^0m^ 'mrpfc ^f^Me RICHTER'S MANUAL OP HARMONY: PRACTICAL GUIDE TO ITS STUDY PBEPARETD ESPECIAIJ:.Y FO^ TH3 CONSERYATOIIY OF MUSIC AT LEIPSIC. BY ee:n"st feiedkich eichtee, UHIYERSITY MUSIC-DIRECTOIl, ORGANIST OF THE CHURCU OP ST. NICOLAI, AND Oh ^ STRUOTOR IN THE CONSERVATORY OP MUSIC. TKANSLATED J?KOM THE LATEST GEEMAN EDITION By JOHN P. MOKGAN, ALUMNUS OP THE LEIPSIC CONSERYATORY OP MUSIC, AND PUPIL OP THE AUTHOIL FOUkTF,E,NtH ^ F^DiTloit. • *, ' ' * ' ^ NEW YORK: G. ScHiEMER, 35 Union Square (West Side). 1883. Entered, according to Act of Congress, in the year 1S#T, oy ' G. SCHIRMEii, bl the Clerk's Office of the District Court of the United States for the Northern District of New fofl TRANSLATOE'S PREFACE In offering to the American public tMs translation of Kichteb's Haemonielehre we need have no hesitation in saying, that we offer a translation of the best text-hook of Harmony which has, as yet, been given to the world. No one knows better than its author the road which one must take to become 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 fuU, to a more smoothly-rounded one which would omit or add sometliing. 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 404358 IV TBANSLATOE S PEEFACE. 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, Eev. John Morgan, D. D., of Oberlin College, for his kind assistance in the work, which, without the aid of his comprehensive knowledge of language in general, and of the German in particular, must have been done much less accurately. JOHN p. MOBGAN. New York, June la, 1867. FROM THE PREFACE TO THE FIRST EDmON. The most immediate occasion for ptiblishing this text book ol harmony is indicated in the title. It was desirable, in connec- tion with the practical course of studies in the theory of music, to put into the hands of the pupils a help for the explanation of the doctrines brought forward, and for their repetition. The quali- ties of such a manual, the author beHeves to be these : It miLst contain tJie most essential, fundamental 'part of tJie musical theory ex- pressed in a manner brief but as complete as possible ; there must be these fundamental features alivays accompanied by reference and guidance to the practical application, in order to qualify for later attempts at composition. The book contains no scientifically theoretic treatise on har- mony, but, although as far as is the case with any system of harmony, it is supported upon a firm basis, is only dedicated to the practical object, which with the scanty means now accessible, would be very difficult to attain in an abstractly scientific way. There has, indeed, ever been a disposition to inquire after a mathematical definiteness in musical rules, and especially youth, opposed to the belief in authority, would like to have everything so clear that no doubt would be possible, much as it shrinks on the other side, from learning, by means of the anatomical knife, to know and understand the blooming life of art ; and it is not to be denied that in this respect a want is found in musical literature, which no one has as yet entirely succeeded in supplying. All attempts VI PREFACE. of tlie sort liave as yet failed to create a really tenable scientifi- cally musical system, according to which, through one fundamental principle all phenomena in the musical realm are found exhibited as always necessary consequences, and what philosophers, mathe- maticians and physicists have accompHshed 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 linlvs for the completion of the whole, in part, too abstract, serving music itseK less than other objects, and with all the understanding of musical things shown in it, still having httle reference to the properly musical, w^hich 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 Httle 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 hkes to busy himself with theory, not, however, so disadvantageous to the advancing student of music that his immediate education must suffer in consequence of it ; and this scepticism, referred to above, might be compared in a certain measure, vdth. that childish mode of procedure, which from over great curiosity, would get at the origin of all things through ques- tions which seldom can be answered comprehensibly enough for the questioner's stage of education. The advancing student of music has to apply his whole power to his technical education, because it will cost him time and trouble enough to attain the stand-point, starting from which he can with greater ease advance towards the position of a real artist. Here the question to be jsked is not Why ? the inquiry of immediate application is, Ebiv ? * It may here be permitted to call attention to a work which miijht be adapted t6 meet a palpable want : Die Katur der Harmonih und Metrik by M. Hauptmann. I I PREFACE. Vll Tlie tiling to be done is, from experience, from the Lt^^t models, to understand, not to calculate, the necessity of cerv^am principles ; later, if education, acquirements, capability and .calling require it, it will be time enough to investigate the lo'hy, 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 cashing, through an espe- cially learned dress or an attractive form, to obtain for them an extended cirde of readers. It contains the doctrine of harmony complete, wdth 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 wiU fol- low, however, in a later volume after the same plan. In closing, stiU 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, fiUed with the works of our great masters, gifted with a poetic mind, think to be able to pluck the blossoms, without learning thoroughly to know and prove the technical aids ; who are of the erroneous opinion that the consecration of beauty which extends itseK over the work of art suffers under the dissection of the material, or that the first natural formations of the latter could never develop themselves to that requisite beauty. No person of talent has ever, without thorough knowledge (to attain which was, to be sure, easier to him than to the less gifted), risen to that height, upon which alone Vm 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 PEEFACE 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 : Generalhass- Uehungen nebst Kurzen Erlauterungen by Benedict Widmann, and Uebungen zum Sludium der Harmonie und des Contrapunhtes, 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 refeiTed to, and, indeed, for exercises which, in part follow the course of my text book, in part aim at other practice. Tho X PBEFACE. work of HiLLER, however, besides the exercises wMcli professedly follow the course of my text book, offers in general a rich material for elaborations of the most manifold kind, not alone for harmonic exercises, but for all branches of theoretic musical edu- cation. Since the exercises in my text book could not of course be exhaustive, and are, for the most part, given only in a suggestive way in order, when needed, to design others after them, both works may here be highly recommended for this object. PREFACE TO THE FIFTH EDITION. It has been my endeavor in this fifth edition, also, which became necessary in a short time after the fourth, through addi- tions, in part through altered verbal expression, to attain that perspicuity^ which a text book of this kind must possess, if it ful- fill its end completely. If I may also venture to hope that the book has been in many directions serviceable and of use, I am still conscious, that in order to reach the simple and luminous representation which is my ideal, many an improvement is still to be introduced. This edition, however, does not differ essentially from the preceding, and I wish, that beside the old friends, thia new edition may gain for itself new ones. EENST FEIEDE. KICHTEE. Leipsic, DecemleVy 1863. TABLE OF CONTENTS. Ihtroduction. — Intercals, .13 PART I. THE FUNDAMENTAL HARMONIES AND THE CHORDS DERIVED FROlil THEM. CHAPTER I. — The Triads of the Major Scale, 21 XL— The Triads of the Minor Scale, ^ 40 III. — The Inversion of the Triads, 47 rv. — ^Harmonies of the Seventh (Vierkldnge), .... 54 V. — The Inversions of the Chord of the Seventh, . . .59 VI. — Secondary Harmonies of the Seventh, 64 VII. — The Inversion of the Secondary Chords of the Seventh, . T? Vni. — The Chords of the Seventh in connection with Chords of Other Tone-degrees, . . ■ 81 IX. — On Chords of the Ninth, Eleventh and Thirteenth, . 88 X.— Chromatic Alteration op the Fundamental Harmonies. Al- tered Chords, 91 XL — On Modulation op a Passage op Music, • • • .102 PAET II ACCIDENTAL CHORD FORMATIONS. TONES FOREIGN TO THE HARMONT. XII. — Suspensions, . . 105 XIII.— The Organ-Point Stationary Voices 123 yr CONTENTS. OllAPTEK PAOy XIV.— Passing Notes. Changing Notes, • • • • 128 XV.— Passing Chords, , 138 XVI. — On the Means for Modulation, . • • • ,141 PAET III. PRACTICAL APPLICATION - OF THE HAEMONIES. THE EXERCISES IK THEIR USE IN THE PURE HARMONIC STRUCTURE. XVII.— The SnirLY Hahmonic Accompaniment to a Given Voice, . 157 XVIII. — Extension of the IlAnMONic Accompaniment, ... 173 XIX.— On the Development of Melody, 176 XX. — On Development op the Accompanying Voices, . . , 183 XXI.— The Exercises in the Three-voiced Movement, . . .187 XXII.— On the Two-voiced Movement, .193 XXIII. — Harmonic Elaboration of a Given Voice in Melodic Devel- opment, .... 195 XXIV. — The Five-voiced ]Movement, ..... • 203 XXV. — The Six, Seven and Eight-voiced Moa^emknt, - , 206 XXVI.— On the Music^\l Forms of Close, • • ... 213 Index of Subjects, • • i • • • 216 JUST PUBLISHED! IN CONNECTION WITH THIS WORK ADDITIONAL EXERCISES BY ALFRED RICHTER. PR. 50c NEn INTRODUCTION. Of the elementary knowledge for whicli general instruction in inu^ 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 differeno3 ; //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 o, being the higher, will come upon the second, the c, higher still, upon the sixth degrtu , -625:: 4; ■\&^ Ig \0 \0 ; ^^ The numbers of the degrees produced thus, will be expressed in the following manner : 1 2 3 4 5 678 «9- TUSIZ ^ ■^' iv- ■** -e*- •6>^ -e^ Unison ov Prime. Second. TIdrd. Fourth. Fifth, Sixth. Seventh, Octav*. 14 c\ 'c I ^ HARMONY, As a rule, we reckon only to the octave, and begin the series again with the tones which lie above, and so on with each new octave, so that the ninth degree becomes a second^ the tenth a third, the eleventh di fourth, and so on ; just so the fifteenth becomes the octave, the sixteenth the second again. Reasons, however, which find their explanation in the principles of harmony and theory in general, give now and then occasion for designat- ing tones which lie above the octave, according to the actual number of the degrees. The series of intervals from the octave upwards will, there- fore, receive the following double designation : Octave. Ninth. Tenth. Eleventh. Twelfth. Tldrteenth. Fourteenth. Fifteenth. mi Second. Third. Fourth. Fifth. SixtTu Seventh. Octave. Greater distances between two tones, are simply reduced to their rela tion in the lower octave. More Particular Deter fnination of the Intervals, It is easy to see that the above presentation of the intervals, is based apon the diatonic major scale of C, and that the relations of the tones which lie between are not affected thereby. In like manner, they are re- garded throughout, as based upon the first tone of the diatonic scale, whereas, it is conceivable that any tone of the scale can be taken at pleas- ure as lower tone, whereby the numbers of the degrees would be altered^ and at the same time, small differences in the degrees themselves appear. In order to gain a clear view of the matter, in the midst of these mani fold variations, it will be well to note carefully the following principles : : The series of intervals shoiun ahove, in which the lowest tone is first "^one of the major scale, which forms the series itself, serves as foundation jfor all determinations of intervals. These intervals are called major, j 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 alter their designation, but only renders a more particular determination of them necessary. Thus, for example, if to the fifth f a sharp is in any way attached, it remains always & fifth, but requires, however, a more particular deter mina« MANUAL OF HARMONY. 