LIBRARY 
 
 OK THE 
 
 University of California. 
 
 GIFT OF 
 
 Mrs. Jämes L; de Fremery. 
 
 Cla s 
 
EDWARD SCHU BERTH & CO. 
 23 UNION SQUARE, NEW YORK. 
 
RIC TITER'S 
 
 MANUAL OF HARMONY: 
 
 PRACTICAL GUIDE TO ITS STUDY 
 
 PREPARED ESPECIALLY MB THB 
 
 CONSERVATORY OF MUSIC AT LEIPSIC. 
 
 BY 
 
 ERNST FRIEDRICH RICHTER, 
 
 TOTVTSRSITY MUSIC-DIRECTOR, ORGANIST OF TUE CHURCH OF ST. NICOLAI. AND It 
 oTRUCTOR IN THE CONSERVATORY OF MU8I0. 
 
 TRANSLATED KEOM THE LATEST GERMAN EDITION 
 
 By JOHN P. MORGAN, 
 
 ALUMNUS OF THX LEIP31C CONSERVATORY OF MUSIC, AND PUPIL OF THE AUTHOR 
 
 SEVKV'/EKXTif i;i'-ITH)N. 
 
 NEW YORK : 
 G. SC HIE MER, 
 
 IS'.)' i. 
 
I frjf 
 
 Entered, according to Act of Congress, in the year 1867, by 
 
 G. SCHIRMER, 
 
 In the Clerk's Office of the uistrict Court of the United States for the Northern District of New York. 
 
 6100 
 
TRANSLATOR'S PREFACE 
 
 In offering to the American public this translation of Richter'! 
 Harmonielehre we need have no hesitation in saving, tnat we 
 offer a translation of the best re.ri-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 one 
 which would omit or add something. 
 
 A few clauses or words which seemed necessary for clearness, 
 have been enclosed in square brackets. 
 
 The whole work has been performed as a pleasant duty to a 
 
 235911 
 
IT TRANSLATORS 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, Rev. Jokn 
 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. 
 OTuw 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 bt 
 these fundamental features always accompanied by reference ana 
 guidance to the practical application, in order to qualify for late- 
 attempts at composition. 
 
 The book contains no scientifically theoretic treatise on hai 
 mony, but, although as far as is the <*ase with any system oi 
 harmony, it is supported upon a firm basis, is only dedicated t< 
 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 
 eo clear that no doubt would be possible, much as it shrinks on the 
 other side,from learning, by means of the anatomical knife, to know 
 and understand the blooming life of art ; and it is not to be denied 
 that in this respect a want is found in musical literature, which 
 no one has as yet entirely succeeded in supplying. All attempts 
 
PREFACE. 
 
 of the sort have as yet failed to create a really tenable äcientifi. 
 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 in musical 
 text books of a scientific basis, has not, however, hitherto verified 
 itself, because it in part as application of single learned investiga- 
 tions, was just as little able to create a system complete in itself, 
 with indubitable conclusions, and in part, as a fanciful structure, 
 was utterly without scientific basis. * 
 
 Still, rightly regarded, this deficiency is perceptible only to the 
 riper and educated musician, who likes to busy himself with theory, 
 aot, 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 
 Btand-point, starting from which he can with greater ease advance 
 towards the position of a real artist. Here the question to be 
 .sked is not Why ? the inquiry of immediate application is, How ? 
 
 * It may here be permitted to call attention to a work which might be adnpted U 
 meet n palpable want : Die Natur der Har?n<mis und Metrik by M. Hauptmann. 
 
PBEFACE. VU 
 
 The thing to be done is, from experience, from the best 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 the why, and all knowl- 
 edge obtained from experience will be an aid not to be despised, 
 for discovering also the laws of nature pertaining to music. 
 
 This practical aim in view, the author was at pains to give the 
 exhibition of harmony, and of the propositions resulting from 
 observation and experience, in a simple and clear manner, and since 
 he destined the book for study, 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 
 
riii 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 
 
FROM THE PREFACE TO THE THIRD EDITION 
 
 Although in the present edition also, the methodical order of 
 the former ones has been retained, still it has received material 
 additions. The exercises for many subjects of instruction have 
 been increased in number, where it seemed necessary. 
 
 As concerns the last, some books have appeared lately which 
 are in a measure related to the present manual, viz : Grneralbafsft- 
 Uebunyen nebst Kurzen Erläuterungen by Benedict Widmann, and 
 Uebuiyjen zum Studium der Harmonie und des Contrapnnkies, 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 works 
 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 PKEFAClü. 
 
 work ot HiLLEit, 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 foi 
 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, wxien needed, to design others after them, both works 
 may here be highly recommended for this object. 
 
 PREFACE TO THE FIFTH EDITION. 
 
 It has been my endeavor in this fifth edition, also, which 
 became necessary in a short time after the fourth, through addi- 
 tions, in part through altered verbal expression, to attain that 
 perspicuity, which a text book of this kind must possess, if it ful- 
 fill its end completely. If I may also venture to hope that the 
 book has been in many directions serviceable and of use, I am 
 still conscious, that in order to reach the simple arid luminous 
 representation which is my ideal, many an improvement is still tc 
 be introduced. This edition, however, does not differ essentially 
 from the preceding, and I wish, that beside the old friends, this 
 new edition may gain for itself new ones. 
 
 ERNST FRIEDR. RICHTER. 
 
 Leipsjo December, 1863. 
 
TABLE OF CONTENTS. 
 
 Introduction.— Intervals, 
 
 18 
 
 PABT I. 
 
 THE FUNDAMENTAL HARMONIES 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, 4.7 
 
 IV.— Harmonies of the Seventh {Vierklänge), .... 54 
 
 V.— The Inversions of the CnoRD of the Seventh, . . 59 
 
 VI.— Secondary Harmonics of the Seventh, 64 
 
 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, . 88 
 X. — Chromatic Alteration of the Fundamental Harmonies. Al- 
 tered Chords, 91 
 
 H. — On Modulation of a Passage of Music, .... 108 
 
 PAKT II. 
 
 1CCTDENTAL CHORD FORMATIONS. TONES FOREIGN TO THE HARMONY. 
 
 XII.— Suspensions, . 105 
 
 XIII.— The Organ-Point Stationary Voices 123 
 
XI" CONTENTS. 
 
 OHAPTKB HG» 
 
 XIV. — Passing Notes. Changing Notes, ... 28 
 
 XV.— Passing Chords, ... ... . AÖti 
 
 XVI.— On the Means for Modulation, .... .14) 
 
 PART III. 
 
 PRACTICAL APPLICATION OF THE HARMONIES. THE EXERCISES IS 
 THEIR USE IN THE PURE HARMONIC STRUCTURE. 
 
 XVII.— Ths Simply Harmonic Accompaniment to a Given Voice, . 157 
 XVIII. — Extension of the Harmonic Accompaniment, . . 173 
 
 XIX.— On the Development of Melody, 176 
 
 XX. — On Development of the Accompanying Voices, . . 188 
 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 Movement, ■ . 206 
 
 XXVI.— On the Mdsial Forms of Close, . . . 218 
 
 Index of Subject«, IKS 
 
JUST PUBLISHED! TN COXXECTIOy WITH TIIIS WORK: 
 
 ADDITIONAL EXERCISES by ALFRED RICHTER. 
 
 Price, 50 cents net. 
 
 INTRODUCTION 
 
 Of the elementary knowledge for which general instruction u. 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 differenca 
 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 degrto . 
 
 The numbers of the degrees produced thus, will be expressed in the 
 following manner : 
 
 1 2 3 4 5 6 7 8 
 
 Vni*o* « r Prims. Second. Third. Fourth. Fifth. Sixth Seventh. Orta—. 
 
U MAN UAL -OF HARMONY. 
 
 As a rule, we reckon only to the octave, and begin the series ag-ain 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 
 second again. 
 
 Reasons, however, which find tbeir 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 : 
 
 Octave. Ninth. Tenth. Eleventh. Twelfth. Thirteenth. Fourteenth. Fifteenth. 
 
 ■«■ *■ - 
 
 Second. Third. Fourth. Fifih. Sixth Seventh. Octave. 
 
 Greater distances between two tones, are simply reduced to their rela 
 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 tonea 
 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 shown above, in which the loivest 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. 
 
 Tims, for example, if to the fifth (? a sharp is in any way attached, it 
 remains always -a fifth, but requires, however, a more particular dete-uiina- 
 
M A N U A L O F H A A' M O X Y. U 
 
 lion, since it Las evidently become a different fifth from what it was otig- 
 inally. 
 
 Or, 
 
 Since now such alterations of the intervals take place through ohromati 
 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 tht 
 major scale, taking ha 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 iutervals result. 
 
 3-. If the upper tone of [most] major and perfect intervals be raised, a 
 Bmall 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 
 
 Prime. Second. Third, Fourth. Fifth. Sixth. Seventh. Octave. Ninth. 
 
 To 2. 
 
 Minor Minor Minor Minor Minor 
 
 t m: 
 
 f 
 
 •» •#■ ■*» 
 
 Second. Third. Sixth. Seventh. Ninth. 
 
 To '6 
 
 Augmented Augmented * Augmented Augmented Augmented 
 
 "fe 
 
 Prime. Second. Fourth. Fiflh. Sixth. 
 
 To 4. 
 
 Diminished Diminished Diminished Diminished Diminished 
 
 77iiri Fourth. Fißh. Seventh.. Octave. 
 
 •Augmented thirds, sevenths and ninths do r.^t occur in harmonic relations. Aug 
 wented octaves are to be regarded as augmentert primes. 
 
It) MANUAL OF HARMONY 
 
 Remark. — Diminished primes, seconds, sixths and ninths, are harmonically inoon 
 eeivable, although they can he conceived of ir melodic relations, i. e„ m 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 tone has b«en 
 raised, notwithstanding that a like interval would result, if the upper tone were kir 
 ered, lies in the peculiar relations of all the intervals in regard to their inversion, whica 
 will be spoken of farther on. 
 
 General riete and Classification of the Most Used Intervals, 
 
 Pkimks. Skoonds. 
 
 Perfect. Augmented. Major. Minor. Augmented. 
 
 =ZT„3=I 
 
 illäü 
 
 = >#— l -^ #*- 
 
 Thirds. Fourths. 
 
 Major. Minor. Diminished. Perfect. Augmented. Diminished. 
 
 pp^^==%E££pp 
 
 Fifths. Sixths. 
 
 Perfect. Augmented. Diminished. Major. Minor. Augmented. 
 
 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 Er- 
 stand thereby, not well or ill sounding ones, whicb, to be sure, can be 
 expressed by these two words, but by the first, we understand such an 
 Btand 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. 17 
 
 The first are called complete consonances, the 'ast incomplete. 
 The dissonances are the major and minor second, major and minor 
 Berenth, 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 octatH. 
 1 4*5 8 
 
 ■&■ *»■ ^ 
 
 b. Incomplete. 
 The niajcr and minor third, and the major and minor sixth. 
 
 ■-%- 
 
 II. DISSONANCES. 
 
 The augmented prime, the major, minor and augmented second, the 
 diminished third, the augmented and diminished fourth, the augmented 
 and diminished fifth, the augmented sixth, the major, minor and dimin 
 ibhed seventh, the diminished octave, and the major and minor ninth. 
 
 Augmented \ Mujor. Minor. Aug. 2 
 
 
 *j$* *£ Hi- jfc — p *£ 
 
 Aug. Dimin. 4 Aug. Dimin. 5 Aug. 6 
 
 Major. Minor. Dimin. 7 Dimin. 8 Major. Minor. 9 
 
 * f* f* 
 
 •Later in the instruction 111 harmony, follows a farther eyplauatiou af th<> peculiar 
 «elations of the fourth. 
 
18 MANUAL OF HARMONY. 
 
 Inversion (Versetzung) of the Intervals. 
 
 As was already indicated above, in determining the intervals we begiu 
 as a rule, with the lower tone. If, however, there is occasion to determine 
 the relation of two tones, taking the upper tone as the starting point, the 
 intervals found are called intervals below. 
 
 Thus, for examp e. /W • is d, the fifth from g ; g, however, 
 
 m 
 
 fron, 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 be removed below 
 the original lower tone. Since particular reference is had to this inversion 
 in various kinds of composition, an explanation of it may follow here. 
 
 The diatonic major scale will, by means of this inversion, assume the 
 following form : 
 
 Intervals above: 1 
 
 2 3 4 5 6 7 8 
 
 ** A "2. 
 
 V 
 
 fa—"**- 
 
 ©** a ö- » g. v Q V9 
 
 y 2 — *- 
 
 interval» below : 8 
 
 5, 9- «S 
 
 7 6 5 4 3 2 1 
 
 There result thus, the following series of numbers : 
 
 
 12345678 
 
 
 8 7 6 5 4 3 2 1 
 
 It 
 
 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 
 d:minished, and the diminished augmented. 
 
 In the following table is exhibited a view of all the inversions : 
 
 Obiuinal 
 
 (itckvair. 
 
 Primes. Seconds. 
 
 Perfect. Augmented. Major. Minor. Augmented. 
 
 OCTAVKS. SrVBNTHS. 
 
 Perfect. Diminished. Minor. Major. Diminished. 
 
 EE3 
 
 led. 
 
 ;>< 
 
 iK 
 
MANUAL OF HARMONY. 
 
 U) 
 
 Thirds. Fourths. 
 
 Major. ifhur. Diminished. Perfect. Augmented. Diminished. 
 
 Sixths. F:fthb. 
 
 Minor. Major. Augmented. Perfect. D.minished. Augmented. 
 
 Fifths. 
 Perfect. Augmented. Diminished. Major. 
 
 Sixths. 
 Minor. 
 
 Augmented. 
 
 _ -g _ E rg:.-^[i- [:^"=:c=3-orz^E-EiQ^z^EiiE : 
 
 =E£ 
 
 1 
 
 Fourths. Thirds. 
 
 Perfect. Diminished. Augmented. Minor. Major. Diminished. 
 
 3=T 
 
 e^ü^ü^iPf 
 
 Major. 
 
 sevenths. 
 Minor. 
 
 Octaves. 
 
 Perfect. Diminished. 
 
 
 g 
 
 kg 
 
 Major. 
 
 Augmented. 
 
 Primes. 
 
 Perfect. Augmented. 
 
 \=^E^E^^0^^0E^^l^^^\l 
 
 An exact, certain knowledge of this essential inversion of the intervals 
 »s 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 
 
 must of necessity give the following dim- 
 
 inished fifth 
 
 Just so the perfect fourth belongs originally to the consonances, siao* 
 
20 MANUAL OF HARMONY 
 
 by inversion it is converted into the perfect fifth, in the same manner as 
 the perfect fifth can only produce the perfect fourth, and never in any case 
 does a dissonance result from the inversion of a consonance in the octave. 
 Mention is made of this here because, in particular cases which are men 
 tioned farther on, the fourth' requires a similar treatment with some 
 dissonances, which induced some theorists in earlier times, to explain it 
 simply as a dissonance. 
 
 It will likewise be clear that the augmented octave, as also the ninth, 
 cannot be inverted, since they never can become intervals below. 
 
 Other kinds of inversions, such as those in the tenth and twelfth, which 
 produce entirely different results, may be passed over here, since they ex- 
 ercise no influence upon our next studies. 
 
 Since a complete and certain knowledge of all intervals is indispensable 
 for the following harmonic studies, the practice of them in writing, as als« 
 an oral solution of given intervals, will facilitate much their correct com- 
 prebv«ioi2 ) — which exer'.iwd •*■* to »»e repeatedly employed. 
 
HARMONY. 
 
 Combinations of simultaneous tones, formed from different intervals, 
 according to certain fundamental principles, are called in geneial, Harmo- 
 nies. Chords. 
 
 The doctrine of harmony makes us acquainted with the different species 
 aud 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 HARMONIES AND THE CHORDS DERIVED 
 FROM THEM. 
 
 Among the various kinds of chords which can serve for the harmoni" 
 foundation of a composition, those which present themselves as indepen 
 dent, without a definite connection with others, can be easily distinguished 
 from those which indicate plainly a connection with other chords, and ar 
 therefore not independent. 
 
 To the first belong the most of the triads, to the last the chords of the 
 seventh. These two kinds form the fundamental harmonies, from which 
 all remaining chords are derived. 
 
 CHAPTER I. 
 
 Tlie Triads of the Major Scale, 
 
 A triad is formed by a combination of three different tones. Of these, 
 *ie lowest is called fundamental tone, to which its third and fifth are 
 ded, e. g- 
 
 t= 
 
22 MA N UAL OF HARMONY 
 
 These triads, formed upon c, g and a, present, however, a difference as tt 
 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 perfect 
 fifth. 
 
 A tr'ad with major third and perfect fifth is called a 
 MAJOR TRIAD 
 
 A riad with minor third and perfect fifth a 
 MINOR TRIAD. 
 
 Hex «uk. — The explaDat on of other kinds of triads cannot follow until farther on. 
 
 As the diatonic scale makes up the content of a key, and forms the 
 foundation of the melodic successions, so also the triads, which are founded 
 upon the different steps of the scale, will form the essential part of the 
 harmonic content. 
 
 Natural Connection of the Triads of a Key. 
 
 The triad which rests upon the first step of a key, is indeed the most 
 Important, the one which determines the key ; there stand, however, others 
 in the nearest connection with it, which make clear its position. 
 
 In the natural presentation of the triad in thirds, the lowest tone showa 
 itself as fundamental, the fifth as highest tone, and at the samp, time as 
 ts culmination. 
 
 Each farther addition of a new interval would either alier 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 
 's here the fifth, will thus form the fundamental of the one nearest 
 standing triad, while c will in the same manner form the culmination, the 
 fifth of the other, the fundamental of which would be F. 
 
 The connection of these three chords can be most plainly presented in 
 the following manner : 
 
 3.9= 
 
 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 ; tiiat 
 they form the fundamental features of the key, and that they are, and must 
 
M A N V A L F IIA ji M ON i 
 
 23 
 
 be tbo.se most frequently employed in practice, if the key is to present 
 itself clear and distinct. 
 
 On account of their importance also, especial names have been given to 
 them. The one first found, standing upon the first degree of the scale, 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 scale. 
 they present themselves to us thus : 
 
 I IV v 
 
 and they show themselves collectively, as major triads 
 
 Application of the Harmonies Discovered. 
 
 In the application of these three, as well as of later chords, we 8 vail 
 ourselves of the four-voiced manner of writing. 
 
 Remark. — The theoretical chord combination can be well presented, to be sure, three- 
 voiced in manifold relation. It would, however, detain us longer from our practical 
 aim, and may, for this reason, be reserved for a special presentation. The four-voiced 
 movement will always maintain its importance as the foundation of all kinds of com- 
 position. 
 
 We regard, however, each harmony not as a mere mass, as compositions 
 for the piano-forte often present them, but divide its component parts intc 
 ^our different voices. 
 
 The upper is called Soprano, the lowest Bass, these two together are 
 :alled the outer voices : the voice next below the Soprano is called Alto, the 
 3ne next above the Bass, Tenor; these two together are called middle-voices. 
 
 The arrangement of these voices in the manner of a score is as follows, 
 ind the triad may be exhibited thus : 
 
24 MANUAL OF HA R M ONT. 
 
 Fjr the upper three voices especial clefs are used, which confonu in.ttei 
 to their lompass than the above used violin [G] clef, and vHiich will ba 
 Bpoken u: 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 o/ 
 writing for the piano, (upon two staves). 
 
 The distribution of voices in No. 5, rnav be exhibited thus 
 
 Soprano. 
 
 A LTO. 
 
 Tenor. 
 
 §lli^=!Eh=i=h=!=l=i^b|^l: 
 
 mmmmmmmmimzi^ti 
 
 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 oi 
 music itself, the observance of which will afford the safest foundation for a 
 later free use of the materials for composition. By exercises %n the pun 
 harmonic structure is the judgment sharpened, the sense for the true 
 and correct formed, and the taste purified. 
 
 Remark.— Inasmuch as every composition should exhibit seit', through a correct 
 *se of all means at command and the purity resulting therefrom, (pu.ity is here syuouy- 
 nous with natural expression), the term pure harmonic stnu-tum in a general sense, 
 would require uo farther explanation, as being a matter of cuinse. In a more narrow 
 »ense, however, under pure harmonic structure we understand something farther, which 
 in more nearly and better indicated by the expression of like meaning, strict harmonic 
 ttructure, strict style, since this can be used in distinction to free style, whereas, properly 
 gpeaking, no antithesis of the pure structure, such as, perhaps, impure structure, is to be 
 assumed, since, as frequently as the latter iu fact may occur, it were certainly to b« 
 designated as false, while the free structure might be essentially founded upon the legiti- 
 mate of the pure structure. 
 
 As was indicated ahove, by jure harmonic structure is understood in a narrower bpub^ 
 
M A N U A L OF II A R M _V )' Jft 
 
 *ucn « une as in the natural development of all torn relation», allow» ihe fevdatthjrt 
 
 from the legitimate, and only such as do not toi«h that which is essentia'., fundamental 
 jf, in what precedes, the idea of pure harmonic structure is determined iu 8 geuera 
 way, still its boundaries are not yet drawn ; and just this is a poiut which gives rse to th 
 more difficulties for the beginner, as the boundaries are so very variously determined bj 
 the theorists themselves. This difficulty has occasioned many of them, especially s<-nie 
 later ones, to omit entirely to speak of the pure construction, of the strict ßtyle; indeed 
 to begin immediately with composition, and teach the laws of harmony from its inci 
 dents. Whether this indulgence to youthful impatience, which does not willingly busy 
 itself with the abstract, this inclination towards premature living creation, before the 
 organic has developed itself to the capability for creation, can produce anything really 
 mature, need not be further investigated here. 
 
 Let those who follow the views of this book and conform their studies to them, aa 
 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 -vhich is forbidden to them, but 
 will unfold itself so much the more fully, and with a more living power, upon ;i basis 
 conformed to nature. The real mastery has ever been able to make itself apparent 
 most genially within prescribed bounds, whereas the most lawless conceits frequently 
 furnish proof of morbidity and weakness of mind. On the other hand, the pupil cannot 
 be justified in making use of exceptions to given principles, which may perhaps be found 
 in the works of the greatest masters, where the rule is concerned ; or, in any case, to wish 
 to produce compositions, when the thing to be done is to work out exercises theoretically 
 •well. 
 
 The three chords thus far knov<j, being applied in the four-voice 
 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 most 
 adapted for doubling, more rarely the fifth and third, and, indeed, the 
 latter, in many cases which will be shown later, is not to be doubled at all 
 
 In order to accomplish the connection of two triads, the following rale 
 is to be observed : 
 
 If a tone occurs in both of two chords which are to be count dei, it w 
 to bt retained in the same voice, e. g. 
 
 Ifl^i^ 
 
2fi MANUAL OF HARM OAT. 
 
 In the Example a, C occurs in both triads as common tone ; the Sopiano 
 which gave the first C, retains it also as fifth of the next chord. Just sc 
 in Example b, in which the Gr of the Alto affects the connection. 
 
 The remaining voices vroceed to the tones which lie nearest to them, as 
 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 inaependently 
 hd in such a manner, that none appears with any other in parallei 
 
 FIFTHS or OCTAVES. 
 
 In or dei- 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 the Movement of the Voices in Respect U. 
 each other. 
 
 One voice can progress with another in 
 
 Parallel [direct] motion (motus rectus), 
 Contrary motion, (motus contrarius) and 
 
 Oblique motion, {motus obliquus). 
 
 The parallel motion arises, if two voices rise or fall at the same time, e 9 
 
 i 
 
 They progress in contrary motion if the one rises and the other falls, e g 
 
 
 rr 
 
 The oblique motion arises, if, of two voices one remains upon the same 
 tone while the other moves on, e. g. 
 
 
MANUAL OF IIA R HON > 
 
 27 
 
 Thcae three kinds of movement of the voices oocur in chord connections 
 m a mixed 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« 
 iug voices. 
 
 The above mentioned faulty movement of the voices in parallel octavts 
 and fifths, can only appear in parallel motion : if, for example, two 
 voices progress by degrees jr skips in the following manner : 
 
 This fault is regarded as such for all voices. 
 
 The following connections of harmony contain both faults * 
 
 smmmmmssm 
 
 t) ; : 
 
 In Example a, are parallel octave skips between Soprano and Bass; in 
 Example b f octave progressions between Alto and Bass, and in Example c, 
 between Tenor and Bass. Parallel fifths are to be found in a, between Alto 
 and Bass ; in b, between Teuor and Bass, and in f , 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 the 
 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 VZ, CI the oblique motion in respect to one voice, and at 
 h and C, the contrary motion of all voices in respect to the Bass, is to b« 
 applied, *. g. 
 
 13. 
 
 §iH=ii=i=i=!=li 
 
2g MANUAL OF HARMONY. 
 
 Rema&k. — The reason for the prohibition of octaves, witn whi.'h is con ected that « 
 the progression in unison, can be easily found in the neetssary independence of the voice». 
 It is more difficult to discover the ground for the prohibition of the profjresnon 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 
 Mk lullowiug 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 *h« 
 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 
 ehord, sc 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 - i l^P=3=l =g==gg=EP 
 
 The sevenths, however, neither form, properly, new chords, nor do they lie, (according 
 to the idea of a seventh) outside of the circle of the original chord, and only serve to indi- 
 cate the relations of two choids, and to make the connections of the harmonies mor-s 
 intimate and firmer. 
 
 Everywhere now, where the perfect fifth appears, it will cairy in itself its character 
 of boundary ; the remaining constituents of the chord, (as it were the content of thfe 
 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, iu 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 withe <ut con- 
 nection, e. q 
 
 15. 
 
 Illii^iff; 
 
 i i 
 
 llililiilB 
 
 At concert« ths diminished fifth, however, which in the dominant «hord oi Um 
 •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 aftei 
 the perfect fifth, its connecting chiracter makes itself felt, whereas, before the perfect 
 
MANUAL OF HARMONY. 
 
 fifth, lea\ing cut 01 the account its farther laws of progression, the latter immeil'rteij 
 iteps outside of the circle of connection of both harmonies. 
 Compare the following examples, 
 
 16. 
 
 J ^* 
 
 e*--i — s r — gj e^-af-*« — i t ~ur~^ 1 r 
 
 fi ^ S - 3B — F- g — g^ ^ ?b I fl^" a -I E 
 
 If, however, instances oi' the following sort are frequently found in composition» of 
 the stricter style : 
 
 17. 
 
 we may assume that the doubling of the diminished fifth (the/,) requires a double pro 
 gression of the same, and that the fifth-succession is thereby justified, because it lies is 
 the middle voices ; that, however, the following progression could not be called pure, 
 
 18. 
 
 9- 
 
 partly because they come forward too prominently in the upper voice ; partly because 
 the above condition of the necessary double progression is wanting, although instance! 
 such as No. 16. c, are often to be heard. 
 
 Hereby it becomes clear, also, why such parallel fifths as arise from passing notes, 
 in many cases do not sound so unpleasant as those spoken of above, for which reason 
 many theorists recognize them as faultless ; which, at any rate, cannot be unconditional! j 
 admitted, since many of them are based upon other false voice-progressions, (for exam- 
 ple, upon covered fifths), and it is not to be denied, that with a very open position and 
 sufficient duration of the same, the unpleasantness of their operation becomes per 
 eeptible. 
 
 Tt is not the place here, to treat at greater length of these relations, and there would 
 be much to say on many points ; as for example, concerning the progressior ->f the fifth 
 of the augmented chord of the sixth and fifth, wlüch would here carry us too far. 
 Individual cases will bring us back to this point in connection with our prnct.oJ 
 exercises 
 
SC MANUAL OF H A R AI S 1 . 
 
 If the sense of the foregoing representation should still be too obscure to the begin- 
 ner, yet with more advanced knowledge, and exercises, and necessary frequent 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. 
 
 HlHil 
 
 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 oi 
 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 : 
 
 C: I V I IV V I 
 
 Rkmark. — These, as well as all subsequent exercises, give an indication in what wa* 
 and manner our practical exercises will proceed. They are always tobe continued s*.- 
 long as the point under consideration makes it necessary. 
 
 The situation of the upper three voices of the first chord, which arc to 
 be added, will yet give us occasion for important remarks. 
 
 * The figure over the Bass-note indicates the proper interval for the Soprano of the 
 first chord. — Eo 
 
MANUAL OF HARMONY. 
 
 31 
 
 We have already seen in Example 5, that the situation of the voices .n a 
 chord can be very different. This situation of the voices is called the 
 vosition 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. 
 
 
 The first position of the chord a is in b 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 G and E ; on the other hand, in </, 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, c. g. 
 
 22. 
 
 hp^h^hi 
 
 m 
 
 mmM^mmi 
 
 At a 9 the chord appears in open position ; by a transposition of the Q 
 between the Alto and Soprano in close position b; just so at c and (/. At / 
 the G of the Soprano of the cho»-d e 9 is placed an octa\e lower betweui the 
 A.lto and Tenor. 
 
 In this sense, however, the following situation of the voices (No. 23) 
 would not be open position, for by the transposition of the Tenor, the 
 situation of the apper voices would not be altered, b f and onlv tu« 
 
32 
 
 MAS UA L OF HA R M NT. 
 
 transposition of the Soprano would produce the real open position of the 
 chord, c. 
 
 23. 
 
 Even if the open position allows the chord to appear fuller, still it is 
 Dot always to he applied, and, for our first exercises, is not clear e.iough to 
 the view ; so that we will for the present, write them in close position. 
 
 Remaek. — It -will always be better in the beginning to work out the examples in 
 close position, and only to use the opeu position later, from the examples of the second 
 fend third part onward, in which last they necessarily present themselves. In the begin- 
 ning, the pupiL in the use of the open position, stumbles now and then upon iifficulties, to 
 overcome which cannot be our immediate object, and which had therefore better be 
 evaded. 
 
 The various positions do not generally appear single, but occur com 
 bined, according as the leading of the voices requires. 
 
 If the position of the first chord is determined, the following chords ai 
 n j longer so free, as to their position, that each can be chosen at pleasure, 
 but it is regulated according to the rules for the connection of chords 
 already given, pages 25 and 26. 
 
