. It can only be remarked in general, that the progression of the voices by 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 Modulation. 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 quickly 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 cast 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 : 2*0. C: F: :I F: V 7 Efe: V 7 This example shows plainly, how the extended modulation, which 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 Ei> 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 kind of modulation used, since the same can serve for both the above designated kinds. The first arid simplest means will be THE TOXIC TRIAD OF THE NEW KEY itself. If. however, this triad is already a component part of the nrst key, then what succeeds only, and particularly the subsequent dominant harmony of the new key, will really determine the intended modulation. Thus, in the Jit AN UAL OF HARMONY. 143 following example at a, no modulation will be felt, w. ile at 6 we hear the key of G-roajor plainly only when we come to the third harmony : Iii case of more distant keys the minor triad can, to be sure, as tonic triad, have 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 ft. 6 6 5 5 C: I r: i C: I C: I A: V i C: I K: V As ansatisfying 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 deciiled. 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 natu~allj followed by the dominant, which first completes the modulation. 8S-1. I T-H-T-r Ha" rd~tT F^s^f .|=4-i:^3ii:z&:|7f^p-r < ^-[:::ii^-|^iB - t -B'-^S- J ~o L - - I --tT C )- 1 - -u> - 1 '-- o- 1 A IE C: 1 Q: I V 144 MANUAL OP JTARMONT. Upon the arsis it will not indicate the key eo definitely : 2*5. 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 le 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. Prom C-major we can reach all keys, except Ei?, .E aud F$, (it can remain undetermined for the present whether major or minor) thus : From C to i>: C F: C G: C A: i486. 2C~ Q ffl" ~ffl <2 &~^ f ? 1 ^ TT^" >^ \ . Tfv\ G>^~^Gf^ r -I &^^^<9 \ & ^w & 1 & x/S ^ f ^ C 4V> C - Ab: -- C li^tg l?S:zi=- -rP- -s- ^ ^ jc ^-^ I S^Ei^=feEEE 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 aTid so -entli of the dominant harmony, &c. MANUAL OF HARMONY. 14g REMARK. It only need be mentioned, that these modulation* ot. nlso be reached through other positions of the chords, e. g. C D: or: ^_^ . , a s> a 2r. tf we wish to modulate in the same manner into the three keys whicfc ire 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. ^-om C to E|>: C E: C FJi 288. CT" The modulation from the minor can be formed thus : From AWB: A D: A : A F: 3=^:-fe=X^~^ -& P^~^ "F= 2 9. fczi-iitr: -JS. 2. ~ * ++ T7 ^ A G: - n^^.>3 ' g"""""c> fc^ -Hn "fLizzrzzr^irkzssirzigzzitt z To the remaining keys C, Dl?, Eb, F^ and Ab, by means of a connecting chord : From A to C: A Dfr: A 290. Ab: y=^U|*= * ** 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. for the connection of harmonies and especially of the keys, it will, how jver, 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, jince its entrance is much milder, particularly in those cases in which rfeverth and fundamental of the dominant harmony would be obliged to enter tree at the same time. The following examples present the use of this chord : Prom C to Bjj. Beside this application, this chord shows, by means of its enharmonic nature, a farther, peculiar capability. Tlif following chords, entirely like as to sound, but variously written : 1 long to four different keys, viz. : in the first form to F minor, in tLi second to D minor, in the third to B minor, in the fourth to AP minor. Through this circumstance a fourfold modulation is possible : From C to F: C r> : C B: C AT>: Sinv.0 now all the chords of the diminished seventh can appear in tha ^r three positions, as the piano-forte shows most plainly, MANUAL OF HARMONY. 147 295. 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 296. with enharmonic change, adapts it, in connection with the latter, for mod- ulation into certain keys, e. g. From C to B: E|j D: 297. JL"S=SS'^iy9--saB==. C: Y* B. 11 V i Efe: V 7 D: n- i V i Although, in the above, the means were sought out with which to pasa 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 by means of the triads of various dtgreet . From C to D through the triad of the third degree : 29. ===rr ===*?s - 2- rt &% - 5 - U- From C to i) through the triad 148 MANUAL OF HARM ONI Of the fourth degree : Of the fifth degree : Qfthe vfafft degree -fi 299. Of the seventh deyret From C major to E through the triad Of the second degree : Of the fourth degree : SOO. ~7C~ P Of the fifth degree . & a- rr "" Of the seventh degree : & d .n .^n S ^Q ^ it ^Q .o 3 u3: g . 2 - -Ji-, > 5 '^ 8 zzz:z^^^iiD2:^z^^~ nz 3_3jiS:_a2Q_ These indications may suffice for learning to form other modulations according to the same principles. Extension of Modulation and its Completion tlirough the Cadence. The process shown above, for passing from one key- into the other, was based upon the simplest and most natural means. If we wish to carry out more at length a digression into a new key, the above means must, to be sure, serve to this end, they are not however applied so suddenly and directly, but the before mentioned passing modulation ia used, and the new key introduced only gradually. The use of the cadence- formulae will, however, establish the ultimate key in the best manner. To this end we can form for ourselves the following kind of problems, e. g. Let a modulation be made from C major through t> minor, A minor, and G major to E minor. This problem would be solved something in this manner : aoi. / \EEEE: ET=F- EiEEEEFE^EliE=t:SEii=E \ C; ID: vn. A: vu. Q.