15 tion, since it has evidently become a diferent fifth from what it was odg- inally. Or, \ Since now such alterations of the intervals take place through chromati- cally raising or lowering them, the following various and more definitely determinative designations are made use of: 1. Seconds, thirds^ sixths, sevenths and ninths, which result from the \ major scale, taking its Jlrst tone for lower tone, are called major; primes j fourths, fifths and octaves perfe ct. 2. If the upper tone of the majo r interv als be lowered a small half-step, minor intervals result. 3. If the upper tone of [most] major and perfect intervals be raised^ a small half-step, augmented intervals result. 4. If the lower tone of most perfect and minora intervals be raised a" half-step, diminished intervals result. ' Tol. Perfect Major Major Perfect Perfect Major Major Perfect Major I \ Prime. Second. Third, Fourth. Fifth. Sixth. Seventh. Octave.- Ninth. To 2. Jfinor Minor Minor Minor To 3. Second. Third. :fe: -^Q- Miitor Siasth. I Augmented Augmented * Augmented SevenGi. Augmented Ninth. Augmented 4*. Prime. ■-fe *J ■-ii^-- To4. Diminished Second. Diminished Fourth. Diminished Fifth. Sixth, Diminished Diminithed $^=l ■^^- M Tldrd. Fourth. '1^ FiftJi. Setenih,. Octavs. ** Augmented thirds, sevenths and ninths do r/>t occur in harmonic relations. Aug mented octaves are to be regarded as augmented jjrimes. 16 MANUAL OF HARMONY, Kemark. — Dimiuislied primes, seconds, sixths and ninths, are harmonically incon- ceivable, although they can be co'^.ceived of ir melodic relations, i. e., in reference to progressing intervals, not to those which sound together. Remark on the Formation of the Diminished Intervals. The reason why, in the formation of the diminished intervals, the lower tone has been raised, notwithstanding that a like interval would result, if the upper tone were low- ered, lies in the peculiar relations of all the intervals in regard to their inversion, which w^ill be spoken of farther on, ,/■' General Vieiv and Classification of the 3Iost Used Intervals, r HIKES. Perfect. Augmented. Major. Skconds. Minor. Mai)or. Tmuus. Minor. Diminished. Perfect. FOUUTIIS. Augmented. Dimiuislied* ====^l=;=b3z] __.3j^~a:J===tt3; I- i V Perfect. Fifths. Augmented. Diminislied. Major. Sixths. Minor. Augmented. cc -¥- m *q .be c a 1^ Sevkxtiis. Octaves. Ninths. Major. Minor. Diminished. Perfect. Diminished. Major. Minor. El^iit Division of the Intervals into Consonances and Dissonances* If we speak in music of consonant and dissonant intervals, we urider- etand thereby, not well or ill sounding ones, which, to be sure, can be expressed by these two words, but by the first, we understand such as stand in a pure, satisfying relation to each other, which does not require a certain farther connection with other intervals ; by tho last, such as defi- nitely indicate a farther progression, and without it would have no Batisfying 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 seventh, and all augmented and diminished intervals. From this we derive the following general plan : I. CONSOITAN'CES. a. Complete. " The perfect primcj perfect fourth, perfect fifth and perfect octaw. 1 4*6 8 -^9- •^ -^ 1^ h. Incomplete. The major and minor third, and the major and minor sixth. I ^ II. DISSONAN^CES. The augmented prime, the major, minor and augmented second, th« diminished third, the augmented and diminished fourth, the augmented and diminished fifth, the augmented sixth, the major, minor and dimin ished seventh, the diminished octave, and the major and minor ninth. Augmented 1 3tujor. Minor. Aug. 2 Dimin. 3 I ^ I -^ ^^ ^ ^-9, \w3^ Aug. Dimin. 5 Aug. 6 Aug. Dimin. 4 ?* Major. Minor. Dimin. 7 Dimin. 8 Major. Minor. 9 :^«- ;^^3: •Later in the instruction in harmony, follows a fiftrther explanation jf the pecnliar relations of ihe fourth. 1 18 MANUAL OF HARMONY. Inversion (Versetzung) of the Intervals, As was already indicated above, in determining the intervals we begin as a rule, with the lower tone. If, however, there is occasion to determine the relation of two tones, taking the upper tone as the starting point, the intervals found are called intervals below. Thus, for examp'Cj |=fe is c?, the fifth from g ; g, however, from d the fifth below. It is easy to see that the interval cannot be al- tered by this. It becomes different, however, if the upper interval 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 dbotei 1 i -<5i2- Intervals lelow : 8 7 (9-- : G-i 6 7 i^p: There result thus, the following series of numbers : 12345678 876543 2 1 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 the octave. I 2. All MAJOR intervals become minor, all minor major, the augmented^ / diminished, and the diminisheePvugmented. j In the following table is exhibited a view of all the inversions : / Oriotnai, 1»TKRVAL8. tllTBBSIOW, Peimes. Perfect. Augmented. Major. Skconds. Minor. Augmented. -os__. '^^l^^l^^^^^^ Octaves. Perfect. Diminished. Minor. Sevenths. Major. Diminished. m ■i^'i'- ■M=m F MANUAL OF HARMONY, 19 Major. Thirds. Minor. Diminished. Perfect. Fourths. A ugm ented. Dimin ished. (§m^^^ii^^]^^^^Mtm Minor, Sixths. Major. Atcgmented. Perfect. Fifths. Diininished. Augmented. ai-^^^tiEJ^EE-- i§isIE Perfect. o_- FiKTHS. Sixths. Augmented. Diminished. Major. Minor. Augmented. S« b« * b*^ V :rsi.-^[iz: Perfect. Fourths. Diminish ed. A ugmented. Thirds. Minor. Major. Diminished. '^^^-M^-^'^E^^E^M Major. Sevenths. Minor. Diminished. ■C=T ==fgf^E[: Octaves. Perfect. Dimi7iis7ied. Minor. Seconds. Major. Augmented. Primes. Perfect, Augmented. ^ g:=:z77Zi|_gi=z^^:^izz=:^^irrrE_ g — zg:- |ii^iz=t;rr^^ An exact, certain knowledge of this essential inversion of the intervals iS not alone important for the exercises in double counterpoint, but greatly facilitates comprehension and insight, in simple harmonic structure, for which reason their study is urgently to be recommended. A few more remarks may follow here : The reason why, in the first table of intervals, (page 16), all diminished intervals were formed by raising the lower tone a small half step, and not by lowering the upper, is clearly to be seen from the above table of inver- 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 1-= zz must of necessity give the following dim- inished fifth W^ Just so the perfect fourth belongs originally to the consonances, since 20 MANUAL OF HARMONY by inversion it is converted into the perfect fifth, in the same manner aa the perfect fifth can only produce the perfect fourth, and never in any case does a dissonance result from the inversion of a consonance in the octav^ Mention is made of this here because, in particular cases which are men tioned farther on, the fourth requires a similar treatment with some jj dissonances, which induced some theorists in earlier times, to explain it 9 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^sian, — which ex^rtiflcs «*« U« he repeatedly employed. / HARMONY. Combinations of simultaneous tones, formed from different intervalsi according to certain fundamental principles, are called in general, Harmo- >, Chords. The doctrine of harmony makes us acquainted with the different species and kinds of chords, and shows their natural treatment. This consists in the right and natural connection of the chords among themselves, that is, in the transition, the resolution, the commingling of one chord into and with the following. PAET I *HE FUNDAMEKTAL HARMONIES AND THE CHORDS DERIVED FROM THEM. I Among the various kinds of chords which can serve for the harmonic foundation of a composition, those which present themselves as indepen- dent^ without a definite connection with others, can be easily distinguished from those which indicate plainly a connection with other chords, and are therefore not independent. To the first belong the most of the triads, to the last the chords of the seventh. These two kinds form the fundamental harmonies, from which all remai»ing chords are derived. ^ CHAPTER I. The Triads of the Major Scale, A triad is formed by a combination of three different tones. Of these, he lowest is called fundamental tone, to which its third and fifth are dded, e. g, ' •m. 22 MANUAL OF HARMONY- These triads, formed upon c, g and a, present, however, a difference as t( their intervals. While the triads of c and g are formed here by majoi thirds 2indi perfect fifths^ the triad of a contains a minor third a,nd perfect fifth. A triad with major third and perfect fifth is called a MAJOR TRIAD. A triad with minor third Sind perfect fifth a MINOR_TRIAD. Remark. — The explanation of other kinds of triads cannot follow until farther on. As the diatonic scale makes up the content of a key, and forms the foundation of the melodic successions, so also the triads, which are founded upon the different steps of the scale, will form the essential part of the harmonic content. Natural Connection of the Triads of a Key, The triad which rests upon the first step of a key, is indeed the most important, the one which determines the key ; there stand, however, others in the nearest connection with it, which make clear its position. In the natural presentation of the triad in thirds, the loioest tone shows itself as fundamental, the fifth as highest tone, and at the same time as ts culmination. 2. ^ imz: Fifih. Fundamental. Each farther addition of a new interval would either ali.er the chord, or present tones already there, doubled. The next triad standing in connec- tion with this must, to be sure, as an independent chord, lie outside its tone- mass, still, however, support itself upon one of its tones. This tone can only be found in the outer limits of the chord, viz : in c and g. G, which is here the fifth, will thus form the fundamental of the one nearest standing triad, while c will in the same manner form the culmination, the fifth of the other, the fundamental of which would be F. The connection of these three chords can be most plainly presented in the following manner : /I V . ry— ' ^— t F O Q / It is especially to be remarked of these three triads which stand in the closest connection, that their tones contain all the tones of the scale ; that they form the fundamental features of the key, and that they are, and must MANUAL OF HARMONY, 23 l)e those most frequently employed in practice, if the key is to piesent itself clear and distinct. On account of their importance also, especial names have been given to them. The one first found, standing upon the first degree of the scale, if called -~__ , THE TONIC TRIAD. ) /The second, upon tlie fifth degree, G THE DOMINANT TRIAD. — ' The third, upon the fourth degree, 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 tJie Harmonies Discovered, In the application of these three, as well as of later chords, we avail ourselves of the four-voiced manner of writing. Remark. — The theoretical chord combination can be well presented, to be sure, threcr 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 into ^our different voices. The upper is called Soprano, the lowest Bass, these two together are called the outer voices : the voice next below the Soprano is called Alto, the one next above the Bass, Tenor; these two together are called middle-voices. The arrangement of these voices in the manner of a score is as followaj and the triad may be exhibited thus : Trwor. Bam :x 2i MANUAL OF HARMONY. For tlie upper three voices especial clefs are used, which confoim better to their compass than the above used violin [Gr] clef, and which will be spoken of later. For our next exercises, we select for the sake of an easier view of the whole, not a separate staff for each voice, but will use the usual form of writing for the piano, (upon two staves). The distribution of voices in No. 6, may be exhibited thus : 6. SOPRAKO. Alto. Tenoe. Bass. ^i^ijpll^-lpg^ 3-==g-r= j izrgzzz qz^oiziz q^zgizzi j^zg — : — o — ^^ A twofold consideration of these various voices will take place : first in relation to the progression of each voice for itself alone, then in its relation to the remaining voices, both of which must be "pure and well-constructed The result of the fulfillment of these two conditions is called 'pure lead ing of the voices. This purity of the harmony and its progression is attained through seeking out and practicing the natural and legitimate of harmonic com- bination. Hereby arises the so-called pure harmonic structure^ also called strict style^ which prescribes rules and laws which proceed from the nature of music itself, the observance of which will afford the safest foundation for a later free use of the materials for composition. By exercises m the pure harmonic structure 4it the judgment^ sharpened^ the sense for the true and correct formed^ and the taste purified. / Remark. — Inasmuch as every composition should exhibit, '^elf, through a correct use of all means at command and the purity resulting therefrom, fpuv ity is here synony- mous -with natural expression), the term pure harmonic strwfure in a general sense, would require no farther explanation, as being a matter of cuurse. In a more narrow sense, however, under pure harmonic structure we understand domethiug farther, which is more nearly and better indicated by the expression of like meaning, strict harmonic structure, strict sti/le, since this can be used in distinction to free s^yZe, whereas, properly speaking, no antithesis of the pure structure, such as, perhaps, impure structure, is to be assumed, since, as frequently as the latter in fact may occur, it were certainly to be designated as false, while the free structure might be essentially founded upon the lef/iti' mate of the pure structure. As was indicated above, by pure harmonic structure is understood in a narrower sens^v MANUAL OF HARMONY. 