 This connection of chords and the leading of the voices of the first 
 exercise, No. 20, may follow thus: 
 
 •2 1. 
 
 
 The natural relation of these chords to one another becomes dear bj 
 the above simple example, if we observe accurately their connection, 
 especially, however, from the last two chords does the close sonnection. 
 the mutual completing of one another, become plain. The feeling oi 
 return, of rest, of satisfaction, which lies in this connection of chords 
 adapts them for forming the close. This form of close through the domi- 
 nant chord, which resolved itself into the tonic triad, is called, if the lattei 
 falls upon th • rythmical accent, the authentic close. [Cadence]. 
 
A X UAL OF UA R M N Y 
 
 25. 
 
 BFEESEF 
 
 Another form of close, which is formed by '.he subdominant triad, u 
 »bove, No. 20, Example 4, is called the plagal close. 
 
 itl=f 
 
 26. 
 
 m 
 
 g=EE^=8 
 
 Of these and other kinds of close, we cannot speak more at length, untü 
 later 
 
 In order to become expert in writing the succession of chords which 
 occurs if the Bass progresses by degrees, (as in Example 24, F — G), it will 
 be to the purpose to write the successions IV-V and V-IV, in various 
 positions and keys. 
 
 Note. — The expression by degrees is used Lere, as elsewhere in similar connection, U> 
 denote from one degree to the next, in distinction to by skips, viz., from one degree U 
 another at a greater distance. — Ed. 
 
 The Triads of the Remaining Degrees of the Major Scale. 
 
 All triads of the remaining degrees of a scale will, to be sure, belong 
 to one and the same key, but will not indicate it so decisively as, for exam- 
 plo, the combination of chords V-I. 
 
 These triads are called, to distinguish them from the primary triads, 
 
 SECONDARY TRIADS. 
 
 They are situated upon the second, third, sixth, and seventh degrees of 
 the scale. 
 
 27. 
 
 ?Pl3=e! 
 
 The triads of the second, third, and sixth degrees, appear as minor 
 triads, since their thirds are minor and their fifths perfect. 
 
 The triad of the seventh degree is materially different from the other», 
 
34 MA N UAL OF HA R M .f 7 . 
 
 because that, beside the minor third, it contains a diminished fifth ; foi 
 this reason it is called the 
 
 DIMINISHED TRIAD 
 
 We select as an easy distinguishing sign, for the minor triad, a small 
 numeral for the designation of the degree upon which it 'is situated, to 
 which, in the case of the diminished triad, we add a 0, as above vii°, a 
 manner of writing which the theorist, Gr. Weber, has introduced. 
 
 All the triads of the major scale can now be exhibited thus : 
 
 WEE äUb — &— g g — * 
 
 Remark. — The beginner must be very careful not to conceive of these chords, at their 
 appearance, as all tonic triads, a misunderstanding which renders insight into harmonic 
 «ombmationa much more difficult. As long as C major is the ruling key, the triads of 
 G, F. D. etc., are nothing else than the chords of the various degrees of this key of 
 major, and belonging to it, and no mention will be made of G major, F major, d min^r 
 so long as these keys do not appear as independent. 
 
 Hereby arises an ambiguity of the chords, -which should be particularly noticed 
 lach triad can belong to various keys. The major triad of C can be : 
 
 C: I F: V G. IV 
 
 -illl^fil 
 
 li, therefore, in respect to this chord, C major is spoken of (expressing the key in the 
 general use of language), this is true only in the first case, if the C major triad oecu 
 pies theirs« degree ; in all other cases, however, it is incorrect 
 
 Application. 
 
 In the connection of these chords, as well among themselves a»s also 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 tw 
 consecutive chords) ; in the last the progression of the voices must be in 
 contrary motion, according to a rule mentioned above, (page 26), in order 
 to bring out the inner connection of the chords. 
 
 See Translator's note on pa»e S3. 
 
M AX UAL OF HARMON Y. 
 
 a. The Bass progresses by skips 
 
 b. NB. 
 
 30 
 
 ilglllgllilp 
 
 ii IV u \ 
 
 m=i 
 
 As in this example, the skips in the Bass from the second degree have 
 been treated, the same can be treated beginning from all other degrees, so 
 that tones common to the 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, aud 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 iu 
 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. 
 
 II 
 
 mEmmn 
 
 Remark —The reason, however, -why exactly this tone should be conceirea at «indole, 
 eiuce this ould also be the case with any tone at pleasure, is founded upun 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 iu the circum- 
 stance, that the upper voice progresses a whole step, aud is yet inor« 
 noticeable if it is contained in the outer voices, as in Example 32 fit a. 
 
 32. 
 
 iiliiiiüüf 
 
36 
 
 MANUAL OF HARMONY. 
 
 By the contrary motion of the Bass at b, the hading of the voieei 
 oan be improved ; in like manner, by the contrary motion in Example c. 
 although here also a covered fifth shows itself between Soprano and Tenor 
 (See the Remark on Example 34). 
 
 Remark. — In tie cases brought forward above, we do not speak of absolute fault* 
 h 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 firmns, of a 
 motive, or on other grounds important for the composition, is unavoidable. The 
 improvement is here only presented from a theoretical stand-point. Concerning the 
 covered fifth in No. 32 c f a farther explanation follows at No. 34. 
 
 The unpleasantness of the covered octaves spoken of ceases at onoe if 
 ths upper voice progresses a half step, e g. 
 
 33. 
 
 fe 
 
 fUPfi 
 
 s 
 
 (illiiilli^illillf 
 
 h. The Bass progresses by degrees. 
 Here the contrary motion should always be applied, e. g. 
 
 35. 
 
 pHitfcrNid 
 
 3SEP1Ü 
 
 wmmm 
 
 N 
 
 
 
 
 
 P_-=-^— : 
 
 ■-^m 
 
 ^=^ T f- 
 
 y 
 
 H III 
 
 better: NK. 2. 
 
 SH=g=l =Eff E; I^ EpfeEg^g 
 
 mmwmmmmFMimmwm 
 
 Mm^mmmi 
 
 mmmimmmimi 
 
MANUAL OF HARMONY. 
 
 Remarks on these chord-eon neet ions. 
 
 In all progressions of voices such as that used at NB. 1, and sub.sequen 
 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. 
 
 jj^ plpg^ PP^BK 
 
 36. 
 
 m^mmmmimimmit 
 
 The leading of the voices at b is to be preferred. 
 
 If these covered fifths occur in the middle voices, they are moru allow- 
 able, because they are less perceptible. 
 
 36. 
 
 I 
 
 
 II 
 
 m 
 
 m 
 
 At NB. 2, the doubling of the third of the second chord is not always 
 to be applied, since in general, the doubling of the seventh degree (in 
 Example 34, the B of the second chord), is to be avoided. 
 
 Concerning the treatment of this tone, which is called leading tone, i 
 fuller discussion will be given in connection with the following exercises ' 
 
 Exercises to be Worked Out. 
 
 4 Nß - ^ 5.^ 
 
 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 s regular harmonic or melo lie 
 progression is called Sequence. 
 
38 
 
 MAX UAL OF HARMONY. 
 
 This consequent progression of the Bass, occasions alsc a like rcgula 
 leading of the remaining voices. 
 
 The treatment of this example, according to principles of chord-con 
 »eetion laid down above, by sustained tones, e. g., 
 
 3§. 
 
 iliiliHB 
 
 w=£=m^m 
 
 =F 
 
 would not admit of the attainment of this end ; the progression musi 
 rather follow in such a manner, that the chord of the second measure it 
 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. 
 
 Trr|T g3 pg£S^I 
 
 Ü3E 
 
 -G— 
 
 In the first example, on account of the sequence, the covered octaves 
 3poken of above will likewise be allowable, if they are not found in 
 outer voices. 
 
 In the third measure of Exercise No. 4, we meet with a chord, which 
 thus far we have not used. 
 
 The Diminished 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), or 
 
 the upper or lower tone progresses alone over against the other, (b, c), 
 
 a kind of progression which only becomes plain through actual chord-ccn- 
 
 ection. 
 
 u. i>. c. (I. «■ Invereton. 
 
MANUAL OF HAhMONY 39 
 
 The third following the diminished triad (<?), exhibits the tiiad of the 
 first degree (C) as incomplete, by omission of the fifth. 
 
 Since, according to the relations of the intervals in respect to inversion 
 before explaiued, (page 18, 19,) an augmented fourth results from the dimin- 
 ished fifth, its progression must also appear in inverted order. See 40 c. 
 
 The fundamental tone upon which the diminished triad rests, is called 
 
 LEADING TONE. 
 
 It is found again as third iu the dominant triad, and as fifth in the triad 
 of the third degree. 
 
 41. 
 
 Hü 
 
 Since the leading tone of itself comes out very distinctly, it is not 
 doubled in the simply harmonic four-voiced movement. 
 
 Just so its progression one half step upwards can be effected, if the 
 next following chord contains this tone. 
 
 This tendency to progression lies in the melodic character of the leading 
 tone, inasmuch as it stands as half-step before the fundamental tone of 
 he scale. This is noticeable particularly in the case of the dominant 
 riad, if the leading tone is contained in tlj upper vokfc, as a in Example 
 42. operates more satisfyingly, than b and c. 
 
 42. 
 
 This inclination upwards shows itself less in the middle voices, as at d. 
 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. 
 
 Il 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 iu 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 82, (the authentic close), shows itself in a still more definite man 
 ner in the last examples. 
 
1(1 
 
 Ma X UAL OF HARMON Y. 
 
 As the natural relation of the cnord of the dominant to me 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. 
 
 U=i=yh$dE$dtt 
 
 mummm^ 
 
 Besides the triad of the second degree, the triad of the sub-dominant b 
 also adapted for this formation of the close, e. g. 
 
 44. 
 
 The closing formulae [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 3Iino)' Scale, 
 
 a. Primary Triads. 
 
 The nrimary triads of the major scale were found upon the first, fourth 
 and fifth degrees. Upon the same degrees we find also the primary triads 
 of the minor scale. 
 
 The relation, however, in which the dominant triad stands to the tonic 
 shord, 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 
 
MA NU siL OF II AR H S f 
 
 41 
 
 -6- — : 
 
 \-0- 
 
 m 
 
 15. 
 
 Nl 
 
 
 By this means the formation of the dominant triad in minor, becomet 
 exactly like that in major, thus : 
 
 y 
 
 A major. 
 
 
 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. 
 
 47. 
 
 C minor. 
 
 
 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 
 *s often necessary melodically, the plagal close proves a (see page 33), 
 which cannot be conceived of at all as at b* 
 
 4§. 
 
 91 
 
 ^i^Sf|EEE^p^pB 
 
 The three primary triads in minor can be thus exhilited in their natura 
 relation according to previous explanation ■ 
 
 IT I V 
 
4L' 
 
 MANUAL OF HARMONY. 
 
 The minor scale, as it forms the basis for the formation of harmon : «i 
 will therefore h • the following : 
 
 ;>o 2li 
 
 1 1 i 1% $ 
 
 Reäaek. — All other forms of the minor scale, such as : 
 
 51. 
 
 w descending ■ 
 
 52. 
 
 
 depend upon melodic conditions, which do not allow the step of an augm.ei.il setona 
 from the sixth to the seventh degree, found in No. 50. 
 
 These forms have no influence upon the harmonic formation in itself considered ; the 
 harmonic foundation, however, has a reflex influence upon the minor scale itself, as the 
 allowing examples show • 
 
 \ 
 
 S3. I 
 
 $3S 
 
 
 ^■» £ ha _•*:_ 
 
 ^^f^ 
 
 The last case, in which the descending scale even exhibits the step of an augmented 
 second B-A b, which in future, in chord-connections we shall carefully' avoid, explains 
 itself thereby, that B was necessary as component part of the chord, A},, however, in 
 order not to destroy the minor character of the passage, which is done very perceptibly 
 through A, while, in the ascending scale, (in the first example), this (minor character) is 
 already perfectly secured through the minor third, Fb. 
 
 b. The Triads of the Remaining Degrees of the Minor Scale. 
 SECONDARY TRIADS. 
 After the establishment r.f the minor scale, the secondary triads appew 
 in the following form : 
 
 54. 
 
 -^r 
 
 =EFiEElEl 
 
MANU At, OF HARMONY. 43 
 
 The second degree gives a dityiinishcd 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 : 
 
 „. b. c. d. e. f. 
 
 _ 6 
 
 iiO 1V V VI VII 
 
 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. 
 
 — ©-ffS 
 
 I^lllilife^ilirtta 
 
 I u o iv ' V VI 
 
 Its introduction is most tolerable, if the augmented fifth h prepared, 
 that is, exists already in the same voice as constituent part of the preced- 
 ing chord, (at (I). 
 
 Remark. — There is something peculiarly foreign in the chord of the third degree, as 
 well of the major as of the minor scale, so that this harmony, even when it appears 
 jimply as minor triad in the major scale, is very difficult to connect naturally and effec- 
 tively with other chords, and therefore seldom occurs. 
 
 Most of the practicable chord-connections exhibited above will occur in 
 other relations, and not allow the augmented triad to be recognized as 
 [triad of the] third degree of the minor scale. The augmented triad, 
 .vhich is much used in the later music, belongs to the chromatically 
 lltered harmonies, which will be explained later under the name Alte^M 
 Chords. (See Chap. X, Altered Chords). 
 
u 
 
 MANUAL OF HARMON J 
 
 Application. 
 
 The principles of the cjnnection of harmonies an I leading of th 
 roices, already developed, will also have application here, and particularl 
 in the connection of the fundamental chords in minor, what was saic 
 »bout the progression of the leading tone comes very distinctly into view 
 jince 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. 
 
 ÄüülfS 
 
 'z^m^E^m 
 
 Hence, in the often recurring connection of the chords of the fifth and 
 sixth degrees, the progression of the leading tone will be necessarily always 
 upwards, whereby, in the triad of the sixth degree the third appear 
 doubled, e. g. 
 
 %_ r ^ r _^ r r r r -^fe 
 
 58. 
 
 la^S Bgm ^B 
 
 Arc. 
 
 ^mmmmm=i=^imi^i 
 
 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, hr 
 »»ample : 
 
 59. 
 
 rämn 
 
 Reu ark — The practice deviates, in certain and especial cases, from this ru.a. It wiD 
 ö* well, however w uccustore 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 tht 
 vractv < is and should be only a well founded exception, whereas the observance of tb« 
 rule can De instanced in numberless cases. 
 
if AN UAL OF HARMOXY 
 
 4b 
 
 Extvcises in connecting the Triads of the Minor Scale, 
 
 1. 2. 
 
 3. 4. 
 
 3 t 53 S 3 5 5 
 
 51 
 
 M^^ö^SPö 
 
 Me in a r 7k s on these Exercises. 
 
 A chroinatvo sign over a Bass note without a figure, as, for example, 
 in the third measure of the first exercise, refers always to the third of the 
 Bass. This 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 
 
 t by 3, 5, 8, or l or in full, by 5 
 
 * 3 
 
 One reason fo/ indicating it by 5, is found in the third and sixth exer- 
 cises. Here the introduction of the triad of the third degree in minor 
 has been attempted, whereby it was necessary to indicate that the fifth 
 is raised, since it likewise forms the seventh degree of the minor scale. 
 
 The figure 3 or 5 over the first chord of some of the examples, indicates 
 its position. See, in regard to this, the remarks to the next exercises, 
 (page 50). 
 
 . The working out of an exercise will confirm the fundamental feature 
 hitherto developed. We select for this purpose the first exercise. 
 
 (51 
 
 sLt Ujagg il 
 
 ?m m 
 
 m 
 
 S=SE 
 
 mn 
 
 The first principle of the connection of chords (by com action of tones 
 it the same voice), is here everywhere observed, and for *his reason thf 
 
46 
 
 MANUAL OF HARM ON T. 
 
 Alto, in the third measure (at NB.), makes the faulty step of an atigmente^ 
 second from F to G$. 
 
 In order to avoid this fault (according to page 44), it will be necessary 
 to let the Alto progress from Fto 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. 31 
 where the connection of tones does not take place in the same voice), or 
 the Soprano retains the B and the Tenor goes from D downward to the 
 G$, the Alto from F to E, whereby the close position is forsaken, and this 
 and the following harmony appear in open position : 
 
 63. 
 
 nnma 
 
 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 minoi 
 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 tht 
 following manner the chords hitherto discovered : 
 
 View of all Triads of the Major and Minor Scale», 
 
 _ Major. 
 
 64. 
 
 g=l: 
 
 i 
 
 I ii in IV V vi vii° 
 
 Minor. 
 
 T n° III' iv V VI vi,o 
 
 Major triads are found 
 
 in Major: in Miner' 
 
MANUAL OF HARMON T 
 
 in Major: in Min, 
 
 Minor triads 
 
 EEgEE^Hbö 
 
 II in VI 
 
 in Major: in Minor : 
 
 Diminished triads fe EE^zzz: z=jzg:=zj ^ [| 
 
 VII II" Tu 
 
 in J/inor: 
 
 Augmented triad Av ~ f ~g rr 
 
 CHAPTER III. 
 
 T7«e 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 chord?, ü 
 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. 
 
 Hkmark. — It should he well remarked, that only transpositions of the Bass to another 
 lüiervnl are here spoken of, and that the before mentioned transpositions of the other 
 voices into close and open position, and to various intervals, by no means essentially alter 
 the chord* 
 
 Two of the inversions are possible with the triad : 
 
 a. If the Bads receives the third of the triad, therre arises the cHCir 
 
 or THE SIXTH. 
 
 Fundamental chord. Chord of the eivth. 
 
 C5. fez 
 
 -V- Third 
 
 of the fundamental chord. 
 
 * Tlie word t> <y».sposki'n is here used in its general, not its technical sense. — E«x 
 
4S MANUAL OF HAB MONT. 
 
 h. ff thb Bass receives the fifth of the triad, there arises the chore 
 
 OF TUE SIXTH AND FOURTH. 
 
 Fundamental Chord 
 
 chord. of the sixth and fourth. 
 
 t>«. 
 
 i 
 
 Fifth 
 
 of the fundamental chord. 
 
 The chord of the sixth is indicated by 6 over the Bass tote, that of the 
 sixth and fourth, by • e. g. 
 
 6 
 6 4 
 
 07 
 
 . üi 
 
 c c c 
 
 C: I I I 
 
 The letter shall in future serve for indicating the fundamental tone, and, 
 as before, the numeral to indicate the degree, whereby, as can be seen in 
 Example 67, only the situation of the fundamental tone can be taken 
 into consideration, not, however, the casual Bass. 
 
 Remark. — As the fundamental tone of the chords of the sixth and of the sixth and 
 fourth in Example 67, is always C, and not the Bass notes E and G, so the chord itself -will 
 not lie upon the third or fifth, but upon the first degree, since, in fact, these are no newly 
 formed chords, but only chords brought into another position by the Bass, and therefore 
 derived chords. 
 
 Every triad can appear in such inversions. 
 
 Application, 
 
 By the use of the inversions of the chords, not only does the leading oJ 
 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 th« 
 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 up}. er 
 three voices is conditioned only by the leading of the voiojs, and asile 
 from this, has no essential influence upon the chord itself. 
 
MANUAL OF HARMONY. 49 
 
 The chord of the sixth can therefore occur in the following forms : 
 
 6§. 
 
 g-F-l-F-g—F-i-F-^-F-— b=ö^zh=€=ztt 
 
 The use of the chord of the sixth and fourth is more rare thui uont of 
 the chord of the sixth, and requires certain conditions which .shall {,r men- 
 tioned later. We meet it oftenest in the formations of the close. Tht 
 Bass tone, the fifth of the original chord, is best adapted for doubling, and 
 the chord will appear in the following and similar forms : 
 
 mmmmpmm^ßtmi 
 
 In the connection of these chords with others, no farther mechanic»! 
 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 b« 
 better judged of in relation to the whole. 
 
 Exercises. 
 
 70. 
 
 §3B: 
 
 
 m^mmmmmmwk 
 
 ö 
 
 Sü^n^üi^ 
 
 G G 
 
 4. 3 6 6 4 3 6 G G 4 3 
 
 5 - 6 6 o o e % * 6 - I % % 6 
 
bO 
 
 MANUAL OF HARMONY. 
 
 6 
 
 6 6 7- 3 6_ _6 6_ _6 £3 _ 
 
 #66 «6 
 
 » 6 
 z *a — k. 
 
 b 5 10. 
 
 3 6 6 
 
 9— =r-r~X=±^ 
 
 g^fezg a 
 
 6 # 
 
 6 
 4« 
 
 iiüifa^iiü^is 
 
 
 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 the 
 sixth. It occurs oftenest in this situation. It may here be called to mind 
 that its fundamental tone is not doubled, because of its being the leading 
 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 it« 
 fundamental position is already given, page 38. 
 
 In the most usual cases the progression of the Bass is as follows ■ 
 
 Tl 
 
 . SS 
 
 »ad the progression of the remaining voices thus ■ 
 
 y>2. 
 
 ±=^d^:r^:sbd:- 
 
 4 
 
 gzzgifcsffiz^g: 
 
 3=3? 
 
 ^^^rS^i^i^^l 
 
M A .\ L'AL F HA li MONT 
 
 ft] 
 
 It is evident from the above Examples, that the inversion of the diiuiu 
 ished fifth, viz., the augmented fourth, will not necessarily, iu /out -voiced 
 movement, have the same progression as was given above, tivo-voiced, pag 
 38. We see, in the first example and others. 13 and F of the Soprano au 
 Alto progress to C and G. 
 
 73. 
 
 II 
 
 'J he similarity of this chord, in sound, to the dominant chord of the 
 fttJOith to be shown later, often induces beginners to lead the diminished 
 fiftu downwards, even if it has converted itself by inversion into the aug- 
 mented fourth ; this, as the above examples show, is necessary only in ca^e 
 i*. rokUy lies above the fundamental as diminished fifth, and a progression 
 f f th following sort : 
 
 T4. 
 
 §=5^i§y 
 
 '& faulty on account of the parallel fifths. 
 
 Remark. — It may yet be remarked here, that parallel fifths, of which the one fiftu u 
 diminished and the other perfect, are to be allowed if the diminished follows tht per 
 fat fifth, but not vice versa, e. g. 
 
 /.'>. 
 
 good. 
 
 
 goo 
 
 m 
 
 d. 
 
 -© — 
 
 <=-s>— 
 
 \3l 
 
 not good. 
 
 Ü 
 
 im=k 
 
 6 
 
 m 
 
 G 
 
 3 
 
 — &- 
 
 m 
 
 
 
 m 
 
 Compete 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 : 
 
 »6. 
 
 6 _6 6 _6 
 
52 MANUAL OF HARMONY, 
 
 letter: not: 
 
 ~e, ^ -\— 2— f —s .—* --1— f=J=| :— «£=£3 
 
 6 6 6 6 6 
 
 ^^ 
 
 11111 
 
 no/ : 
 
 —Jig p 
 
 5 1 P— 
 
 5 6 
 
 Mi 
 
 6 6 
 
 6 
 
 süp 
 
 JLr—S- — 
 
 6 
 
 =1— F=ö— 5 
 
 6 
 
 _5 2- LL_ 
 
 6 6 
 
 §>fc^= 
 
 =N=^e=* 
 
 ?=E=E 
 
 -N 
 
 =!^E 
 
 3=K= 
 
 The diminished triad of the second degree iß 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 A'oices moving in contrary motion to the Bass, e. g. 
 
 J>J. 
 
 66 66 66 66 6 6 6 6 
 
 r. 
 
 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 voi«es, e. y 
 
 % 
 
 3*E 
 
 r|:z|z«z 
 
 ^0 
 
 —S— 
 
 =ff 
 
 
 
 ° 5? 
 
 6 
 
 6 6 
 
 6 
 
 Ac 
 
 m 
 
 E$E 
 
 ^Ep 
 
 ^m 
 
 — (OL- 
 
 Z-lE 
 
 iB 
 
 78. 
 
 Covered octaves, as in the 2d and 3d measures between Tenor and Basa. 
 
 re not to be avoided in such cases. It can be deduced from this, that to 
 
 single progressions of the voices which are contrary to rule, thai especial 
 
 importance is not to be attached, in opposition to the consequence op 
 
 the whole, tvhich otherwise belongs to them, since the construction of the 
 
MANUAL OF HARMONY. 
 
 53 
 
 details, although It must be as perfect as possible, will always be sc ordi- 
 nate to that of the whole. 
 
 Remaiik. — It is not to be ignored, that the principle laid down above :an easily b 
 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 cxpe 
 rience and practice. 
 
 Concerning the Signs of the Thorough-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 : §), if a chromatic 
 elevation of the interval a half-step becomes necessary ; instead of which, 
 however, a J or t3 is often set after the figure {e. g., 6JJ or 6Q, 5£.) Other 
 figures will find their explanation later in connection with the chords 
 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. I 
 
 mwmm 
 
 (m 
 
 mi 
 
 The chord of the sixth and fourth is frequently preceded by the triad 
 M the fourth or second degree. 
 
 SO 
 
 FFfr^F 
 
 mm 
 
54 MANUAL OF HARMONY. 
 
 As decidedly now as the chord of the sixth and fourth indicates the 
 close, having also a decided influence in the modulation into foreign keys, 
 just so weak is the effect of its entrance under other relations, so that its 
 proper use is subject to certain conditions, which will be treated of later. 
 
 CHAPTER IV. 
 
 Harmonies of .the Seventh (Vierklänge), 
 
 The harmonies of the seventh are founded upon the triads. They result 
 from the addition of a tbird to the fifth of the triad, which [third] forms a 
 seventh from the fundamental. 
 
 7 7 
 
 §1. 
 
 mmmm 
 
 Not only the various kinds of triads, but also the various kinds of 
 Sevenths will afford manifold harmonies of the seventh. 
 
 The General Properties of the Chords of the Se vent h. 
 
 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 
 tbe 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 tho 
 voices. 
 
 The Dominant Chord of the Seventh in Major and Minor. 
 
 The chord of the seventh which is most important, and occurs oftenes* 
 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 the major triad and minor 
 tventh. 
 
 ». i=t#=E&ig;=S 
 
MA X UAL OF IIA R M N Y. 55 
 
 In the fundamental position it is marked by a 7 over the Bas« note, and 
 our method of notation, indicated by V7 
 
 7 
 
 7 t 
 
 • IMEi^ 
 
 83 
 
 O: V 7 
 
 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 
 
 §4. 
 
 S 2 — g— 1 — ft— c - ff => — T — ^r — 
 
 7 
 
 mbmwmm=mi 
 
 C: V 7 I a: V 7 
 
 Remark. — It is to be remarked here, that the triad folio-wing the chord of the seventh 
 is 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. 
 resulting union with a triad, is called 
 
 RESOLUTION OF THE CHORD OF THE SEVENTH, (Cadence). 
 If the union of the dominant chord of the seventh with the tonic triad 
 follows in the manner exhibited in No. 84, or in a similar way, it is ealled 
 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 reyrfar resolution of the 
 dominant 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 oJ 
 he Bass, which contains the fundamental, is regarded as given, an upward 
 rogression of the seventh will appear impossible : 
 
 85. 
 
 Ü :-icif 
 
&€ 
 
 MANUAL OF HARMONY. 
 
 •ren if, as at b, a third voice is added ; whereas its downward progrewiioB 
 %ffords full satisfaction : 
 
 86. 
 
 Since tLs 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 cnord 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 what 
 has been said before concerning the leading tone, (page 39) ; its progression 
 will follow a half-step upwards, and b will, therefore, not appear so nat- 
 ural as a : 
 
 «. 
 
 Id the Example 87, b, 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. 
 
 §§. 
 
 m 
 
 
 I 
 
 fiiiiliHK 
 
 This downward leading of the third (leading tone) is therefore to b« 
 applied under the following conditions : 
 ff, If it does not He in the upper, but in a middle voice, e. g. 
 
 89. 
 
 seldom practicable. 
 
 
MA NUA.Ü OF IIA R M .V Y. 
 b If the Bass progresses in contrary motion, e. g. 
 
 90. 
 
 
 S=^K 
 
 The reason of the second rule becomes evident, if we observe the cov- 
 ered fifths in tha last Example b, between Alto and Bass. 
 
 The leading rf the fifth of the chord of the seventh is free. While, 
 for the mojt part, it is crowded a degree downwards by the seventh, reasons 
 may exnt 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 ol 
 what was said of tbe fundamental and the diminished fifth in the diminished triad, (page 
 38). Both intervals are found again in the dominant chord of the seventh. 
 
 Application. 
 
 Except in the formation of the closes, the dominant chord of tho seventh 
 is, 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 o» 
 the complete close is not produced. 
 
 This takes place particularly in cases where the seventh of the chord 
 ties in the upper voice, whereby the close becomes incomplete, or, if the 
 dominant chord of tho 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 imbsion 
 of an interval. This interval, however, can only be the fifth, seldom the 
 third, while the omission of the fundamental or the seventh, would entirety 
 alter the cbord and reader it incapable of r« cognition. 
 
58 
 
 At A X UAL OF HARM A V 
 
 91. 
 
 c. rarely : rf. 
 
 liipiiplllilf: 
 
 In tf, b, d 9 the fifth is omitted, in c, the :hird, and in each case 
 the fundamental doubled instead, which doubling affords, by means of the 
 tone which is allowed to remain stationary, the closest connection with the 
 fallowing 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; tht> 
 omitted interval will, in most cases, be the fifth of the fundamental chord. 
 
 Exercises. 
 
 92. 
 
 feililliliill^IililE 
 
 Ü^EE^S 
 
 6 
 
 um 
 
 3 
 
 -© — a 
 
 6 
 _ » 6_ 6 7 6 4 7 
 
 |i?E6EE|Ei|E^jpl|=^i^ 
 
 6 
 
 17 
 
 I 
 
 5. 3 
 
 
 These exercises require no farther explanation. It has been alieadj 
 mentioned, that the chord of ".be seventh, in the position known to us now 
 
MANUAL OF HA KM XT. 39 
 
 U iLdicated by 7, also that the sharp found under it, or in general, all 
 •hromatic signs which occur without figures opposite to then, have refer 
 Doe to the third from the Bass tone. (See page 55.) 
 