-V- MANUAL OF HAXMONY In connection with the addition of the cadence, the folbwing is Is be >bserved : If the modulation takes place through the chord of the sixth and fourth of the tonic triad of the new key (see page 148), then the succession of the dominant chord with its natural progression will be sufficient fi effecting the cadence, e. g. 302. In other cases the extended cadence, or the known closing formulae will be requisite (see page 40) in order to determine the final key. As the simplest of such closing formulae the following are commonly used : In other positions : 303. I ^ r f? ~r ic usi EnEt ij :iac ip L i__ L _ Q * i=r= r iEE=iE=S=i=TE A p^=i -i=G,-=t - J n fi ' - - 1 L ilEE -rp r~ &- i . If the Bass progresses by degrees to the following new chord, 01 emains stationary The following examples show the application : 154 MANUAL OF HARMONY. 3 -E3 3= , . . Octaves : d. e. 835 - Here it is well, if one voice be at the same time led in the contrar movement or remain stationary, as in Example No. 335 (t f b, C. It i not so well, if all voices go in parallel motion ((}). REMARK. Although the above rule will suffice in so many cases, still it cannot always apply, as the above Example, No. 335 d, shows, which is not to be reckoned among' those which exhibit a first rate leading of the voices, since the progression from U chord of the sixth, c f is a very forced one. We must remember also, what has been said before concerning the cadencing pro- gression 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 thoM which pass over ^* wViol-Btei>. 160 M A NUAL OF HA RMOVY. In the exercises exhibited above, the octave always shows itself as 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: 336. Even as fifth of the chord it is not to be called good. REMARK. With the covered fifth, the lower voice will always be the fundsmenwtl the chord. Covered fifths in the outer voices are to be refected if the upper viict tkips. a, b, c. ff. *. ] ~~ " """ 338. Wherever a seventh makes the connection of the harmony firmer, as at b f (1 9 C, the progression of fifths appears more covered and less harsh. Covered octaves in the outer voices are not to be unconditionally rejected if the upper voice skips. 339. r~ i^ g r \ ^~^\ I" : I . Here also tliose 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 (1 and e Covered fifths and octaves in the outer voices are to be rejected if botk voices skip. MANUAL OF HARMONY. 163 ^ J-- r cuip' r ' "* "T ^nn r T r SIO. 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 fifth* and octaves at all. 341. giJL-fi, - J --- 5-J> -- 4 --- g NX^-g - ft - a Covered Fifths and Octaves in the Middle Voices. Although the leading of the middle voices must be just as pure *< that of the outer, still their situation, which is much covered by the latter allows them occasionally a greater freedom ; this particularly applies to the 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: a-L - - Covered Fifths and Octaves between the Outer and Middle 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 aiechani oal rules. Here are some examples : 313. 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. "^-g i "TVQ i y&^ ~^f3 1 __ t'g J._. Q _t_a__ J _ 1. _ ^.1 __ I_J _ r ^"T*-^; L __j __ I _ _ t cv I n T- i- r--! T''~1 ~i:^i~ "raz ^Ei^ I=3^EI^3E=l=fes=fc=f=3Z i E 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-harmonit structure, without regarding the higher requirements of art : Avoid, indeed, covered fifths and octaves as much as jwssible ; consider them, however, as safe if on the one hand, an otherwise natural, yood con. nccti m of harmony takes place, or on the other, considerations of a higlier sorl prevail ; such as melodic voice-movement, application of definite motives, etc. MANUAL OF HARMONY. 168 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 thai 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. P Thus it only remains to alter, in this case, the harmony itself, and seleel aother marking of the fun dame ntal tones. The following alteration can take place : 346 or: 347. 587 m B D 7 G 7 587 l. 347 b. itezrsrz Exercises. -&- . C- F Bb l*J4 MANLAL OF HARMOHY. ' P :/V~~ s *'. i 848. The following exercise : GCOD 7 GCOAD 7 O we will work out in this manner : 1. 2. 4. 5. zz iris~ TZ^ ~ T~ s> I ~g~^ ~ T~ g |-g : F-S : l-^^l-g-j^e |-g f^^^-g fgg PF 240. The faults of this work are indicated by figures. The movement of all the upper three voices, by skips in parallel motion, at No. 1, is not good, since it offends against the first principles of all har- monic connection and is by no means necessary. A leading of one or two voices, by skips, can take place only if through a third voice (by a tone remaining stationary or by a contrary motion), iht 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. 