25 #r3C» « une as in the natural development of all tone relations, allows the fewest dtjressiom from the legitimate, and only such as do not touch that v)hich is essential, fundamental. If, ia what precedes, the idea of pure harmonic structure is determiued iu a genera way, still its boundaries are not yet drawn ; and just this is a point which gives rise to th more difficulties for the beginner, as the boundaries are so very variously determined hy the theorists themselves. This difficulty has occasioned many of them, especially some later ones, to omit entirely to speak of the pure construction, of the strict style ; indeed, to begin immediately with composition, and teach the laws of harmony from its inci dents. Whether this indulgence to youthful impatience, which does not willingly busy itself with the abstract, this inclination towards premature living creation, before the organic has developed itself to the capability for creation, can produce anything really mature, need not be further investigated here. Let those who follow the views of this book and conform their studies to them, as also all who have to go through a strict school, be assured, that their freedom for future creation will by no means be lost by means of that which is forbidden to them, but will unfold itself so much the more fully, and with a more living power, upon a basis conformed to nature. The real mastery has ever been able to make itself apparent most genially within prescribed bounds, whereas the most lawless conceits frequently furnish proof of morbidity and weakness of mind. On the other hand, the pupil cannot be justified in making use of exceptions to given principles, which may perhaps be found in the works of the greatest masters, where the rule is concerned ; or, iu any case, to wish to produce compositions, when the thing to be done is to work out exercises theoretically well. The three chords thus far known, being applied in the four-voice, movement, will give occasion for remarks and observations, from which certain fundamental features and rules are to be established. Since the triads only contain three tones, one component part (interval) 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 rule is to be observed ; /If a tone occurs in both of two chords which are to he connected, it ij / io he retained in the same voice, e. g. / 26 MANUAL OF HARMOIi T, In the Example a, C occurs in both triads as common tone ; the Soprano, which gare the first C, retains it also as fifth of the next chord. Just so m Example h, in which the G of the Alto affects the connection. The remaining voices vroceed to the tones which lie nearest to them, aa at a the Alto from G to A, the Tenor from E to F, &c. If in tjjOQ chords no common tone appears^ the voices are independently led in such a manner^ that none appears with, any other in parallel FIFTHS or OCTAVES. In order to explain this faulty progression more exactly, we must first' make the necessary explanation of the movement of the voices in refer- ence to each other. The Melation of the 3Iovefnent of the Voices ifi Hespect to each other. One voice can progress with another in Parallel [direct] ormtion (motus rectus). Contrary motion, 1 , (motus contrarius) and Oblique motion, I ^ {motus obliquus). The parallel motion arises, if two voices rise or fall at the same time, e. g. S. f—s) ' T— r— ^- :Ezizi=:t:=i=?=:Ez4:-- -^—:: i They progress in contrary motion if the one rises and the other falls, e g 9. ■^ ^ ;i^ ^A f-T i The oblique motion arises, if, of two voices one remains upon the same tone while the other moves on, e. g. \ Jzz El^J^z:fiiiiz=LL=3=i^=:pz±zi£z=:i izr-_:s: 1:^^11=8 MANUAL OF HARMONl. 27 These three kinds of movement of the voices occur in chord connections \n2kmixed manner. Thus, in Example No. 7, h^ the parallel motion showii itself between Soprano and Tenor, the contrary motion between Soprano, Tenor and Bass, and the oblique motion between the Alto and the remain- ing voices. The above mentioned yawZ^y movement of the voices m parallel octaves and fifths^ can only appear in parallel motion : if, for example, two voices progress by degrees or skips in the following manner : 11. \im^^^ This fault is regarded as such for all voices. The following connections of harmony contain both faults: In Example a, are parallel octave skips between Soprano and Bass; in Example h^ 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 h^ between Tenor and Bass, and in c^ between Soprano and Tenor, as also at the same time between Soprano and Bass. The best means, to avoid- these and similar faulty progressions, is, for the above Q.^Sef,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 mttioUj or, if the following chord contains the same tone, remain stationary. The other voices then move on to the tones of the new harmony which lie nearest to them. Thus in Example 12, d the oblique motion in respect to one voice, and at b and Cf the contrary motion of all voices in respect to the Bass, i? to be applied, e. g. 13. i^i^iii=iiliiS 28 MANUAL OF HARMONY. Reiiark. — ^The reason for the prohibition of octaves, ^ith whiisb is ton ected that _ ■•• iliiiliil^l^gS^ 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 ofi"ered 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 of them, frequently the first principles of chord-connection are violated, and other much worse faults easily arise. Much which follows will lead us back to this point, and with a more mature insight, the subject will be particularly discussed. Exercises, To bring musically into connection the three primary triads, with observance of the rules thus far established, will be the next exercise. We select for this purpose the following Bass progression : /— '" ■ " / ^- -©— ._-<2_. u '.Z—^U. -s>— il^^i C: I IV ^P=P^ 4. 3=1 liff Remark. — ^These, as well as all subsequent exercises, give an indication in what way and manner our practical exercises will proceed. They are always to be continued so long as the point under consideration makes it necessary. The situation of the upper three voices of the first chord, which are to be added, will yet give us occasion for important remarks. * Ihe figure over the Bass-note indicates the proper interval for the Soprano of thw first chord. — Ed. MANUAL OF HAB.MONY. 31 "We have already seen in Example 5, that the situation of the Toicos .n a chord can be very different. This situation of the voices is called the 'position of the chord. Close and Open Position, A chord appears in close position, if the upper three voices lie so near to each other that neither the Soprano nor Tenor, if transposed an octave, can appear between the two other voices, even if the Bass is somewhat removed, e. g. 21. i^iEin: mmmmmmt The first position of the chord a is in ft so altered, that the former E of the Tenor being placed an octave higher is given to the Soprano ; in c, th« case is the same, with the two tones Gr and E ; on the other hand, in d^ tha C of the Soprano is placed an octave lower. In all these transpositions the situation is indeed altered, but not the close position. It is otherwise if the chord appears in open (also called dispersed) posi- tion, which is the case if either the Soprano can be placed between the Alto and Tenor, or the Tenor between Alto and Soprano, so that thereby the close position results, e. g. I 22. liH^i^E^ L. \=^^^^^^^^ At a, the chord appears in open position ; by a transposition of the Q- between the Alto and Soprano in close position &/ just so at c and d. At / the G of the Soprano of the chord e^ is placed an octa\ e lower between the Alto and Tenor. In this sense, however, the following situation of the voices (No. 23) would not be open position, for by the transposition of the Tenor, tha situation of the upper voices would not be altered, h, and only thf 32 MANUAL OF HARMONY, transposition of the Soprano would j)roduce the real open position of the i chord, c. 23. ^lis^^l^l i^g=E=^f=|EEj Even if the open position allows the chord to appear fuller, still it i§ not always to be applied, and, for our first exercises, is not clear enough to the view ; so that we will for the present, write them in close position. Remark. — It will always be better in the beginning to work out the examples in close position, and only to use the open position later, from the examples of the second and third part onward, in which last they necessarily present themselves. In the begin- ning, the pupil, in the use of the open position, stumbles now and then upon difficulties, to overcome which cannot be our immediate object, and which had therefore better be evaded. The various positions do not generally appear single, but occur com bined, according as the leading of the voices requires. If the position of the first chord is determined, the following chords ai no longer so free, as to their position, that each can be chosen at pleasure, but it is regulated according to the rules for the connection of chords already given, pages 25 and 26. This connection of chords and the leading of the voices of the first exercise, No. 20, may follow thus ; =SeI|eIeIeIe3eWe|J 24. 0: I V I IV The natural relation of these chords to one another becomes clear by the above simple example, if we observe accurately their connection; especially, however, from the last two chords does the close connection, the mutual completing of one another, become plain. The feeling of return, of rest, of satisfaction, which lies in this connection of chords adapts them for forming the close. This form of close through the domi- nant chord, which resolved itself into the tonic triad, is called, if the lattef falls upon th » rythmical accent, the authentic close. [Cadence], MANUAL OF HARMONY, Zh 25. ^:3:,^^dti£.o^rx^ ii^ii^i Another form of close, which is formed by the subdominant triad, as above, No. 20, Example 4, is called the jplagal close. ) -l-x— 26 IV I Of these and other kinds of close, we cannot speak more at length, unti) 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-Y and V-IV, in various positions and keys. Note. — ^The expression by degrees is used here, as elsewhere in similar oonnection^ t* denote from one degree to the next, in distinction to by skips, viz., from one degree t* another at a greater distance. — Ed. T7ie Triads of the Me^naining Degrees of the 3Iajor 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- plfs, the combination of chords V-I. These triads are called, to distinguish them from the primary triads, SECONDARY TRIADS. They are situated upon the second, third, sixth, and seventh degrees of the scale. 