 CHAPTER V. 
 
 The Inversions of the 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 Ban,?, and 
 
 The third, if the original seventh is given to the lower voice. 
 
 In close position the inversions present themselves thus : 
 
 93. g: = g=:g = : g==: -EE 
 
 A comparison of these inversions of the chord of the seventh, witti 
 those of the triad, shows plainly their analogous position : 
 
 6 
 
 »i. 
 
 5 £>»' # 
 
 (i) b») 
 
 r 7 G 7 G 7 G 7 
 
 These derived chords receive their designation from the position ol 
 th eir 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, chord 
 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. 
 
30 
 
 MANUAL OF HARMOtrY 
 
 It needs only to be remembered here, that in these inversi' ns, just as 
 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 
 ouslj distributed among the upper voices, e. g. 
 
 95. \ 
 
 _a — , — o — _,©o_ _a — T — ——-j 
 
 ) ■ .1,1,1 „j^+H-g feg^ 
 
 66— -4 4- — - 
 
 55 --3 3--- 
 
 W <fcc 
 
 Application. 
 
 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 *xi«t in the case of the derived chords, in which the two tones, the 
 fundamental and the seventh, eithei appear again, or become seconds by 
 
 96. 
 
 — © — F— i 
 
 E-?=iz:?=t = s£^fel=zl[ 
 
 Progression of the Chord of the Sixth and Fifth. 
 
 Since the original seventh shows itself likewise, over against the Bass 
 tone in the chord of the sixth and fifth, as dissonance, as diminished fifth, 
 the progression of which was discussed above, (page 38), 
 
 97 
 
 . S3 
 
 i 
 
 the rssolution of the chord of the sixth and fifth will naturallv take 
 place thus : 
 
 ... I SEJgHEEtt 
 
 Q 7 U 
 
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 iuto 
 
 the fifth. This is, however, only apparent, for that it forms the foundation 
 
 of this connection of harmony, the marking v elow G7 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 othei 
 reasons, immediately in the character of these voices, which is to be found 
 more in mediation and connection of the harmonies, than in laying their 
 foundation, which belongs to the Bass. 
 
 Remark. — Deviating progressions of the fundamental in these eases, such as a freer 
 leading of the voices in certain relations would give, are not hereby excluded, only ther« 
 must be an inner connection of the chords. 
 
 Progression of the Chord of the Sixth, Fourth, and Third. 
 
 We find again here, beside the seventh and its inversion, the diminished 
 fifth or its inversion, the augmented fourth : 
 
 [g o ^_ 
 
 99. ^ =^s=— o ~ ^^ 
 
 The resolution of this chord follows thus : 
 
 a. b. 
 
 G 7 C G 7 C 
 
 The Bass, the original fifth, can progress in both of the given ways. 
 Prof/rt'ssion of the Chord of the Second. 
 
 This chord has the peculiarity, that the original dissonant intervals, tht 
 seventh and the diminished fifth, can only occur in their inversions, at 
 second below, and augmented fourth bcloiv. 
 
 The progression of this chord is as follows : 
 
 2 6 2^ 6 
 
 Thus the resolution of the chord of the second is effected here thioug* 
 khe chord of the sixth. 
 
 We can perceive in these resolutions, that they are all based upon th* 
 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 G 7 C or V? I. 
 
 These resolutions will, therefore, themselves form cadences, ovAy not 0« 
 w> 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. 
 
 m 
 
 9- g-^Fg==|i=: ^=$^g— -F= ^^F -g=F=5=j^^=j 
 
 a 
 
 6 
 
 •"> 
 
 Q 
 
 Est 
 
 6 
 
 5 
 
 •*■ a ^ *t 
 
 !>. The Chord of the Sixth, Fourth, and Third 
 
 or : 
 
 wMmw&mwmtMmtwm 
 
 4 
 
 3 G 
 
 mmmmmw^=£m£^^mi 
 
 SH£g 
 
 1 
 3 
 
 5wmmmm\m=i 
 
MANUAL OF HARM ONI 63 
 
 C. The Chord of the Second. 
 
 =ilgi3^!Üi^^gi!f!i!3 
 
 5 ■*• ° "* G 
 
 •2 o ~ 
 
 2 2 6 2 G 9 ß ■ •** Ä **■ 
 
 flfi^IIlEIIlE^löi^J 
 
 103 
 
 Exercises in the Use of these Chords. 
 6 6 
 
 1. 5 G G 3 2 G £ 
 
 SI 
 
 4 
 3 3 
 
 87 
 
 i;|E=sIl^El^Eli=^li=ji^l= 
 
 3 2 G 3 
 
 4 7 
 
 i^iiIiJÜElEE=S=ii*=frEEl 
 
 4 6 
 
 3 G 4 3 6 
 
 lääü 
 
 t=Bt 
 
 g^|^H=^J|p_^|^E^|=|^ 
 
 r^-ri t f 
 
 87 
 6 3 
 
 ihEifc 
 
 £ 6 6 7 
 6 2 6 jar 5__ _ 4i _ 
 
 f 
 
 3 6 
 
 67 
 
 4« 
 
 £4 67 
 
 8. 6 f __ ffl 3 2 6 3 G__ _4J_ 
 
 Observation— The markiug 8 7 in the next to the last measure of the 
 second, fouith, and fifth Examples, denotes that the seventh should nr.t 
 appear with the chord itself, but follow after the octave. 
 
ft4 MANUAL OF HARM ONI 
 
 CHAPTER VI. 
 
 Secondary Harmonies of the Seventh. 
 
 While in the case of the triads, three primary chords are requisite i* 
 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 
 anders the key certain, and the natural progression of which to the tonio 
 triad represents the key. 
 
 Remark.— The manifest fact, that the seventh of the dominant chord of the seventt 
 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 : 
 
 I. I* Major: 
 
 10-1. 
 
 -Ä- — 5 — -- 
 
 h "7 m 7 
 
 I ":— 1: &z g= -^ ==Jb 
 
 7 "7 m 7 1V 7 
 
 VI ~ VII" 
 
 b. In Minor : 
 NB._ J^; & 
 
 "Tp n° 7 UVj iv 7 Vly vu° 7 
 
 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 m»j 
 be distinguished : 
 
MANUAL OF HARMONY 
 
 in Major : 
 
 a. Major triads with major JO _ aEizzisz: ^ "is™ 
 
 seventh. ' &=¥=■%= * » A 
 
 o: ^ n> a: vi 7 
 
 N15. Major triads with minor seventh always form dominant c/mrat 
 tf the seventh. 
 
 in Minor: 
 
 h. Minor triad with -Q- 
 
 major seventh. (a) ~fe not used as fundamental harmony. 
 
 =BI 
 
 in Major: 
 
 C. Minor triads with minor 
 seventh. 
 
 Diminished triads with minor 
 seventh. 
 
 Diminished triad with diminished seventh. 
 The augmented triad with major seventh. 
 
 48 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, iu Chapter X. 
 
 Application of the Secondary Chords of the Seventh in Major* 
 
 The seventh or its inversion, the 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 the 
 seventh, viz., one degree downwards toward the fundamental, if the latter 
 noves by fifths or fourths, downward or upward. 
 
 If accordingly the progression of the principal intervals of the chord it 
 ound, 
 
 106. 
 
 iPIgüPi 
 
MANUAL OF HARMON i. 
 
 for the remaining intervals, no new rule is necessary ; the third wili bt 
 led one degree upward, while the progression of the fifth can be in either 
 direction. 
 
 a. b. e. 
 
 107. 
 
 C: \j IV n 7 V 
 
 Remark. — The deviation from this rule in the progression ine third in Example 
 107 b, is occasioned by the circumstance, that the covered octave, which would appeal 
 in the regular ascension of the third a whole step, e. g., 
 
 10§. 
 
 :S:= 
 
 g=i=g=f: 
 
 II 
 
 i rog=P ^^B 
 
 was avoided thereby. See page 85, Example 32. 
 
 Whether, however, as in Example 107 C, the leading tone should be doubled in th« 
 succeeding chord, or the following covered fifths be preferred, 
 
 109. 
 
 nas 
 
 §is 
 
 i 
 
 will depend upon circumstances which can only be judged of in the application to par 
 ticular cases. 
 
 Natural (Cadencing) Progression of the Secondary Chords of the 
 Seventh in Major. 
 
 a. of the first degree. 
 
 or : not : 
 
 110. 
 
 good : 
 
 a __ — ^--r a _ g g — g— 1 — s> — r— g-sr— a» — • 
 
MANUAL OF HARMONY. 
 
 57 
 
 vnth omission of the fifth : 
 
 +*■ 
 
 b. of the second degree. 
 
 
 without fifth : 
 
 
 mnimmummmwm 
 
 c. of the third degree: 
 
 & ■» 
 
 without fifth . 
 
 SSSte^lSI 
 
 mm^m^m=mm 
 
 not: not: 
 
 C: in 7 vi — 
 
 d. of the fourth degree (Seldom with Viis resolution). 
 
 not good: 
 
 ^ 5 ^ ■*>■ 
 
 wm 
 
 
 
 "*>-© 
 
 
 
 
 without fifth : 
 
 
 \m 
 
 -EE^I 
 
 =N 
 
 ^3= 
 
 =h 
 
 =%£*=$=!= 
 
 
 
 P 
 
 ? * 
 
 
 -g~T- <S - 
 
 
 
 
 =^=5= 
 
 h 
 
 =^= 
 
 =f= 
 
 -H-.=f = 
 
 
 
68 MANUAL OF HARMONY. 
 
 e. of the girt, degree. 
 
 without /i, ih : 
 
 mifmmmmmmimmm 
 
 mmwmmmFm 
 
 f. of the seventh degree, 
 
 not good : 
 
 mmmwrnm^M 
 
 gEEEEg-^^l5=P 
 
 C; vh° >y m 
 
 xcithoiU fifth: 
 
 :4El=iE^l3=1^1=l=EE 
 
 H= 
 
 HI 
 
 
 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 man)' 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 the 
 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 car. 
 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 Ihe progressions of all chords of th« 
 ■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 
 »step of a fourth upward or a fifth downward. This progression is the 
 
MANUAL OF HARMONY 
 
 60 
 
 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 
 Lb added, is based, (see page 38 and 50), viz., that to the tonic triad. 
 
 ai 
 
 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 b), 
 because otherwise, perfect fifths would arise ; (See No. 112 a), 
 
 12. 
 
 % 
 
 mmm 
 
 i 
 
 or a skip must be used, as at b, 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. 
 
 Rxmark. — Whether the reason of this is, that in the seveuth with its above used 
 progression, the character of the ninth lies, (as some theorists assert, that the domiuan 
 chord of tb<j 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 mere comprehensive, and 
 does not l.-ar the situation in the middle, cannot here b>i further «ivestLzated. 
 
70 MANUAL OF HARMONY 
 
 TJie Freer Treatment of the Third and Fifth in the Chord of 
 
 the Seventh. 
 
 Various progressions of these intervals have already been used in th« 
 previous connections of chords. The fifth goes upwards and downwards, 
 the third likewise, sometimes goes a degree upwards, and sometimes makes 
 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. 
 
 a. b. not good. c. 
 
 ■*+ ^ ja 
 
 -ffl G- 
 
 114. 
 
 •f~ 5 -6- 
 
 That this leading is also possible in the middle voices, if the position 
 admits of it, is shown at c. 
 
 The hading of the Soprano at h 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 
 TritOll II §, because it contains three whole steps. More of this sub- 
 eequently. 
 
 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 
 »f most of the sevenths in the secondary chords of the seventh, reudera 
 necessary a careful introduction of them, which consists in their pre- 
 varation. 
 
 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 by 
 a tie. 
 
MANUAL OF HARMONY. 
 
 71 
 
 Such preparation of a tone is contained already in the first connections 
 of chords previously shown, e. g. 
 
 15. 
 
 II 
 
 
 It can be said here, that C of the Soprano in the second chord is pre- 
 pared by the C of the first chord ; likewise the G 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 : 
 
 11C. 
 
 
 C: V I T IV 
 
 \j IV IV n 7 v 
 
 
 C: in IV j vii : 
 
 II IV Til" 7 I 
 
 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 b« 
 bserved : 
 
 a. The preparation takes place upon the unaccented part of th* 
 measure (arsis) and must 
 
 I>. at least, be of as long duration as the succeccdiug seventh ; it can 
 indeed be lonjrer but not shorter, e, g. 
 
MANUAL VF HARMONY 
 
 117. 
 
 mm^$ 
 
 g It- U- 
 
 \l 
 
 Remark — The preparation of the sevenths forms one of the most important jwrts o4 
 the doctrica of harmony, and is to be carried through and practiced with much car«, 
 because up:>n 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 m a concrete case by the position and relations. (Page 44 — Remark). 
 
 These exceptions occur mostly with the minor sevenths, a3 the less harsh, as those o* 
 the second and seventh degree, and va then always softened by good leading of the 
 roices. 
 
 An especial exception, however, to the necessary preparation is formed 
 Dj the seventh of the dominant fihord, 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 casea. 
 
 Of its farther use the following may be remarked 
 
 The iominant seventh does not, to be sure, require preparation, yet its 
 free entrance demands the presence of the fundamental, if the leading oi 
 the voices is to be ^ure aad without harshness. 
 
 1§. 
 
 — g— 1-jgg ^-g^— g -\ a . -t^ ja FF 
 
 ggJSppSs]5z8^£I 
 
 Rimabk. — The so-called passing sevenths, wliich of course, as such, cannot be pr«r 
 oared, conform to the rules of the passing notes, which are explained later Concerning 
 ihe passing sevenths, see Chapter XVIII. 
 
 The seventh also of the seventh degree in major and minor (m the last 
 3ase, the chord of the diminished seventh), by reason of their especial 
 character do not by any means always require a preparation. 
 
MANUAL OF HARMONY. 
 
 Exercises. 
 
 7 7 6 G 47 
 L-l-g- 
 
 :a 
 
 2. 8267 5 66 47 
 
 4 7 
 
 §». 
 
 ^ ; 
 
 Il^üglUiliP^I 
 
 4. G " *► 7 _ 7 5 6 6 7 
 
 The Connection of the Chords 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, but 
 remain stationary, e. g. 
 
 120. 
 
 §i: 
 
 C: n 
 
 mmm\ 
 mm 
 
 7 7 
 
 Here the third of the 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, th« fi'lh will always be wanting in each 
 alU'-nsift nhuld. 
 
74 
 
 MANUAL OF HARMONY. 
 
 
 121 
 
 7 7 
 
 •I 
 o — , 
 
 m^^E^m^m^ 
 
 VI IV<r VII « III -y VI. 
 
 The following rule may therefore apply for connections of harmony o» 
 this kind : 
 
 If two or more chords of the seventh follow each other in the funda 
 mental position, the fifth is omitted in each alternate chord. 
 
 4 
 1-3 3 6 
 
 Exercises. 
 
 6 
 6 5 
 
 122 §BE^fEpE^ 
 
 =f=^. 
 
 2. 3 6 7 7 
 
 6 
 6 4 
 
 um 
 
 llül 
 
 4 
 
 4-5 77777366 62677 
 
 ■ or s» 
 
 Application of the Secondary Chords of the Seventh in Minor 
 
 The use of the secondary chords of the seventh in minoK is more lim 
 ited. Many of them show themselves, to be incapable, or indefinite and 
 ambiguous, for chord-connections as they were applied in major, others 
 form, in their cadencing progressions, heavy, unmelodic steps of the voices. 
 
 A chord of the seventh formed as the first degree gives it, can afford 
 no prog-es.sion analogous to the above, since the following chord conneotios 
 Is not conceivable. 
 
 123 
 
 % 
 
 Ü 
 
 m 
 
UANUAL OF HARMO N Y. 
 
 Rkmark. — Even if with the above combination of intervals, progre 
 formed, such as perhaps : 
 
 ri 
 
 121. 
 
 :5g: 
 
 m 
 
 73 6 
 
 •till this wouid hardly be admissible as proof that we have in this a progression of I 
 ehord of the seventh of the first degree in minor. 
 
 The resolution of the chord of the second degree is into the dominant 
 and is very frequently used. 
 
 G-r-zi r— g igsp— r — S» S ? 1 
 
 125. { 
 
 
 ^ gj^ i 
 
 A progression of the ehord of the seventh of the third degree is n<* 
 lpossible, 
 
 26. 
 
 
 " m '7 VI 
 
 it is ambiguous, however, and might be better adapted to C major than to 
 A minor. (See Altered Chords). 
 
 It may be remarked here, in addition, that the fifth in this chord, as 
 augmented interval, will always go upward one degree. 
 
 The chords of the fourth and sixth degrees are unusual, because the 
 leading of the voices in their resolution becomes inconvenient and un- 
 ;^clodi . 
 
 127. 
 
 2— - 
 
 good: 
 
 
 *-— B 
 
 :«==«: 
 
 iT=^*: 
 
 EzS L^t ^ E^^^^feifEi 
 
 F 
 
76 
 
 128 
 
 MANUAL OF HARMON: 
 
 
 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. 
 
 
 1 
 
 As the fundamental of this chord (leading tone), progresses a halfstef. 
 bo 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 : 
 
 ■a. *>■ 
 
 130. 
 
 lM^^Ä£=i 
 
 II; 
 
 #* * 
 
 »hereas the position at b and C gives to the third greater freedom. 
 
 Remark. — The natural progression of this chord, as well as of the chord of the seventh 
 of the seventh degree in major, to the tonic, has occasioned the older teachers of har- 
 mony to find th t basis of it in the dominant harmony „/ 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 f. we refer to that whicl is -«aid later (in Chapter IX.) of the cficrd of the aiulh 
 
MANUAL OF HARMONY 
 
 77 
 
 jre cau only bring forward here as reason for the view offered, that this assumptic i of 
 the che rd of the ninth is needless and far-fetched, and that for practical purposes, the 
 simplicity 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 iu 
 addition the following : 
 
 The diminished seventh, as the mildest of all, needs no preparation 
 (See page 72). 
 
 Exercises. 
 
 7 6 6 7 
 
 7 7 
 
 — (S 
 
 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 chorda 
 thus far explained, and to test the rules and remarks laid down, have some- 
 thing inflexible and stiff in their structure, because the great number of 
 chords of the seventh could only appear here in the fundamental position 
 and because the introduction of many of them upon our present stand 
 point, which did not allow us the selection of other means, was difficult, and 
 could only appear forced. 
 
 "What follows may serve as explanation of them: 
 
 The fundamental of these chords of the seventh makes everywhere the 
 cadencing skip of a fourth or fifth, as is to be seen from the leading of the 
 Bass, only, in the third exercise of Nos. 122 and 131, there is found, seem- 
 ingly, an exception. In the fourth measure of the third exercise of No. 122, 
 the Bass tone, to be sure, remains stationary, the progression of the funda- 
 mental is, however, contained in a perfectly regular manner in the tw« 
 chords: A7, D 7 . 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 iu the fiftk 
 
MAX UAL OF HARMONY. 
 
 measure of the third exercise of No. 131, where the progression of the 
 fundamental A7-D takes place with a stationary Bass. 
 
 ]n the second Exercise of No. 131 the chord of the seventh 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 the samt 
 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 
 «neue in the same manner as has already been explained above. 
 
 6 4 o 
 
 H 3 1 
 
 - 5 <S- 
 
 0:1> I 7 IV 
 
 There is need of no new rule for the progression of all these chords il 
 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. 
 
 las 
 
 6 4 
 5_ 6 _ not: 3 6^ 2^ 4 
 
 AH these inversions of the chord may be used, only the last, the chord 
 of the second, will most seldom be in place, since the resolution into tta 
 
MANUAL OF HARMONY. 79 
 
 dbord of the sixth and fourth could only occur in rare case», 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 
 monies 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, 
 
 6 4^ 
 
 131. 
 
 9= — g-j ^^g^^g^^E 
 
 appear more satisfying, because the seventh lies above the fundamental. 
 
 The chord of the diminished seventh requires a manner of progression 
 
 «imilar to the foregoing e. g. 
 
 6 
 & £ 4 6 
 
 56 or .-5 6 3 6 2J4 
 
 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 chorda 
 of the sixth and fifthj and of the fourth and third, in this manner : 
 
 136. 
 
 are to be regarded as faulty, has been already mentioned above, (page 76). 
 •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 abovt 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 tfu 
 former only to be felt as such in reference to the key 
 
MANUAL OF HARMONY 
 
 Exercises. 
 
 6 6 
 
 6 6 5 5 
 
 6 
 6 5 
 
 6 6 6 
 8. 2 5 6 5 2 6 2 6 5 
 
 ü 
 
 6 4 
 4. 5 ö 267366 6 5 
 
 ^l^IiiePI?äöi=l== 
 
 5. 5 
 
 2 6 2 6 6 5 
 
 6. 32626 42 65 7 7 _ 
 
 f 6 
 
 7 7 3 6 5 J 
 
 5 J 6 ß 
 
 mm 
 
 S: 
 
 f 
 
 7 3 6 7 
 
 5 * 
 
 * 7 6 6 7667 
 9. f 6 7 « 5 I ,. 7 7 < 4 4 It 
 
 « 4 
 
 5 6 _^ 3 * 2 
 
 m^im^mMw^£^= 
 
MANUAL OF HARMON T. 81 
 
 CHAPTER VIII. 
 
 The Chords of the Seventh in connection with Chords of the 
 various tone-degrees other than those thus far used. Deccp' 
 live Cadences. 
 
 The known rule, that the seventh must, in the resolution, progress one 
 degree downwards, verifies itself, to be sure, completely, in the connections 
 of chords previously shown, but it has as little positive authority as any 
 thing else which, under other conditions, and in the great variousness of 
 chord connections, is subject to necessary alterations. 
 
 In the movement of the seventh or of its inversion, the second, every- 
 thing depends upon the progression of the fundamental. If this is of 
 such sort, as in all the cases hitherto shown, that without the downward 
 progression of the seventh no intelligible and satisfying result would be 
 produced, then also the above rule will have full application. 
 
 The progression of the fundamental, however, can entirely set aside this 
 direction of the seventh ; it can either remain stationary or even pro- 
 upwards, e. q. 
 
 1 4 
 
 13§. 
 
 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 
 net 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. 
 
go 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 x>rogression of the seventh by de 
 yrees downwards. 
 
 a. Connection with the sixth degree. 
 
 In Major. In Minor. _ 
 
 O: V 7 v, ^L-* ^^ a: V 7 VI 
 
 This chord-connection (deceptive cadence) occurs very frequently. 
 The effect of this progression is not so decided with the inversions oi 
 the chord of the seventh, and is therefore more rare : 
 
 In Major. In Minor. 
 
 £ 6 4 6 6 
 
 5 ^ 36 2 4 56 
 
 140 
 
 " C: V 7 vi ■ ■ a: V 7 VI 
 
 Connection with the third degree. 
 
 better position ; 
 7 6 _ 7 6 7_ G 
 
 1 *** ' fe~^:z^z^"~|:~i : ^^' 9 i=|:~®: : Er^3^| E 
 
 Remark. — The attempts with the inversions of the chord are omitted here and in warnt 
 follows ; they are easily made. 
 
 This progression becomes more decided under the application of modu- 
 lation : 
 
 7 6 7 G 7_ 6 
 
 142. ^=|^^^^=^-=5^g 
 
 C: V 7 a:V -_* S 
 
 The connection with the triad of the third degree is also possible id 
 minor, but this as dissonant chord (through the augmented fifth) will make 
 t farther succession necessary. 
 
 143. 
 
 
 III' VI 
 
 a: v 7 
 
 2 TAf connection with t?'iads, the seventh remaining stationary. 
 
MANUAL OF H A R M X Y 
 A. With the second degree. 
 -0 
 
 «3 
 
 1 it. 
 
 not : impracticable in Minor. 
 
 - »- . — - jo - 
 
 95E 
 
 '7 
 
 I), TFi7A the fourth degree. 
 
 I'k Major : 
 
 145. 
 
 ^6 
 
 ,5, 
 
 /» Minor . 
 
 ; —f-,-*^ 
 
 I Ci 'S 1 Ct Cd — 1 — na s 1 «.- - > iL 
 
 Ä ■*■ — = 
 
 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 : 
 
 «A Degr 
 
 3d Degree : or : 
 
 6 
 
 116. 
 
 
 Minor : &d Degree, 
 ö 
 
 mm?mm 
 
 C: V-, 
 
 Y 7 a':V 7 
 
 If we modulate into other keys, the possibility of new connections 
 extends itself greatly, e. g. 
 
 a. With a downward progression of the seventh. 
 
 better 
 
 fe — * "— ^ - \ —o^jy,— P— g— ^Sg— q g| -jZg |^_^-g|— ^ — [ 1 
 
 C: V- 
 
 C: V. 
 
 V~ F: V-v a: V-r G:yn° 
 
 7 ü: * 7 Wi ' 7 
 
 1). TAe seventh remaining stationary. 
 
 C: V 7 Efc>:V 7 C: Y~ B,,: V 7 a: V 7 C: V 7 a: V~ G: V' 7 
 
 3. The connection cf the chords through an upward progression of t hi 
 levenih. 
 This case can occur with the common cadence (V — I). 
 a. With an exchange of the progression of various voices- 
 
M 
 
 119, 
 
 MANUAL OF II ARM ON 7. 
 
 not : 
 
 7 
 
 7 6 7 6 
 
 7 
 
 Through the step of a third, of the Bass, the downward progression of 
 the seventh becomes impossible, since the covered octave occurring thereby 
 
 150. 
 
 ä 
 
 ■«. — tt 
 
 si 
 
 is in any case faulty. 
 
 In the remaining voices this progression of the fundamental cannot W 
 introduced. 
 
 151. 
 
 ^=E=?=^iiE 
 
 §i =^^=JE£=^^^^g 
 
 A.11 these Examples are faulty. 
 
 fo. The fundamental remaining stationary : 
 
 152. 
 
 g?^|g - 
 
 ~-%=^* — F — g^^g^=^g — F— g g =^ 
 
 g=S 
 
 4 
 ^3 G 
 
 g o g- 
 
 W *■ 
 
 1 
 
 
 l=e^l 
 
 The fundamental serves -here as so-called stationary voice. (See later: 
 Organ point). It must however lie «/ a distance from the seventh, and 
 the following progression would be faulty : 
 
 153. 
 
 a 
 
 g 
 
 ^ü 
 
MANUAL OF HARM OS Y. 86 
 
 C Through cliromatic alteration ana with modulation. 
 
 r< & 
 
 4 7 4 ß # 4 7 
 
 fl 7 u_3 3 5_ 2__ £ # J 
 
 C:V 7 G:V 7 ^ 
 
 enharmonic: 
 
 % 
 
 _o 2 5 7 u« 7 3 
 
 C: V 7 Q: V 7 V 7 b: vii» 7 C: V 7 FJ: V 7 
 
 d. Through contrary motion of the Bass with modulation into other 
 keys 
 
 7 C:V 7 b|,:vu» 7 a: V 7 d: vii<> 7 C: V 7 F: V 7 
 
 (See above, No. 149.) 
 
 •«• ^P^^^^^i 
 
 The foregoing catalogue of chord-connections gives only an indication 
 of possible combinations. The object of them was to call attention to 
 the manifoldness of harmonic progression and its capability for con- 
 struction. 
 
 Concerning the worth of these and similar chord-combinations, criticism 
 can only decide in especial cases, since their right use becomes possible 
 only with a proper attention to their introduction, their succession, their 
 rythmical weight ; in short, their whole situation. 
 
 The particular character of a piece of music, the peculiarly formed 
 leading of the voices through the application of a motive or thought, and 
 the like, can lead to such combinations of harmony ; to apply them, however, 
 upon speculation, to produce new and strange forms in any case, in ordei 
 to appear original, would probably in few instances so succeed, that th« 
 intention would not be apparent. 
 
 Exercise», 
 
 6 
 
 7 7 
 
 , 5 «. g j^ ZLjrj3B§ nm?TT^ i 
 
 4 
 
 m^^wm^s^E^mm 
 
se 
 
 3. 3 
 
 MANUAL OF HARMONY. 
 2-4 6 fi 
 
 •1 
 7 3 
 
 — (2-t-S>- 
 
 6 - 
 
 6 
 6 4 7 
 
 I E^M4=£N -j ^l7T^ff 
 
 i^sililiii^^^liü^li^l 
 
 4 7 
 
 5. open position. 3 6 7 6 J? 
 
 lü^llü^lü^Ülü IUI 
 
 6 7 
 
 3 4 S 
 
 -&- 
 
 4 G 
 
 3 4 2 5 
 
 7 
 
 7 $ 
 
 6 7 6 6 4 6 7 
 
 7. 4 I 6 J3T 6 5 4 3 6 6 4 g 
 
 5 _p _5 5_ 
 
 4 7 
 
 ÜpE 
 
 I= ^Hp-l_j - O-T- 
 
 d=zt 
 
 SB 
 
 Remahk. — The ope« position of the 5th exercise has reference to a leading of the voices 
 adduced page 84 ; farther on, it can be abandoned again. 
 
 The Secondary Harmonies of the Seventh Connected with fliords 
 of other Tone-Degrees or Keys. 
 
 A few more connections of chords with secondary chords of Ifct. seventh 
 may here follow. To adduce all cases of the kind would be &i impossible 
 as it would be without object. 
 
 a. With regular progression of the seventh. 
 
 C: n 7 m ii 7 b: V 7 C: m 7 IV ir; 7 F:V 7 CilV^OtV-jr 
 not: letter: 
 
 ifppilipliliilill^f «flop 
 
 a: a?* III VI iv 7 V iv 7 V VIjQiVy j te» 7 » «m»« 7 
 
 b. TFtf/i /re« progression of the seventh. 
 
3. AN UAL F H A R M N 1 . 87 
 
 not : 
 
 C: n ? G: V~ C: 117 o: vii ^ C: 117 a: V7 0: 11- i>: vii u ^r 
 
 Rem abk.— The reason wl v the last example is not good, lies in these called erou 
 nlatiir. therein found, the explanation of which follows later. 
 C. The seventh remaining stationary. 
 