850. i i ^r & I r ,^ G D The next exercise^ K Eiy A B : S^= Fj 7 B 7 5*. &-SESE: with the following treatment : 354. gives us opportunity to speak of a fault which bears the name, UNHARMONIC C R 0-S S - R E L A T I N . The unharmonic cross-relation (relatio non harmonica) belongs to the unmelodic progressions, and consists in general in this ; that upon one tone immediately follows the same tone IN ANOTHER VOICE, chromatically raised or depressed, as here upon the G of the Alto the G$ 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 instancea brought forward in which the unharmonic cross relations o<;cur in a per- fectly natural manner, without examining the reason why they do not sound faul ty. Some of them will be here adduced : 355 HANUAL OF HARMONY. 167 SrzrcizSzii^T s^zr :tf^-j tt^ ' zr 'riitz~ T- s== |g^^ g --F ^--jg-f 115 F~ =5= * : ^f^~p z ^iff = i =:=: F".' 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 9 b, r/ ? or through contraction (drawing together) of natural, but for the metrical construction, too cir- cumstantial harmonic connections, at c f d, , f, h The first needs no proof, and there is only the observation to be added, that this kind of cross-relations would probably occur mostly with smallei divisions of the measure, and the above notation in half notes is rare and therefore unsuitable, because through it the simple harmonic foundation is 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. Let these examples be compared with those tinder No. 355, at C 9 e t h. 158 MANUAL OF HARMONY. 9 AL these conditions, through which cross-relations are most endurable we wanting in the following and similar cases, which are therefore faulty or: z^ g t^Lr^T=z4^^==lf-=^ -gg - g-Vsr- :n~ 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 tempo, 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 Tritonus. The tritonus is contained in the diatonic major scale, and embraces the 'listance from the fourth to the seventh degree (in the C major scale th augmented fourth F B.) This step from F to B embraces three whole tone-steps, whence its name \B derived : 35. BSH 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 : of which the one must remain disregarded in its progression, if tha is transferred to one voice : nieog the melodic secession be formed thus: MANUAL OF HARMONY. 169 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, 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 above. '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 (b), e. g. I ^ ~ T g>~~ ~':~T~g~~r~ If it occurs upon one chord, its entrance is not unexpected, and the eai 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 tivo maj. ? 5T- E A F S T S> r*r ^E= , E=: oo D^ o A e Oy e 2. Harmonic accompaniment to a given middle voice. This exercise, which belongs properly to the contrapuntal labors, cannot begin too early. It is introduced, for the present, with the addition of thfi fundamentals. MANUAL OF HARMONY. 171 ALTO C Exercise. G F G C 367 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. 36. Df G C 6 6 ^ @ 6 1 I The foregoing can answer as a three-voiced movement ; through the addi tion of the Tenor it will assume this form : StfO. B: -zfezz^-zdr- 22 4fE ^-- tjzzgrzqiiz^z^izs! :_ g 7 ^__ \^ _ pg_[f 2G9A. I OlV C F C F o C-* F F C F C D 4. D _ o c-. A~ D K AY D 6 C F .__. -CL ? Ei A D 172 MANUAL OF HARMONY. 6. - 1~5 - r - T -- r ^ - T -- T -- i-s r -- ( i EifcEEEHcE * g - or: i?-tE- }=_}_-_:{: - j -- i ij -- j -- } --- H s D 7 a B|j o A Tenor voice would be treated in like manner. =#?=t^- I D 7 Exercise. TENOB. C G A F C G~ O 37O. Sketch of the Bass and Soprano : 371. I :^=p^:p=:f^=p=:T=::p=^p JEEEEEE -* Q t -IF Pour-voiced : 372. Exercises with ffiren Tenor. 3726. C G 7 C G A D G 7 C 3. C 6 3E C A D C G 7 C AADB 4. B These exercises are to be continued, until the sketching of the Bass, as well as the leading of the voices in general, is perfectly pure and certain. At the close of this chapter it should be remarked, that to a good car- rying out of these four-voiced movements, a good position of the vokes ii MANUAL OF HARMONY. 173 especially necessary ; the boundaries of the voices themselves must not be overstepped, the distance from one voice to the other must Lot be too great, neither must it be too small; this, however, does not apply to two voices, which, for example, meet upon one tone. In this relation let the following rule be noted : Of the upper three voices, the distance from one to the next must not be greater than one octave, The relation of the Bass to the Tenor, however, admits of exceptions. KEMARK. To set the present exercises in the Bass, will not be to the purpose since they would appear exactly in the former manner, as figured Basses. They can poly be set tor free harmonic treatment. CHAPTER XVIII. Extension of the Harmonic Accompaniment. To a given voice in whole notes, the harmonic accompaniment in half* notes interchangeably in the other voices. This can take place, Through two chords, Through change of the situation of one chord, Through suspensions. The exercises will be marked in the same manner as heretofore. Exercise. F i. BG 373. The Bass can be sketched in this manner : 8T4 !i^ In the second and fourth measures, sevenths of secondary chorda of th seventh show themselves without preparation. 174 TL ^ kind are called passing sevenths. They start from the fun Jamenta; of th; 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, given the following four-voiced movement . 375. 267 2 6 8 7 The same exercise with a richer change of harmony can be given in this nunner : C FFJ GG|.. AC-b D D G C - 376. Zrk~C T T ^ T <> I m Treatment : 877. y~cp .