27, i U III VI VIlO 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 others 34 MANUAL OF HARMONY. I because that, beside the minor third, it contains a diminished fifth ; for this reason it is called the DIMINISHED TRIAD. We select as an easy distinguishing sign, for the minor triad, a small numeral for the designation of the degree upon which it is situated, to which, in the case of the diminished triad, we add a 0, as above vu°, manner of writing which the theorist, G. Weber, has introduced. All the triads of the major scale can now be exhibited thus : as. ^=^^=:^g^|=g: I 11 m IV Re»ark. — 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 harmonio combmations much more difficult. As long as C major is the ruling key, the triads ol 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 particuUJy noticed Each triad can belong to various keys. The major triad of C can be; 29. i^n*^ C: I F: V G; IV / If^ therefore, in respect to this chord, C major is spoken of (expresning the key in the] general use of language), this is true only in the first case, if the C major triad occu pies the first degree ; in all other cases, however, it is incorrect. Application, In the connection of these chords, as well among themselves as al&u with, those found before, no new rule is at present necessary. Several things which are new will, however, appear in connection with it. The Bass can move either by skijys or by degrees* In the first case there will always be connecting tones (like tones in two consecutive chords) ; in the last the progression of the voices must be in contrary motion, according to a rule mentioned above; (page 26), in order to bring out the inner connection of the chords. • See Translator's note on page 33. MANUAL OF HARMONY, a. The Bass progresses by skips. b. NB. 30 \mmm^^^ II IV / '-1S-B F=^F=«=T=g- IP; ^i II VI &c. As in this example, the skips in the Bass from the second degree have been treated, the same can be treated beginning from all other degrees, so that tones common to the two chords always remain in the same voice. To this rule there are, however, in many cases, exceptions. In Example 30, at NB., is found a progression of the voices formed according to the above rule, which contains an unpleasant covered octave between Tenor and Bass, and which is certainly improved by the following progression. Even if, in the last case, the local connection of the tones fails, still the inner connection is present, since the D of the Soprano in the first chord can easily be conceived as doubled through the lower octave, whereby the connection immediately becomes apparent, as in Example No. 31 : 31. feiEpi I mm^^ Remark. —The reason, however, why exactly this tone should be conceived as double, since this cjuld also be the case with anj; tone at pleasure, is founded upon the fact that it is the fundamental, the tone which gives to the whole chord its determination. The unpleasantness of the covered octave mentioned, lies in the circum- stance, that the upper voice progresses a whole step, and is yet more noticeable if it is contained in the outer voices, as in Example 32 at a* J b. _ c. y 32. mm^^^^^ I S6 MANUAL OF HARMONY. A By the contrary motion of the Bass at hy the leading of the voice* can be improved ; in like manner, by the contrary motion in Example c, although here also a covered fifth shows itself between Soprano and Tenor (See the Remark on Example 34), Remaek. — In the cases brought forward above, we do not speak of absolute faults. If the leading of the voices is entirely given into our control, much can be avoided, which under other circumstances, for example, in the treatment of a cantusfirmus, of i motive, or on other grounds important for the composition, is unavoidable. The I improvement is here only presented from a theoretical stand-point. Concerning the covered fifth in No. 32 c, a farther explanation follows at No. 34. The unpleasantness of the covered octaves spoken of ceases at once if ths upper voice progresses a half step, e. g. 33. iim^il^J^lilf^P 1>, The Bass progresses hy degrees. Here the contrary motion should always be applied, e. g. 31. NB. 1. tetter : piiill^MiiglSiillilfL^ m^^^^wi letter. ' tetter . II lit NE. 2. —9.- liS^^iliiiElil^lPJli^ ll^ieE^i'^E^I^S=i ui IV IV i^l^fiiii^i^i^lli: lii V Ti V IV MAirUAL OF HARMONY. Zl MemarJcs on these Chord-connections^ In all progressions of voices such as that used at NB. 1, and subsequen gimilar places, it is better to double the third of the second chord, in ordel to avoid covered fifths. Their unpleasantness is more noticeable if the chords appear in open position, e. g. w^M^m^^^i 35. ^^iw^mM^^^^ The leading of the voices at h is to be preferred. If these covered fifths occur in the middle voices, they are moru allow- able, because they are less perceptible. 1^ zr ^ja iiii-iEi 36. At NB. 2, the doubling of the third of the second chord is not alwayi 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 tonCy a fuller discussion will be given in connection with the following exercises" 37 4i Si E^E^EEgl^gl ^EEEi z^gE^: ^i^^imm^m H « 1 1 -s) — © NB. 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 melciia progression is called Sequence, 88 MANUAL OF HARMONY, This consequent progression of the Bass, occasions also a like rcgulaf leading of the remaining voices. • The treatment of this example, according to principles of chord-con- Election laid down above, by sustained tones, e. g., 38. :=:o— 6* 25*- :^=::|: i &C, ^^^mi would not admit of the attainment of this end ; the progression must rather follow in such a manner, that the chord of the second measure is brought into the same position which that of the first measure occupied^ whereby the connecting tone D, does not remain in the same voice. NB. 39. Ill VIlO In the first example, on account of the sequence, the covered octaves spoken of above will likewise be allowable, if they are not found in outer voices. In the third measure of Exercise Nu 4, we meet with a chord, which thus far we have not used. The Diminished Triad, It rests upon the seventh degree of the major scale, and is more depen- dent than the triads found thus far, since it plainly indicates a progression, which indication is efi'ected 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, {h, c), a kind of progression which only becomes plain through actual chord-con- ection. Jn'V6r»ion. 10. - TT) — ^-^ — F— g- -G F— (g->^- ^gg — V' i MANUAL OF HAKMONT. 39 The third following the diminished triad yd)^ exhibits the triad cf the first degree (C) as incomplete, by omission of the fifth. Since, according to the relations of the intervals in respect to inversion before explained, (page 18, 19,) an augmented fourth results from the dimin- ished fifth, its progression must also appear in inverted order. See 40 e. The fundamental tone upon which the diminished triad rests, is called, LEADING TONE. It is found again as third in the dominant triad, and as fifth in the triad of the third degree. *^ viio V III / 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 stajids 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 ttj upper voic<;, as a in Example i2, operates more satisfyingly, than b and c. 42. I S^pEi^i=iEi?rfEfe£i^a^=[^ g— --^-^ vS— — ©- wmwi^m^^mmmmii This inclination upwards shows itself less in the middle voices, as at d. Most intolerable in many cases, in such chord-connections, are skips in the upper voice (at c), whereas, on the contrary, skips in the middle voices (at e) are to be used, if the Bass is led in contrary motion. In Example 39, third measure, is found a doubling~liB4 progression of the leading tone, contrary to the above rule. Both took place on account of the sequence contained in the example, which allowed no alteration of the position or the progression of the chord. Concerning more Extended Formation of the Close* The formation of the close through the chord of the dominant, noticetl I on page 32, (the authentic close), shows itself in a still more defnite mao* i Her in the last examples. 40 MANUAL OF HARMONY, As the natural relation of the chord of the dominant to the tonic triadj 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. :=d=t ifemiiiiiii "v" :l^l E3E 1 Besides the triad of the second degree, the triad of the sub-dominant is also adapted for this formation of the close, e. g. 44. m!^=^M^i IV The closing formulce [cadences) produced by this chord-connection, will assume more definite form through the application of the chords to be shown later. CHAPTER II. The Triads of the Minor Scale* a. Primary Triads. The primary triads of the major scale were found upon the first, fourth and fifth degrees. Upon the same degrees we find also the primary triads of the minor scale. The relation, however, in which the dominant triad stands to the tonic chord, that is, as it becomes plain through the formation of the close pre- viously shown, renders the chromatic alteration of one tone of the minor 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 o'laracter of a leading tone, e. g. i MANV^L OF HARMON r. 41 t_ffl- 1 15. NB. -G fi • By this means the formation of the dominant triad in minor, becomes exactly like that in major, thus : A minor. a A major. "■ wm^m^ a: V A: V cr briefly expressed : The dominant triad in major and minor is always a major triad, A comparison of the form of close of both modes shows this plainly 4T, C major. C minor. b §— I— <9— — ©— 1— o- E|Efer=; ^--s —"^y-— =1^^%==': :==.— ;: That, however, the sixth degree of the minor scale is not, in a harmonic sense, capable of any such chromatic alteration by elevation a half-step, as is often necessary melodically, the plagal close proves a (see page 33), which cannot be conceived of at all as at &• Iti A minor. a. 4§. EL^i^y=kidrJ:EEbriEiEEf3l=l^=l tl^ i=i^l=i^f=^l=iei=[E The three primary triads in minor can be thus exhilited in their natura relation according to previous explanation : 49. g: # IT I V 42 MANUAL OF HARMONY. I ITie minor scale, as it forms the basis for the formation of harmonies will therefore be the following : o,^^ ^-^ \.v-y^'^ a^a- ' 50. iiE== Hemark. — All other forms of the minor scale, such as : depend upon melodic conditions, which do not allow the step of an augmented second 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 following examples show ; 53. ^laiiP ^M^M\ J I &c, lI '—- iiu'i:— re :B=1 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, Eb. !>• The Triads of the Remaining Degrees of the Minor Scale* SECONDARY TRIADS. After the establishment of the minor scale, the secondary triads appe&f in the following form : 54.. m uo NB. IV V VI vu® MANUAL OF HARMONY. 4S The second degree gives a diminished triad, as before the seventh degree of the major scale ; in like manner a dimdnished triad is found upon the seventh degree. The sixth degree forms here a major triad. The third degree exhibits a new form of the triad. It contains a major third and an augmented fifth, and is therefore called THE AUGMENTED TRIAD. The constrained or forced character of the connection of this chord with other chords of the same key, allows it seldom to appear as fundamental harmony of the third degree of the minor scale. The following examples may serve to prove this : a, b, e» d, e» f» 55. 6^ ^ -g-g- VIlO 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. ^^s#r%M=fi# 91 '-^-G- '^:^^^m^m\ 11° VI Its introduction is ' most tolerable, if the augmented fifth is prepared, that is, exists already in the same voice as constituent part of the preced- ing chord, (at (JD). Remark. — There is something peculiarly foreign in the chord of the third degree, &» well of the major as of the minor scale, so that this harmony, even when it appears simply as minor triad in the major scale, is very difficult to connect naturallr and effec- tively with other chords, and therefore seldom occurs. Most of the practicable chord-connections exhibited above will occur in other relations, and not allow the augmented triad to be recognized as [triad of the] third degree of the minor scale. The augmented triad, «vhich is much used in the later music, belongs to the chromatically filtered harmonies, which will be explained later under the name Altered Chords. (See Chap. X, Altered Chords). 14 MANUAL OF EARMONl, Application, The principles of the connection of harmonies an I leading of th voices, already developed, will also have application here, and particularl in the connection of the fundamental chords in minor, what was saic about the progression of the leading tone comes very distinctly into view since the step of an augmented second, occurring in the minor scale between the sixth and seventh degrees, as well as descending, between the seventh and sixth, is to be avoided as unmelodious, if both tones, which contain the step of an augmented second, belong to different harmonies, e. g. 67. -k- '-h.