 „. b. ^ c. (I. G 6 
 
 C: n 7 IV :i 7 vi n 7 I n 7 I V 
 
 The last chord-succession is often used. It forms a delay of the caden- 
 cing progression of the second degree to the fifth, through the inserted 
 chord of the sixth and fourth of the tonic triad. Its chord of the sixth 
 also often appears between this chord and its resolution, as in Example C. 
 
 The chord of the diminished seventh is often used in like manner: 
 
 Here also the natural progression is only delayed through the chord of 
 the sixth and fourth. 
 
 The mechanical combination of such chord-successions may be left to 
 personal practice and investigation. The advantage of it will lie in the 
 insight gained into the relations of chords, and therefore is not to be 
 esteemed so insignificant as it might at first appear ; this [practice] will, 
 i' fact, stand in about the same relation to composition, as the technical 
 studies and preparatory exercises, to the practical bringing out and repre- 
 sentation of musical works. Both produce aptness and skill, educate the 
 powers, and render intellectual productions possible. 
 
 It may here only be remarked in addition, -that the relation of the 
 seventh to the fundamental and Us progression must always be regarded 
 as the criterion of the above combination. If this is pure and the remain- 
 ing voices form nine of the before mentioned faults, then the chord- 
 ombination can bt used for particular cases. 
 
 Exercise: 
 
 7 6 
 
 5 6 6 5 
 
 1G1. 
 
 ^Wt^tr- rf^^ ^EEeg m^t 
 
88 
 
 MANUAL OF HARMONY. 
 
 ikfe^^ 
 
 =P 
 
 i=£ 
 
 ;iü 
 
 4 7 
 7 3 5 6 2 
 
 ^mmmimimM^mmmmm 
 
 6 6 
 5 4 
 
 6 
 
 6 
 
 4 T 
 
 ° I*- 
 
 6 6 7 6 6 7 
 
 5. 3 547S 6 7654S 
 
 7 
 55 6 
 
 6 7 
 
 4 5 
 
 Sfe^Eg^J3Ep j3=jpsgi^j^t 
 
 7. 5 
 
 6 21 $ 2 6 
 
 -r-~ Ö--r-(2- 
 
 ÜäliE gEEg^EE'Eg 
 
 7 5 
 
 87 
 * 
 
 iÖieEg 
 
 £^ 
 
 7 6 
 
 6 7 
 
 4 t 
 
 llfefell^l 
 
 IE 
 
 Remark. — Many of the cases above adduced could not be taken up in these exercises, 
 because they are based upon modulation, which is not particularly explained until later. 
 (The sixth exercise niakjs a little application of modulation.) Many of the above Ex- 
 amples would also have become smoother and less stiff and strange, by the application 
 of modulaiioa 
 
 CHAPTER IX. 
 
 On Chords of the Ninth, Eleventh and Thirteenth. 
 
 Iv most text-books are found extended discussions respecting these chord. 
 formations. 
 
 Tbe views which can be plausibly maintained respecting them are van 
 ous. and will lead to the same practical result. We can assume 
 
At A N A L O F II A R M O A i . &> 
 
 Either that this combination of intervals is to be regarded and treated 
 «w real chords ; 
 
 Or, that they, as unessential chord-formations, eiflier belong to the sua 
 pensions, or arise accidentally on account of a voice remaining stationary 
 
 In the first case, the explanation of their use, especially through theiy 
 inversions, becomes very extended; and also obscure, (since in the fou' 
 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 : 
 -ZZHZX. TT/s' -LL 
 
 162. 
 
 Tn 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 Ol 
 of the fundamental ; and cases cf the following sort, where both to~.« 
 enter free 
 
 l«:s 
 
 ^=m 
 
 we to be censured on account of their stiffness and want of connection 
 TV ; * preparation can be effected thus: 
 
90 
 
 MA A UAL OF HARMONY. 
 
 164. 
 
 g^lgiifeilllli 
 
 9 
 
 7 
 
 :~g— r 
 
 9 6 
 7 4 
 
 sr 
 
 
 %iS 
 
 IIow far the first examples are to be reckoned as belonging to the sus- 
 pensions, and the last to other accidental chord-formations, cannot be 
 explained until later, in Part II. 
 
 Remark. — From the chord of the ninth in major they derive the chord of the seventh. 
 of the seventh degree, which we have treated of fully before ; likewise the chord of tht 
 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. fe= 
 
 mm 
 
 Through this arises, with the first, the complication that we must accept of too chords 
 •f the seventh of the seventh degree in major ; one, the natural cadence of which is the 
 Following : 
 
 166. 
 
 i 
 
 the other as derived from the dominant chord of the seventh, while it remains the sim- 
 plest way to refer to the character of the leading tone upon which the above chords 
 rest. 
 
 That many musical text-books accept also of secondary chords of the 
 seventh and 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 : 
 
 167. 
 
 
 1 3 
 
 1 1 
 
 1 1 
 
 9 
 
 9 
 
 7 
 
 7 
 
MA NUAL OF Ha R MO .V Y. 91 
 
 In the pure four-voiced movement they can, of course, never be applied. 
 since, through the necessary omission of many intervals, they will appeal 
 «imply as suspensions, e. g., 
 
 1 4- 
 
 16§. 
 
 
 and even in the polyphonic movement they will not distinguish themselv«« 
 at all, in their character, from the suspensions ; in the more free style, 
 where they also appear without preparation, they can be regarded as 
 changing notes. 
 
 CHAPTER X. 
 
 CJiromatic Alteration of the Fundamental Harmonies, Altered 
 Chords. 
 
 The chromatic alteration of one or several intervals of the fundamental 
 harmonies has a double effect : 
 Either it produces a modulation, 
 
 Or, it gives to the chord a new formation not hitherto used by us. 
 If, for example, the major triad is altered in this manner, there arise 
 a. Modulations : 
 
 .« 9 . gj EzB ^^EpSgg fei 
 
 Through C», the diminished triad of the seventh degree in D major or 
 D minor, or the second degree in B minor ; 
 
 Through E?, the C minor — triad; 
 
 Through Ei? and Gb, the diminished triad of the seventh degree cf D? 
 major and minor, or the second degree of Bi? minor. 
 
 The last two alterations are mere transpositions of the same chord into 
 vther keys, viz., C? major and Cjf major. 
 
 to. New Formations: 
 
 ■ TO. glj=tll=PI=gf=j^^|li^ 
 Of these, the formations a, &, d, f, can indeed be produced accident 
 
MANUAL OF HA VMONY. 
 
 ally thrcugh by-tones (passing tones); they have, however, n. harmoni« 
 value. 
 
 It is otherwise with the formations at c and e 9 which maintain harmoni 
 (accordliche) significance. 
 
 The first form of the triad (c) is known under the name of 
 THE AUGMENTED TRIAD. 
 
 Tins chord was found before upon the third degree in minor (see page 
 U) ; it appears seldom, however, in this situation, as has been previously 
 mentioned, but more often as triid of the first, fourth and fifth degrees 
 in major, with chromatically raised fifth. 
 
 Its origin from the passing tone (G$) to the next following (A) is easy of 
 explanation, as also its progression, which is determined through this tone 
 (Gfr as augmented interval. 
 
 171. 
 
 The inversions of this chord can also be used. 
 
 6 G 
 
 172. 
 
 fellfifel^Iil^ 
 
 C: I iv v I iv vno 
 
 Although these chords appeared for the most part in passing, or throngb 
 preparation of the augmented fourth, they can also enter free in case of & 
 rapid change of the harmony : 
 
 I «. I '.I 
 
 173. 
 
 ÜB 
 
 §IiHeü3^If| 
 
 To the augmented triad can be added not only the dominant seventh, 
 whicL occurs most frequently, but also the major seventh of the first and 
 fourth degrees. 
 
 a. The augmented triad in connection with the dominant seventh: 
 G 
 
 174. 
 
 
 4 
 
 a e 
 
 mmmmii 
 
 mm^mmmmsmm^js 
 
MA NUAL OF IIA R M N Y. 
 h. In connection tvith the seventh of the fust degree: 
 
 93 
 
 175. 
 
 
 C. TA« addition of the seventh to the augmented triad of the fourth 
 degree is very rare : 
 
 4 
 
 3 G 
 
 176. 
 
 — ^ — g — F — g — g — t- — a — g — L—i.yi—g- _-rr 
 
 4^ 
 
 iftltllilglil^lf 
 
 (J: IV-r vii» 
 
 In all these chord-connections thus far, the cadencing Bass progres- 
 sion, (e. g., V-I I-IV) has been used: some examples, however, may show, 
 that these chords treated of can also be used with chords of other degrees, 
 and a various progression of the Bass. 
 
 7 
 5*6 
 
 177. 
 
 7 
 
 5 J G 
 
 
 6 5 - G 
 
 5 4 3 5 X 
 
 .% 5 9 8 J- ; 3b 
 
 
 1 
 
 ^^ i ^^==^ em = il 
 
 C: V* d:vh 
 
 6 7 65 
 
 555 76 5 I « 
 
 t t #5 J ■#■ u« -J- 1 
 
 1 T d: V C: m 
 
 These occasionally strange and rough sounding harmonic combination» 
 acquire significance only through the situation which they occupy, and 
 especially, if in a certain degree an inner necessity leads to them. 
 
 If it is the province of a text-book to call attention to the possibility of 
 such harmonic formations, it is ai«o its duty to warn the beginner against 
 oyer valuing the worth of such stimulants; to advise him in general, not 
 
MANUAL OF EAR MONI 
 
 to occupy himself with such things and speculations, until he is fuUy 
 versed in the treatment of the simplest harmonies of the simple pur* 
 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 <A 
 harmony, and turn away the sense from the chief thing to secondary 
 matters. 
 
 Exercises. 
 
 1- 5 53 5 5$ 3 6 
 
 its. asjE^f* ~ 
 
 5 - 
 
 3 
 
 m^fi^iii^! 
 
 
 3 2 _ _6J 5 
 
 53 5 55 6 2 
 
 6 63 
 5 4 
 
 
 6 5 6 
 
 5 4 7 if 6 7 7 
 
 era 
 
 ^ 
 
 Sl^^l 
 
 :t=i=f 
 
 7 6 
 5 3 53 5 — 
 
 NB. 
 6 3 53 6 
 
 
 Remark. — In the fourth exercise the augmented fifth has been used, even with the 
 minor triad of the second degree (at NB), which in this connection does not sound un- 
 natural. This would correspond to the formation/* before in Example No. 170. It 
 is seen from this, that with a natural leading of the voices, many new chord-formations 
 can be gained. 
 
 , _g, (which also occurs 
 
 From the formation e of example 179 : 
 
 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 : 
 
 r». |=Ed|f=^l 
 
 According to its progression, which is determined by the augmented 
 tixth, the original chord belongs here to G minor, the fourth degree of 
 which, C minor, with a raising of the fundamental, goes to the fifth degree 
 
 Wherever this chord appear* with its natural progression shown abeve^ 
 
MANUAL OF IIA EM GAY. 85 
 
 Example No. 179, the last chord shows itself as dominant The 
 proof of this lies in a few harmonies formed like the augmented chord of 
 the sixth, the augmented chord of the sixth, fourth and third, and the 
 augmented chord of the sixth and fifth, the explanaticn of the basis rf 
 which follows farther on. 
 
 Remark. — The relation, in which the augmented chord of the sixth stands to the jmt 
 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 
 onbj (the fifth of the original chord) can be doubled in the four-voiced 
 movement : 
 
 l§0. \ 
 
 gsj^gggfjfjjjE 
 
 Of the remaining positions of the original chord (the so-called double 
 diminished triad), the first (fundamental position) can be used three- 
 voiced, but very seldom, the third (second inversion), also four-voiced, only 
 however, in a very open position. 
 
 a. b. not: not: better: 
 
 Remark.— Tbe 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 place 
 referred to. 
 
 Thus the formation of the triad in No. 170. d will be like the following, wh : ch is 
 found in C major : 
 
 letter in open position: 
 
 182. ^=lz:pll=^=|;^lg^=^| 
 
 " o: vno * * 
 
 This chord bears, in many text-books, the name : harsh diminished triad, {hart ver- 
 minderter Dreiklang). 
 
 The like chords, if they may be so called, appear generally only accidentally, in pass- 
 ing, and their progression proceeds in accordance with their intervals, that is, augvwiied 
 intervals progress one degree upwards, diminished intervals downwards. 
 
 The chromatic alteration of an interval <tf the chord of the seventh ha* 
 
96 MANUAL OF HARMONY. 
 
 been, in part, already mentioned, where to the chromatically altered triad 
 the seventh was also added (page 92). This occurred with the augmented 
 triad. 
 
 Among the remaining secondary chords of the seventh, the chro.natie 
 alteration of one receives an especial importance. This is the -ehori 
 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 
 
 183. ^=2—-S=\l 
 
 a: u« 7 
 
 gives the following inversions : 
 
 6 4 £ 
 
 5 3 2 
 
 Of these inversions, the second is the most important and is much as©d 
 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 hased upon that of the fundamental chord, that is, as 
 the chord of the seventh of the second degree leads most immediately to 
 the dominant, so also will this. 
 
 If the fundamental of this chord is omitted, the augmented chord of the 
 sixth, already found, arises, the progression of which to the dominant u 
 hereby explained, (see page 94) ; 
 
 86. 
 
 mmm 
 
 a: ii° 7 V a, ii° 7 V 
 or, for comparisor with No. 179, in G minor : 
 
 Chro. raising Am./, chord of the si.rth, Aug. chord of 
 
 Fundair trial chord : of the third: fourth and third : the sixth : 
 
 «: ii ! f g: ii° 7 V c°» V 
 
MANUAL OF HARMONY. <St 
 
 Remat. Ft may he mentioned here, that the formation of tlie Augmented chord 
 of the sixth, fourth and third can be already reached through the harsh diminished tnaa 
 (hart verminderter Dreiklang) mentioned page 95, to winch a Beventh is added; that 
 the resolu ion, however, must become a different one, since that was considered to be on 
 the seventli degree, while this is found upon the second. 
 
 Instead of the fundamental of this chord, the ninth . f the fundamental 
 chord can be added, whereby the 
 
 AUGMENTED CHORD OF THE SIXTH AND FIFTH 
 arises. 
 
 Its origin is as follows : 
 
 without Fundamental : Inversionx : 
 Fundamental with ninth: with elevation a. b. £ c. 25 
 
 chord: of the third : 5 ;5 yy. 
 
 &„ & *' 
 
 a: h° ^ 
 
 Of these chords, the one resulting from the first inversion <t, 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 producer 
 var all el fifths: 
 
 1§0. 
 
 mmsm 
 
 These progressing fifths, which do not belong to the most unpleasaut ones, 
 are avoided either through an earlier resolution of the fifth (the original, 
 above-mentioned ninth as suspension), as in the following Example {(f), or 
 through a skip of the same into the third, whereby the augmented chord of 
 the sixth results (b), or most frequently, by the third and fifth remaining 
 stationary while the sixth and the Bass tone progress, whereby the chord 
 of the sixth and fourth is inserted before the resolution (c), which chord 
 can be here regarded as a prolongation of the suspension. 
 
 not : better : 
 
 Remark. — The addition of the ninth does not justify explaining this harmony as f 
 chord of the ninth ; the ninth has here, as everywhere, the same character as sispen 
 don, as appears very plainly from the progression a; just so the progression at h are 
 
»8 
 
 MA X UAL OF HA R M . N Y 
 
 C ausw ■>. < completely to the treatment of the suspensions, as it alsc (a* fifth in the abort 
 chord) i v quires a preparation. 
 
 It wou<d follow f'nm this, that this harmony should be taken into consideration first 
 in conue« ciou with the suspensions, it was however necessary to mention it here, be- 
 sause the question of the origin was under discussioa and it was not the intention, by 
 the above <"spres<ed view, to oppose x generally received appellation 
 
 Exercises. 
 » 60 $ 2 
 
 6 7 
 
 •••• z^m ^m mm^mmimm 
 
 7 6 5 4 
 
 $4 3 
 
 9!pt 
 
 
 =3= ± 
 
 -o — *- 
 
 4 
 
 3 6 
 
 Ifcjgjgzfc 
 
 ESj 
 
 3 - $ i 
 
 3=f 
 
 G * 
 
 4 J 2 
 -s>- 
 
 6 7 
 
 7 4 5 
 
 a 
 
 B 
 
 i 
 
 I 
 
 : Mg = r-F F g- Psr— g- 
 
 L ^- : o ; 
 
 At the close :>f this chapter we survey once more the broad field which 
 was opened in it for harmonic formations. We have found much which is 
 generally knowu and adapted for use. Much appeared to us unadapted 
 for use and worthless. Nothing however showed itself in its original condi- 
 tion, everything had received an addition, experienced an alteration, in a 
 certain sense, adornment. This forsaking of the original gives us occasion 
 to refer once more to that which was remarked on page 03. 
 
 A long time indeed elapsed, before these harmonic transformations 
 were discovered, and a still longer, before they became common property; 
 much, which until now is unadapted for use, may with time be developed, 
 but, in order that the healthy inner germ may not be lost, we cannot ad- 
 vise the direction of the whole effort, out of desire for originality, to the 
 discovery of new harmonic forms, or the immoderate use of then, and devia- 
 tion from the primitive. 
 
 Since all these transformations serve more for adornment, and it might 
 be said, for the more elegant carrying out of the simple fundamental idea, 
 we may venture to usa them only with discrimination if we do not w<sh to 
 overload the work of art, and thereby ourselves be reckoned as without 
 taste. 
 
MA A' U AL OF H A R M X Y 
 
 '..'.» 
 
 At the close of the exhibition of all essential harmonies and their moBt 
 immediate use, may still follow a brief view of them, their varieties and 
 derivatives. 
 
 View of all Chords belonging to a Major or ßlinor Key. 
 
 I. FUNDAMENTAL HARMONIES. 
 
 a. The Triad. b. TTu chord of the seventh. 
 
 A. The varieties of the Triad. 
 Major, Minor, Diminished, Augmented. 
 
 Major Triads. 
 
 Of the Major Scale : Of the Minor ScaU 
 
 *=> 
 
 C: I IV V a: V VI 
 
 Minor Triads. 
 
 Of tht Major Scale : Of the Minor Sea, 
 
 3=5=* 
 
 C. ii in vi 
 
 Diminished Triads. 
 
 Of the Major ScaU : Of th e Minor ScaU i 
 
 C: vn° a: n° 
 
 Augmented Triad of the Minor Scale. 
 
 II P —The remaining augmented triads see under II. : Altered Chord». 
 
 Inversions (Versetzungen) of the Triads 
 
 a. The chord of the sixth. 
 
 b. The chord of the sixth and fourth. 
 6 
 4 
 
100 MA XV a L of harmony. 
 
 BS The Varieties of the Chord of the Seventh,. 
 
 ft. The dominant chord of the seventh or primary chord of the se.tnth 
 
 b. Secondary chords of the seventh. 
 
 a. Dominant chord of the seventh (major triad with minor seventh)* 
 
 Formed alike in Major and Minor : 
 7 7 7 
 
 H3g= 
 
 C: V 7 o: V 7 a: \-j 
 
 h. Secondary chords of the seventh 
 1. Major triad with major seventh 
 
 In Major. 
 
 o: T 7 iv 7 
 2. Minor triad with minor seventh 
 
 In Major. 
 
 O: ii 7 my vi 7 
 8. Diminished triad with mir.or seventh 
 
 In Major : 
 
 i — 
 
 C: vii«: . 
 
 4. Diminished triad with diminished seventh (chord of the diminiahtd 
 seventh) 
 
 6. Augmented triad with major seventh 
 
 In, Minor : 
 k: Ul'y 
 
MANUAL OF IIA k M N Y 
 
 101 
 
 Inversions (Versetzungen) of the Chords of the Seventh. 
 
 a. ^'t chord of b. The chord of the 
 
 the sixth and fifth : sixth, fourth ami third . 
 G 
 
 § I 
 
 e. The chord of 
 the second : 
 
 ~ I qjg r Z ~~^ ^ a " 
 
 II. ALTERED (chromatically changed) CHORDS. 
 The augmented triad, formed from the major triad : 
 
 In Major: 
 
 C: T **■ IV V 
 
 1>. The augmented chzrdof the sixth, formed 
 1. From the minor triad with raised fundamental (so-called doubl« 
 diminished triad) : 
 
 
 2. From the chord of the seventh of the second degree in minor. (See 
 the following chords) : 
 
 C. The augmented chord of the sixth, fourth and third; 
 
 d. The augmented chord of the sixth and fifth— both formed from 
 the choid of the seventh of the second degree in minor : 
 
 Raising of 
 the third : 
 
 Second 
 
 Inversion . 
 
 IL 
 
 1ÜS|=^| 
 
 Without Fundamental, 
 aug. chord of the sixth . 
 
 &* 
 
 BE 
 
 With the ninth from 
 
 the Fundamental 
 
 and without the latter. 
 
102 
 
 MANUAL OF HARMONY. 
 
 CHAPTER XI 
 
 On Modulation of a Passage of Music (eines Tonmtun). 
 
 The term modulation has a various signification. Formerly was un.ler 
 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 nest be important, to learn 
 rightly to recognize and determine each occurring modulation (digression 
 into a foreign kev) ; 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. 
 
 mmiMMmäiii^=?m 
 
 §l£EES 
 
 J Ö 7 ,7 
 
 (s a modulation to D minor in the third measure, because CiJ-E-G-B'2, 
 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 unmia- 
 takable. 
 
 The dominant chord of the seventh, as also the chord of the diminished 
 seventh, are, as the chief means of modulation, never to be mistaken ; all 
 the remaining chords are ambiguous, that is, they can belong to severaJ 
 keys. 
 
MANUAL OF HA R I/O N 7. 103 
 
 Thus the G major triad belongs not exclusively to G mnjor, 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 forme-l first through the dominant harmony of the seventh with ita 
 derivatives. 
 
 The musical ear itself proceeds very simply in the apprehension of a 
 modulation : it always apprehends the foreign haru>\>y as belonging to 
 that key, which is nearest related to the ruling one. 
 
 Thus, for example, in 
 
 103. g^fef^E 
 
 if — i^r-tts 
 
 the major triad of D in itself considered, would belong to ♦be \cy of D 
 major ; in connection, however, with C major, it will be most incu^diately 
 recognized as dominant to G major, and the following chords first can de- 
 termine which key becomes the ruling one. 
 
 There follow here some more exercises for practice in searching out tl 
 modulations ; for the farther discussion of this subject see Chapter XVi 
 
 Exercises. 
 
 9 
 
 i 
 
 3 68 5 
 
 .»4. m ^ mmmm^m^=?^m^. 
 
 C: I G: V 7 I C: IV V 7 I d: vii u 7 i 0: I » 7 V I 
 
 6 
 
 %.-?- £ § 4 5 2 
 
 y.ct — & 
 
 6 * •* 
 
 _*. 3 6_7b >? 5h 2_ _3_G_ _2iL _ _<L 
 
 6 7 Ü 6 6 
 
 4} *• 6 6 J 2 6 7b - 5 3 
 
 G 2 6 4-5 5 ö 6 g 
 
 -&■ 5; ■ 
 
101 
 
 * 2 
 
 MANUAL OF HARM OKT. 
 
 7 
 
 6 
 6 5 
 
 4 J 
 
 6-3 6 6 33 i 
 
 m 
 
 50 4 3 G 8 7 
 
 — r 
 
 ÜIHS 
 
 :t=fr 
 
 4b 4 6b 6 
 
 2 3 4 5 
 
 6 6 
 5 5 
 
 mm iS^lipülfilf^i 
 
 Kü=4 
 
 5 
 
 6 6 
 
 5 5b 
 
 4 7 3 2 6 
 
 f 
 6 3 
 
 ÜS 
 
 SEüö 
 
 6b 
 
 4 6 
 2 5 
 
 t=t 
 
 6 7 
 
 The modulation can be indicated in the same manner as in the fir it 
 exercises, accoiding to which the letters indicate the key and the 
 Roman numbers, m>> *vj know, the degrees upoD which the ihords in que» 
 Hot r«at 
 
MAN SAL OF HARMON. I0h 
 
 PART II. 
 
 aCCIDENTAL CHORD-FORMATIONS.— TONES FOREIGN TO TI1K 
 HARMONY. 
 
 CHAPTER XII. 
 
 Suspensions. 
 
 The simultaneous progression of all voices to the following chord, par 
 fcicnlarly 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 n<ixt 
 harmony. 
 
 The most important manner of thus linking harmonies together, and the 
 one tc 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, vhich has to progress one degree dowmcards, 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 pass 
 over into the harmony until later. 
 
 In the following connection of harmony : 
 
 195. 
 
 
106 
 
 M A .V U A L OF HA RM0S7 
 
 the Soprano can linger upon the C during the entrance of the secoLd chori, 
 and pass over later to the B in the following manner : 
 
 196. 
 
 Just so a suspension can be formed from Example No. 195, through the 
 delaying of the Tenor : 
 
 197. 
 
 
 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 
 Dne of the otner 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 b» formed with a descending progression of c- voie* 
 by degrees, under the following conditions ; it must 
 
 1. Be prepared, and. 
 
 2. Resolve itself. 
 
 There will, therefore, be three things to observe in connection wirb tha 
 suspension : its preparation 'he suspension itself and its position, and 
 its resolution (progression). 
 
MANUAL OF HARMON J 
 
 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 
 
 tnroagh trie octave of the Fundamental: 
 
 IDS. 
 
 Through the third: 
 
 
 4: 3 
 
 
 Through the ßßh: 
 
 — A n I 
 
 6 4 33 
 
 * 15 si 
 
 C: I G: V vi C: I IV 
 
 Through the dominant seventh: 
 
 
 I I 
 
 Pf^£f^!ii^^P==== 
 
 5 - 
 4 3 
 
 9 8 
 
 3 
 
 
 V 7 a:V 
 
 The preparation takes place upon the arsis, the suspension itself 
 enters at »he 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. 
 
 b. The Suspension. 
 
 The entrance of the suspension at the thesis has just been mentioned , 
 its position in other respects should be still more particularly expla'.nc« 1 . 
 
 The suspension can appear in any voice, before an interval of tk 
 trvad.—befcre the seventh, enly in rare cases. 
 
108 MANUAL OF HARMONY. 
 
 8uspe?isions before the Octave of the Fundamental: 
 
 109. 
 
 m*& m 
 
 7 6 
 
 7 6 Ä- -£. J. 
 
 m= ^5^m " i -g -K-= 
 
 C: V T I 
 
 Before the third: 
 
 -c-o 
 
 I I a i-g— 
 
 £illli 
 
 5 - 3 ~ 
 
 4 3 ■*■ •*■• ^ 
 
 ü§!Mi=e^p^ie 
 
 C: IV I 
 
 Before the flfth rarely, only in certain positions: 
 
 J 
 
 PöÖE^ii 
 
 2 
 
 
 _<2 I_ 
 
 "c^ - 1 V 
 
 4 4 - 
 
 3 2 -- 
 
 ^1 
 
 1 
 
 » 5 v*4 
 
 ܧ1 
 
 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 ot 
 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 npver come into a dissonant position («), except as in the fol- 
 lowing Example h, where the octave is diminished. 
 
 800. 
 
 
 ) ~ 8 7b 88 7b 
 
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 downwards. 
 
 Remark. — Ways of resolution which deviate from this will be shown later. 
 
 Here it is further to be observed that 
 
 Tbe tune 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 "eeeive 
 it without disadvantage to the harmony. 
 
 a. not: b. better: c. nut: d, NB. 
 
 201. 
 
 mk^ä^i^^Eß^M\[ 
 
 e— T -% 
 
 $-iZ— i 
 
 mm==\mm^m\mmMm 
 
 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, wbich, in the 
 Alto, has the suspension A. Both reduplications are faulty, especially be- 
 cause they concern the third and fifth of tbe chord. In Example d at 
 NB., the reduplication takes place with tbe fundamental. In this caso 
 tbe effect is better, especially if the consistency of the leading of the »oiee» 
 necessitates it as in the following movement : 
 
 Fundamental : 
 
 Third : Fifih : 
 L J | ^ %J j 
 
 sssil 
 
 Remark. — It may still be remarked here, that the doubling of the fund \ment»l 
 always assumes the distance of at least an octave, and that the doubling in 'inison ii 
 faulty, e, g 
 
 4 1— rc 
 
 SEE 
 
 The suspension can indeed appear in such proxi 
 with the voice which lies next to the lowest. 
 
 ty, only between Bass »nd Temr, or 
 
 The lowest voice, commonly the Bass, has, however, as the one which 
 determines tbe chord, the power of counterweight against tbe dissonance 
 
no 
 
 MANUAL OF HARMONY. 
 
 of the suspension ; reduplications are therefore admissible, if they aw 
 based upon a good leading of the voices, e. g. 
 
 »03. 
 
 — r- g 
 
 6 9 
 
 mwmmmmmm 
 
 t 
 
 mmmmmmmmmmmi 
 
 The faulty progression of the Soprano and Bass in the last example W 
 «ornes clear, if the suspension as mere delay of the progression of the 
 voice, is taken away, through which means the open octaves appear : 
 
 201. 
 
 -g— =■ 
 9. — 
 
 s 
 
 §t 
 
 The relation is the same with the fifth-successions, which are covered 
 through the suspension : 
 
 205. 
 
 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 unpleasantnesg 
 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 : 
 
 200. 
 
 m^im$^=ii 
 
 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 tlem is impossible; to reject them alwayi 
 would confine us too much 
 
MANU A L F I! A R M N Y 
 
 11 
 
 The suspensions in the Bass, which occur oftenest before the third oi 
 
 the chord (or, which is the same thing, before the chords of the sixth and 
 of the sixth and fifth), allow of no reduplication in the oth'.r voices. 
 
 ao7. 
 
 i=E^^=l^ä=Eizl^^t^^^l 
 
 (pi^feEEf^^^^l 
 
 m 
 
 w 
 
 The suspensions before the fundamental and the fifth rarely show them- 
 »elves practicable. 
 
 (tiüiüi=g^=E^I| 
 
 20§. 
 
 ^3^mmm mmm\ 
 
 The indication of the suspensions in the Thorough-Bass notation is, in 
 part, contained in the previous examples. 
 