^ _ 1 &^ i _ 2H_|5_5_ =5=tszH :p=pi*3l cr- 17^= ii^rg^iir ( 5^CGnr=2'-na:i--^r| &EiE^feEEEEtEE~=k=EtS -EH 7b E!H5=-2^ t 6 - 8 ' [\ The next exercise will exhibit the use of the suspensions. F 8(7 C D G F Bjy C^ P . fefc^-~^=. iJgE|-a-|i=gzr|i^ = }= Treatment: 879. "P" f 9 8 MANUAL OF HARMONY. ^__e- . T ~ g ._ t~ ?~ a \ |f 7 fi 98 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: O Haupt voll Blut und Wunden. A Ai DA D. E E A E * A 380. fa:=J:=sL-= o C G A-, n G c D~ G E A /Ts E Tbe treatment of this choral can, according to the above exercise \)+ e f flowing : 178 VAN UAL OF HARMONY. ^ 1 1 -I- ^ [- _\ J_J_ J l J. a I_J_ I . -+- j _j_ i . _--- _? ^"^f" frFf r^ = ' g. l ' i__ I !__' i_ , I J_ _,, _ After sufficient practice and certainty in the management of the 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 Development of Melody, WE are not to treat here of the invention of a melody, but of its devel- opment, and, what is most important for our harmonic exercises, to treal of it in order to learn, by the elaboration and fashioning of melodies, tc' know and use what in them is essentially harmonic. All will here depend upoi the recognition and comprehension of the following principles : MANUAL OF HARMONY. 17, Every melody, however extended and developed it may be, has a founda tion just as simple as those we have used, as exercises, in our last examples Every harmonic leading of the voices, however complicated, admits, 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 th following melody, which we will write down in the simplest manner according to the above mode with indication of the fundamental tones. 382. Both melody and harmony are, as selected, simple, and the latter may be carried out, four-voiced, in the following manner : T T xj_T~ ^ .G~~ QT- i_;zii-^<2= Before we proceed to a farther development of this movement, it becomes nocesary 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 ot a composition), or it can be a whole, separated and bounded by means of ntithesos. 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). MANUAL OF HARMONY. The more complete treatment of this subject belongs to *ho doctrine o* Form.* That the above movement will form a period, is seen in the closa af the whole, and it will be necessary, above all, to seek out the separatin, point of the divisions. This point of separation is very often discovered in the cadences, which 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 ign f stands. The first division, the thesis, would accordingly receive seven, the antithesis six measures, each of which can be rythmically altered so as to eontain four* measures. This may take place in the following manner : 384. 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. g., into 4 > 9 , 3 or [ measure, admit of easy accomplishment, e. g. * ^^f~^ T ^^=|=p-7-| == r li =^|-=j=^|= tytj ~^qr : I CI p I u 5 1 * 1 *y &c. ;if; &C. Ac. We proceed now to the tonic variations of the melody, and add to it passing and changing notes, e. g. 36. =p^z^^^:f:= trzt=fzi * See the -work of this author " Die Grundzuqe der mtm7- ilisthen Formen." (Leipnq O. Wiarand.) of 179 Still rieh - I .^^r -- _ 3~T I--T _p^ i 1 1-- i,-, I . '^- " 180 MANUAL OF HARMONY. - B We may remark concerning the octave parallels in the middle voices, to be found in the third measure of this example, that they are to be regarded as faultless if they do not occur singly, but appear only as a means of additional strength, in a more extended succession, for the inten- sification of a harmonic and melodic progression. The movement is, in this case, to be regarded as three- voiced. As little independent worth as this example has, it still served, here, to show of what development the simplest melodic and harmonic movement ia capable. The advantage of the contemplation and recognition of these melodic and harmonic relations is too great to allow us to forbear to furnish another example in the following interesting movement. The fundamental harmonic progression is just as simple as that shown efore. 39. This movement forms a period; the middle close is easily found in the half-cadence of the seventh measure. We omit here the various kinds of measure, and select the following division : ii MANUAL OF HARMONS. 181 The develop raent of the upper voice may take place in the following tanner reference being had to the harmonic progression : 391. What part the other voices can take in melodic development, the follow- ing movement from the E[? major quartette of Beethoven will show: 392. VlOLINO I. VlOLINO II. VIOLA. VIOLONCELLO. ~i - T- 1 1 T ' T *^ A comparison with No. 390 will show the melodic and harmonic variations. There now follows still another alteration of the original melody, out of the game composition : 182 MANUAL OF HARMONY. *' i ii J ^ ___ ^"""Sl ' >^ The other voices show themselves in th< following alteration : 394. ^g g * ~~ii^^j_ ' ' '^~~j -J-* ~~* ~* * * . ^-y-i-r * '~ -MzBBS3=HgB ^bF^^- *- Q:rb-t-3=^Sf ^&&ZB. These hints in reference to melodic development may, here, suffice, and be left to personal practice or special guidance. REMARK. The mechanical element in the whole proceeding should not occasion mis- take; foi just so certain as it is that in composition one does not always proceed in the wav shown above (even if Beethoven, in the later alterations of these original