-^ smmm mm^^mi VI VI Hence, in the often recurring connection of the chords of the fifth and sixth degrees, the progression of the leading tone will be necessarily alwayg upwards, whereby, in the triad of the sixth degree the third appear douhled, e. g. ftS. -fe fe^, &c. li-ZZfi- M^^^^l^==l=l'^M 1 VI VI VI VI VI Thus, it would not be possible to exhibit in a correct form the example given under No. 57 by unless we make use of a mediating tone, such as, fjr example : I 59. 9^ i Ruf ARK. — The practice deviates, in certain and especial cases, from this rule. It wiH tN? well, however, to accustoo* 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 thi vrachce is and should be only a well founded exception^ whereas the observance of th« rule can be instanced in numberless cases. MANUAL OF HARMONY. 45 JEx^vcises in connecting the Triads of the Minor Scale* 1. 80. *S= t -3^ , EeM=El^lMlE?^rElE^gf^l / 3 % 5Jf A 3 % §L^=^i|if=gE-L^gEg^EE^^£^=[ 6« — I- g f^JgE ^^E^lEE^i^-E^^^g^r^^^ Memarks on these Exercises, A chiromatio sign over a Bass note ivithout a figure, as, for example, in the third measure of the first exercise, refers always to the third of the Bass. This raikjing 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 attemj)ted, 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. Set, in regard to this, the remarks to the next exercises, (page 50). The working out of an exercise will confirm the fundamental features hitherto developed. We select for this purpose the first exercise. 61. NB. asiiiiiUiipeiS s The first principle of the connection of chords (by connection of tonea h: the same voice), is here everywhere observed, and for this reason thr I 46 MANUAL OF HARMONY. Alto, in the third measure (at NB.), makes the faulty step of an aTigmented Becond from F to Gjf. In order to avoid this fault (according to page 44), it will be necessary to let the Alto progress from F to E, and to lead the Soprano from B to GJ, 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 GjJ, the Alto from F to E, whereby the close position is forsaken, and this, and the following harmony appear in open position : 63. Farther remarks, which the difficulties in the leading of the voices in reference to the chords of the fourth, fifth and sixth degrees of the minor scale render necessary, are in especial cases to be left to practical guidance. Before we proceed to the farther use of the triads, we will exhibit, in the following manner the chords hitherto discovered : / View of all Triads of tJie Major and 3Iinor Scales* I Major. 64. / =f=i^: ^1 I 11 III IV V VI yu9 Minor. piiiEi=iife^ iio III' IV V VI vno in Major: Major triads are fotind in Minort I IV V V Vi MANUAL OF HARMONY, 47 in Major : in Minor : Minor triads ife:z:g:=zi:iizS:=:q — i^^-— ]?|:z^p^ Diminished triads Augmented triad II III VI in Major : in Minor , W =h=z]=m =^^l VIlO in Minor: iii^^ lU' CHAPTER III The Inversions of the Triads, The Chord of the Sixth, the Chord of the Sixth and Fourth. The appplication of the triads, and indeed of all fundamental chords, is not limited to that use of them in which the fundamental lies in the Bass^ as in all previous examples; the Bass can also receive the third or fifth of the fundamental chord. Hereby arise transformations of the fundamental chords, which are called IN'VERSION'S of the chord. REMARK. — It should be well remarked, that only transpositions of the JBass to another intervttl are here spoken of, and that the before mentioned transpositions of the other voices into close and open position, and to various intervals, by no means essentially alter the chord.* Two of the inversions are possible with the triad : a. If the Bass receives the third of the triad, there arises the CHORir OF THE SIXTH. C5. p Fundamentnl chord. Chord of the siatih. i TVdrd of the fundamental chord. ♦ Tlie word Po^^posiiun is here used in its general, not its technical sensa — >Blik 48 MANUAL OF HARMONY, b. If the Bass receives the fifth of the triad, there arises the chohd OF THE SIXTH AND FOURTH, Fundamental Chord chord. of the sixth and fourth. ««•§; -^ Fifth of the fundamental chord. The chord of the sixth is indicated by 6 over the Bass note, that of the sixth and fourth, by ?;«. ^. 67 ceo 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 Dot lie upon the third or fifth, but upon the^r«^ degree, since, in fact, these are no neydy 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 ot the harmony receive more variety, but the movement of the voices, and particularly of the Bass, becomes thereby more flowing. According to the above noticed rules for the doubling of an interval of the triad (page 25), it will also be better in the case of the chord of the sixth, in the four-voiced movement, to double the fundamental of the original chords and the doubling of the Bass tone in the chord of the sixth (that is, the original third), can take place only if the natural leading of the voices requires it, or if thereby certain faults can be avoided. That the leading tone, even if it lies in the Bass^ is to be excluded from this doubling, may be yet remarked after what was said on page 39. Just so, it needs merely to be mentioned, that the position of the upper three voices is conditioned only by the leading of the voiojs, and aside from this, has no essential influence upon the chord itself. MANUAL^ OF HARMONY. i9 The chord of the sixth can therefore occur in the following forms : 6S. J^E-i:ziE=iEzzE-gz=:t= ^— tizrzziEizgizib: 1_ && ll^i^fi^i^El^ilil The use of the chord of the sixth and fourth is more rare than ttittt of the chord of the sixths and requires certain conditions which shall \yn men- tioned later. We meet it oftenest in the formations of the close. The Bass tone^ the fifth of the original chord, is best adapted for doublirg, and the chord will appear in the following and similar forms : ■g a m\=^m^^mwm^^ <&c. m^^m=m%mmmmM A In the connection of these chords with others, no farther mechanicaK^je^ ^ % rules are necessary beyond those already given ; we likewise omit the mere >*^ ^ 3 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 b6 better judged of in relation to the whole. ^ Exercises, <• ^ ?o. ^SEE^^EgEEE^lE^fcElEJEJE 6 4 3 -& J- laizi: I §^=^:E^E!=S^ --5)- ili^liiiil 1 |^^5=?'£=i=s,— i25--i=r=^P^=z=ii:= 6 43 m^^ I 50 6 6 MANUAL OF HARMONY. •7. 3 6 6 6 6 6 1 3 m^^m^^m^M=t^^^^^^^-^i J3r 6 6 « 6 ^ 9- 3 6 6 g^ii^^ig^i^P=P^ PIPB^P|g^ ^ 6 JS- 6 4Jt i^i!iE^=s =^=^~;=^F=; .-^|i[:=pi|ir— p--|rp— ^-|== 11. §ip$^EE^-=EE I— p. 6 -t-i- m i RemarJcs 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 Baes. The natural direction of the diminished triad in its fundamental position is already given, page 38. In the most usual cases the progression of the Bass is as follows • •71, W^=^^^:^^ and the progression of the remaining voices thus 72. :®zt:5z::idiJ?z::^z:dzi«^zi:®z:l[ 6 6 6 6 m^MimwMmmmwMw MANUAL OF HARMONY, 61 It is evident from the above Examples, that the inversion of the dimio. ished fifth, viz., the augmented fourth, will not necessarily, \x\ four -voiced movement^ have the same progression as was given above, two-voiced^ pag 38. We see, in the first example and others, B and F of the Soprano an Alto progress to C and G. d: 73. rdlO *Jhe similarity of this chord, in sound, to the dominant chord of the st'Jviith to be shown later, often induces beginners to lead the diminished fiftli do-jmrnards^ even if it has converted itself by inversion into the aug- inenVjt'. fourth ; this, as the above examples show, is necessary only in caf:ie i<: ro?.yly lies ahove the fundamental as diminished fifth, and a progression <• f th following sort : 74. i i=^^l ts faulty on account of the parallel fifths. Remark. — Tt may yet be remarked here, that parallel fifths, of which the one fifth is diminished and the other perfect, are to be allowed if the diminished follows the per feet fifth, hut not vice versa, e. g. _____——— good. good. /5. not good. Oompi-te 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 : I »6. 6 G not pure. -(S- G- ll^^i IV vuo f 52 MANUAL OF HARMONY, "better : not: _6 TllO 11 and uther»> > The diminished triad of the second degree in Minor allows another treatment, since its fundamental can be doubled. The succession of two or more chords of the sixth, with a progression of the Bass by degrees, as in Exercise 70, No. 3, and others, will render pecessary one or more voices moving in contrary motion to the Bass, e. g. '.i inM^m^mm 6 6 6 6 6 6 -T-^^«»— I 6 6 il^^^^fg^isi=-if3 i i The series of chords of the sixth of the 5th ana 6th Exercises m No. 70 can, to be sure, be carried out in various ways ; best, however, if the con- sequent succession of the Bass is retained also in the remaining voices, e. g 78. ii^i^ Covered octaves, as in the 2d and 3d measures between Tenor and Bass, 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, that especial importance is not to he attached, in opposmoN to the consequence op THE WHOLE, wMch otherwise belongs to them^ since the construction of th« MANUAL OF HARMONY. 5B details, although it must be as perfect as possible, will always be sul Drdi« flate to that of the whole. Remark. — It is not to be ignored, that the principle laid down above can easily h misunderstood by the beginner; however, the laying down of the principle was not t be evaded, and it may be added here, in order to avoid possible error, that a decision ia these things, in the last instance, belongs only to a judgment fully matured by expe- 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 : 0), if a chromatic elevation of the interval a half-step becomes necessary ; instead of which, however, a jf or tl is often set after the figure {e. ^., 6^ or 6t], 5t3.) Other figures will find their explanation later in connection with the chorda which they concern. Formation of the Close through tl^ CTiord 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. E=i: l=iiii^ 79. 1 The chord of the sixth and fourth is frequently preceded by the triad of the fourth or second degree. l-^-jr=d=I=^- 80. —&—. .-5|. EifEtE2EtE3^^ ._!_ J_^ i ^^m 64 MANUAL OF HARMONY, As decidedly now as the chord of the sixth and fourth indicates the close, having also a decided influence in the modulation into foreign keys, just so weak is the effect of its entrance under other relations, so that its proper use is subject to certain conditions, which will be treated of later. CHAPTER ly. Harmonies of the Seventh ( Vierklange), The harmonies of the seventh are founded upon the triads. They result from the addition of a third to the fifth of the triad, which [third] forms a seventh from the fundamental. 81. Not only the various kinds of triads, but also the various kinds of ■evenths will afford manifold harmonies of the seventh. The General Properties of the Chords of the Seventh, The chords of the seventh are not so independent as the most of the triads, but indicate definitely a progression, so that they never alone, but only in connection with triads, afford anything complete or finished. On the other hand, they will render the relations of the chords to each other closer and more intimate, and by means of this quality furnish in particular excellent means for the connection of chords and for the leading of the voices. The Dotninant Chord of the Seventh in Major and Minor, The chord of the seventh which is most important, and occurs oftenest IB 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 mi»cf eventh. §2. 0: V V^ o: V V^ 7 7 MANUAL OF HARMONY. 55 In the fundamental position it is marked by a 7 over the Bas.i note, and in our method of notation, indicated by V7 83 .§! C: V^ l^i G: V. The relation in which the triad of the dominant stands to the tonic triad, has become clear principally through the formation of the close shown before, (see page 33). The close will come out still more clearW through the use of the dominant chord of the seventh. The following combination of chords will show the formation of th€ elose : 84. l=i:El=|^b|Ei 'JSSLZ 11=11=11 C: V- Remark. — It is to be remarked here, that the triad folio-wing the chord of the Beventh is incomplete ; m 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 called CLOSING CADENCE. For the leading of the voices, the progression of the intervals of the chord of the seventh will furnish important observations. We observe first the closing cadence as the regular resolution of the dominant chord of the seventh especially. The seventh, as the essential interval of the chord, is, by its relation to ihe fundamental, confined to a definite progression. If the progression ol he Bass, which contains the fundamental, is regarded as given, an upward regression of the seventh will appear impossible : a. —G- 85. Hi^^l 56 MANUAL OF HARMONY. even if, as at h, a third voice is added ; whereas its downward prcgressioi affords full satisfaction : 86. p^^{=ig=[j Since the 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 chord 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 h will, therefore, not appear so nat- ural as a : »7. i!: :bi^ 5_«2- i In the Example 87, &, the third, is given to the upper voice, which ren- der the unpleasantness of its progression quite perceptible. This leading becomes tolerable if the third is found in a middle voice, «. g. i 88. teniiifiiiiii / This downward leading of the third (leading tone) is therefore to be applied under the following conditions : a* If it does not lie in the upper, hut in a middle voice, e, g. seldom practicable. 