 If the suspension lies in one of the three upper voices, its interval from 
 the Bass is given at the same time with the resolution, e. g., | % 9 8 76 
 the remaining figures determine the chord where it becomes necessary, 
 e. g., the chord of the sixth | ^ the chord of the sixth and fourth 5 ^ 
 
 or 1 1 
 
 If the suspension lies in the lower voice, the chance intervals of the 
 remaining voices are likewise indicated by numbers, e. g., |Z> or i n case 
 cf the chord of the seventh 4—; the dashes which follow denote that the 
 
 voices retain their tones during the resolution of the suspension. 
 
 The suspension in the Bass is also marked by a diagonal stroke above it 
 and the corresponding chord set over the tone of resolution, which 
 plainer as concerns the latter, e. g. 
 
 209. 
 
 H^ÜI^^HÜPIÜB 
 
 \ o 
 
 6 
 
 \ 5 
 
 6 
 \ 5 
 
 I^fggi iE£^E55gIi|slfElj=B 
 
 In the succeeding examples the first manner is chosen, as the most 
 twmmon. 
 
112 
 
 MANUAL OF HARMONY. 
 
 210. 
 
 Exercises. 
 
 5 7 6 5 7 
 
 5 o •& 5-43 2. 3 6 9 g 
 
 '7 v 7 ' 
 
 IV V^ I ii- 
 
 5 
 4 33 
 
 4 3 6 2 - 98 7 4 33 
 
 mm 
 
 5 - 6 
 
 32- 7 6 7 5 
 
 4- 
 
 31] 6 J? 
 
 6- 7 - 
 5 4 4 3 
 
 -s^ 
 
 a*! 
 
 "fTF 
 
 g=sfc 
 
 ££S 
 
 5 - 
 4 - 
 2 - 
 
 zd: 
 
 :Ez. 
 
 98 26625 6 
 
 :EZ 
 
 8* 
 
 -si — g— J 
 
 7 
 6 4 
 
 5 9 8 3 
 
 3=F 
 
 7 7 6 
 
 5b 3 5 
 
 ÜE^EN»g^S^^^g^Bjg 
 
 5- 6 
 4 3 5 
 
 7 jar 
 
 4- 6 
 6-5 63-4 27 765 
 
 6 65 — „ o 5 — 5 — 
 
 9 8 7 5 6^ 4J^J _ 7. %_J>_ 4 3 2 6 28 — 
 
 5J- 
 £3-6 6 
 312 6 2 — jt_ 3— 5 8 
 
 -Sh-.-r- 
 
 EEppPS 
 
 3 6 9 8 7 
 
 
 6 
 5 6 
 
 6 6 7 6 
 
 4 5 3 7 5 
 
 4- 5-6 
 
 3 2 6 4 3 4 
 
 ll^^lgiil^=^«=g^l^f^^ 
 
 5^ 
 
 7 6 5 5 3 7 
 
 :=zj=zj: 
 
 iztzJ 
 
 It will be to the purpose in the working out of these and the succeed, 
 ing exercises, to separate the voices and write each upon an especial staff. 
 This notation, in 'he manner of a score, affords a better view of the course 
 
MANUAL OF HARMONY. 113 
 
 of each particular voice, aud is in general a useful preparatory exercise in 
 score reading. 
 
 Here, however, it becomes necessary to write the voices, which, in tin» 
 pure harmonic structure, must always be conceived of as voices to be sung, 
 in the clefs which have always been allotted to them, the knowledge ol 
 which is indispensable to every musician. The knowledge of these clefs 
 can be very soon attained by attentive practice, and through comparison 
 with those already known. 
 
 REMARK. — The knowledge of the Alto and Tenor clefs is requisite <br the understand 
 irg and rending of scores, since many voices and instruments are exclusively or partially 
 written in these clefs, aud the Soprano clef itself, which occurs more rarely, afforoa 
 with various instruments, which are tuned in a particular way, an especial facility in 
 reading. 
 
 The clef which is used for the upper three voices, Soprano, Alto, and 
 Tenor, is called the G-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 once 
 marked [middle] C, and in such a manner, that for the Soprano this C ifl 
 found upon the lowest, for the Alto upon the third, and for the Tenor upoa 
 the fourth line, e. g. 
 
 Soprano-cleß. Alto-clefs. Tenor-cleft. 
 
 The most common compass of the voices exhibits itself in these clef» 
 thus- 
 
 
 ^==zj=;=;~ *~ g=p~|: zx:zEz£ : 
 
 ^jjfffl I l_l_l i ij. 
 
 "TlTlTiTI 
 
 :t-t 
 
 ■ ß — F - I — I — i — I — r- 
 
 
Ill 
 
 MANUAL OF HARMONY. 
 
 Resia <k. — The orig\i of these various clefs from the most simple foundation fiom th» 
 eo-ealled Tnblature (commonly a 6ystem of ten lines, upon which all the voices wer% 
 written, with especial designation of the lines upon which the principal tones, F, C, O, 
 «me u stand) is interesting, its farther explanation would here, however, lead us 
 loo far. 
 
 The easiest method of impressing these clefs upon the memory, ii 
 probably, to observe accurately the position of the C-triad in the various 
 voices, whereby the tones which lie between and on each side are easily 
 faind out. 
 
 Tims the position of the complete C-triad, with doubling of the fund»- 
 mental, will be : 
 
 In the Soprano : 
 
 p=« 
 
 In the Alte : 
 
 £iE*!£= 
 
 In the Tenor, lest in the position -f ^g- — »-Q-- 
 the chord of the sixth and fourth : j* # " Q~ 
 
 of the i 
 
 The carrying out of the first exercise of No. 210 in these olefs follows 
 here : 
 211. 
 
 Sopran 
 
 P 
 
 e- 
 
 
 + ~TE: 
 
 =m^^35^mm 
 
 HiH 
 
 ISSÖ^i 
 
 ^^i^m^m=wmmm 
 
 n 
 
 C: I V IV" Yj I 117 V~ 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 be necessarily exchanged for the close position where necessity aD<* 
 sonforinity with the end in view require it. 
 
MANUAL OF HA R MO NY 
 
 IIP 
 
 In this exchange of the position of the voice», the following rules must 
 oe observed : 
 
 The voices can never, simultaneously, move by degrees or skip out of their 
 necessw-y positio?i from one chord to another (foreign one), except <.n indi- 
 vidual cases in the transposition of one and the same chord into uhet 
 positions. 
 
 Any voice can forsake its piosition, if one or more remain stationary upon 
 one ton\ 
 
 The following carrying out of Exercise 8 of No. 210, will make this 
 plainer 
 
 212 
 
 BOTBAN- 
 
 Alt*. 
 
 5 NB 
 
 
 §s§ 
 
 
 G 6 6 
 
 9875 62664 537 
 
 -&- 
 
 G — C 
 
 e: i — it 
 
 7 aO ? 
 
 EH Blj C 7 F 7 
 
 — 7 ii° 7 B!,:iii V} I IV IF:V^ I 
 
 
 1_ -(2—s, 
 
 NB. 8 
 
 I 2 — ©- r S- 
 
 
 =g=p rjxqfa g 
 
 7 6 
 
 3 7 6 
 
 - 6 
 4 3 4 7 6 
 
 D* g o F 7 B? c o c KW a° 7 D 7 « 
 
 g. vif i iv B,:V| I n o: i iv VI n°{ V 7 » 
 
 The following may serve as explanation of this treatment. 
 
 The close position in which this example begins, is forsaken in the fifth 
 measure, in which the open begins, and remains until in the eleventh 
 measure the close position again appears. 
 
116 MANUAL OF HARMON*. 
 
 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 ia 
 already present and remains stationary (as here the F in the Baso;; 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 come» 
 into a better position. At last the close position is attained again Jirougb 
 the better and free leading of the Tenor in the tenth measure. 
 
 Suspensions from Bcloiv Upward. 
 
 Suspensions from below are only in a few isolated cases to be regarded 
 a& such ; most progressions of this kind arise out of the suspensions from 
 above, before treated of, through contraction (abbreviation) of the sam* 
 vith a farther succession in a upward direction, e. g. 
 
 213. 
 
 from : 
 
 mmMm 
 
 ■77 
 
 The suspension from below can take place in connection with the pro 
 gression of the leading tone : 
 
 214 . -* 4-^a=d=i 
 
 also with several intervals, which progress a half-step upwards, especially 
 with those altered chords, which receive augmented intervals through 
 elevation, e. g. 
 
 215. 
 
 ^| Sgpj i|^^i 
 
 — , I .. _ I I 
 
 m^m^^m 
 
 Observe here, that as before, the tone of resolution (harmonic tone) 
 jaust 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 htuinony. (See pag« 
 74). That, in the above application, it is to be considered as suspension of the leading 
 tone, requires no farther explanation. 
 
M A N UAL OF HARMONY. 1 17 
 
 Of other suspensions, especially those which progress a ivhole step upwards: 
 
 Bi a. 
 
 v ■&■ -ee- 
 
 c.^ j a.^ , e. . . 
 
 1 — I— — j— i -© eÜ=i * x ?*?-. -*-£ A a4. r 
 
 «inn! show, of themselves, the unnaturalness of their progression ; and 
 jome 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. «■ ( &• jjj * . , i d :_i#| I e - - — > 
 
 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: 
 
 ..*. isifeiife 
 
 The chord of the sixth and fourth frequently shows itself as double 
 suspension, e. q. 
 
 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 Bass, progress at the same time 
 and > v this mean« form a new harmony 
 
118 MANUAL OF HjlHMONI 
 
 For example, by progression of the Bass : 
 
 B20. ) 
 
 5 9 6 5 
 
 C: V. 
 
 iitaiiiiiiiEf 
 
 I — n-r V I I IV ii r I a: vii°« i 
 
 By progression of more than one voice : 
 
 - ATTJ J __ b ' 
 
 221. 
 
 
 C: I ii V« vi 
 
 I IV vii° vi 
 
 In all these examples the resolution of the suspension ensuci regularly 
 during the progression of the remaining voices to a new harmony, of which 
 the resolution-tone is, itself, a component part. 
 
 Remaek. — It may here be remarked, in explanation of the view concerning chords oi 
 the ninth expressed in Chapter IX, that many places in which the ninlli occurs, and 
 which are recognized by many as chords of tbe ninth, can be explained ui 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 niuth, il 
 the above explanation of a suspension of a ninth with the use of three chords were no* 
 much more simple and did not lead to the same result, and, a-s with all subsequent ex 
 nmples, present itself in the same manner : 
 
 Suspension of a ninth 
 with two chords: 
 
 with three chords : 
 
 222 
 
 — -J , j^J ! _• — -J jT^J j ^ 
 
 ■fmmmm^mmm 
 
 Concerning the ninth whicn enters free, we will speak later in connection with th* 
 Organ-point. 
 
 It mav still be added as completion of what was said in Chapter IX, that as a reaso« 
 against independent chords of the ninth, the impossibility may apply, of bunging them 
 into such inversion with the fundamental that the latter is brought into immediate 
 proximity with th; ninth, as can always take place with the chords of tin. aavonth, t. p 
 
MA N UAL OF HAR M o JF > 
 
 11Ö 
 
 223. 
 
 y—9-. 
 
 ' z^5— J— ä — «=E — 2 EfciEE 
 
 In trie same manner /our chords can be applied with the suspension, i! 
 t stands before a harmonic tone, which is not contained in the remaiuing 
 «ices, e. (j. 
 
 2 3 4 
 
 Without suspension : 
 2 3 4 
 
 22-1. 
 
 I^^^ ^B 
 
 9 5 6 
 
 i 4 
 
 
 C: I IV it vn° vi 
 
 3 
 
 1- 8 7 
 
 Exercises. 
 
 5 G 
 
 4 4 7 4,7 
 
 7 7 
 
 225 
 
 G 7 6 6 5 4 6 
 
 -2. 8J3__ 2 6-4 5 - 5 4 6 - ff 3 6 747 
 
 5 6 7- „ 6 6 
 4_6_7_ 4- 3 _ _ 3. 3 6 9 7 4 7 9 4 — 
 
 Ö j? 
 
 4 4 9 6 6 
 
 6 6 2 3 6 7 5 4 7 
 
 5 >r 5 
 
 4. 8 7 ff 4 2^ 6 70 9 6_— 4 6_- 6 7 
 
 5 6», 5 
 
 46 5» 5. j 676-46- 
 
 g^rtHfaig a rf-rrnrTF ^^ 
 
 7 
 
 6 6 6 «• 4 6 6 6- 
 S 7 6 547 824 4 Ö 
 
120 
 
 9 6 7 
 
 MANUAL OF HARMON\ 
 
 5 
 
 4 6 
 
 7 - 
 
 4 3 2 7 3 
 
 6 
 
 7 4 7 
 
 :®=5L 
 
 Ü^i^ÜÜHÜ 
 
 r> 5 
 
 6 4 7 
 
 gpE=^ ^^^ 6Bg=fe^S 
 
 7. 8 
 
 4 7 
 
 9 3 2 5 
 
 fi- 
 
 ß 
 
 -5*- 
 
 ^ 
 
 5 
 6-43 
 
 -o- 
 
 3 6 
 
 (2- 
 
 üüllil^iü 
 
 7 6 7- 
 
 4 — 65 7- 5 — 
 
 I 326 4 il 3 96 7964 3« 
 
 Between suspension and resolution, other tones can be inserted in ih* 
 same voice. 
 These can be : 
 1. Tones which belong to the chord, e. g. 
 
 & ! _ -_ I •** I 
 
 £zz^Ep33-E ^=p= -5-E ziEpz^äzEö :?E=: EE 
 
 220. 
 
 2. Tones 'oreign to the harmony, changing notes, e. ^. 
 
 227. 
 
 
 *■ jfe p^^^f»==s s g=ffig= B 
 
 The explanation of these and similar instances is completed through thf 
 exhibition of the passing and changing notes found farther on. 
 
 Instances also occur, in which the suspension receives no resolution 
 it all, e. g. 
 
 * oi- 
 
 Usually in this manner : 
 
 22 S 
 
 
 They have arisen from the following passages, by omission 
 
MANUAL OF HARMONY. 
 
 121 
 
 -I r> 
 
 22». 
 
 •■» ♦_#__( | i *L_ _-fH_ | I J | . . 
 
 * 7 i 
 
 Ztr- 1 -^ 
 
 Z 
 
 II 
 
 Alttici])atiO)l. ( Fbrawswa/iwM!.) 
 
 The anticipation of a tone, which is more rarely used than the saspen 
 »ion, is the opposite of the latter, and consists in this, that one or more 
 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 oi 
 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. 
 
 Anticipation in the Basis : 
 
 In the Soprano : 
 
 In several voire« : 
 
 230. 
 
 t t n ' r y f \ f v 
 
 '>: 
 
 
 JI1 
 
 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 rythmical 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 thai 
 intended at the entrance of the chord, as in the known closing 
 
 which is 
 h rmula 
 
 231. 
 
 I I 
 
 z * % * 
 
 Aa antithesis to anticipation may yet be adduced the after-sty-iking of 
 harmonic tones, which has a similarity with the suspensions, in so far, as 
 also life preparation and resolution take place, but differs apain, mat» 
 
122 MANUAL OF HARMONY. 
 
 rially rh its character expresses itself more in the metrical and rythmical 
 movement, for which reason it also always appears in more extended suc- 
 cessions ; the suspensions, however, appear under entirely other conditions*. 
 ^ngly or in greater numbers. 
 
 The following Bass would be a succession of such after-struck tones: 
 
 «32. 
 
 XT 
 
 |^=g^|^==z=|^--Jz£^= 
 
 = 2 5. 
 
 
 ^^^^^^^^^ 
 
 , ! I I 
 
 Here would also belong that unison passage from the overture to 
 Leonore " (No. 3) of Beethoven : 
 
 233. 
 
 -a— - 
 
 -5> v 
 
 
 
 ^ aI-^!— aJ^ Ut» — nc*-4g— lvp-f ür . f F — ■ I— , 
 
 
MANUAL OF HARMONT VI» 
 
 CHAPTER XIII. 
 
 The Or(/an Point, Stationary Voices. 
 
 Ak 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 tc 
 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 oe 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- 
 foint, some examples may follow 
 
 a. Organpoint upon the tonic: 
 
 i f ^ M i r i i f Ft r * * * 
 
 »31. 
 
 
124 
 
 MANUAL OF HARM NT. 
 
 Upf i the dominant: 
 
 I I 
 
 i i ' if 1 i i f r t t *■ *■ * 
 
 m 
 
 
 ^^PpilfegplWpil 
 
 i r f i 
 
 II 
 
 d. Upon both at the same time : 
 
 J * J * * * * * **ii J I I j 
 f +- P §»• P §#• -r ■*• ' I f r i 
 
 11^=1^1 
 
 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 which the Bass tone harmonically belongs ; 
 
 3. The last chord of the organ-point must likewise be in harmony 
 A>ith it. 
 
 The first takes place at the beginning or close of a period or division 
 of one and upon the thesis ; the second and third oommonly by mean.' 
 of the fundamental of a triad, as in Example No. 234 a 9 C 9 (l^ or at b 9 
 through the chord of the sixth and fourth. 
 
 Care should be taken, further, that the chords foreign to the Bass tone 
 do 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 digressions violating the character of the organ-point 
 which is only to be Lund in the holding firmly together of various 
 chord ■ combinations. 
 
MAKVAL OF HARMONY. 
 
 125 
 
 This the following organ-point would be faulty in this regard . 
 
 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 a, the progression of the B[? 
 in the Alto (in the first measure) is determined by the leading of tha 
 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. 
 
 d=J-zJ: 
 
 I I 
 
 wmn 
 
 ÜEE 
 
 The plagal close can, however, ensue with the organ-point of the tonic r 
 
 
 237. 
 
 The end of the organ-point is indeed to be just as carefully treated a* 
 its entrance. In the examples brought forward above, this always taken 
 place through a cadence. In this case it presents no difficulty, except m 
 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 car:fullj 
 »bserved, e. g. 
 
12« 
 
 HAN UAL OF BARMOKT. 
 
 
 See^e 
 
 i^pl 
 
 ÜÜ 
 
 i r i 
 
 Breaking oflF in the following manner would not, however, be good: 
 
 i I V 
 
 I I 
 
 i i i i r j r "i r f f 
 
 Stationary Voices. 
 
 Upper or middle voices remaining stationary upon one tone, in the man 
 oer of the organ-point before described, are much more rare than the 
 latter, and require greater caution in their treatment. 
 
 Sustained tones of this kind only conform to the character of these 
 voices if chords not belonging to them appear very rarely in connection 
 with them, since such voices do not possess the power of counterweight 
 against foreign chords, which is peculiar to the Bass or the lower voice as 
 the determining one. 
 
 Thus the organ-point of Example No. 234 a, being transposed into the 
 upper voice, will in the last measures, sound very unpleasant : 
 
 210. 
 
 
 r f f ~" r Hf 1 f i . 
 
 I I ! 
 
 while the following tone, prolonged as dominant, is better because the laM 
 chords of the example belong to it : 
 
 911. 
 
 illiilliii^iiiifeisiil 
 
'AN UAL OF HARMONY. 
 
 1*7 
 
 As example of effective use of stationary voices and prolonged tones 
 *nd for their treatment, a place can be adduced in the " Gloria " of Che 
 cubiiii's Mass in C-major,where the violins hold Ab for a length of time 
 while the choir and instruments takiug part, carry out below it their par 
 ticular melodic and harmonic progressions; just so the D of the violins 
 in the introduction to the overture " Meeresstille und glückliche Fahrt ; 
 of Mendelssohn Bartholdy. In both cases but few chords can be foui 1 
 to which the prolonged tone would not be harmonic. 
 
 Under this head may also be reckoned the Trio of the Scherzo of Beet- 
 hoven's Symphony in A-major, which is based throughout upon the A 
 which shows itself sometimes as stationary tone in the upp.r and middle 
 voices, sometimes as organ-point in the lowest voice, and serves throughout 
 the whole piece as basis. 
 
 Stationary tones in the middle voices are to be treated with the same 
 care, as those in the upper voice. In instrumental compositions they 
 always appear strengthened according to the circumstances ; in the four 
 voiced movement they occur rarely and not in too great length, e. g. 
 
 . - ' — . ^-: II III 
 
 242. 
 
 Remark. — As completion of what was said of the chorda of the ninth, the following 
 may here still find place : 
 
 In the foregoing Example b, if the stationary voice be included [in the reckoning], 
 * complete chord of the ninth is found in an inverted position with regular resolution. 
 It has already been remarked in objection to the chords of the ninth, that their inver- 
 sions cannot be so used that fundamental and ninth are brought into immediate 
 proximity, as in the case of the sevenths. That they can occur together at greater dis 
 tsuces, as above, furnishes no ground for regarding them as independent chords, sine 
 they occur only in the relations there found, viz., in connection with a stationary tone 
 tLe character of which is, however, also to bear harmonies foreign to it, as, for exainpK 
 m the case with the following uiuth, which certaiulv forms no chrni of the ninth. 
 
 343. 
 
 ■ 1 i i 
 
 g^^gg f^gPPEpE 
 
128 
 
 MANUAL OF HARMONY 
 
 If we wish to mark by numbers the harmonic progression above th« 
 organ-point, they must always have reference to the stationary tone in tta 
 Bass, whereby in many cases the otherwise general marking of the chords 
 is altered. 
 
 Thus the organ-point found under No. 234 b, could be marked thus ■ 
 
 14 gj = g =f 
 
 ÜH 
 
 Such a manner of marking is only used for especial purposes, on ac- 
 count of the difficulty of reading it and also its incompleteness, for which 
 reason, in scores where a figuring is introduced, we often find with the 
 organ-point the words tasto solo, which indicates that, with the otherwise 
 customary organ accompaniment, only the organ-point itself is to be given. 
 
 CHAPTER XIV. 
 
 Passing Notes. Changing Notes. 
 
 Among the tones foreign to the harmony are especially to be reckoned 
 the passing and changing notes. 
 
 The first arise through the filling out, by means of tones lying between, 
 of greater or smaller harmonic voice-steps, e. g. 
 
 215. 
 
 
 fe^Hüfc=U 
 
 -Un-J . 
 
 -I 1-= — , — I — \-*-m-&—. — I 1-^-©--,— I — n-i— — i — i — u h--;h-5— r r 
 
 The notes marked by a cross x form the pass, those marked with 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. 
 
MA N UAL OF IIA R M <> X V 
 o 
 
 216. \ 
 
 12* 
 
 Tie passing notes found under a of Example No. '245 are called dutr 
 tonic, those under b 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 he 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 upoi 
 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. (Nc 
 247 b). 
 
 a. * Ä *_ *~^ ^^ 
 
 247. 
 
 ^^m^^mm^mm 
 
 
 The changing note can therefore appear in skips, it must however be 
 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 
 Dotes 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, has 
 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 
 
 248. 
 
 määmm 
 
 w 
 
 This applies particularly to the changing notes introduced by skips. 
 
 It is otherwise if they appear in a progressing series, whereby they tak* 
 ou 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. 
 
 4- 
 
 21». 
 
 — g— : ■ J—: & \ £ '• 
 
 III 
 
 Those changing notes below, which fall upon the unaccented part, require 
 only partially the minor second. Thus, in the Example No. 250 a, the 
 formation will not necessarily be like b 9 while c is not so good as (I. 
 
 250. 
 
 mmmmmm 
 
 Definite rules on this head cannot be given ; it is also unnecessary, in a 
 .»ach as every musical ear will certainly find that which is right. 
 
 Ü km ark. — The third of the triad bears the changing note as whole step better than 
 Lb fifth and octave. Since -with the latter the changing note can appear at the same 
 time as seventh, so that the succession only can determine in respect to it. 
 
 Changing 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 chord-tone because they are always formed diatonically, and govern 
 themselves according to the key and modulation. 
 
 I I 
 
 251. 
 
 We often meet with figures, in which changing notes above and below 
 the chord note are made use of one after the other, e. g. 
 
 * * * * ** * * 
 
 252. jL~i 
 
 um 
 
MA.' UAL OF HARMi XI. 
 
 131 
 
 Upon this is founded also the following often occurrkg manner of em 
 bellisbment : 
 
 253. 
 
 Passing and changing notes can occur in all voices. If this takes plase, 
 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, 
 
 254. 
 
 päI EgE^ Pf PP^= 
 
 :^=q=q: 
 
 1 
 
 -a 5j- 
 
 I l 1 I 
 
 Si 
 
 -j- — "I ^— p- — y~ — 
 
 light, by the use of the above by-tones, assume the following form : 
 
 255. 
 
 » ■ i [ 
 
 I . I 
 
 J I 
 
 gstel^Sitafepl 
 
132 
 
 MANUAL OF hARMONY. 
 
 * . * * 
 
 — ? £ • * i ' ' ' * — ' ' i ' i 
 
 * $ I J J- ä i 1 J. J 
 
 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 was 
 before remarked iu connection with the suspensions, that no voice receive* 
 the harmonic tone which in another is introduced through a changing 
 note, e. g. 
 
 256. 
 
 -1-4— 1-J-^ l I J J -rr 
 
 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. 
 
 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 sucb 
 figures formed through changing notes, other considerations arise, aa the 
 following passage shows; this to be sure, cannot be conceived of as a four- 
 voiced vocal movement : 
 
 r 
 
 In the case of the regular passing notes, like regard is to bo had to theii 
 approximation to harmonic tones, and figures such as No. 259 it, b, d« 
 not appear so pure as c 9 (l, e. 
 
MAX UAL OF HARMON V. 
 h. c. d. 
 
 153 
 
 259. ifeE5=~ E3E ^^^l Q ~—l—^-—^^-^^ f 
 
 . • I I • I I I • 
 
 More rapid figures allow this approximation more readily, e. g. 
 
 260. 
 
 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 : 
 
 2G1 
 
 • p 3-r=wrf^ r M^ ^=^ 
 
 Open octaves formed with passing tones cannot occur, because the first 
 of them will be harmonic as much as the second. 
 
 262. 
 
 0^sZ 
 
 m 
 
 On the other hand, in the following instances, the passing notes will not 
 «orer the open octaves, and consequently will be considered as faulty ' 
 
 263. 
 
 
 Ebmark. — The last kind of octaves would find application m instrumental movimenu, 
 wider the condition of intended strengthening and reduplicaticu. 
 
134 
 
 MANUAL OF HARMONY. 
 
 In like manner the entrance or progression of the changing note lit 
 parallel movement is to be called faulty if it takes place in the following 
 manner ■ 
 
 better : 
 
 261. 
 
 _4_rfj[_J_ J_#L 
 
 -y- 
 
 — ' — r — °" T^ g — ' 'S 1 ~ & — I — "^ — ~ m ~^~" m~V 
 
 i I 
 
 ^rHEt 
 
 Ö 
 
 It 
 
 The last example is better because the octave progression appears 
 covered. 
 
 Passing and Changing Notes in more than one Voice at the 
 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. 
 
 r—r-, J. _ . 
 
 265. 
 
 ^ffA^^^=f=^= 
 
 * SL 
 
 9£ 
 
 ++*.%*. ~± „ 
 
 m 
 
 =e; 
 
 t 
 
 m 
 
 The free movement of the voices with the use of the passing notes can 
 also produce parallel seconds, fourths, fifths, and sevenths, of all kinds, 
 which require great caution in their treatment, and on account of their 
 disagreeable effect are only to be allowed singly, and in a very favorable 
 position. 
 
 Progressions in fourths are good if a third voice is added as third 
 below : 
 
 266. Jfe— 
 
 
 Single fifth -successions arising from passing notes are occasionally met 
 with in good compositions, which, however, is no reason for recommending 
 
MA N UAL OF HA R M N Y. 
 
 155 
 
 them as faultless. (See that which is said concerning fifth-suucasionj 
 page 27 and what follows). 
 
 Just so the harshness of the seventh-successions can only be alleviated 
 through favorable position and good leading of the voices throughout; 
 indeed, through tempo, movement, etc. 
 
 In contrary movement the various intervals of the passing notes often 
 give to the passage an especial, peculiar coloring, and contribute much to 
 the independence of the voices, but they must not appear too numerously 
 »r.d in too many voices at the same time. 
 
 267. < . | 1 | i . I F-i f\\ "^ 
 
 Here also it will be found, that those passing notes, which, outside of the 
 eimply 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§. 
 
 :=«==r-tffe 
 
 
 ^ 2 
 
 'm^^m^m^m 
 
 In all such places everything depends upon the question, wr ether at the 
 hange of the harmony the voices are in a position which allows thew 
 o form their progression regularly. 
 
 Changing notes can occur in various voices : 
 
 a. In tivo voices : 
 
i36 
 
 MiNUAL OF HA R MO VT. 
 
 in pa ''UA motion 
 I -m- 
 269 
 
 wmmmmm 
 
 in contrary motion . 
 
 870. 
 
 Hüll 
 
 b. lu three voices : 
 
 271 
 
 C* In /ow? - voices ■ 
 
 23Z # # m— tC 
 
 **■ 
 
 I I 
 
 Remark. — The most of the above examples can also have the force r.l 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 vould be likely to 
 pronounce changing notes of the following sort, good : 
 
 good 
 
 «73, 
 
 — '# ftj k*m & "* if*" "J ~ U J J ' ' m ^ 
 
 Jhauging notes can also be of longer duration, than the harmonic not 
 to which they are joined, e. g. 
 
 27 
 
 4. *raf*5tptefey^^^»=ööi 
 
MANUAL OF HARMONY. 131 
 
 The significance, in composition, of the subjects explained in ('hapten 
 XII., XIII. and XIV., is great enough to subject them t«> a careful inves- 
 tigation ; as a thorough knowledge of them contributes materially to th 
 
 understanding of the inner harmonic structure. We have still to speak 
 concerning their relation to the pure harmonic structure — the object of 
 our immediate studies. 
 
 Since on page 24 the term "pure harmonic structure" was only spoken 
 cf in a general way, it becomes necessary to consider the question mora 
 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 embellish-ment, 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 (Künsteleien) 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 ivhich are struck free and the figures formed there- 
 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 it. the use of the harmonies, and for the learning of 
 a good and pure leading of the voices, the elaboration of chorals or simple 
 movements in the manner of chorals is directly suggested as most to the 
 purpose, this also will not exclude the use of those means in so far as they 
 serve not merely for embellishment but for the development of the lead 
 ing of the vones. 
 