melodies, could uot, sometimes, proceed otherwise), in even so great a degree was it her* our only object partly, to set in the right light the relation of our previous exercises to the practical side, and partly, to gain a clear insight into complicated compositions them- selves. As concerns the accompanying voices, they arose of themselves out of the simple manner of harmonizing, required little alteration, anj showed themselves, even if subordinate, still not on that account insig nificant. It yet remains to speak concerning other kinds of accompaniment, whiol will be done in the next chapter 183 CHAP1ER XX. On Development of the Accompanying Voices. THE l.'ist examples of the foregoiBg chapter have already shown in what auanner the accompanying voices take part in harmonic, metrical and melodic development. There are, however, still other kinds of accompaniment, which are known inder the name of THE FIGTJRATED ACCOMPANIMENT. This is not adapted to the character of the vocal parts, and may be used for them only in a very limited manner. In the following investigation, instrumental music only will be treated of. By figurated accompaniment is understood the kind of accompaniment arising through metrically uniform transformation of the simple chord tones, e. g. harmony: figurated accompaniment : 395. pt soru kinds of accompaniment. This m;>y be p.-eceded by the following remarks : // the figures repeat themselves uniformly (V. g. in broken chords), then [84 MANUAL OF HARMONY. all the rules of the harmonic leading of the voices are to l>e ol served at the CHANGE OF THE CHORDS, as wett as in the reduplication. We must not write : 396. but somewhat in this manner : 397. 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 : better : not : 39. r ~ I r -z=l dt:=r^=T4 not better : The harmonic figuration also affords the means for forming one-voictc movements in greater perfection. The examples will begin with this : 399. One voiced: MANUAL OF HA8MONY. 186 That these movements are calculated for an instrument, probablj" such s a violin or clarionet, is easy to be seen. -IOO. Two voiced : Three voiced: In the middle voices: in tho lower voice: in the upper voice: in two voices: The figuration in the four-voiced movement, after thes-e attempts witt the above example, will be equally easy of acoomplishmer t. 186 MANUAL OF HARMONY Instead of this we prefer to select, as an example of manifold figuration, thu following passage from the above quoted quartette movement of Beethoven. IO1. h H - l^*"*' 1 I [-- ' -* -0- -+ * pizz. = -[- L ' ~\~ "" *"^| f - ^ ^ I 4 i ; I] T ^ 9 ; "^- -^ s^ - a * f-a jp^ irl_J^^a * __ aim t=dtE MANUAL OF HARMONY. 187 * This whole rich development rests upon the foundation given in Nos. 890, 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. The Exercises in the Three-voiced Mo *ment. WITH few exceptions, the four-voiced form of writing Ws 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 arr- especially calcu- lated to make the leading of the voices more skillful and many-sided. We begin, as before, with the problems with figured B isses. 402. 188 MANUAL OF HARMVNY. 4 6 63 65 1- 6 5 "1 1 t~T~ rr 2f_J i= 3 _2_ i^L. t -41 The three-voiced movement is sufficient, indeed, for the triad, but Un- loading 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 rale, 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 : 2 3 403. ==pgl p rtIZ^LT-?pSl- 6 a In the fourth measure is found, at NB., the chord of the sixth and fourth of the diminished triad, E-Gr-BS>. It stands instead of the chord of the second, Bb-C-E-G-, of which the fundamental C is here omitted. For four' voices, this place would stand thus: MANUAL OF HARMONY. 186 -101. Concerning this chord, compare what is mentioned page 155. In the fifth measure a fourth represents the chord. Now, altlough i fourth can neither in the three-voiced nor in the two-voiced movemei.^ 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. 4O5. Four-voiced, the above place in Example No. 403 would, complete, stand thus: 406. In the eighth measure of Example No. 403, the chord of the sixtfc, fourth and third is, by the skip of the Alto, formed complete. The tcpth 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, become* a third. Four-voiced this becomes plainer : 100 4O7. MANUAL OF HARMON? I- The closing measure of Example No. 403 shows, through ih that the triad can appear, in such cases, even without third and nfth. 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. 40. IF" . 2- =-F=F j i F -r T- 1 il==iil=ii=?-il^llil 6 75 65 4ft- 43 6t) Clt==t . r_ _ . | r D 6 C 411. 413. Treatment 6-57 i|W ^- ^r r^ i * i F v -* NB. In the fifth measure at NB. appears the real ninth-suspension (through '.he position of the voices), as second, which occurs very seldom, and onlv 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- eion of the seventh, and governs itself according to the progression of thf latter, e. g. 192 MANUAL OF HARMONY. or: Inversion : 413. Exercise in a middle voice. TENOK. D A B|j C OKD D A As npper voice, the selection of the Alto is here most to the purpose. 415. 