89. 9J MANUAL OF HARMOXY. 57 b« If the Bass progresses in contrary motion^ e. g, a. 6. not: 90. i=r_?: mm^\ The reason of the second rule becomes evident, if we obserye the cx)V- ered fifths in the last Example &, between Alto and Bass. The leading of the fifth of the chord of the seventh is free. While, for the most part, it is crowded a degree downwards by the seventh, reasons may exist connected with the leading of the voices, for allowing it to pro> gress a degree upwards, as Example 88 h 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 he led by degrees^ upward or downward. Remark. — By the progression of the third towards the seventh, we are reminded of ^ what was said of the fundamental and the diminished fifth in the dimmished triad, (page 88). Both intervals are found again in the donUnant chord of the seventh. Application. Except in the formation of the closes, the dominant chord of the 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 of the complete close ia njil. produced. This takes place particularly in cases where the seventh of the chord lies in the upper voice, whereby the close becomes incomplete, or, if the dominant chord of the seventh falls upon the accented part of the measure (thesis), since in the complete close (cadence) the tonic triad must f^l there. (See page 33). Besides this, the chord often appears incomplete through the Omission of an interval. This interval, however, can only be the fifth, seldom the thirdy while the omission of the fundamental or the seventh, would entirely alter the chord, and reader it incapable of r« cognition. a MANUAL OF HARMOJsY. e, rarely: a. 91. §i; :g^.-.-^^ Sili :I^liy^ In a^ bf df the fifth is omitted, in c^ the third, and in each cas« the fundamental doubled instead, which doubling affords, by means of the tone which is allowed to remain stationary, the closest connection with the following chord, and allows the tonic triad to appear again complete, which was not the case in the previous resolution. (See No. 84). We add the following remark upon the omission of an interval in the cjiord : / Through the leading of the voices a chord can appear incomplete ; the , /omitted interval will, in most cases, he the fifth of the fundamental chord. Exercises. *Vf^ , 3 6 f) - 1.^ 7 6 6 4 7/ =1 1 1/^ s^i^il^ll^il^^I^SI ^iiliegl^lipgl^^il^Jii^ 6 6 ^6 6 7 lE $^= |gg^| g^|^g |gE^: I "/IglL^l^l^li 6 43 U ili/ 6 47 5. t giE^iE^E^EJE^ 7 6 t ^ 6 4 J6 6 7 4 t :p-i ^-tijg— azii=t— 3-i=ig-ib ^=^ 67 4:% ii These exercises require no farther explanation. It has been already mentioned, that the chord of the seventh, in the position known to us noWj MAKUAL OF HARMOKT. 59 is iiidicated by 7, also that the sharp found under it, or in general, all chromatic signs which occur without figures opposite to them, have refer ence to the third from the Bass tone. (See page 55.) CHAPTER V The Inversions of 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 Bass, and The third, if the original seventh is given to the lower voice. In close position the inversions present themselves thus ; 93. , ^__:iL. i A comparison of these inversions of the chord of the seventh, with those of the triad, shows plainly their analogous position : m^^^^ 94. 6 4 These derived chords receive their designation from the position of their intervals : The^rs;^ 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, choi'd of the second. Their designation in the Thorough-Bass notation is to be seen above, in Example 94. 50 MANUAL OF HARMONY 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 ously distributed among the upper voices, e. g. .G -g k^blEl^ElEEkiEii 95. 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 ene direction, the tendency to the same progression (resolution), will also ^xist in the case of the derived chords, in which the two tones, the fundamental and the seventh, eithei appear again, or become seconds by inversion. 96. b-S«z i; J5 :s£^ l\ Progression of tJie 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 fifih^ the progression of which was discussed above, (page 38), 97, i?; m fche resolution of the chord of the sixth and fifth will naturally tak€ place thus : , •«.. if^_^=[f MANUAL OF HARMONY, 61 Tte progression of the fundamental, as before given, does not appeal here, since the Gr of the upper voice is sustained and transforms itself into the fifth. This is, however, only apparent, for that it forms the foundation of this connection of harmony, the marking below G7 C, of Example 98 proves. That however, the Soprano, or a middle voice, cannot in notes carrj 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 cases, such as a freer leading of the voices in certain relations would give, are not hereby excluded, only there must be an inner connection of the chords. Progression of the Cliord 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 : 99. ^- g '^ — The resolution of this chord follows thua^: a. h, a^LI^ 100. 9: ^ The Bass, the original fifth, can progress in both of the given ways. Progression of the Chord of the Second, This chord has the peculiarity, that the original dissonant intervals, the seventh and the diminished fifth^ can only occur in their inversions, aa second below, and augmented fourth below. The progression of this chord is as follows : 2 6 2 6 101. m^mm^m G^ C ^ G^ ^^' Thus the resolution of the chord of the second is effected here thiough i \ Ihe chord of the sixth* We can perceive in these resolutions, that they are all based upon the aa*.ural progression of the dominant chord of the seventh, which before 62 MANUAL or HARMONY, was called cadence^ for we find everywhere the same marking of the funda- mental G7 C or V7 I. These resolutions will, therefore, themselves form cadences^ onl}? not 0! j ro 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 I>oni- ? inant Chord of the Seventh in various positions. a. The Chord of the Sixth and Fifth. 102. 9J 6 5 "G7 (J s— -f-'g- 6 5 -I (5-^_-« I i~^^EM-^^'^¥^f^EE.^^=] 6 5 -©- 6 5 b. The Chord of the Sixth, Fourth, and Third. 1: 4 3 — p-gg-^ g— I^^I^L^;i3E3 g=^|^^l;=^|=^^£^p^t^Ei^|^^^Egfj^j e^^^iiiiifl 4 3 4 3 ^^^E^:^ ^-i=TS 2 MANUAL OF HARMONY. C. The Chord of the Secoud. 63 ^_c__^.^ It— s: ^m G 2 ^ 2 ^iz:z?35is;^Ei«:ifes=Fi6Li|^:P:zFJ^^S Exercises in the Use of these Chords, y^ 1- 5 6632G 47 / O 4: 6 / 2- 3 3 G 6 5^ 9__H 3 2 4 6 3 G 4 7 F/ 4. 5 1 2 G 4 3 G G 4 3 -s— e- t i? 87 L^ 6. G 2 G 87 G7 4« zziip- 4 3 G iiiziSE^- G7 4« ^^|:_rS§=^z:y^_J=— 1-^| 6 t ^ 3f f G 3 G7 4S ^n^fii^iiei^i ;^Se Observation. — The marking 8 7 in the next to the last measure of the second, fourth, and fifth Examples, denotes that the seventh should net appear with the chord itself, but follow after the octave. 64 MANUAL or HARMOlfT. CHAPTER VI Secondary Harmonies of the Seventh, While in the case of the triads, three primary chords are requisite to 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 renders the key certain, and the natural progression of which to the tonic triad represents the key. Remark. — The manifest fact, that the seventh of the dominant chord of the seventh 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^ liarmonies 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- damental to the triads : VI o- VII'' 6. In Minor : NB. NB. -&- IC ^m^ T7 -^ 11° *- m^T ^"''^7 ^'jT ■^"°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 may be distinguished : MANUAL OF HARMONY. in Major: 65 a. Major triads with major ^^- seventh. in Minor: mim^i VI- C: r;^ IV J a: vijT- NB, Major triads ivith minor seventh always form, dominant chords of the seventh. J^r----Mvn:Sr^IfiaT with major seventh. in Minor. gg not used as fundamental harmony. a: .r^ C, Minor triads with minor seventh. in Major: in Minor: C: ii-r d. Diminished triads with minor seventh. in Major: in Minor wm^m§=^ C: vno. v.^C.^ Diminished triad with diminished seventh, \^ fl y&g augmented triad with major seventh^ as 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, \& very seldom used, and ambiguous. Remark. — We find this chord again, with another foundation, in Chapter X. Application of the Secondary Chords of the Seventh in Major, The seventh or its inversion, 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 tha7i that already found in case of the dominant chord of the seventh, viz., one degree downwards toward the fundamental, if the latter moves by fifths or fourths, downward or upward. If accordingly the progression of the principal intervals of the chord if ound, 106. ±=§: m 65 MANUAL OF HARMONY. for the remaining intervals, no new rule is necessary ; the third will be led one degree vpward^ while the progression of the fifth can be in eithef direction. b. e. lor. — JlL -os>— fl C: IV "7 Remark. — The deviation from this rule in the progression of the third in Example 10*7 b, is occasioned by the circumstance, that tlie covered octave, which would appeal m the regular ascension of the third a whole step, e. g., ~;^ 1 10$. ^^-^<2 m. i was avoided thereby. See page 35, Example 32. Whether, however, as in Example 107 C, the leading tone should be doubled in the •ucceeding chord, or the following covered fifths be preferred, 109. g ^^ -r 1 — ©-='^-3^ rr i •^ :g: w 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: ^iil^ilili^iiilillll:!^ 110. ' iippE^^^E^=EilP=^ C: .^ good: not or : not . — g-r-gg— r-g-r-g— r-^- i^^^m. MANUAL OF HARMONY, udth omission of the fifth : 67 -^- ;I^Elil^^l^^i m^m\^^=\^^^^: h* of the second degree. ii^rEiil^^_^Hil — f- ilUgM mmm C; II- without fifth : not: 1— « C 1— « 1 1 — (0____1L. ©— c. of the third degree vnthout fifth: l|iir^1^:ltiiiii^ilSg f^-Si^glE^S^^gS ^^ not: C : III ry VI «o<. not: d. of the fourth degree (seldom with this resolution). 1-^3 I ^ «=— 5- 9= ^1^5^ jg ;i: not: c: iv^ viz' no< without fifth : ^iHiii^ii 9!=!: =f=i:zf=? 1^1^ 1 not: 68 MANUAL OF HARMONY, €, of fh« sixth degree. withoui /l/lh: ^^^mm^Bimmm not : C: vi-y not . II /. of the seventh degree. not good. tetter : -^^'-=\^^^^^ =^-+- g : ^=m^^^\^^\^^\^^^\ not : C; \u9rr in l^W^l^^^iM: ?if^eii 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 " woi," "not good" which, for the most part, refer to the leading of the Bass, (inasmuch as this, with other necessary voice-progressions, produces these faults,) are, in many cases, only to be understood from a theoretical stand point, while such cases and similar ones in the practice, even in the so-called pure harmonic structure, must often be judged according to the principle before expressed, (pages 52 and 53). Since the theory has not yet succeeded in furnishing positive rules for all cases of the kind, the true and false, the admissible and inadmissible in this respect, can only be dis- tinguished by means of complete harmonic edv-cation and a really musically educated ear. More about this follows later. Concerning the especial Progression of the Chord of the Seventh of the seventJi Degree, In the above found collection of the progressions of all chords of the •eventh in major, under No. 110, that of the seventh degree^ analogous with the others, has been led to the third degree^ that is, the progression of the fundamental takes place, as with the other chords of the seventh, through a step of a fourth upward or a fifth downward. This progression is tho MANUAL OF HARMONY moie 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 oftener, upon which the diminished triad^ to which here the seventh is added, is based, (see page 38 and 50), viz., that to the tonic triad. 5. ....