188 MAMJAL OF HARM , NT. 
 
 Among these is especially tobe reckoned the use of the suspensions and of 
 the regular passing and changing notes. 
 
 In accordance with the foregoing, the strictnessof 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 ae 
 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 
 
31 A XU A L OF HARMONY. 
 
 lifo 
 
 »75 
 
 I I G J < I I i I 
 
 
 Iiül-l^i|^il|il:^ 
 
 it 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 
 rach harmonies as are assigned to smaller divisions of the measure, as in 
 the following examples : 
 
 276. 
 
 a. b. | 
 
 flp^pPsppli 
 
 2 7b 
 
 m^mmimwi^ 
 
 fUE 
 
 277. 
 
 wmm 
 
 P 9- 
 
 I I 
 
 0' 
 
 
 0-ß 
 
 im 
 
 The peculiar manner of appearance of the chord of the sixth and fourtb 
 in Exanqle No. 276 a and c, as well as of the chord of the seventh in c, 
 k only to be explained through the ensuing progression (in the chai acte 
 
141» 
 
 MANUAL OF HARMONY. 
 
 of the passing notes) of all voices, by degrees^ to their nearest goal— the 
 chord of \he thesis in the following measure. 
 
 These toices can be still more easily recognized in th*"'* 1 character m 
 passing, if one voice is allowed to remain stationary, for example, the 
 Bass of No. 277 a, or the upper voices h. (See above, No. 277). 
 
 The leading of the voices in No. 276 a, has arisen from the application 
 >f 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. 
 
 2T§. 
 
 _£J_A- 
 
 ±=i= 
 
 IppiSP 
 
 ,-^rfH=g= 
 
 ? H§=§üs^^H 
 
 m 
 
 xIemark. — 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 oi 
 less weight. Passing chords will show themselves in the following manner : 
 
 279. 
 
 1 I I P I ' I l ri I -P 
 
 i I 
 
 6 
 
 6 4 
 
 7 5h 9 8 7 
 
 2 4 H5 
 
 SilPii^l^ii^i^liaa 
 
 :p=p: 
 
 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 detiate from them. In the 
 first case, which is mare frequent, no farther remark is necessary ; in the last 
 it will depend upon a flowing melodic leading of the voices, as well in them- 
 
MAN UAL OF HA R M A T Y . Ul 
 
 «elves, as also in relation to each other, whether formations of this kind are 
 .o bo 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 
 ■passi7ig chords, and that all such passages are to be judged after taking 
 into account the rythni, 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 wa 
 are to treat of the best means for effecting a modulation. 
 
 The art of modulation consists in finding out those harmonies whici:. 
 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 jor, seek out the new key as a 
 goal, and take it for a length of time as basis. 
 
 In the first case it will avail itself of the simplest means, make its ap- 
 pearance with decision, but soon leave the new key, and perhaps, indeed 
 not allow it to attain to a definite development of itself; in the second case 
 it is commonly prepared and worked out gradually by various means, and 
 endeavoring to impress the new key upon the ear, will probably also lead tc 
 a close. 
 
 Thus, in the following example : 
 
 -t-i-J J-J U -j 
 
 SSO. 
 
 I ! I ! " I I I f """ 
 
 066 G 
 
 ■#-}£ 6 4 5 62 G 47 
 
 the modulation will be transient and frequently charging, without forsak- 
 ing materially the principal key, C-maicr. 
 
142 MANUAL OF HARMO*!. 
 
 This kind of modulation is only adapted for the nearest related keys 
 and although more distant ones can be reached by especial and decided 
 means, still in their development very natural and organic combinations 
 must prevail, if they are not to appear unintelligible. 
 
 In the next example, however, the more distant key becomes the goal, 
 whirh is gradually reached ; the original key is entirely forsaken, and the 
 Dew one takes its place : 
 
 . ... i bJ-L M k-iij-iuJ 
 
 2S1. 
 
 p^l^päüü 
 
 5b V 
 
 C: I »b: vu° 7 Bb:I f: V 7 Efe: V ? 
 
 This example shows plainly, how the extended modulation, which sett 
 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 Eb 
 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- 
 züge der musikalischen Formen und ihre Analyse." — (Leipsic, G. Wigand.) 
 
 We make use at present of the formation of such modulations as exer- 
 eises, 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 and simplest means will be 
 
 THE TONIC TRIAD OF THE NEW KEY 
 itself. 
 
 If, however, this triad is already a component part of the nrst key, then 
 what succeeds ouly, and particularly the subsequent dominant harmony of 
 the new key, will really determine the intended modulation. Thus, in tha 
 
MANUAL F HA R M O N Y . 
 
 ua 
 
 following example at a, no modulation will be felt, w lie at b we hear the 
 key of G-roajor plainly only when we come to the third harmony : 
 
 
 77 
 
 m 
 
 Jl 
 
 In 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 (b) 
 
 283. 
 
 ^aFr^f=ftf^ ^^pE^^I 
 
 •)•: 
 
 ;eifi^f==fE^=ü?=i^i 
 
 ÖldÖE^Ii^lE|=[E==EEEE= 
 
 91 
 
 ^^^ Hm ^ß ZEm 
 
 C: I a: V 
 
 i C: I k: V 
 
 As ansatisfying as the tonic triad shows itself to be, for modulation, 
 tn the way used above, in as great degree has one of its inversions (the 
 ■chord of the sixth ar.rl fourth) the quality of rendering such modulation 
 particularly decided. For just as it naturally takes part in the closing 
 «aJence (sec pages 19 and 53), so it produces at its entrance the 
 fee'ing cf 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-all} 
 followed by the dominant, which first completes the modulation. 
 
 384. 
 
 eeiiiiipifiitpiiiiSö 
 
 6 
 
 4 8 
 
 I fe^jg^P; 
 
 C- 1 G: I V 
 
144 MAX UAL OF WAR 21 N I. 
 
 r Jj. Dri the arsis it will - aot indicate the key so definitely : 
 
 1§5. 
 
 b^ % 
 
 1 6 
 8 4 
 
 
 All examples given above, however, point to a still more potent mean» 
 of modulation, viz., 
 
 THE DOMINANT HARMONY. 
 
 The triad, as well as the chord of the seventh of the dominant, shows 
 itself as the most natural and best means of digression, since, through it, 
 (which applies especially to the dominant harmony of the seventh) the key 
 is most unmistakably determined : 
 
 The modulation through the chord of the seventh of the dominant can 
 be effected without intermediate chord in the following manner. 
 
 According to the principle that that connection of harmony will b« 
 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 and F£, (it can 
 remain undetermined for the present whether major or minor) thus : 
 
 From C to u: 
 
 !i§6. 
 
 
 Db: or: 
 
 o_I?ö. 
 
 7 * 
 
 Ab: 
 
 ^fe#*Sf^i^^fif=gM 
 
 «^ 
 
 Everywhere in these examples the like tones, which are connected wiifa 
 each other by a tie, mediate the transition to the dominant of the next 
 key; thus, from C major to 1) minor, the tones G and E, which become 
 fifth and sc fiith of the dominant harmony, &c 
 
MANUAL OF HARMONY. 145 
 
 Remark. — It only need he mentioned, that these modulation!» «ut. also be reached 
 through other positions of the chords, e. g. 
 
 C — d: or: ^_^ 
 
 2S r. |p|jppEi||§|f=f[i 
 
 If we wish to modulate in the same manner into the throe keys which 
 arc wanting above, it can be done by means of an inserted chord (in the 
 simplest manner, by a triad), which then supplies the missing ionnec 
 tion e. g. 
 
 "•-om to E^: C — E: C — Ffi 
 
 — If rüp|ifl|^pitipipp[ 
 
 The modulation from the minor can be formed thus : 
 
 From AtoB: a — d: a — e: a — F: 
 
 289. fe^-^^^^^Ö^gl^lET^pi^Eg^j 
 
 iF * * s- = 5 «a 
 
 — G 
 
 
 To the remaining keys C, Di?, Ej?, F$ and A?, by means of a connecting 
 chord : 
 
 From A to C: A — Dtj: a — Bj: 
 
 2f)0. 
 
 a FJ: a Ab: 
 
 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 a< 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 : 
 
14 e MANUAL OF HARMON 7. 
 
 '291. 
 
 ff tt W ■w k 
 
 r cr Mie con 
 
 »ver. 
 
 nection of harmonies and especially of the keys, it will, how' 
 •, 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 
 »11 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 
 ieverth and fundamental of the dominant harmony would be obliged tn 
 enter tree at the same time. 
 
 The following examples present the use of this chord : 
 
 From C to Bfe. C — B: C — d: a — b: 
 
 Beside this application, this chord shows, by means of its enharmonic 
 nature, a farther, peculiar capability. 
 
 Tlit» following chords, entirely like as to sound, but variously written : 
 
 2Ü3. 
 
 ÄÖÖ 
 
 l long to four different keys, viz. : in the first form to F minor, in 
 tui second to D miuor, in the third to B minor, in the fourth to Af 
 minor. 
 
 Through this circumstance a fourfold modulation is possible : 
 
 C to k: C — u: C — b: C — atj: 
 
 Sin^e now all the chords of the diminished seventh can appear in th« 
 follow. xw three positions, as the piano-forte shows most plainly, 
 
MANUAL OF HARMON T. 147 
 
 295. 
 
 ami each of them, thrc ugh 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 to b: E(j — d: 
 
 297. 
 
 C: V 7 b n° 7 i V i Efe: V 7 i>: n" 7 i V i 
 
 Although, in the above, the means were sought out with which to pass 
 quickly from one key into the other, still (since it will not always be the 
 intention to carry out a modulation quickly and decidedly), for the fur- 
 therance of skill the exercises can be extended and given out in th< 
 following manner : 
 
 From, one key into the other by means of the triads of various dccjre** . 
 
 From C to D through the triad of the third degree : 
 
 298. iE = ^F ::z -5^=r « — ft 
 
 From C to D through the triad 
 
148 MAX UAL OF HARM0K1 
 
 Of the fourth degree. : Of the fifth degree : Of the sixth degre* 
 
 2T fl c: 5 ^ ■©- 55 
 
 Of the seventh degree 
 
 -I 
 
 i" — ^? 
 
 From C maj^r to E through the triad 
 
 0/7/<« 8»jo?m2 t/e[7'-ec : Of the fourth degree : Of the fifth degree . 
 
 * p s= ^ * fr 87 
 
 (?/ t/te seventh degree : 
 
 f=#ÄEi#~l 
 
 These indications may suffice for learning to form other modulations 
 according to the same principles. 
 
 Extension of Modulation and its Completion through 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 is 
 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 d minor, a minor, 
 and G major to e minor. 
 
 This problem would be solved something in this manner : 
 
 »01. 
 
 ,0 _ _ !_ . ' I 
 
 C: I d: vii° 7 a:vii° 7 G;V 7 b:V 7 
 
M A X U A i OF II A H M O X ¥ 
 
 US 
 
 In connection with the addition of the cadence, the folbwing is t-> he 
 •bserved : 
 
 If the modulation takes place through the chord of the sixth and fourth 
 of the tonic triad of the new key (see page i43), then the succession ot 
 the dominant chord with its natural progression will be -ufficieut f<>i 
 effec ting the cadence, e. g. 
 
 :J0'2. 
 
 -%: 
 
 " S -fe 
 
 mm^m 
 
 In other cases the extended cadence, or the known closing formulae 
 be requisite (see page 40) in order to determine the final key. As 
 simplest of such closing formulas the following are commonly used : 
 
 will 
 the 
 
 30:$. 
 
 =t 
 
 iimiiiiüii 
 
 In other positions : 
 
 
 I 
 
 IE 
 
 6. 
 
 1- 
 
 SIEVES 
 
 ;il3^3=!l|=ili 
 
 6 
 7 •** ^ 5 
 
 mmmm 
 
 
 m 
 
 In other position» : 
 
 mmmmmmmmmm 
 \mmimmmmmwmwm\ 
 
 If these cadence- formulas be added to the modulation itself, according 
 to the position of the last chord, then it is completed. 
 
 This may be shown in connection with some former examples. 
 
 The modulation from C to Et?, No. 288, closes with the fifth in th« 
 Soprano. To this is added the cadence in the position which answers tc 
 this last chord, e. g. 
 
160 
 
 MA NU AL OF U ARM ON Y. 
 
 301. 
 
 'tE^^^mm^mm 
 
 b 5fe 
 
 ~<* V9 & ?g 
 
 5b 6 4b 7b 
 
 ^M^lE£kmn^äm=^& 
 
 The following modulation from C to a in No. 286, would require i 
 oadence in this position : 
 
 From C to a : Cadenct 
 
 !IlIll|lfili|II|IB 
 
 305. 
 
 6 
 
 mmmmmMmms 
 
 The modulation from C to B with use of the cadence under No. 3^3 b I 
 
 From C to B : Cadence : 
 
 300. 
 
 
 307. 
 
 ^ifeäppiSppSf 
 
 ^^=s^ 
 
 3sfc 
 
 US 
 
 To close, we present an example of a more extended problem : 
 
 From G through e minor, major, nnil u]y minor to A\) major. Cadence 
 
 Jk _- ■ — ^- T -J — l--. — i — k-.—j---,- 
 
 90K. 
 
 
 Those indications will be sufficient to enable us to form for ourseJ»ei 
 manifold problems. 
 
MANUAL OF HARMC NT. 161 
 
 PART III. 
 
 PRACTICAL APPLICATION OF THE HARMONIES. -THE EXER013E8 
 IN THEIR USE IN THE PURE HARMONIC STRUCTURE. 
 
 Through the following bints respecting the manner most to the purposa 
 in the use of the harmonies, the principles until now developed will be, at the 
 same time, still more exactly explained, extended, and made complete. 
 To this end, individual cases will furnish opportunity for farther remarks. 
 
 CHAPTER XVII. 
 
 Tlie Simply Harmonic Accompaniment to a Given Voice. 
 
 It may first be remarked, that here, only simply melodic progression of 
 a voice will be discussed ; all other elements of a melody, as, for exam- 
 ple, its metrical and rythmical development, will be for the present 
 excluded. 
 
 I. Harmonic accompaniment to a Soprano. 
 
 We select the following simple exercise : 
 
 ■^mmmmwmii 
 
 p- 
 
 To facilitate the work, those fundamental tones, which can serre as the 
 harmonic foundation, will be added in the manner used before. 
 
 c 
 
 ffiF 
 
 3,0. ^H^SI^i^g 
 
 With every harmonic progression, the leading of the Bass is the most 
 important point. 
 
 Wo turn our attention therefore first to this, and write its progression 
 perhaps, in the following mauuer : 
 
152 MA N UA L O F H A U MONY 
 
 9T in the follow tag way : 
 
 31 *.&mmmm=\^\i 
 
 The addition of the middle voices will now present no difficulties 
 
 313. 
 
 Soprano. 
 
 C G C 
 
 mmmmmmmimi 
 mmmimimmt 
 
 Let this working out of the exercise serve, for the present, for the expl» 
 nation of the exercises themselves. 
 
 The next exercises will give opportunity for becoming acquainted with 
 the principles of a good leading of the Bass, as well as of melodic voice» 
 in general so far as the simplest harmonic progression requires... 
 
 Examples worked out in a faulty manner can best serve this end. 
 
 Exercise with indication of the fundamentals : 
 
 - .. ^m=immmmm\=m 
 
 Simauk. — In the treatment of this and the following examples we use the viol 
 eirf for the sake of saving room, and write the voices together on two staves ; for Ü 
 pcreoual work of the pupil, however, we recommend, most earnestly, the manner of n 
 tit f i m used in No. 313. 
 
 The working out of this exercise E?ay be as follows : 
 
M A N U A L OF fi A R M N T 
 
 IM 
 
 315. 
 
 a§§=IIi 
 
 
 ■FSS 
 
 ^^^PSSI 
 
 6 
 
 There appears nowhere in this example a transgression of any rule of 
 progression and chord-connection thus far known, and still, on accoui.t oi 
 the stiff, uncertain, and powerless Bass, it is to be rejected entirely. 
 
 Except in the case of the organ-point, a good harmonic leading of the 
 Bass allows it to remain stationary only if its continuity is conditioned 
 by necessary preparation of a tone, or compensated for by a decided pro- 
 gression of the other voices. 
 
 The previous example also contains the chord of the sixth and fourth 
 twice, which may give us opportunity to add what is farther necessary con- 
 cerning the use of this peculiar and difficult chord. 
 
 Of the Use of the Chord of the Sixth and Fourth. 
 
 The rare use of the second inversion of the triad, the chord of th 
 sixth and fourth, has its reason in this, that its appearance depends upon 
 certain conditions. 
 
 First, we find it oftenest in connection with the cadence-formations, as 
 former examples show. 
 
 Then, it appears in a like character in connection with modulation. 
 <See page 143). 
 
 It can probably also enter free in both cases, it must then, however, be 
 regarded not as a passing chord, but always appear upon the *hesis. 
 
 Except in these cases, it appears most naturally as tonic, lebminant, oi 
 sub-dominant triad, under the following conditions : 
 
 a. If the fourth is prepared ; 
 
 I». If the Bass progresses by degrees to the following new chord, or 
 -emains stationary 
 
 The following examples show the application : 
 
 3lt>. 
 
 
 E- IJJ^?| = E=g:j; = S--gg: E — 
 
 mmmwdWMmmmwmm 
 
154 
 
 MANUAL OF HARMONY 
 
 Q 
 e" 7 ^- 
 
 
 =g-i 
 
 ili^ 
 
 o 4. 5 
 
 liülp 
 
 In the Examples at a, it appears most naturally, because it rests upon 
 tonic, dominant and sub-dominant, while upon other degrees (b) it easily 
 produces the feeling of a modulation. 
 
 Used upon the arsis (beside appearing under the above conditions), it crd 
 also appear with preparation of the Bass. 
 
 " . I I J 
 
 317. 
 
 ^s^PP^ 
 
 gj=^: 
 
 i=*mmmmEmi 
 
 The chord of the sixth and fourth shows itself in all these examples, 
 either as passing chord (upon the arsis), or, as above, in the character of th« 
 suspension upon the thesis ; with preparation of the Bass upon the thesis, 
 it appears much weaker. 
 
 i i 
 
 31§. 
 
 litany 
 
 6 4 
 4 3 
 
 Not unfrequently it will appear as itself a suspension, whereby th« 
 preparation of the fourth is perfectly justified. 
 
 319. 
 
 ^=kg:=W.^l = J^i=:|J^=EE 
 
 ^mmm^mm 
 
 4 6 
 
MANUAL OF HA R M 9 iV V. 
 
 155 
 
 In tin second case still more decidedly, because it arises with a rarely 
 occurring chord (that of the third degree). 
 
 That the chord of the sixth and fourth, however, can also enter free in 
 connection with a leading, by degrees, of the voices of smaller measurat 
 divisions, in passing, as : 
 
 6 6_ 
 
 320. 
 
 will require no farther explanation after what was said in Chapter XV., of 
 the passing chords, and after the examples, Nos. 276, 279. 
 
 Remark. — The often necessary preparation of the perfect fourth in the chord of tue 
 sixth and fourth, has led many theorists to reckon it anions the dissonances. 
 
 In the introduction to this system of harmony, in the division of the intervals (page 
 16), it is introduced among tbe consonances; and also (page 20) the reason of this view iß 
 given. 
 
 The doubtful relation of the perfect fourth, and the necessity of its preparation occurs 
 only over against the Bass, or the lowest voice, and, in fact, in the choH of the sixth 
 and fourth only, since in the chord of the sixth, fourth and third, itself, tb>» necessity of 
 preparation is not always found ; between the other voices the perfect fourth is to be 
 treated just as any other consonance. 
 
 "With the real dissonances this is not the case, for these retain their ch»»-a Mv every- 
 where, whether they appear above, below, or in the middle. 
 
 The chord of the sixth and fourth of the diminished triad will soldom 
 be appropriate for use four-voiced, because it appears too iucompleto. 
 
 321. 
 
 fe=i= 
 
 ^Eli 
 
 m 
 
 9F=- 
 
 6 
 
 4 6 
 
 1 ■"*" 
 
 m 
 
 On the other hand, it will occur in three-voiced composition, where it 
 often takes the place of the chord of the second. (See later, the thrse- 
 toiaed movement). 
 
 Besides the condition of a good harmonic progression, viz., that the B* « 
 itself should form a good and intelligible foundation for it, the secoi ' 
 requ'rement is, 
 
 THAT THE PROGRESSION SHOULD ALSO PE MELODIC 
 
156 
 
 MANUAL OF HARMONY. 
 
 Among the uuinelodic progressions have alwajs beei r igt:ly reckoned 
 eertain skips. 
 
 Tbe succession of two fourths and ßfths in the same direction, e. g. 
 
 322. §-~= 
 
 
 mmwm 
 
 These skips are improved thus 
 J23 9^^~-i^P=f: 
 
 m 
 
 
 i 
 
 E\ * skips of a sixth, if the situation and compass of the voices admits 
 of it, are better carried out by skips of a third in a contrary movement : 
 
 lietter : better : 
 
 Augmented interval-steps and skijis are tobe avoided as unmelodic ; 
 diminished are, however, good. 
 
 not : better : not : better : 
 
 325. B: r ^EE3= =LEZEE3= =t==] = J^ 
 
 better: not: better: 
 
 i 
 
 * 
 
 \i 
 
 Deviations from this rule are often found ; they find their explanation in 
 a formation of melody, or in the especial character of the composition as a 
 whole. The observance of the rule in theoretical labors will always be 
 very improving. 
 
 The skip into the major seventh is to be entirely avoided ; that intc 
 the minor seventh can be used, but only in ease of an inversion of tht 
 tame chori. 
 
 not: not: 
 
 The las*-, perhaps, with the following progression of harmony : 
 
 not very good : not: not: 
 
 .__ \fo — r -o — -,-ka — . -. r ba — J25 
 
 32T, 
 
MANUAL OF HARMONY. 
 
 \b\ 
 
 These few observations contain the principal features of a good 
 melodic leading of the voices, and especially for the next (simply harmonic) 
 exercises, prove themselves sufficient. It should still be remarked, that 
 these rules apply, not alone for the leading of the Bass, but in general for 
 all voices. 
 
 The exercise given under No. 314 can, with an improved progression ol 
 the Bass, be worked out something in this manner : 
 
 328. 
 
 aa§ b. 
 
 2 8 7* 
 
 las 
 
 c^ 
 
 
 mmimmm 
 
 Exercises. 
 
 c 
 
 SS 
 
 F 
 
 I ' a I 
 
 mmmm 
 
 7 G 7 
 
 It. 
 
 Ci- 
 
 ft 
 
 ==^l^=i 
 
 CG A D G7 C D7 
 
 iiiiliT^Ililil 
 
 n-y G-. C 
 
 The next example will give occasion for the explanation of an impor 
 tant and difficult part of harmonic connection and leading, of voices. 
 
 Exercise, 
 
 B" c 
 
 - 7 u 7 
 
 329. 
 
 mw^mmmmmwm 
 
 Tbe following faulty work may serve for illustration 
 
 330. 
 
 6 6 6 6 7 
 
 5 
 
158 
 
 MA NUAL OF HA R M N Y. 
 
 The faults of this treatment of the exercise consist, firstly, in th« 
 doubling of the third of the second chord through the Bass, which, with- 
 out occasion, gives to this and the following harmony an awkward position; 
 eecondly, in the indicated covered fifth (from the fourth to the fifth measure), 
 and lastly, in the introduction of the seventh by a skip, in the next to the 
 last measure. 
 
 A 5 concerns the last, this can take place with the dominant seventh 
 anly — the fundamental being already present (prepared). (See page 70). 
 
 881. / 
 
 
 e-_ -\~-& 1- — G -——\— G — -pp 
 
 
 More tolerable and less harsh is the free entrance of the seventh, and of 
 the fundamental in contrary motion ; 
 
 1 
 
 332. 
 
 in parallel motion, however, it is either to be rejected entirely, or only applied 
 in connection with especially favorable progressions, if, perhaps, as in the 
 first example of No. 333, the fundamental (G) is already present in the 
 previous chord, although in another voice. 
 
 333. 
 
 mmmmmmi 
 
 The first of the faults instanced above will be corrected in what follows 
 The second is more important, and will give us occasion to speak in 
 general 
 
 OF COVERED FIFTH AND OCTAVE PROGRESSIONS. 
 
 The nature of these progressions has already been spoken of, page 29. 
 
 Covered fifths and octaves arise, if two voices, starting with different 
 intervals, progress in parallel motion to an octave or fifth, e. g. 
 
 ( 'overed fifth» : 
 
 «■ m^M^m^^^M^m 
 
 Covervt octaves : _ 
 
 p!==MSis=fe 
 
 -*-6>— I— © 
 
 
U A NUAL OF HARM N T. 159 
 
 These fifths and octaves become open, if the skip which one or both 
 eoices make, be filled out by the tones which lie between, as is indicated 
 above by the points. 
 
 Since in every four-voiced movement certain covered fifths and octaves 
 can occur, without which the choice of chords, as well as the ending 
 of the voices, would be very much limited, and also, since others are to 
 be avoided, it becomes necessary to take a somewhat nearer view of 
 the manner of their appearance. An attempt to give positive rules for 
 their use, which would be sufficient for all cases, has not yet been success- 
 ful, and would probably with great difficulty succeed ; there are, therefore, 
 onlv general observations to be made, which, however, will furnish a stan- 
 dard of criticism for especial cases. 
 
 Covered fifths and octaves between two voices can occur : 
 
 1. //' one voice moves by a step and the other skips ,' 
 
 2. If both voices skip. 
 In the first case : 
 
 SI. By a step in the upper, and a skip in the lower voi.ee; 
 
 h. By a skip in the upper, and a step in the lower voice. 
 
 In regard to both cases as concerns the kind of voices : 
 
 a. Between the outer voices, 
 
 h. Between the middle voices, and 
 
 C. Between ar. outer and a middle voice. 
 
 Covered Fifths and Octaves in the Outer Voices.. 
 
 They are to be allowed, if the upper voice progresses by a step. 
 
 a. Fifths: b. c. Octanes: d. e. 
 
 
 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 a 9 b, C. It i 
 not so well, if all voices go in parallel motion (d). 
 
 Remark. — Although the above rule will suffice iu so many cases, still it cannot al .vaya 
 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 fr m tLe 
 ehord of the sixth, c, is a very forced one. 
 
 We must remember also, what has been said before concerning the cadeucing pi\^ 
 gression of the Bass, pages 35 and 36, viz., that covered octavea which pass over the 
 leading tone, or in general, over the half-step, are always more tolerable than the«« 
 which pass over ♦'•» whol« ateD. 
 
160 
 
 MANUAL OF HARMONY. 
 
 In the exercises exhibited above, the octave always shows itself *» 
 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. 
 
 :J3«. 
 
 I*||=l 
 
 -ar—jsr 
 
 Even as fifth of the chord it is not to be called good. 
 
 J---G- 
 
 * -* 
 
 Remark. — With the covered fifth, the lower voice will always be the fundamenwil o 
 the chord. 
 
 Covered fifths in the outer voices are to be rejected if the upper vcice 
 tkips. 
 
 338. 
 
 ^l^^^lg[ 
 
 illiiiiiisiiitr 
 
 m 
 
 Wherever a seventh makes the connection of the harmony firmer, as 
 at b, (I, e f 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. 
 
 i^feSP^fefefeSillt 
 
 ~° - "V 
 
 -»v.. #. 
 
 gg^gi^iH 
 
 Here also those case» in which the Bass progresses a half-step (a) show 
 themselves to be most tolerable. What was said in connection with Nos 
 330 and 337 applies for (I and e. 
 
 Covered fifths and octaves in the outer voices are tc be rejected if bot* 
 voices skip. 
 
MANU A L OF IIA RMON V 
 
 101 
 
 II» 
 
 
 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« 
 *nd octaves at all. 
 
 341. 
 
 mm^^mm 
 
 w^^m^mmm 
 
 Covered Fifths out! Octaves in the Middle Voices. 
 
 Although the leading of the middle voices must be just as pure a« 
 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 ouly 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 : 
 
 
 II: 
 
 § : ; 
 
 
 Covered Fifths and Octaves between the Outer and Middle 
 Voices. 
 
 The considerations which are to be taken into account in connection witfe 
 these progressions of the voices, are to be Bought in a good and natural 
 
l62 
 
 MANUAL OF HARMONY. 
 
 connection of harmony, rather than established through mere'j meehani 
 sal rules. Here are some examples : 
 
 8 1 J. 
 
 mm^m 
 
 Pe? 
 
 i 
 
 *2^?_Jzs» 
 
 ?=f=Z 
 
 S=p* 
 
 m^mm 
 
 not good: not: 
 
 sninetiM 
 
 ^mmm^ mf^ f^^ 
 
 An especial kind of covered octaves is still to be mentioned, viz., such 
 as pass over the seventh ; these, in all voices, are to be avoided as faulty. 
 
 344. 
 
 »^SIiIil^iSIi*Ll 
 
 -b> s S±iHA="^:rSh: 
 
 g^m^g^ ^i 
 
 (See page 84.) 
 
 That which was remarked of the octaves, applies also to covered unisons. 
 Between Soprano, Alto and Tenor, the latter are to be avoided entirely, 
 between Tenor and Bass, however, they are to be regarded as covered 
 octaves— according to the postion of the chord and of the voices themselves. 
 
 The cases, in which covered fifths and octaves can appear, are so man- 
 ifold, that it would be superfluous, if it were, in fact, possible, to adduce 
 them all. The above observations may suffice, if we add the following 
 maxim, which, to be sure, is not written for those beginners who still 
 have to do with the technical, or the properly mcchanicallj-harmoni« 
 structure, without regarding the higher requirements of art : 
 
 Avoid, indeed, covered fifths and octaves as much as j)ossible ; consider 
 them, however, as safe if on the one hand, an otherwise natural, (,<ood con- 
 nectirri of harmony takes place, or on the other, considerations of a h'xjJier 
 sort prevail ; such as melodic voice-movement, application of definite 
 motivts. etc. 
 