3__6 I I_<2-_ The same Exercise idth the following determination of chords : DO A 7 B|jG CF B^CY D B|> F o E D A Treatment : 417. m '^TI^lE L_g=I s-- i * - -J'H t^ -- & ~-\ i -- -f - ~ - tr-H T 3 -1 & 64 67 6 * 5 MANUAL OF HARMONY. iy*> The next to the last measure affords the proof, that even the sixth can be suspension. For farther practice, former exercises, which were s;iven for the four- ^oiced movement, may be used. CHAPTER XXII. Chi the Two-voiced Movement. THE great meagreness of the two-voiced movement, in a purely harmonic point of view, allows it rarely to appear adapted for other than contra- puntal labors, in which it first receives actual significance and comes 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 polyphonic move- ment must possess. The omission of one or more intervals will, in every case, necessarily take place in connection with 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 seldom to be introduced, since they appear too empty ; the fourth could only b 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: OFnC-FCAGC Treatment : 19. 6 3 i i E?EE?3=3 T ~ T If 536 63 G 63 <2-_ 194 MANUAL OF HARM CS 7. Tho omission of intervals is plain through a comparison rf the! fun iamental tones of Example No. 418. Want of clearness of the harraony will be rare in connection with this, since each chord explains itself through ts situation, i. e., through the preceding and following harmony. The same exercise with the following marking : F C A 490. . 4J-^-tE g I f tt3i:ir:__ fr- H Treatment: 121. 111=111= -(2- 4 2 F 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- line? tbsy drop the above limitation of a prescribed succession of chorda, MANUAL OF HARMONY 195 CHAPTER XXIII. Harmonic .Elaboration of a given Voice in Melodic 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 our 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. 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. o^ "O^ ^ T* T^^ . T r-[-~rx::T ~r C 11=111=11111 6 6 704 5 -&- _ 9 8 3 7 6 7 6 This treatment, after what has been remarked in connection with the fehree-voiced movemen 4 needs no farther explanation. The harmonic treatment of this melody as middle voice will show it 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. MANUAL Of HARMONS. -. El^f L__?L 1 r~T 1 1 1 r ~ 6 6 7 583984 5 6 987 ^=P&=3= 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. =*= 1IS=* -r art" i r & 6 3 6 3b 2 4 5 6 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 introduce passing and changing notes interchangeably, into the two voices to be added, e. g. e.f. 196. MANUAL OF HARMONY. fi 19? & m 6 5 3 5 ~ 3 7 Of the remaining treatments, that of the cantus firmus in the middle voices will here be given : 427. e.f. 6 7 6 966 _ _ T _ _ m _ f _ a " P^=J_,T^I_ r =?rr ^ii - = i r b^SE^^EE^-:i^EEl t * * - - 9 8 ^ ~ +- As examples of four- voiced treatment, the following may stand here : 428. Given roise : ^f^ia^|^5^EBgEgIEE^^-^T=H| I i- T ff-2 F = F-T ^-=c n^ 1 T- c F ;- 1 1 1 i 198 MANUAL OF HARMONY 429. Fovf-voicd treatment : c.f. ^^-i i 1- -p . -. . . t ft L I 3 98 6 66 5 7 6 74 35t]543 867 =EE=^S ffr-Fi | g^P- a - P P f E NB. 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. irfLf- : w=---~- 1 s i T^fr c.f. p-ai:g-2-= ^HH^P 5 4 3 9 8 7 6 647 5"."g o '._._ j I _i ~T r ZI~LZ3 ^-j?--a -^ ~--\^> r ~ ' "*"-'^ H %: %-E=5L=g:- -%-- - p g o Y& * H *> -iV- It r ~ j 6 '-^~ 1 ~ 7r^ IZ1L tzT^ __tH If we glance at tLe treatments found in this chapter, we cannot fail to tecognize the melodic development of the voices, and herein lies the ground for regarding them as contrapuntal labors ; for exactly in this consists th< 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 voice* move iu 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 taker vip in connection with counterpoint itself. 202 MANUAL OF HARM OUT. CHAPTER XXIV. The Five-voiced Movement. As the doubling of the intervals of a triad is necessary even in iiu 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- lers this reduplication necessary. Farther remarks follow in connection with the examples given. Exercise* 435. = := In the treatment, we can select, according to the position of the voieea, either two Sopranos, two Altos or two Tenors. 436. BOPRANO. ALTO I. ALTO II. TBNOR AM. T-<5 ft 7 - -- n ___ ^ I * fr _ TZ7IIC _ [I _ 1 1 G 6 5 4 2 3 MANUAL OF HARMONY. 203 The oaiue exercise carried out in another manner : P ! 437. SOPRANO I. SOPEANO II. ALTO. TKNOB. BASS. HEF 5iE It pertains also to the independence of the voices, that two voices dc not remain stationary upon one tone or in the octave, if the chords change. In the above example, this is the case in the first and second measures between the second Soprano and Tenor, but here is not faulty, because he same chord only leaves its position, but is exchanged for no other. The following case, however : 43. would be corrected thus : ip' a ^ T ; T* ~|~~T-' g FF _ip_; --o.^^rJp^-:^ _g_ & ' p 1 -- 5rf ' & *-- & *>&& 439. fefcz REMARK. This rule admits, however of frequent exceptions in connectic a with poly- phonic movements, because there other relations present themselves. That the leading of the voices vnll also admit of the doubling of the leading tone, is shown by the third measure of Example No. 437, between the second Soprano and Tenor. A.S in the four-voiced movement, so here in a still greater degree in the 204 MANUAL OF HARMONY. five and more than five-voiced movement, the unavoidablenes of corered fifths, octaves and unisons will appear. That here also the outer voices must progress in pure relations, and a greater freedom be allowed to the middle voices only, may be mentioned again. The following example contains various progressions of this sort : 440 At.TO II. 1_D T I T c * *-) 1 1 TKNOB. R4M. |^EEEE=:SHrfzzt=ttz:t=! . =P=3t=3=if=z=x=K The covered fifth, octave and unison progressions in this example are iudicaied by strokes. The open fifth in the eighth measure, between the second Alto and Bass is not to be avoided, sinco polyphonically the chord of the diminished seventh can, only with difficulty, be made to progress otherwise. The first and second Altoh- in 'fce eighth and following measures could also be made to progress thus : MANUAL OF HARMONY. 