(i :^^ i ^ C: viio VIlO- m -■gr :t mi "=j =g== g:-: VII* r The above Example shows plainly, that the relation of the diminished triad to the tonic triad is not altered by the addition of the seventh, but on the contrary, becomes more decided. It is likewise to be remarked, that, if the chord appears in the above position, the third of the following triad must be doubled, (see No. Ill 6), because otherwise, perfect fifths would arise ; (See No. 112 a), 112. ^ 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. g g — ]- § |g=EE^| mm G 4 Kemark. — Whether the reason of this is, that ic the seventh with its above used progression, the character of the ninth lies, (as some theorists assert, that the dominan chord of the seventh, with added ninth, is the basis of this chord with its resolution)^ which, though similar to that of the seventh, is still much more comprehensive, and dues not bear the situation in the middle, cannot here be further investigated. 70 MANUAL OF HARMONY. The Freer Treatment of the Third and Fifth in the Chord o/ the Seventh, Various progressions of these intervals have already been used in th« previous connections of chords. Thejifth goes upwards and downwards, the third likewise, sometimes goes a degree upwards, and sometimes makea a skip of a third downwards. This all took place principally in reference to, and in avoidance of, covered fifths and octaves. Where these faulty progressions do not interfere, the third especially, can make still other steps, by means of which the leading of the voices often becomes more independent and freer, e. g, a. b. not gooi. c. 114. That this leading is also possible in the middle voices, if the position admits of it, is shown at €• The leading of the Soprano at b 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 Tritoims, because it contains three whole steps. More of this sub- sequently. A difi"erent 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 msiuy dissonances, and particularly of most of the sevenths in the seco7idary chords of the seventh^ renders 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, ttud as harmonic tone^ so that it can be connected bj a tie. MANUAL OF HARMONY, 71 Sucli preparation* of a tond is contained already in the first connectiona of chords previously shown, e. g. 115. 111=^=1^^ ii^l^i: i 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 Gr of the Alto in the Example following. The necessity of the preparation of the sevenths, however, does not result alone from the harsh effect of their entrance if they are struck /re^, [enter unprepared], but particularly from the character of harmonic con- nection and binding of two consecutive chords, which is especially characteristic of the sevenths, and which, without the preparation, would not appear. The preparation of the seventh can now take place in the following manner : 116. I m^^s. r^S^^E^ C: V IV IV IV l3i&^^i^Siii^g=iiE=3 C: III '—<9 i=?2~; IVr viio £11 ly VI ■» 1 1 &c -j \-G IV viio-r I m 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 ba bserved : a. The preparation takes place upon the unaccented part of ths i measure (arsis) and must I h, at least, he of as long duration as the succeeeding seventh ; it can indeed be longei; but not shorter; «, g. 72 MANUAL OF HARMONY. 117. not: %^^$m^M\ r 1 Remark. — T%e preparation of the sevenths forms one of the most important parts — 6 6 5 gmil^iiilpl Apiillcation of the Secondary Chords of the Seventh in 3Iinor, The nse of the secondary chords of the seventh in minor 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 frst degree gives it, can aflbrd no progression analogous to the above, since the following chord connection is not conceivable. 123 ii MANUAL OF HARMONY. Rkmark. — ^Even if with the above combination of intervcUs, progrcflftl ns Ibnned, such as perhaps : \ 1 124. iJ 9^ -§:z m 71 6 Btill this would hardly be admissible as proof that we have in this a progression of i chord of the seventh of the first degree in minor. The resolution of the chord of the second degree is into the dominan< and is very frequently used. 125. ^—"ffi- 7 m [f ^= &e. mmimm\ not: A progression of the chord of the seventh of the third degree is noJ jnpossible, 126. m a: IIP 7- VI i^i5!^Ez=?±5^E --G — not: 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 th« leading of the voices in their resolution becomes inconvenient and un- melodic. t ^ -O. good: 127. ^ r ^~-J^— ¥=\ i^:^=[i^^l^py^^iip[| a: IV ^ vuo 76 12S MANUAL OF HARMONY, •(9- -^ -f^^^v =Ie il a: VI r 11° 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 the seventh degree in major (see page 68), is based upon the natural progres- sion of the leading tone, upon which this chord rests : 129. As the fundamental of this chord (leading tone), progresses a halfstef. 80 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 Cl) must the leading of the third he accurately attended to, because it easily produces faulty progression : 130. if L areas 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 seventBi of the seventh degree in major, to the tonic, has occasioned the older teachers of har« vaouj to find the basis of it in the dominant harmony of 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 Keventh degree. While we refer to that whici is naid later (in Chapter IX.) of the c/icrd of th* ninlik MANUAL OF HARMONY. 77 »re can only bring forward here as reason for the view oflFered, that this assumption of the chord of the ninth is needless and far-fetched, and that for practical purposes, the gimplieity of the harmonic system has been preferred to the more excursive explanatioTi of it. For the application of the chord of the diminished seventh, observe in addition the following : The diminished seventh^ as the mildest of all, needs no preparation (See page 72). 131 . ii^-l 3 6 EE Exercises, 7 6 7 « 6 ?^lr^ b: CZGI 1 2. 3 7 5t ^m=m^ 2E^=l 6 2 6 JS- 3=i The foregoing and all previous exercises of this chapter, which, of course, only have the object to assist us in learDing 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 ffth, as is to be seen from the leading of the Bass, only, in the third exercise of Nos. 122 and 131, there is found, seem- ingly, an exception. In the fourth measure of the third exercise of No. 122, the Bass tone, to be sure, remains stationary, the progression of the funda- mental is, however, contained in a perfectly regular manner in the two chords: a 7, D7. The Bass tone could here remain stationary, because we have already learned the inversions of the dominant chord of the seventh, and can therefore use them. The case is the same in the fiftb 78 MANUAL OF HARMONY. measure of the third exercise of No. 131, where the progression of the fundamental A7-D takes place with a stationary Bass. In the second Exercise of No. 131 the chord of the seventh of the thira degree in minor is used, and, it may he 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 thesam« derived chords arise, which have already shown themselves before with the dominant seventh, viz., the chord of the sixth and fifth, of the sixthy 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 augw.ented, still its progression will ensue in the same manner as has already been explained above. 6 4 o n 5 3 ^ c: t> \j ly There is need of no new rule for the progression of all these chords ^f 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 m Major. 6 4 133. All 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 th* MANUAL OF HARMONY. 79 chord of the sixth and fourth could only occur in rare cases, and at most ns passing chord. We must not allow ourselves to be misled in respect to their usefulness by the crowded position in which these chords are exhibited in No 133. It is only important, as was mentioned before, whether the seventh comes to lie above or helow the fundamental (see page 69), and positions of the chords of the sixth and fifth, and of the fourth and third of the following sort, 134. s i^ll^J^^lil appear more satisfying, because the seventh lies ahove the fundamental. [ The chord of the diminished seventh requires a manner of progression similar to the foregoing e. g. 135. 1.^=1 -M^- 6 f 4 6 2f 4 1(5.^: mm^m a: vii*^.' 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 fifth, 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 as respects the seventh produces no such material difference, as with the chord of the seventh degree in major ; the seventh can lie above 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 thf former only to be felt as such in reference to the key. 80 MANUAL OF HARMONY. 6 6 Exercises, 6 5 137. gJE^zz^-p-nfEp :=F=±=t: =^ 1 2. 3 5 ' — - 3 7 3 2 6 7 7 i^ii^^^llig^iW;i^-l^E; 6 2 6 6 6 5 2 6 2 6 6 __ 4. 5_ 5 2 6 2 6 7 3 6 6 6 6 5 ^— 1- -5i-©- i 6 6 5 0^ 5 2 6 2 6 6 5 7 7 list :^t 6. 3 26 26 42 66 S^i^gg^^^l^i 7 7 H9-IS-- V. 5 « 6 jsr Pi3$E= :rF=C: lat =P f 6 7 7 3 6 5 9 Zl /7 ^-3 _2 7 6 7367 5« ^ 76 6 7667 36 7S6 «77 S44« 10. f 6 7 3 « 2 6 > ■■*, ,^-_. 6 6 4$ ^ -t^izz^l-i^ li T MANUAL OF BARMONT. 81 CHAPTER VIII. TJhe Chords of the Seventh in connection with Chords of the various tone-degrees other than those thus far used, Decep' tive Cadences, The known rule, that the seventh must, in the resolution, progress one degree downwards, verifies itself, to be sure, completely, in the connections of chords previously shown, but it has as little positive authority as any thing else which, under other conditions, and in the great variousness of chord connections, is subject to necessary alterations. In the movement of the seventh or of its inversion, the second, every- thing depends upon the progression of the fundamental. If this is of such sort, as in all the cases hitherto shown, that without the downward progression of the seventh no intelligible and satisfying result would be produced, then also the above rule will have full application. The progression of the fundamental, however, can entirely set aside this direction of the seventh ; it can either remain stationary or even pro* gress upwards, e. g. 13§. f -a Haie^i^gf^MI .C___L_ This leads us to the possibility of connecting the chords of the seventh with chords of tone-degrees, other than those hitherto used. A few known kinds of chord-connections now follow with remarks, in order to be able, in attempts at new formations of the kind, to proceed according to critical principles. We begin with the dominant chord of the seventh. It has been mentioned before, that the resolution of the chords of the seventh in the manner hitherto used is called cadence, and that of the dominant chord of the seventh closing cadence. If any chord other than the tonic triad follows the dominant chord of the seventh, the natural inclination to a close is either delayed or entirely set aside. The expectation of the natural succession experiences hereby a disap- pointment, and for this reason these connections of chords are called D EC EFT I VE CADENCES. Deceptive cadences arise thus every where^ where the progression of the dominant chord of the seventh does not result in the tonic triad, but lead* *o other chords. 82 MANUAL OF HARMONY. Some varieties of them will next be explained. 1. The connection of the dominant chord of the seventh with triads^ other than that of the tonic, with a progression of the seventh by de grees downwards. a. Connection with the sixth degree. In Major. In Minor. C; v^ V. ^^— ^ -^Z—^ a: V^ YI . 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 6 4 6 6 p -^ 36 24 56 M^m^^^^^^^i 140. g *^ C: V^ VI " a: V^ VI t>. Connection with the third degree. "better position . 7 6 7 6 -0- m — 5^ z=g:— Ei=g^— «Ti=:E— g:^-^^iz=Lb C: v. Remark. — The attempts with the inversions of the chord are omitted here and in what follows ; they are easily made. This progression becomes more decided under the application of modu- lation : 142. 7 6 7 6 C: V-r a:V The connection with the triad of the third degree is also possible in minor, but this as dissonant chord (through the augmented fifth) will make I, farther succession necessary. 7 6 -fl « -■= ^-h- ^ ^ rr III' VI a: y^ 2. The connection with triads, the seventh remaining stationary. MANUAL OF HARMONY. 88 a. With the second degree. not : impracticable in Minor. 6 C: V^ n a: V-y iio I), TRif^ if Ae fourth degree. 6 145. ^znfi^iig?. /7i Major : In 3finor : ^ 6 6 6 6^6 ^ — — ^=^ 1— 52?_ -^ 77 "^ TT -^ C: V^ IV a: V^ ^^ 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 : Uh Degree : Sd Degree : or : Minor : Sd Degree. 