MANUAL OF HARMONY. 
 
 16b 
 
 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 moveuiert, 
 the evil presents itself again in another place, e. g. 
 
 345. / 
 
 
 Thus it only remains to alter, in this case, the harmony itself, and select 
 aaother marking of the fundamental tones. 
 The following alteration can take place : 
 
 346 
 
 347. 
 
 1. 
 
 347 b. — Pri?:=5: 
 
 Exercises. 
 
 .a. 
 
 ^=bd=£ 
 
 i 
 
 F Bb 
 
 •<>F d e-» C r F 
 
 Ü5 
 
 O F 9» F 
 
IM 
 
 MAKLaL OF HARMOSY. 
 
 fä 
 
 
 F C d C 
 
 The following exercise : 
 
 D-* G G 
 
 l^f^-ill 
 
 we will work out in this manner : 
 
 1. 2. 
 
 241). 
 
 "*" ^2 _ ~%^~ 
 
 ■» -CT 
 
 7 
 
 IPEf 
 
 ^mmmmmf: 
 
 The faults of this work are indicated by figures. 
 
 The movement of all the upper three voices, by skips in parallel motijn, 
 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), the 
 harmonic connection is preserved. 
 
 No. 2 also contains the same fault, which here becomes still harsher 
 because seventh and fundamental enter free and come thereby into an 
 awkward position, so that one is crowded by the other. 
 
 It has already been mentioned (pages 72 and 158), that the free entrance 
 of the seventh can take only place without harshness, if the fundamental 
 is already present, and can remain stationary in the same voice. 
 
 Thus, none of the following examples exhibit a superior leading of tha 
 voices. 
 
 ^-^^ 
 
 850. 
 
 
MANUAL OF HARMONY 
 
 lt>3 
 
 Probably few of these and similar instances would be excisable for 
 »ore important melodic reasons. 
 
 The following examples may still serve as completion of the free intro- 
 duction of the fundamental and the seventh in contrary motion, mentioned 
 Oil page 158. 
 
 iiiöiiiis^^iiis 
 
 J5I 
 
 The instance No. 2, of Example No. 349, contains besides this, another 
 fault, contrary to the rule laid down above (page 153), in connection with 
 the chord of the sixth and fourth, viz., that th<> Bass should not skip from 
 the chord of the sixth and fourt 1 :. 
 
 The third fault of Example No. 349 consists in the covered fifth, which 
 is thu more prominent in connection with the skip of the Soprano in the 
 same direction, as well as in the general scattered leading of the voices. 
 
 The covered fifth in No. 4 is to be condemned, on the ground that it was 
 not necessary ; that at No. 5 is better ; it can take place in connection 
 with the leading of the Alto, as well as of the Bass in contrary motion. 
 
 The following will be a better working out of Exercise No. 348. 
 
 352. 
 
 
 _e^Ii^fi^lliEl^l=^=i 
 
 „ a— a^a ^ a z: s. ^ 
 
 gf^Hl 
 
 ^Ls==s==a= 
 
 PPPff 
 
 2 6 
 
 Exercises. 
 
 «■ »• wmmmmmmmmwm 
 
 w 
 
 2— ,.-0- 
 
 D~ Q D*, P 
 
 C D a D 7 O 
 
 G D G D 
 
 l^^^fiül 
 
166 
 
 MANUAL OF HARMON 7. 
 
 -<2 C -&— 
 
 tl» G-D-b 7 aDCOD 7 G 
 
 The next exercise, 
 
 rt° 7 B 7 ■ 
 
 353. fijjbfp: 
 
 ^^^^^^1 
 
 with the following treatment : 
 
 354. 
 
 i§i?^=f=HMi= 
 
 gives us opportunity to speak of a fault which bears the name, 
 UNHARMONIC CROSS-RELATION. 
 
 The unharmonic cross-relation (relatio non harmonica) belongs to the 
 unmelodic progressions, and consists in general in this ; that upon one tont 
 immediately follows the same tone in another voice, chromatically raised 
 or depressed, as here upon the G of the Alto the GJJ of the Bass. 
 
 In order to avoid this fault, note the following rule : 
 
 Immediate chromatic alterations of a tone, are to be applied in that voice, 
 alone in which the tone unaltered immediately before occurs. 
 
 Notwithstanding this rule answers, in so great degree, to all theoretical 
 principles of harmonic connection and progression, there is hardly any 
 one, to which so many exceptions in the practice can be shown. 
 
 For this reason, in the books of instruction of later methods, great sus- 
 picion has been cast upon the doctrine of the cross- relation, and instances 
 brought forward in which the unharmonic cross relations 0<5cur in a per- 
 fectly natural manner, without examining the reason why they do not sound 
 faulty. 
 
 Some of them will be here adduced : 
 
 S55 
 
MANUAL OF HARMONY. 
 
 167 
 
 'A^LMAj 
 
 ■ — «■ T-Q? r — » — rj — t — = r — fr —\ IT »~t » — r — 
 
 ■P-r-^- V ■ * - 
 
 iüHl 
 
 
 ^eP^Be^P^J^N 
 
 In all these cases the cross relation appears, not formed through the 
 simply-harmonic leading forward of the voices, but either 
 
 In the character of changing notes at a, b 9 fj, or through contraction 
 (drawing together) of natural, but for the metrical construction, too cir- 
 cumstantial harmonic connections, at c f d 9 C f 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 smaller 
 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. 
 
 ■» *. 
 
 
 z|=t= 
 
 m\m=mm 
 
 r r»r 
 
 <Hsii=eiiiii; 
 
 Let these examples be compared with those under No. 355, at C, d f 
 
 e, h. 
 
£58 
 
 MA XU AL OF H A RMO X F. 
 
 Al. these conditions, through which cross-relations are most endurabl« 
 are wanting in the following and similar cases, which are therefore faulty 
 
 457. 
 
 litgüiöilifill^ll 
 
 \ 
 
 liHII^l^l^^i^lilt; 
 
 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 
 distance 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 
 is derived : 
 
 35§. 
 
 mmmwm 
 
 It is held to be unmelodic and unvocal because each of its tones requires 
 sin especial progression, which tones properly appear assigned to two dif- 
 ferent voices : 
 
 3S ». pp^m^ 
 
 of which the one must remain disregarded in its progression, if the atajr 
 ip transferred to one voice : 
 
 untas* the melodic secession be formed thus: 
 
 Z9ZHZ— t — J U: 
 
 ««1. 
 
MANUAL OF HARM Ob Y. HjJ 
 
 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, 
 
 362. 
 
 ^ä=^g=B 
 
 Hud is just as intelligible and easy of performance, as the tritonus ay pears 
 difficult and refractory. 
 
 Remark. — It nun still be remarked, in this connection, that the tritonus depends upon 
 the diminished triad and its progression, as becomes plain from Example No. :J62 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 & 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) f e. g. 
 
 363. a. b. 
 
 5*a i~±^dE^_ — a L«l-t: 
 
 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 i 
 forced progression is easily produced. 
 
 Formerly the prohibition of the tritonus was extended to the two major 
 thirds, which follow each other at the distance of a whole step, e. g., 
 
 not however : 
 361. 
 
 and it is not to be den.cd, that this progression produces, two-voiced, ti.t 
 
i;j 
 
 MANUAL OF HARMONY 
 
 ume \inpleasant effect, whereas the same three and four-\C!ced, especially 
 if it does not appear in the outer voices, is rendered much milder. 
 
 365. 
 
 £):— ~¥ L — CL - — P — e — 
 
 \\ 
 
 That formerly the step from the fourth to the seventh degree of th« 
 minor scale, e. g., D to Gr£, was not reckoned as tritonus, is founded upon 
 the former usual representation of the minor scale itself, and its harmo- 
 nies. The effect of this step, since it is augmented, remains the same. 
 
 We return again to our Exercise No. 353, and attempt a better treat* 
 ment. 
 
 366. 
 
 « L 
 
 t^jllpl 
 
 immrmmmMMii 
 
 Exercises. 
 
 ~*aE 
 
 I 
 
 33= 
 
 ft: 
 
 i==p=ig==l 
 
 11=11 
 
 n 
 
 wMmmmmmmmi 
 
 
 Df> 
 
 H 
 
 
 lilfrll 
 
 i 
 
 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 th6 
 fundamentals. 
 
Alto C 
 
 MANUAL OF HARMONY. 
 
 Exercise. 
 G o F o a 
 
 17) 
 
 Dn G C 
 
 567 
 
 mmmimmmmtmmti 
 
 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§. 
 
 mmmiwMTä^wm^ü 
 
 G C 
 
 ■or 
 d 7 G C 
 
 pfeEJE=|EiEEJ~JEEE 
 
 i;EiEa= 
 
 t- 
 
 6 
 
 The foregoing can answer as a three-voiced movement; through the addi 
 tion of the Tenor it will assume this form : 
 
 r^llipilgieiliimÜpl 
 
 8ti0. 
 
 ■» ■» ■» 
 
 mmmmmmmMm\ 
 
 Exercises with given Alto. 
 
 »«»»• ü^llllfl1IiilE?!!IlE§ltliF!! 
 
 B 6 C, d e 7 C F 
 
 F Bb 
 
 B, C F g C 7 F 
 
 FC FC 
 
 wm^mmmm 
 
 G-l &—A-0-- 
 
 1 
 
 e C F 
 
 3 7 A 7 
 
 til MP = 
 
 e C-r A^ d ■ £ A 7 b 
 
 HIHI 
 
 Of £ D 
 
i72 MANUAL OF HARMONY 
 
 A Tenor voice would be treated in like manner. 
 Exercise. 
 
 Tenor. C 
 
 370. ^~g^|-_±z:|^— 
 Sketch of the Bass and Soprano : 
 
 n 
 
 371. 
 
 Pour-voised 
 
 372. 
 
 
 -2. *. 
 
 iü§üi PP^i= |^fe[^ 
 
 §a=^Pi 
 
 «~T= 
 
 Exercises with given Tenor 
 
 -Q— 
 
 372 5. gg|g=^^|^^g^g=gj: 
 
 3=3^ 
 
 f=a=T^ 
 
 l=fe^f^^l 
 
 C G 
 
 A Ef A A D GJ^ A — B° E 7 A 
 
 These exercises are to be continued, until the sketching of the Bass, m 
 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 voices hi 
 
MANUAL OF HARMONY. 
 
 173 
 
 «specially necessary ; the boundaries of the voices themselves-, must not 
 be overstepped, the distance from one voice to the other must not be toe 
 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 it 
 greater than one octave. The relation of the Bass to the Tenor, however, 
 admits of exceptions. 
 
 Remark. — To set the present exercises in the Bass, will not be to the purpose sine« 
 they would appear exactly in the former manner, as figured Basses. They can paly 
 be set for fret 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, 
 
 373. 
 
 The Bass can be sketched in this manner : 
 
 JTI 
 
 
 ifl 
 
 p&St 
 
 I^HiliflK 
 
 In the second and fourth measures, sevenths of secondary chords of th« 
 seventh .show themselves without preparation, 
 
174 
 
 MANUAL GF HARMONY 
 
 Tn.s kind are called passing sevenths. They start from the fun lam en ta. 
 of th; chord, and always appear upon the arsis. In such a manner thev 
 can occur in all voices. 
 
 The addition of the middle voices to the above sketch of a Bass, give« 
 the following four-voiced movement . 
 
 375. 
 
 The same exercise with a richer change of harmony can be given in this 
 manner : 
 
 C Fijo-y Ge$o 7 AC 7 b »D G— 7 C 
 
 376. 
 
 3{E5E 
 
 m 
 
 377. 
 
 p 
 
 ^E^=E: 
 
 - r» fe" 
 
 I I f I 
 
 
 
 pflZ-l^ -A^ 
 
 
 ü^if^H^Hi^^i^ 
 
 7b 
 
 4 6 - 8 7 
 
 3b 7 
 
 The next exercise will exhibit the use of the suspensions. 
 
 F Bb c d 
 
 37§. 
 
 Mi * PT 
 
 i-^^i: 
 
 a=ir^=z 
 
 i 
 
 179. 
 
 3* 
 
 , I- -I 
 
 ^-r 
 
 
 "o — 
 I 
 
 FTT^ h»-^^ I * >¥ 
 
 9 8 
 
MANUAL OF HARMONY. 
 
 m 
 
 We pass over the exercises in the middle voices. 
 
 The using of the simply melodic progression in whole notes, as exercise», 
 (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. 
 
 d* b" 7 E £ 
 
 U80. 
 
 ä^g^güi 
 
 öS 
 
 :t=t=p=fz 
 
 O GC Fb° CF CC a Cyjj d — 
 
 mmwmT^w^^mm 
 
 DGC G~ C Df G Ea 
 
 ^äffi^ragöTTjj CTa 
 
 The treatment of this choral can, according to the above exercise, b. 
 *he fallowing : 
 
 3S*. 
 
 mm^mwmmmwm 
 
 m 
 
 s>— ' 
 
 S I 
 
 isfc 
 
 
 =g: 
 
 TT/9 . fZi 
 
 ±e — P- 
 1= 
 
 
176 
 
 MANUAL OF HARM NT. 
 
 rq=3; 
 
 ^--s-T-jzziA 
 
 W^r-r*-»— R -? — l - P 
 
 iri^iiiiiiiftE^ii^ 
 
 
 c y- 
 
 •st=ä==i: 
 
 ■<*■ - •■ \n 
 
 ^ppppp^kä 
 
 
 
 i i f r t ? 
 
 fc 
 
 i j 
 
 §?=üp 
 
 I= i=§ÜHilü^l 
 
 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 treat 
 of it in order to learn, by the elaboration and fashioning of melodies, to 
 know and use what in them is essentially harmonic. 
 
 All will here depend upor the recognition and comprehension of ih« 
 following principles : 
 
MANUAL OF HARMONY. 
 
 IT. 
 
 melody, however extended and developed it may be, has a founda 
 tionjust 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 loam to distinguish the 
 essential notes from the subordinate and accessory work. 
 
 We select to this end the analytic method, and endeavor to develop the 
 following melody, which we will write down in the simplest manner 
 according to the above mode with indication of the fundamental tones. 
 
 SS2. 
 
 <^^m^m 
 
 Ü 
 
 Both melody and harmony are, as selected, simple, and the latter may 
 be carried out, four-voiced, in the following manner : 
 
 J§3. 
 
 
 l=£zaE 
 
 Ä 4» 
 
 mm=m 
 
 
 %^m 
 
 (mmmmmt 
 
 Before we proceed to a farther development of this movement, it becomes 
 necesary to premise what is to be mentioned concerning the rythmical for- 
 mation of a melody. 
 
 A melody can be either a musical movement without definite boundary 
 containing more or less measure«, as it is often found as theme (motive of a 
 Composition), or it can be a whole, separated and bounded by means oi 
 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}. 
 
178 
 
 MANUAL OF HARM OS Y 
 
 The more complete treatment of this subject belongs to the doctrine o* 
 Form.* 
 
 That the above movement will form a period, is seen in the clo*« 
 of 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-oadences, show themselves as plagal in 
 the middle of the movement. 
 
 Such a half-cadence (in general, a close in the dominant) is found in our 
 exercise in the sixth and seventh measures, and the separating point of 
 the divisions of the periods may be assumed to be at the place where the 
 sign 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 
 contain four measures. This may take place in the following manner : 
 
 384. ^m---*^y=$ 
 
 it— r 
 
 :~5— (52- 
 
 — ztr 
 
 mmMmm 
 
 If we add the harmonic accompaniment selected above, we obtain a com 
 plete musical period. 
 
 It needs, also, onlv a glance, to enable us to see that all farthei 
 
 *" 9 q o c 
 
 transformations into various kinds of measure, e. g., into ^. £, S 0r S 
 
 measure, admit of easy accomplishment, e. g. 
 
 llplllpirj 
 
 ÜHHII3PS 
 
 v — *—. — p 
 
 ;: } , 
 
 
 We proceed now to the tonic variations of the melody, and add to it 
 passing and changing notes, e. g. 
 
 S8 «. ^g^ü^^üjü^iüili 
 
 * See the work of this author—" Die Qrundzüae der musik »tischen Formen."— (Leipai* 
 G. V-gand.) 
 
jf,A't/.r OF Ha hJtQJTY. 
 
 179 
 
 t m^m^^m 
 
 Still richo.* ».ee of all by-toret. couM give the following turn.ation : 
 Adagio. 
 
 asr. i 
 
 ll^ji&^lp^il^Eypz^^l 
 
 OrigiiitiUy: 
 
 :£rfe=iE 
 
 <H— 
 
 n — r- 
 
 ^^tfl^ ^B^^ m 
 
 ;^= 
 
 ^ISS 
 
 i 
 
 
 ;e; 
 
 
 f — =^5= 
 
 The simple melodic progression found below, will be easily recognized as 
 the fundamental voice. That, however, the above melody is carried out 
 with reference to the original harmony, will immediately become evident, 
 if we add the other voices with the few deviations conditioned by the upper 
 voice : 
 
 3S§. 
 
 =^*a 
 
 I— I > 
 
 i ♦' ff * i F^ - 
 
 1 J I I — I 
 
 iESEil 
 
 
180 
 
 MANUAL OF HARMONY. 
 
 L a 
 
 i^^fi^PElEÜH 
 
 3 
 
 B 
 
 PIUEi: 
 
 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 
 oase, 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 melodio 
 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. 
 
 3S9. { 
 
 n 
 
 ^fcg: E |ii=|=g=|E| 
 
 g— 
 
 F#3^j 
 
 m^ 
 
 mmmm 
 
 •-V 
 
 
 W= 
 
 mi 
 
 mmm^mmmii: 
 
 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 followir^ 
 division : 
 
 3f»4> 
 
 r r t C i i ii ^ fcsT i 
 
 i 
 
M A X UAL OF IIA K M N i 
 
 l«i 
 
 The development of the upper voice may take place in the following 
 iLanner reference being had to the harmonic progression : 
 
 3!>l. 
 
 &g§^5fes#ai|±ts 
 
 What part the othei \oices can take in melodic development, the follow- 
 ing movement from the Eb major nuartette of Beethoven will show: 
 
 302. 
 
 VIOLIN O I. / 
 
 ?IOL0N0RLLO. \ 
 
 j ^^—gEg ^ s^ ^a 
 
 
 Z L ' '"% i ■?■ ♦ * $ 
 
 foS^ 
 
 ^''?' fc&r ^ 
 
 
 ra=l 
 
 igg^ 
 
 yp:^Iig|p^^ 
 
 ^ 
 
 fe -< 
 
 
 ii^ll^1iiipifl3ill^= 
 
 \ä 
 
 Ö 
 
 S^^^^i^ 
 
 A comparison with No. 390 will show the melodic and harmonic 
 variations. 
 
 There now follows still another alteration of the original melody, out o< 
 Ibe same comx^osition : 
 
182 
 
 MANUAL OF H A R M X 7 . 
 
 393. 
 
 semens 
 
 äfe^=st 
 
 ifcy-r-jgrtg 
 
 "===3 
 
 The other voices show themselves in th« 1 following alteration : 
 
 
 
 3^ 
 t. 
 
 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 war shown above (even if Beethoven, in the later alterations of these original 
 melodies, could not, sometimes, proceed otherwise), in even so great a degree was it here 
 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, vt hio) 
 wiD he done in the next chapter 
 
MANUAL OF HARM ON Y 163 
 
 CHAP1ER XX. 
 
 On Development of the Accompanying Voices. 
 
 The lust examples of the foregoing chapter have already shown in what 
 Banner the accompanying voices take part in harmonic, metrical and 
 melodic development. 
 
 There are, however, still other kinds of accompaniment, which ure known 
 inder the name of 
 
 THE FIGÜRATED 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. 
 
 Simple harmony: Figurated accompaniment: 
 
 a. 
 
 w — £ — ^nrpTT -~^'ip~^^^r 
 
 b. e. 
 
 ?te ~^0-0-0~ir& — t—* 0~0 z s^-'. -»-', f- : i- — '^^'^^'-•^T^i 11 '—-*- * #— -I 
 L - L - ^ hr< > " ^ ^^ ^ -^ 
 
 i 
 
 ^TrfTir 
 
 The accompaniment at a is harmonically figurated. The figures arising 
 therefrom are called also broken chords. That at b is metrically figurated, 
 and that at c is melodically figurated. The figures which have arisen 
 from the last are formed from changing and passing notes. 
 
 Any accompanying voice can be used for such figuration, either alone or 
 n connection with other voices. 
 
 We select the beginning of Example No. 382, in order to attempt som« 
 kinds of accompaniment. 
 
 This may be preceded by the following remarks : 
 
 If the figures repeat themselves uniformly (e. g. in broken chords), then 
 
L84 
 
 MA N UAL OF HARMO N T. 
 
 all the rules of the harmonic leading of the voices are to he observed at 
 the chaxge of the chords, as well as in the reduplication. 
 We must not, write : 
 
 **Q6. 
 
 : H 
 
 * — Ö 
 
 
 but somewhat in this manner 
 
 1 
 397. 
 
 .# ,_«- 
 
 
 1 
 
 At the change of the harmony, the Zastf rcofo 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 : 
 
 i|-p!lliip=^!liP3ppi 
 
 *- « " > " ^ 3 
 
 «98. 
 
 E 
 
 ISr^*rtr 
 
 §i 
 
 ^ ^ g - _ . 
 
 The harmonic figuration also affords the means for forming one-voiced 
 movements in greater perfection. The examples will begin with this : 
 
 
MA N U A L O f if A J; M <> \ Y 
 
 186 
 
 That these movements are calculated for au instrument, probablj sucb 
 
 *s a violin or clarionet, is easy to be seen. 
 IOO. Two voiced: 
 
 
 ÖÜöte?lE 
 
 Three voiced : 
 
 in the middle voice.- 
 
 in the lower voice : 
 
 
 
 
 $3 
 
 in the upper voice: 
 
 _, _ # _n 00-00 
 
 -_ 1 ^- r _»-, , T -— w-m-w-w - 
 
 Ü 
 
 
 iöii^fe^aQ 
 
 in two voices: 
 
 ilUliil^^ilEi: 
 
 
 gil3=^'^M^^=[^==^=:^g 
 
 The figuration in the four-voiced movement, after the?e attempts wit! 
 the above example, will be equally easy of accomplishmer t. 
 
186 
 
 manual of harmony 
 
 Instead of this we prefer to select, as an example of manifold figuration, 
 the following passage from the above quoted quartette movement oi 
 Beethoven. 
 
 401. 
 
 ^-s£ . . . T 
 
 :z^z^zfzLz#ztz#zzz*_zz#— j=^!LL,-"t 7 * * gg-f-r-j 
 
 
 ^^^P 
 
 
 iÖ=L^=£z3z3=^IIzSzI^ztE?-=l 
 
 ±* 
 
 e§=p 
 
 
 SEg 
 
 -p^zzpzzz^z=*zzzz^^L-gzzT= ^^z^ -^— ^zzzz.-pjng: 
 
 hn * 1 ' ! 1 i 
 
 
 I^^^B^^^^ 
 
 s=it^^|^i^ii^^S=S 
 
 aj^^ ^ag ^ s Qzf^ c^EB^ 
 
MA NUAL OF IIA RM NY 
 
 mm 
 
 187 
 
 r* ; '-;-i^;-=E?~"=^iE[ 
 
 ^^^ä§üiiiitefei?^[ 
 
 
 '^Bö^ 
 
 ög=^ 
 
 Tins whole rich development rests upon the foundation given in Noa. 
 890, 301 and 392, and whenever the harmonic change enters, the leading oi 
 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 
 vury 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 formation« 
 of our own. 
 
 CHAPTER XXI. 
 
 The Exercises in the Three-voiced Mo orient. 
 
 With few exceptions, the four-voiced form of writing has been uied for 
 our exorcises 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 13 asses. 
 
 8 7 
 
 6 6 
 5 4 
 
 ß 4 
 
 6 t 
 
 «"• ^MsM^^^^^MWti^M 
 
 ¥ 
 
188 
 
 MANUAL OF HARMONY. 
 
 2S=5 
 
 n-l— t 
 
 i= 
 
 The tLree-voiced movement is sufficient, indeed, for the triad, but the 
 leading of the voices will often result in the omission of one of its inter- 
 vals ; in the case of the chords of the seventh one interval must naturally 
 always be wanting ; this, however, can never be the seventh itself. As a 
 rule, the fifth can be omitted, as has already occurred in the four-voiced move- 
 ment, and the fundamental also in many cases ; the third, as the interval 
 which determines the mode, can only be omitted in a few cases, without 
 producing an especial emptiness. 
 
 The treatment of the exercise is the following, to which a few remarks 
 will be added : 
 
 4 NB 5 KB 6 
 
 $3 
 
 B=* 
 
 £ 
 
 4os - i wm^ mmmw^ mm^^ i m 
 
 -pJE f— f-}r?5 f pl 
 
 7 6 5 4 ß 4 5 
 
 6 a 
 
 1p 
 
 im 
 
 8 NB. 
 
 10 
 
 m*mmmwmm$: 
 
 -O e> 
 
 m^ m* ^^m ^mm 
 
 4 
 G 3 
 
 i^!i|^imiHL!iBE==: 
 
 In the fourth measure is found, at NB., the chord of the sixth and fourth 
 of the diminished triad, E-G-B|?. It stands instead of the chord of the 
 second, Bb-C-E-G, of which the fundamental C is here omitted. For four 
 voices, this place would stand thus: 
 
MANUAL OF HARMONY. 
 
 180 
 
 401. 
 
 Concerning this chord, compare what is mentioned page 155. 
 
 In the fifth measure a fourth represents the chord. Now, although • 
 fourth can neither in the three-voiced nor in the two-voiced movement 
 have the worth of a complete chord, as can the third and sixth, yet, 
 in cases where the chord of the sixth and fourth as passing chord can 
 be used upon the arsis in the four-voiced movement, probably the sixth 
 or third of the fundamental chord can (for the sake of a better lead 
 ing of the voices) be omitted in the three-voiced, so that the fourth alone 
 remains, marking, here, fundamental and fifth of the original chord. 
 
 In the two-voiced movement, the fourth will occasionally take the 
 place of the chord of the second, especially in the case of the passing 
 seventh, e. a. 
 
 405. 
 
 
 it 
 
 Four-voiced, the above place in Example No. 403 would, complete, stand 
 thus: 
 
 406. 
 
 $3lj^E*|§Il 
 
 6b 6 
 #45 
 
 H3=aIp§Ei 
 
 In the eighth measure of Example No. 403, the chord of the sixth, 
 fourth and third is, by the skip of the Alto, formed complete. 
 
 The teeth 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 : 
 
190 
 
 407. 
 
 MANUAL OF HARMONV 
 -4- 
 
 ü 
 
 IPÜI^HPIE 
 
 The closing measure of Example No. 403 3hows, through ih* <»ct*?w t, 
 that the triad can appear, in such cases, even without third and nftü. 
 
 That the omission of the third is often conditioned by the leading 
 of the voices, is shown by the first and second measuren of the next 
 example. 
 
 40§. 
 
 %^ = m^m *m 
 
 SKI-* EEEE: 
 
 mm 
 
 -P-&- 
 
 H f IlIill=!ililHiI===il 
 
 £ 7 6 
 
 5 — 
 4 3 
 
 7 6 
 
 4 - % 
 
 mÄ*i 
 
 
 §11 
 
 The omission of the third takes place best upon the arsis, as here in the 
 last measural division ; upon the thesis, (accordingly at the beginning of 
 the measure), the third should not be wanting. 
 
 Farther exercises are to be left to the especial guidance [of the teacher] 
 
 Exercises in the Three-voiced Movement to a given Upper 
 Voice. 
 
 The following exercise, with indication of the fundamental tones [» U 
 ^e worked out three-voiced : 
 
MANUAL OF HARMONY 
 
 19 
 
 ■"•p^HH 
 
 mmmmm 
 
 & 
 
 110. 
 
 
 i^^f=p^=iiii§giiiE 
 
 fiiiiiiiü^ü^: 
 
 s 
 
 fundume/ital. 
 
 This treatment needs no explanation. 
 
 The choice of the middle and lower voices will depend upon the position 
 of the chords in general. Thus, in a low position, the Tenor as middle 
 voice, will he more suitable than the Alto, just so the Tenor can be selected 
 as lower voice instead of the Bass. 
 
 For the following example the Tenor is selected as middle voice, since 
 its movement attaches itself more to the Bass, while on the other band 
 the simple song of the Soprano appears, of itself, isolated. 
 
 The previous Exercise in more extended harmonic treatment : 
 
 411. 
 
 113 
 
 ig=: 
 
 ffiF— = 
 
 £ A 
 
 G C 
 
 D Gjf° 7 
 
 A F. 
 
 
 _*. 5 6 G -rv •£■ 7 66-57 
 
 In the fifth measure at NB. appears the real ninth-suspension (through 
 '.he position of the voices), as second, which occurs very seldom, and only 
 between Tenor and Bass. In this connection it is to be remarked, that a 
 second-suspension cannot exist, because the second depends upon the inver 
 sion of the seventh, and goverus itself according to the progression of the 
 latter, e. a 
 
192 
 
 M A NU A L OF HARMONY. 
 
 I ] 
 
 413. 
 
 
 I I 
 
 Exercise iu a middle voice. 
 
 Tenor. v A B|j C o k° d — oJ°y d A D 
 
 As upper voice, the selection of the Alto is here most to the purpose. 
 
 415. 
 
 ^=JM= 
 
 ü£i=E[ 
 
 3 6 
 
 era: 
 
 §^i=M^m=M^M^mi 
 
 The same Exercise with r he following determination of chords : 
 
 116 
 
 do A- 7 B|)0 CF B|)C 7 d B[jF gf.0 d A d 
 
 f 5 -®— r— ?5-g- 
 
 iHEit^^ ^^fTT rf^ 
 
 : ff ._i_(a_ 
 
 1 
 
 ( bii^iiÖliilrtliill^ 
 
 / G 6 
 
 G 4 G 7 G * 5 
 
MANUAL OF HAH M ONY. 
 
 litt 
 
 The next to the last measure affords the proof, thai even the sixth can 
 be suspension. 
 