20fi 441. +1 _ 4_ a 4 ct & \- TL*tt the voices, particularly the middle voices, must often cross eaci is shown by the second Alto and Tenor in the second and thiid measures. For practice in the five-voiced movement, chorals especially can be used to advantage. The following may be given here : Choral: Allein Gott in der HoV sei Ehr 1 . G C D C D ? G Dy G K G A 442. G C D A 13 'The work in the five and more than five-voiced movement, requires a. simple and natural Bass-progression, and the less artificial and difficult, the latter, so much the clearer and more intelligible the succession of har- mony itself will become ; this is here the more important, since with the fullness of the chords and the necessity of the free movement of tht voices, very unintelligible progressions can easily arise. Tte beginning of this exercise follows here : 4-13. _. o-d l-T-d H-r 3 "-Rz^if^EEfe: '--'-? 2 ^- '~ i i. i i _i cm_^ i c_i c_i_ u_i.:r , i 6 5 6 6 In the repetition, the following succession of harmony can be applied . 206 MANUAL OF HARMONY G G 444. CHAPTER XXV. /Six, Seven and Eiyht-voiced Movement* THE necessity of doubling or trebling increases with the number of th 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 thia manner of writing, because their intervals, in as much as they are subject to a definite progression, do not allow of multiplication^, 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 : 445. b-voietd : ^voiced: B^EESE^g L=;-gi=t=^=S= 1 T -eoiced : 8-voicfd: MANUAL IF HARMONY 207 Progression to the third degree 4-voiced: ft-voiced : 6- voiced: 1-votctd: ~ ' r | I ~ -- 1 ---- ^^-T Progression to the fourth degree : 4-voiced : ^-voiced : 6-voiced . 7 -voiced : S~voieed : *" V- 49- i* * Progression to the fifth degree : 4-voiced ': 5-w'cedr 6-voiccd : T -voiced: 8-voiced: ^J'~ HI5 t Gt \Q t & S _ r--i C 1 1 , L LC We pass over farther combinations ; to try them, with all inversions, will be of great use. As example of the management of the leading of the voices, the choral found under No. 442, may follow here with six voices : 446. N<> i. & II. Tares . & a. - I "ff |-i "/p t I *_t ^p i T rr LIZI t L r t 'r r~ 6 6 5 208 MANUAL OF HARMONY --6> ___fS __ fi g . . e-s, J -fi I 1 r i 9 T I T i 1 r ?* 1 -Mn ' "1 - -F f - 1 -' 1 -H- | T -F F :p-i-?F , 1 r r r F=T 1=^=^- -e - i & 6 6 6 o 4: 7 |^j * ff- ' n 3|~ _ r ~~~ _ -l -J- i i i | j , fl 6 I 2 6 IP 11 3"~ --- gS<- - nj - ^ T~ Ol --- 5* - T-d -- g^ T S< - -g T^ 1 g "j 4 - 677 3 - fl 50 m __ __ _ _ _ _ _ __ m.5lH i"O ~i ^ !~l ~~T~g ' 1 p g< MANUAL OF HARMONY. 209 J _L*J_ r~T |:=g=iT znziipt E^^^f^Al 1 L-^~?. . J. LL ^-J J--T-J i-T-J J-T- ffiu- iJ <^ ' ^ ' ~ -i~3 a Lg_ P-R^-f-fe 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 number 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. SOPRANO I&II. AiTO. TENOR I&1I. BASS. W=g^ l^yfa-g |-g ^f^T^ T~J- = J^ =fci= "* Vp _ T _ T~_ T & [ S> _ | v T E^ZII .=^ZT - LL- -(Og T W ft -ig- ^-T ~g~rr^|~rr f 210 MANUAL OF HARMONY. f^F- ALTO II. TBNOR. BASS. id .i J | i |-i: ~s i-^-S H -f-f- "T " :p=J !=< =RT-* =g :^p : ' ::::= r ;r= tf : ' p MANUAL OF HARMONY. fl *-~^" 1 ' & & E?EtEEEE=tEt5HEE JZc~ -- ~T~^ -- |p 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 : 4tJ. SOPRANI I. & L ,g' T &5< _r 5 T -a>- [- g |- o rf- io- V IV V Among the half-cadences are also counted those closes in the key of tht MANUAL OF HAfyMONY. 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 either through its inversions or through the chord of the seventh of th eyenth degree, e. g. 450 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 n-V, which effects the close of the first division of the whole period ; in the seventh and eighth measures, however, we find a perfect whole 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 ivhole or authentic cadence in the key of the dominant at the conclusion. (Thus this is no half cadence, sicce the dominant harmony of the seventh renders the modula- tion decided). In the choral treated under No. 446, the first strophe ends with an imperfect whole cadence, the second with a perfect whole cadence, the third with a AaZ/"-cadence to E minor (iv-V), the fourth with a perfect whole cadence in Gr major, the fifth with a. perfect 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 G 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, Accompaniment figurated, 183; harmonic accompaniment to a given voice, 151; 178; 195. After-striking of harmonic tones, 121. Alto, 23 ; alto notes, alto clef, 118. Anticipation, 121. Arsis, 107, 138, 174. Bass, 23; movement, progression of the same, 34, 36, 153, 205. By-tones, harmonic, 128. Cadence, 55, 81 ; whole, half, 178, 213; perfect, imperfect, 62, 218; in connection with modulation, 148. Cadence formula, 149, 150. Cantus firmus, 195. C-clef, 113. Ch.orals, as exercises, 175, 205. Chord, 21. Cherd -formations, accidental, 105. Chords, altered, 43, 91, 101; passing, 138; view of same, 99. , see also Triads, Chords of the seventh. Chord of the sixth and fourth, 48 ; the same in the formation of the close, 53 ; in con- nection with modulation, 143; as passing chord, 139; use of the same, 153. of the augmented triad, 92, 198; of the diminished triad, 155, 188. Chord of the sixth and fifth, 59, 60, 62; the same as suspension, 189; augmented, 97; in connection with modulation, 147. Chord of the second, 59, 61, 63. Chord of the sixth, fourth and second (see Chord of the second). Chord of the seventh, 21, l>4; dominant chord of the seventh, 64, 57, 61, 82, 144; sential, 64 ; the same in passing, 1 38. - of the seventh degree iu major, 68, 78, 90, 200. diminished, 76, 79, b7, 90; in connection with modulation, 146; in the poly- phonic movement, 204. Chords of (he seventh, connection of the same among themselves, 73; in connection with chords of other tone degrees, 81, 83 ; view of the same, 100. Chord of the sixth, 47 ; augmented, 94. Chord of the thirteenth, 88, 90. Chord of the fourth and third, chord of the sixth, fourth and third, 69, 60, 62. Chord of the eleventh, 88, 90. Chord of four tones, 54 (see chord of the seventh). Chromatic alteration, 91. Consonance, 17; complete, incomplete; 17. Contrary motion, 2, 135. MANUAL OF HARMONY. 217 Cenntction of chords, 25, 73, 81 ; local, inner, 86. Close, 32 ; authentic, plagal, 32, 33. see also cadence, -whole close, half clos*, deceptive cadenoe. dosing cadence, 55, 81. Closing formula, 40, 41, 149. Cross-relation, unharmonic, 16t. Deceptive cadence, 81. Degrees, diatonic, 13. Digression (see Modulation). Dissonance, 17. Dominant harm ony, C-triad, chord of the seventh in connection with modulation, 144. Eleventh, 14. Exercises, for practice of the primary triads in major, 30 ; of all triads in major, 8? of the triads in minor, 45 ; of the inversions of the triads, 49 ; of the dominant chord of the seventh, 58 ; of the inversions of the same, 63 ; of .the secondary chords ol the seventh, 73; of the connection of the chords of the seventh among themselves, 74 ; of the secondary chords of the seventh in minor, 77 ; of the inversions of the same, 80; of the deceptive cadences, 85 ; of the secondary chords of the seventh in connection -with chords of other tone degrees or keys, 87 ; of the augmented triad, 94 ; of other altered chords, 98 ; iu searching out modulation, 103 ; of the suspen- sions, 112, 119; of the harmonic accompaniment to a given voice, 151, 152, 157, 163, 164, 165, 170, 171, 172, 173; in the development of melody, 177 ; in the three- voiced movement, 187, 191, 192; of the two-voiced movement, 193; in the harmo nic accompaniment to a given voice in melodic development, 195, 200 ; in the five- voiced movement, 202, 205 Fifteenth, 14. Fifth, 13, 22 ; perfect, 15, 16 ; augmented, 16, 16, 75 ; diminished, 15, 16, 38, 60; fifth in the chord of the seventh, 57, 70. Fifth-progressions (parallel fifths), 26, 28, 51, 79, 97; open, 30, 78; covered, 30, 37, 110, 158, 204; in connection with passing and changing notes, 133; in contrary motion, 201. Figuring, 44, 48, 53, 64, 58, 63, 111, 128. Fourteenth, 14. Fourth, 13; perfect, augmented, diminished, 15, 16; preparation of the perfect focrik, 155; the same as chord, 189, 196. Fourth-progressions (fourth parallels) in passing, 134, 136. Formation of the close, 39, 53, 55. Fundamental harmonies, 21 ; chromatic alterations of the same, 91. fundamental, 21 ; in the chord of the seventh, 67. Half close (half cadence), 178 213. Harmony, 21. Harmony, tones foreign to the, 105. Intervals, division of, 17 ; view of the same, 16, 18 ; inversion of the same, 18. see also omission, reduplication. Intervals, doctrine of, 13. Interval, 13; major, perfect, 14; minor, augmented, diminished, IB Interval steps and skips, augmented and diminished, 156. Intervals above, 18. Intervals bc'oic, 18. 218 MANUAL )F HARMONY. Inversion, 47; cf the trhds, 47 ; of the chords of the seventh. 69, 62, 78 (tee also IB tervals). Leading tone, 87, 39, 56, 76, 116, 159, 203. Major triad, 22, 65. Melody, its development, 176; its rhythmical formation, 177. Middle voices, 23. Minor triad, 22, 33, 65. Modulation, 102 ; means for the sarae, 141 ; its extension and completion, 118. Movement, one-voiced, 184; two-voiced, 193; three-voiced, 187; four-voiced, iSr fi?j voiced, 202 ; six, seven and eight- voiced, 206. Movement, parallel, contrary, oblique, 26 Nachsatz, 177. Ninth, 14 ; major, minor, 15. Ninth, chord of the, 88, 118, 127. Ninth-suspension, 118. Oblique movement, 26. Octave, 13 ; perfect, augmented, diminished, 15, 16. Octave-progressions (octave parallels), 26, 28; open, 30, 110, 133; covered, 80, 86, II, 84, 158, 208; in contrary motion 2 201. Omission of intervals, 57, 73, 188, 193. Organ-point, 123. Outer voices, 1 1. Pass ; passing notes, 128, 134. Passing chords, 138. Period, 177. Plagal close, 33, 41, 213. Position of the chord, close, open, dispersed, 31, 32, 114. Preparation, of the seventh, 70 ; of the suspension, 107. Prime, 13; perfect, augmented, 15, 16. Primary chord of the seventh, 54, 64. Primary triads, in major, 23, 33 ; in minor, 40. Progression, melodic, unmelodic, 155, 156. of the secondary chords of the seventh, 66, 73, 81; see also resolution, out unison, octave, fifth progressions