 For farther practice, former exercises, which were efiveu for the four- 
 voiced movement, mav be used. 
 
 CHAPTER XXII 
 
 On the Two-voiced Movement. 
 
 The great meagreness of the two-voiced movement, in a purely harmoni« 
 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 be 
 admitted in a few cases where the chord of the sixth and fourth can 
 regularly stand, or if it occurs instead of the chord of the second. (See 
 page 188). 
 
 Example: C F b° 
 
 c 
 
 —a — 
 
 
 119. 
 
 A ^ 
 
 ^Mmmmmimmmimm 
 
 5 3 6 6 3 6 6 3 J 
 
194 
 
 MANUAL OF HaRMC N ?. 
 
 Tho omission of intervals is plain through a comparison ->i ihc (ua 
 iaruental tones of Example No. 418. Want of clearness of the haimony 
 will be rare in connection with this, since each chord explains itself through 
 •ts situation, i. e., through the preceding and following haimony. 
 
 The same exercise with the following marking : 
 
 .»«. jp^ 
 
 I 
 
 421. 
 
 Treatment 
 
 i^H=^H=H 
 
 5 - 
 2 - 
 
 mE- m^^ &V TTXT^^ L 
 
 
 \tr- 
 
 ^rr n^ 
 
 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 tue next chapter are also to be considered in this light, 
 pin sq tbey drop the above limitation of a prescribed succession of chorda. 
 
MANUAL OF HARMONY 
 
 196 
 
 CHAPTER XXIII. 
 
 Harmonic Elaboration of a given 
 ment. 
 
 Voice in Melodic Develop 
 
 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 
 incut also. 
 
 The following exercise will make this plainer : 
 
 422. 
 
 -P—0- 
 
 ■#■ ^ -P- ■& ■*■ 
 
 tmmmM^mmmmmmit 
 
 fc 
 
 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 
 .n the previous chapters, if a free, skillful treatment of them is to be 
 attaine 1. 
 
 This exercise will follow, first in three-voiced treatment. 
 
 423. 
 
 _(B- T _(0-s, ^L^-0-^-^-fia. T _s- T - 
 
 '"■"'■ ■&■ • A . A v9- A . 
 
 z-g— a-&t— -E- 
 
 3 7 6 7 6 7_6 4 
 
 iH|f^f^E|[ 
 
 This treatment, after what has been remarked in connection with the 
 three-voiced inovemen* needs no farther explanation. 
 
 The harmonic treatment of this melody as middle voice will show its 
 many-sidedness, and may be recommended as a useful exercise. 
 
 In order to be able to retain the Alto voice, we transpose the melody, foi 
 the sake of the better nosition, to F inaior. 
 
106 
 
 MAX UAL Oh HARMON f 
 
 421. 
 
 
 G G 
 7 683984 5 
 
 fifüIüi^l^g^lllUPilE 
 
 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. 
 
 Ä 
 
 mm 
 
 ms^i^ ^mi^m 
 
 m^mm 
 
 m 
 
 c.f. 
 
 HUM? 
 
 g jer 
 
 •S T i9— > — fS- r Q — Ö 
 
 4 5 
 
 6 3 6 3b 2 
 
 4 5 
 
 mm^ mm mm 
 
 This treatment exhibits a weakness in the third and fourth measures, in 
 the harmonizing of the sustained A of the Bass. In like maimer 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. 
 
 c.f. . - 
 
 ^ 
 
 iaci. 
 
 =1 
 
 £■ 
 
 rn^rn 
 
 m^m 
 
 G 
 
£=£ 
 
 MANUAL OF HARMONY. 
 
 191 
 
 
 »= 
 
 ai^^^^^SI 
 
 6 
 
 6 3 
 
 S 
 
 
 Of the remaining treatments, that of the cantus firmus in the middle 
 voices will here be given : 
 
 427. 
 
 =£3= 
 
 c./. 
 
 iÜifiiiÜ: 
 
 mmmmmi 
 
 gs fm TrrTnrr gf 
 
 9 6 
 
 
 9 8 
 
 ß-0—* 
 
 mm^^m^s^iwmiwm 
 
 As examples of four-voiced treatment, the following may stand hore : 
 
 428 Given rohe: ^_^ 
 
198 
 
 429. Four- voiced treatment 
 e.f. 
 
 MANUAL OF HARMONY 
 
 P-0- 
 
 
 gBj f^ gzrrg^: 
 
 
 pö 
 
 5 
 4 3 
 
 9 8 6 G 6 - 5 
 
 7 6 7_4 3 59 5 4 3 
 
 ^j-g ^^^ gi^Pi^g=E=iE 
 
 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. XI L, page 116). 
 
 The same cantus firmus in the Alto, transposed to D major : 
 
 130. 
 
 / =} 8 J|====P^&ee|: 
 
 g=i=^n Lg.-i^ 
 
MANUAL OF HARMONY. 
 
 199 
 
 j)pEE==§| 
 
 
 pfe 
 
 2 r a ^ 
 
 P 
 
 ?=E 
 
 
 to 
 
 U 
 
 F3e 
 
 ll^i 
 
 
 7 6 5 
 
 m 
 
 
 In the fourth measure are found suspensions in three voices (see pag« 
 117). In the fifth and sixth measures the position of the Alto and Tenor 
 is not good, because the distance from one to the other is more than ao 
 octave. 
 
 Of the remaining treatments, that of the cantus firmus in the Bass will 
 here follow : 
 
 
 Sltiili^itelfciSiiI=^iiEI 
 
 :fczo^zzx^z=T^ 
 
 a — s — tU.siW 
 
 m ^EEH^=m ^^^^ 
 
 ^iii^llS|-liriiiliiis|ii^ 
 
 5 - 
 
 e.f. 4 3 6 
 
 4 
 6 _2 6 2 
 
 6_3366 6 4 
 5 A Jp**r> * 6 3 
 
 mMmmimimmmämmmü 
 
 The introduction of the chord of the seventh of the seventh degree, in 
 the fourth measure, is not clear, because the fundamental lies imm*- 
 liately above the seventh. (See page 69). 
 
 Besides this, its progression does not ensue here according to the leading 
 of the leading tone, but in the same cadencing manner as with the other 
 ehords of the seventh : C^ °-j Fjf. (See pages 68 and 69). 
 
 The treatments of this cantus firmus with a leading of the vo : ces iu 
 which there is more movement, can be carried out in this manner r 
 
200 
 
 M A X UA L OF IIA R M A Y. 
 
 cf. 
 
 t32 
 
 -E-3— — 
 
 
 i^ti^^i^gi 
 
 s 
 
 
 PSF 
 
 i=^=± 
 
 -g— gi. 
 
 4 5 
 
 ->_ # -^ — i--*- - -»it~\ 
 
 m^ mjji ^YTT-nTV'^^ 
 
 m^=mm 
 
 
 sp 
 
 #-^- 
 
 I^Ü^^HH 
 
 iiH:E~=il? 
 
 £=fe 
 
 6_7 
 
 4 
 7 4 3 
 
 The upward progression of the seventh in the next to the last measur« 
 (at NB.), is conditioned by the movement of the Soprano. (See page 84) 
 The treatment of the cantus firmus in the Tenor follows: 
 
 m m m^=F ¥ =m^m 
 
 133 ( 
 
 
 
 Ä 
 
 ES^EEE 
 
 fe 
 
 g 
 
 6 G 6 
 
6 6 
 
 8 4 3 6 4 7 
 
 The third measure gives opportunity to speak of octave and fifth-succes- 
 sion in contrary motion. 
 
 According to the principle developed on page 27 and the following 
 pages, they are just as faulty as those of the parallel motion, and it is to 
 be especially remarked in connection with octave-successions, that thev 
 confine the free movement of the voices ; with the fifth-succcessious, how- 
 ever, the character of separation is rendered much milder by contrary 
 aiotion ; this is particularly true of those which approach each other 
 while those which progress from each other, make the separation or wan 
 of connection more perceptible. (See also Example No. 430 in the 6th 
 and 7th measures, between Tenor and Bass). 
 
 Compare the following examples : 
 
 4'i 
 
 ,.( 
 
 f=^^tzjB=f:zzE=i=g=E=:^=r?~ E=®:=z §ü fb 
 
 
 
 If we glance at the 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 voice:», 
 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 voicei 
 move in quarter notes, the simply harmonic structure can be demonstrated, 
 and thus they may serve the purpose, for the present, of making us under- 
 stand the difference between simply harmonic and contrapuntal treatment 
 of a given voice. The more particular discussion of this can only be taker 
 tip in connection with counterpoint itself. 
 
202 
 
 MANUAL OF HARMONY. 
 
 CHAPTER XXIV. 
 
 The Five-voiced Movement. 
 
 As the doubling of the intervals of a triad is necessary even in th< 
 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. 
 
 4 
 
 2 3 
 
 «■«• §:3^EE 
 
 £S 
 
 
 plUK 
 
 In the treatment, we can select, according to the position of the voice*, 
 either two Sopranos, two Altos or two Tenors. 
 
 mmmmmwimmms 
 
 -© — IS- 
 
 m^s^ ^m^^m 
 
 I 6 4 
 
MANUAL OF HARMONY. 
 The ouiLe exercise carried out in another manner : 
 
 iilifcil=iilii=l 
 
 20a 
 
 437. 
 
 BoFBANo I 
 
 »OPE A. NO 
 
 * 
 
 H ' Jr 
 
 ff3=' 
 
 1BE' 
 
 g 
 
 
 iH 
 
 IEI^sl=i=iIl 
 
 It pertains also to the independence of the voices, that two voices do 
 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§. 
 
 jfehfrFJ 5 * 
 
 6 6 7 
 
 5 
 
 would be corrected thus : 
 
 439. 
 
 ^P^F^^^i 
 
 ^ 
 
 
 i^llilliüi^ 
 
 Remark. — This rule admits, however of frequent exceptions in connectif a with poly- 
 phonic movements, because there other relations present themselves. 
 
 That the leading of the voices will 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 
 
2Ö4 
 
 MANUAL OF HARMONY. 
 
 five and more than five-voiced movement, the unavoidableness 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 
 
 ROPBANO II. 
 
 — >. P— HO <S>- 
 
 
 6 8 7 
 9 8 4 J 
 
 11111 
 
 j^^^H!*! 
 
 
 The covered fifth, octave and unison progressions in this example are 
 indicated by strokes. The open fifth in the eighth measure between the 
 second Alto and Bass is not to be avoided, since polyphonicalhj the chord 
 of the diminished seventh can, only with difficulty, be made to progress 
 otherwise. 
 
 The first and second Altot in "he eighth and following measures could 
 also be made to progress thus : 
 
MANUAL OF E A Ä M A * 
 
 20f> 
 
 üsyiiä^B 
 
 441. 
 
 SEI 
 
 l^ü^if 
 
 TL»t the voices, particularly the middle voices, must often cross each 
 Jther is shown by the second Alto and Tenor in the second and third 
 measures. 
 
 For practice in the live-voiced movement, chorals especially can be used 
 to advantage. 
 
 The following may be given here : 
 
 Choral: Allein Gott In der Hüh' sei Ehr*. 
 
 G — C DCJD 7 GD 7 G ■ Ga 
 
 pr— ^~- 
 
 U 
 
 ^\t^^=im=&m&M 
 
 Da ■ a 
 
 Be G D 
 
 W UUIJL U*^ m 
 
 - i n - i- 
 
 s 
 
 The work in the five and more than five-voiced movement, requires a 
 simple aud 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 th< 
 fullness of the chords and the necessity of the free movement of tl,i 
 voices, very unintelligible progressions can easily arise. 
 
 The beginning of this exercise follows here . 
 
 443. 
 
 =b=t 
 
 ii ' r i i > i ■ 
 
 SL J. J ± | J «L 
 
 mm^Mm^wwm^m 
 
 G 
 5 
 
 1 ' 
 
 ' Vi/ 
 
 In the repet :4 ion, the following succession of harmony can be applied 
 
206 
 
 MANUAL OF HARMONY 
 
 444. 
 
 7 
 
 4 — u 
 
 ^Hl^=I^SH 
 
 ±-T4=d=±ir:d- 4= 
 
 he 
 
 CHAPTER XXV. 
 
 T/te Sise, Seven and Eiyht-voiced Movement. 
 
 The necessity of doubling or trebling increases with the number of the 
 voices which are added ; it will also often occur in connection with 
 an independent leading of the voices, that the voices cross each other 
 The simplest harmonic progressions become here, in a still greater degree, 
 fundamental condition of the possibility of such polyphonic movements 
 and it must be remarked, that many chords are not adapted at all for this 
 manner of writing, because their intervals, in as much as they are subject 
 to a definite progression, do not allow of multiplication^, 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 : 
 
 ^-voiced : 
 
 la — g ~~ 
 
 i45. 
 
 6- voiced : 
 
 eeee^e^eeee=eefeie:^ö 
 
 i= F-g — g T^ g=db g g g LT^g *— t 
 
 V n» s •#■ ■» — •» 
 
 lliiiö== 
 
 (Si 
 
 ^ ^ggB= B= — 
 
MANUAL IF HARMONY 
 
 207 
 
 Progression to the third degree 
 
 4-voiced: 5-voiced: b- voiced: 1 -voiced: 8 voiced • 
 
 §i 
 
 
 Progression to the fourth degree : 
 
 4-voiced: 6-voiced: 6-voiced. T -voiced : S-voieed: 
 
 §n=y 
 
 =£ 
 
 Il^^Him 
 
 Progression to the J?/VA degree : 
 
 4-voiced : 5-vo*eed ; ü-voiccd : 1-voiced : 9-voiced : 
 
 P 
 
 .ffl (5(2. 
 
 ] C © 1 g, C g, c 
 
 IE 
 
 n 
 
 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. 
 
 »or» a no I. & II. 
 
 la 
 
 taci . A IL 
 
 =fc 
 
 "Igt— T— g gl' 
 
 
 Ä=E 
 
 
 EQ^^ 
 
208 
 
 MANUAL OF HARMONY 
 
 mm 
 
 || 3 -5^ T= r:Ei = x=^fc:f:=p-i=fz=:.pa: _ 
 
 -J==i=fa=d=jBfc 
 
 I« Bh 
 
 
 =F rt F 
 
 •4-^-, 
 
 —4 1— r 1 1— r- « - 
 
 d= 
 
 6 
 
 4 7 
 
 2 6 
 
 iii^^il^j^^fl^ggEg-lil 
 
 A 4- 
 
 —s- 
 
 _e>: 
 
 I J T- J— 
 
 
 M=e=ee1 
 
 e ± e ^3eee*e3 
 
 J L 
 
 BEE 
 
 ?tl^ü^Ü=^3= 
 
 7 
 4 3 
 
 i33 
 
 T—l ! 
 
 -l—ts , 
 
 -fS t*~ 
 
 l=t=f: 
 
 —I- © U ■' 
 
 pigiSi?#Ji^ 
 
 5»=^= 
 
 J I 
 
 > — ~t i — , — i 
 
 i^^^ii?eiiiiii^Illii 
 
 fe 
 
 :— d 
 
 I I 
 
 u 
 
 i iii i i i J a J 
 
 I EEE2=dE£=dEEEE==t=3£ EE=E=£t=2Efc): EEEl 
 
 a 
 
 G 3 - 
 
 7 7 
 
 55 S 
 
 EE3EEJ5EESE? 
 
 ?IgPiÜÜE 
 
ANUAL OF HARMONY 
 
 209 
 
 3 
 
 -j Ut-4 
 
 3E 
 
 i£t 
 
 A 
 
 ^^g^^^g ^^^B 
 
 
 7 - 
 4 3 
 
 Since in polyphonic chorus-movements, all the voices do not always work 
 at the same time, as in a ohoral-treatment, the movement often appears 
 only three ami 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 he introduced, without detriment to the clear 
 ess and intelligibility. 
 
 447 - ^ , i_ """" 
 
 \ f mmmmimimmi^M 
 
 i 
 
 TlNOR I 
 
 I ill. J 
 
 
210 
 44§. 
 
 Soprano I 
 
 Bam. 
 
 f-. 
 
 iii 
 
 F^z^: 
 
 & 
 
 MANUAL OF HARMONY 
 
 LH—TT " T= = j 
 
 ee 
 
 §g=p^l^ 
 
 =)=* 
 
 ÖpÜ^ 
 
 HE£ 
 
 f o 
 
 =t=F 
 
 :*E 
 
 wmm 
 
 §i£*£: 
 
 ffi 
 
 V 
 
 ^^ 
 
 1 I r 
 
 A • ♦ 
 
 =p 
 
 93 
 
 -"a CM- 
 
 P 
 
 s 
 
 S3 
 
 JP 
 
 
 &=?==g 
 
 IHIIIIeeI^I^ 
 
 a: 
 
 ^HHi-ilit 
 
 ^sfes=d 
 
-# (5 r-ß 
 
 MANUAL OF HARMONY 
 ß—0 
 
 211 
 
 
 I^HI1e= 
 
 — d- 
 
 
 fc=±===fc 
 
 #*=r1f g^üJEEE 
 
 In eight-voiced chorus-movements, for which, as a rule, tht customary 
 four voices are used twice, the latter are not always found employed aa 
 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 : 
 
 4 49. 
 
 SOPBANO I. <fe II. 
 
 I. A II. \ 
 
 m mmmm^m^m 
 
 Bam 1 A II. 
 
 mmmm- 
 
 J_ T __! 4- 
 
 (2 p- 
 
 
 I 
 
 §il3£E 
 
212 MAX UAL OF HARMONY 
 
 -l flUj— T -^ 1— r , ■ 
 
 iii=iii=lii^^igii 
 
 The difficulty of this manner of writing is, in the case of polyphonic 
 movements which are divided into two different choirs, met by this, that 
 *here two or more choirs work together, it is not altogether the tonica) 
 difference, but often the metrical, which separates the voices; itisalway* 
 to be presumed, however, that the harmonic succession takes place in tb 
 simplest manner, and never in rapid changes. 
 
 The above is generally to be understood when we speak of twelve or six 
 teen-voiced choruses, movements, etc., and single pieces of Bach only 
 are found, where eight and more voices (among which, however, iustru 
 mental voices are to be reckoned), are treated obligato. 
 
 These hints concerning the polyphonic movement may here suffice, sine, 
 the rest, with thorough knowledge of harmony, can be left to per 
 sonal study and the inclination for polyphonic movements. Concerning 
 its application, however, we may farther remark that the use of th. 
 polyphonic form and its manner of treatment above shown, will have appli 
 cation mostly in compositions for choirs ; in instrumental music, however 
 e. g., in orchestral works, will not find place (as the taking part, si so man) 
 instruments of various kinds allows us to suppose) in the compass adduced 
 for this last, in the majority of cases, the four-voiced movement will lx 
 sufficient, concerning the farther treatment of which only the actual 
 instruction in instrumentation can give information, since here the rela- 
 tions of reduplication (even if often approaching the manner shown above), 
 moat still be subject to other principles. 
 
MANUAL OF HARMON F. 218 
 
 JHAPTER XXVI. 
 
 On the Musical Forms of Close. 
 
 Several kinds of close have already been mentioned (pages 32 and 33) , 
 in relation to the authentic close, farther remarks followed on pages 40 
 and 53 ; in the course of the wi.ole treatise, however, no farther opportu- 
 nity has been given to take up til« subject, so that a fuller explanation of 
 these and other kinds of close 3iay here follow : 
 
 The forms of close are immediately divided into 
 
 The authentic close and 
 
 The plagalic or plagal close. 
 
 The authentic close has the formula V-I, the plagal close IV-I (or in 
 minor : V-i, iv-i), as was before remarked. 
 
 Both kinds are used not only at the conclusions of whole compositions, 
 but also at the close of the principal parts, of the periods, and their 
 divisions. The more particular discussion of this point belongs to the 
 doctrine of Form. (See the book referred to, page 142). 
 
 If the plagal close concludes a piece, it seldom stands alone, but suc- 
 ceeds the authentic close ; in a composition in minor it also frequently 
 leads to major, e. g. 
 
 150. 
 
 
 J 
 
 1 
 
 a 
 
 auth. 
 \ | close 
 
 
 playal 
 
 clone 
 
 
 \h^ 
 
 — G— 
 
 m 
 
 
 i 
 
 immm 
 
 =\i 
 
 (9c 
 
 \ 
 
 r 
 
 III j 
 
 — =T=F 
 
 
 \ i *> 
 
 m 
 
 124- 
 
 -V- 
 
 1 i- 
 
 - i r 
 
 In the last case, as in the above example, it is introduced by means of a 
 modulation. 
 
 The closer (cadences) are also divided into whole and half closes 
 'cadences l. 
 
 By the first is understood the same which is comprehended under the 
 authentic cadences. In the case of the i<-J nie cadences a farther distinction 
 is again made between perfect and imperfect ones. 
 
 The perfect whole cadences are those in which the Bass receives the 
 
214 
 
 MA N UAL OF HARMOXY 
 
 fundamentals of the dominant and tonic, and the Soprano the fundamental 
 of the tonio, e. g. 
 
 not: 
 
 51. { 1 
 
 If this is not the case, they are called imperfect, e. g. 
 
 152. { 
 
 
 ^mmmwMm^^M\ 
 
 If the Bass progresses from the dominant to another degree, they a<e 
 ealled deceptive cadences. 
 
 453. 
 
 mm 
 
 mmmmmmm 
 
 fa. &c 
 
 mmmmm 
 
 See the examples, pages 82 to 85. 
 
 The half-cadences have the formula I-V, e. g. 
 
 451. 
 
 a 
 
 They consist therefore in this ; that the dominant triad completes the 
 movement. 
 
 Besides the tonic triad, other chords of other degrees can precede th« 
 dominant in the formation of a half-close, e. g. 
 
 455. 
 
 ma^zmm*m^i - 
 
 Among the half -cadences are also counted those closes in the key of thi 
 
MANUAL OF HARMONY. '215 
 
 dominant which are formed by a modulation into the same ; with which 
 however, the modulation itself is not, in a definite manner, effected through 
 the fundamental positiou of the dominant harmony of the seventh, but 
 either through its inversions or through the chord of the seventh of the 
 •eventh degree, e. g. 
 
 This is, however. tixi 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 il-V, which effects the close of the first division of the 
 whole period ; in the seventh and eighth measures, however, we find 
 & 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 whole or authentic cadence 
 in the key of the dominant at the conclusion. (Thus this is no hol) 
 cadence, sicce the dominant harmony of the seventh renders the module 
 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 half-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 
 if the smallest, as well as of the more extended movements, an i 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. 
 
 Aeeotrtpanimer.t figurated, '83; harmonic accompaniment to a given Toice, 151 ; 171; 
 
 195. 
 After-striking of harmonic ♦'ones, 121. 
 Alto, 23 ; alto notes, alto clef, 118. 
 Anticipation, 121. 
 Amis, 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, 213; in connection witfc 
 
 modulation, 148. 
 Cadence formula, 149, 150. 
 Cantus firmus, 195. 
 C-clef 113. 
 
 Chorals, as exercises, 175, 205. 
 Chord, 21. 
 
 Chcrd-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 cot* 
 
 nection with modulation, 143; as passing chord, 139; use of the same. 153. 
 
 <>f 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, 6%; dominant chord of the seventh 54, 57,61,82. 144; «•■ 
 
 sential, 64; the same in passing, 138. 
 
 of the seventh degree in major, 68, 78, 90, 200. 
 
 diminished, 76, 79, 87, 90; in connection with modulation, 146; in the poly- 
 phonic movement, 204. 
 Chords of the seventh, connection of the same amoDg themselves. 73; in connection wfck 
 
 chords of other tone degrees, 81, 86; view of the same, 100. 
 Chord of the sixth, 47 ; augmented, 94. 
 CJiordff the thirteenth, 88, 90. 
 
 Chord if the fourth and third, chord of the sixth, fourth and third. 59, 60, 62. 
 Chord of the eleventh, 88, 90. 
 
 Chord of four tones, 51 (see chord of the seventh). 
 Chromatic alteration. 91, 
 Consonance, 17; Complete, incomplete 17. 
 Contrary motion, 26. 135. 
 
MANUAL OF UAKMONY. 217 
 
 Cvnntction of chords, 25, 73, 81 ; local, inner, 85. 
 
 Close, 32 ; authentic, plagal, 82, 83. 
 
 see also cadence, whole close, half close, deceptive cadence. 
 
 Closing cadence, 55, 81. 
 
 Closing formula, 40, 41, 149. 
 
 Cross-relation, uuharmonic, 16fc. 
 
 Deceptive cadence, 81. 
 
 Degrees, diatonic, 18. 
 
 Digression (see Modulation). 
 
 Dissonance, 17. 
 
 Dominant harmony, 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 i 
 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 of 
 the seventh, 78 ; 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 tin 
 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 ; <>f the augmented triad, 
 94; of other altered chords, 98; in searching out modulation, 103; of the suspen- 
 sions, 112, 119; of the harmonic accompauiment 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 
 nie 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, 15, 16, 75 ; diminished, 15, 16, 8C, 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, 54, 58, 63, 111, 128. 
 
 Fourteenth, 14 
 
 Fourth, 13; perfect, augmented, diminished. 15, 16; preparation of the perfect fourlk 
 155; the same as chord, 189, 196. 
 
 Fourth-progressions (fourth parallels) in passing, 134, 136. 
 
 Formation of the close, 39, 53, 65. 
 
 Fundamental harmonies, 21 ; chromatic alterations of the same, 91. 
 
 Fundamental, 21 ; in the chord of the seventh, 67. 
 
 Half close (half cadence), 178 218. 
 
 Harmony, 21. 
 
 Harmon;/, tones foreign to the, 105. 
 
 Intervals, division of, 17 ; view of the same, 16, 18 ; inversion of the same, 11 
 
 see also omission, reduplication. 
 
 Intervals, doctrine of, 13. 
 
 Interval, 13; major, perfect, 14; minor, augmented, diminished, 16 
 
 Interval steps and skips, augmented and diminished, 156. 
 
 Interval* above, 18. 
 
 Jnten-us bt'ow, 18. 
 
218 MANUAL )F HARMONY. 
 
 Tnvetaion, 47; cf the trhds. 47 ; of the chords of the seventh. 59, 62, 78 (*e* also I» 
 
 tervals). 
 Leading tone, 57, 39, 56, 76, 116, 159, 203. 
 Major triad, 22, 65. 
 
 Meloiy, its development, 176; its rhythmical formation, 177. 
 MicLlle voices, 23. 
 Minor triad, 22, 33, 65. 
 
 Modulation, 102 ; means for the same, 141 ; its extension and completion, 148. 
 Movement, one-voiced, 184; two-voiced, 193; three-voiced, 187; four-voiced, it : At» 
 
 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, 138; covered 80, S6, II 
 
 84, 158, 208 ; in contrary motion, 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, 81, 82, 114. 
 Preparation, of the seventh, 70; of the suspension, 107. 
 Primi 13; perfect, augmented, 15, 16. 
 Primär chord of the seventh, 54, 64. 
 Primarii triads, in major, 23, 33; in minor, 40. 
 Progressi on, melodic, unmelodic, 165, 156. 
 . of the secondary chords of the seventh, 66,73, 81; see also resolution, out 
 
 unison, octave, fifth progressions <fec. ; connection of the chords. 
 / «duplication, of intervals, 25, 39, 48, 58, 70, 95, 109, 111, 132, 202, 206. 
 Resolution, of the chord of the dominant seventh, 55, 60 ; of the secondary chords of th« 
 
 seventh (in major) 65; (in minor) 74; of the suspension, 106, 10 i, 116, 120. 
 Scale (see Triads). 
 
 Secondary triads, in major, 33 ; in minor, 42. 
 8eeo7idarg chords of the seventh. 64, 78, 86. 
 Second. 13; major, minor, augmented, 15, 16. 
 
 Second- progressions (second parallels), in passing, 184; with changing notes, 186. 
 Second, step of the augmented. 44. 
 Sequence, 37. 
 
 Seventh-] rogressions (seventh parallels), in passing, 184; with changing notes, 136. 
 Seventh, IS; major, minor, diminished, 15, 16; passing, 72, 176; preparation, 70; th* 
 
 same without preparation, 72, 77, 158, 164. 
 Sixth, 13; major, minor, augmented, 15. 16. 
 Signatures. 53. 
 Soprano. '}'*■ «"oratio notes, soprano c.ef, 118. 
 
MANUAL OF HARMONY. 219 
 
 Stationary voices, 123, 126. 
 
 Structure, pure harmonic, 24, 137. 
 
 Style, pure, strict, free, 24; pure, 137. 
 
 Subdominant triad, 23. 
 
 Suspension, 105, 108; in the bass, 111; from below upwards, 116; in MTeral roi«e«, 
 
 117, 199. 
 Tenth, 14. 
 
 Tenor, 23; tenor notes, tenor clef, 113. 
 Thesis, 107, 138. 
 Third, 13, 22; major, minor, diminished, 15, 16; in the chord of the seventh, 166, M 
 
 7C (see Leading tone). 
 Thirteenth, 14. 
 
 Thorough-bass notation (see Figuring). 
 Tonic triad, 23, 142. 
 Triad, 21 ; major, minor 22 ; dominant triad (in major) 23 ; (in minor) 40; tonic triad, 
 
 23 ; (in connection with modulation) 142 ; subdominaut triad, 23. 
 
 duuble-diminished, 94 ; harsh-diminished, 95, 96 ; augmented, 43, 65, 92 ; dimin- 
 ished, 34, 38, 43, 50, 65. 
 
 Triads, of the major scale, 21, 33, 43, 99. 
 
 of the minor scale, 40, 42, 46, 99 ; natural connection of the same, 22 ; view ol 
 
 the same, 46, 99. 
 
 Tritonus, 70, 169. 
 
 Twelfth, 14. 
 
 Unison, 13. 
 
 Unison progressions, 27 ; covered, 161, 206. 
 
 Voices, movement of the, 26, 55 ; (see Progression, Ac.). 
 
 Voices, compass of the, 113. 
 
 Voices, relation of the, 113. 
 
 Voices, outer, 23 ; middle voices, 28 ; development of the accompanying voioea, 146. 
 
 Vordersatz, 174. 
 
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