6 6 146. ^zmg :i=^=J=g_3='^ ^ ^ ^ I ^^^ C: V-y vi-y y^ Illy Yiy a:Vy a: Y^ IIF^ VI If we modulate into other keys, the possibility of new connectit^ns extends itself greatly, e. g. a. With a downward progression of the seventh. better : 147. C: V^u:V^ C: V-y b:viio*- a: V^ F: V^ ArVo-GiTii" ll. The seventh remaining stationary. 148. -i=q==r=i2^^~q= •tf pfellil^miiliim^ C: Vy Ei^cY-y C: Vy Bb: V^ a; V.^ C: V^ a: V^ G: V^ 3. The connection of the chords through an upward progression of thi seventh. This case can occur with the common cadence (V — I). a. With an exchange of the progression of variou* voice i' •r MANUAL OF HARMONY, 140. i" Fl^— =ii — - ^N^^ ^^-^Ei?^ ^ 7 6 7 6 7 77 ;5. 6 7 6 ^: -'S-^-j?- =[= ^^^_ E^E i^-^r =t^- Loz^fzi?:^ ^©i i Through the step of a third, of the Bass, the downward progression of the seventh becomes impossible, since the covered octave occurring thereby 150. 1 1 is in any case faulty. In the remaining voices this progression of the fundamental cannot btf introduced. 151. §:=^^^|^5^=^5£^5^ All these Examples are faulty. b. The fundamental remaining stationary: 152. The fundamental serves here as so-called stationary voice. (See later : Organ point). It must however lie at a distance from the seventh, and the following progression would be faul,ty : 153. MANUAL OF HARMOST. C> Through chromatic alteration and with modulation. 7 4 6 4 7 154. f |iii^; 0: V-r G: V. 77 ^ -&- ^=e 1= ^n^rmonjc .* T5€: # u« 7 C: V- G: V. ?' I Vy «: viiOy C: V-j- FJ: Viy d. Through contrary motion of the Bass with modulation into other keys. 155. C: V^ d: Vy C: V^ b^: yxiP^ a: V^ d: vuO^ C: V^ F: V.^ (See above, No. 149.) 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 the intention would not be apparent. Exercises fSr-<^ MANUAL OF HARMOI^ T, Mm=\ 4 7 3 6 6 4 7 It: fc:. 3E -G>~ tip: 2 5 :t=:n: l^^f: 6 6 6 5 6 5 5 7 6 5 — ©- n^^^^igiirsi^ippi, 6 6 4 7 5. open position. 3 6 6 7 6^7 6 7 4« §^E^E=: 4 6 6 3 4 2 5 7 7 tf i '7. ^ 4 I 6 J8^ ^— rz-zziczilz::] §L=iE 6 6 4 6 7 5 4 3 6_6_ 4 % 6 4 7 iffi=l^^lEE^1-^JI-^ii -C i; \ Remark. — ^The open position of the 6tli exercise has reference to a leading oi the voices adduced page 84 ; farther on, it can be abandoned again. The Secondary Harmonies of the Sevetith Connected tvitJi ^fhords of other Tone-Degrees or Keys. A few more connections of chords with secondary chords of ihc seventh may here follow. To adduce all cases of the kind would be ij\ impossible as it would be without object. a. With regular progression of the seventh. .5.. pr^teiiptei^iil^il^ C: II- -'t iif^ K:'V.r C: m^ IV not: pppipSipiEil^Sif iiftfeO IIP VI VIjGlV^ A Wty A ir«».y With free progression of the seventh. MANUAL OF HARMONY. 87 noti 15S. m&m^^w^sm^^sm C: 11^ G: V-y C: ii-y o: viiO,r C: n- r7 ^7 C: II. Remark. — The reason why the last example is not good, lies in the so called <^-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. fezz:i:=i:^ ^=[1= Through this arises, with the first, the complication that we must accept of two chords »f the seventh of the seventh degree in major ; one, the natural cadence of which is th€ following : ±=:f=zg==rr 166. feziii zgizizitE E3Z ,5 tC 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 diff'er 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 : 7 13 11 9 7 167. mmmtm MANUAL OF HARMONY. 91 In \hv. pure four-voiced movement they can, of course, never be applied, since, through the necessary omission of many intervals, they will appear simply as suspensions, e. g., :;=^-^.— -d=r^^^=:d: 1 16S. and even in the polyphonic movement they will not distinguish themselves 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. CHAPTEH X. Chromatic Alteration of the Fundamental JBCarmonies, 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 : Through Cjf, the diminished triad of the seventh degree in D major or D minor, or the second degree in B minor ; Through El?, the C minor — triad ; Through El? and Gj?, the diminished triad of the seventh degree of Di? major and minor, or the second degree of Bt? minor. The last two alterations are mere transpositions of the same chord into ffther keys, viz., Cl? major and Cjjl major. I>, New Formations: Of these, the formations a^ &, d^ fy can indeed be produc »d accident 92 MANUAL OF HARMONY. ally through hy-tones (passing tones) ; they have, however, nc harmonic value. It is otherwise with the formations at c and e^ which maintain harmoni (accordliche) significance. The first form of the triad (c) is known under the name of THE AUGMENTED TRIAD. This chord was found before upon the third degree in minor (see page 43) ; it appears seldom, however, in this situation, as has been previously mentioned, but more often as tria^d of the first^ fourth and fifth degrees in major, with chromatically raised fifth. Its origin from the passing tone (Grjj) to the next following (A) is easy ol explanation, as also its progression, which is determined through this tone ifi^) as augmented interval. ITl, M^MeI^e^. l^. i *a I The inversions of this chord can also be used. 1Y2. Although these chords appeared for the most part in passing, or through preparation of the augmented fourth, they can also enter free in case of a rapid change of the harmony : 173. EpppEJli^l 4 3J3 m £EEtEEE: 1 To the augmented triad can be added not only the dominant seventh, which occurs most frequently, but also the major seventh of the first and fourth degrees. a* The augmented triad in connection with the dominant seventh: 7 51 mm EJ tSEES^g a MANUAL OF HARMONY. 98 b. 175. In connection with the seventh of the first degree : j*c _^ Jffi ^*^ g,_ ^^^^^^^^^^ -G 1 IV C. The addition of the seventh to the augmented triad of the fourth e IS very rare : 7 5% 176. — d:i-_g — L_ 6 6 t <2 ©- ;[=! m^pi ^^ ^^^^^ 1 i In all these chord-connections thus far, the cadencing Bass progres- sion, (c. r- minderter Dreiklang). The like chords, if they may be so called, appear generally only accidentally, in pass- in<7, and their progression proceeds in accordance with tlieir intervals, that is, augmented faatervals progress one degree upwards, diminishti.i intervals downwards. The chromatic alteration of an interval -'f the chord of the seventh ha? 96 MANUAL OF HARMONY. been, in part, already mentioned, where to the chromatically- alteted triad the seventh was also added (page 92). This occurred with the augmented triad. Among the remaining secondary chords of the seventh^ the chroroatio alteration of one receives an especial importance. This is the <;hord of the seventh of the second degree in minor ^ which, in the following fornii produces chord-formations much used. The chromatic raising of its third a: iiO,j- gives the following inversions : 183. fe=g- 9! 6 4^ 5,32 \^\. fez: :o-zrT— J5«iz55®z:*^o«zzizFE Of these inversions, the second is the most important and is much dsod, the rest are unusual. The chord resulting from the second inversion is known under the name of THE AUGMENTED CHORD OF THE SIXTH, FOURTH AND THIRD. Its progression is based upon that of the fundamental chord, that is, as the chord of the seventh of the second degree leads most immediately to the dominant^ so also will this. a: iio^r V 1S5. If the fundamental of this chord is omitted, the augmented chord of tTie sixths already found, arises, the progression of which to the dominant if hereby explained, (see page 94) ; With ami union of the Funddmental : a: 110,7 V A, iio-j- V or, for comparisor with No. 179, in G minor : 'burt) Chro. raising Aug. chord of the sixth-, Aug. chord of Fundamental chord: of the third : fourth and third: the sixth : MANUAL OF HARMONY. 97 Remauk. — It may be mentioned here, that the formation of the augmented chord of the sixth, fourth and third can be ah-eady reached through the harsh diminished tria^ {hart verminderter Lreiklang) mentioned page 95, to which a seventh is added ; that the resolu ion, however, must become a different one, since that was considered to be OD the seventh degree, while this is found upon the second. Instead of the fundamental of this chord, the ninth of the fundamental chord can be added, whereby the AUGMENTED CHORD OF THE SIXTH AND FIFTH arises. Its origin is as follows : toithout Fundamental : Inventions : Fundamental with ninth: with elevation a, J8' b. ^ c. 2f chord: of the third: 5 3 Of these chords, the one resulting from the first inversion a^ the aug^ mented chord of the sixth and Jifth, is best adapted for use, the others are rare. Its natural progression is likewise to the dominant, but always produces varallel Jifths : ISO. ^^if^|fE^l=i£^HFE These progressing fifths, which do not belong to the most unpleasant one«, are avoided either through an earlier resolution of the fifth (the original, above-mentioned ninth as suspension), as in the following Example (a), or through a skip of the same into the third, whereby the augmented chord of the sixth results (&), or most frequently, by the third and fifth remaining stationary while the sixth and the Bass tone progress, whereby the chord of the sixth and fourth is inserted before the resolution [e)^ which chord can be here regarded as a prolongation of the suspension. ifiMn Remark. — ^The addition of the ninth does not justify explaining this harmony as a chord of the ninth ; the ninth has here, as everywhere, the same character as suspea- aion, as appears very plainly from the progression ay just so the p'-og^ression at b and 98 MANUAL OF HARM CNT. C ans-wers completely to the treatment of the suspensions, as it alsc (as fifth in the ahort chord) requires a preparation. It would follow from this, that this harmony should be taken into consideration first in connection with the suspensions, it was however necessary to mention it here, be- cause the question of the origin was under discussion, and it was not the intention, by the above expressed view, to oppose a generally received appellation. 6 Exercises, 6^ t 2 «^iiiii4i^^^ii=iji^ilii: At the close 3f this chapter we survey once more the broad field which was opened in it for harmonic formations. We have found much which is generally known and adapted for use. Much appeared to us unadapted for use and worthless. Nothing however showed itself in its original condi- tion, everything had received an addition, experienced an alteration, in a certain sense, adornment. This forsaking of the original gives us occasion to refer once more to that which was remarked on page 93. A long time indeed elapsed, before these harmonic transformations were discovered, and a still longer, before they became common property ; much, which until now is unadapted for use, may with time be developed, but, in order that the healthy inner germ may not be lost, we cannot ad- vise the direction of the whole eflfort, out of desire for originality, to the discovery of new harmonic forms, or the immoderate use of them and devia- tion from the primitive. Since all these transformations serve more for adornment, and It mighk be said, for the more elegant carrying out of the simple fundamental idea, we may venture to use them only with discrimination if we do not wish to overload the work of art, and thereby ourselves be reckoned as without taste. MANUAL OF HARM0N7. 99 At the close of the exhibition of all essential harmoaies and their moat immediate use, may still follow a brief view of them, their varieties and derivatives. View of all Chords belonging to a Major or 3Iinor Key, I. FUNDAMENTAL HARMONIES. a. Tlie Triad. b. The chord of the seventh. A« The varieties of the Triad: Major, Minor, Diminished, Augmented. Major Triads. Of the Major Scale : Of the Minor Seal* : -^ &- C: J IV V Minor Triads. Of the Major Scale : O; II a: V 71 Ofth^ Minor Seals: ifcz^ g g S e^ Diminished Triads. Of the Major Scale : Of the Minor Soal« i C : viio A : ii" yn9 Augmented Triad of the Minor Scale. $=h^ a: ni' If B.— The renjaining augmented triads see under II. : Altered Chordi. Inversions (Versetzungen) of the Triads a, Tlie chord of the eiasth. 6 n b. The chord of the sixth and fourth. 6 4 100 MANUAL OF HARMONY, B. The Varieties of the Chord of the Seventh. a. Tlie dominant chord of the seventh or primary chord of the seventh b. Secondary chords of the seventh. A. Dominant chord of the seventh (major triad with minor seventh). Formed alike, in Major and Minor : 7 7 7 C: V. Y o: V.^ a: Viy lb. Secondary chords of the seventh 1. Major triad with major seventh In Major. C: Tj lYj 2. Minor triad with minor seventh In Major. In Minor. VI. In Minor, C: 11 Y Illiy VI Y 3. Diminished triad with mirror seventh In Major: In Minor : f^ C: vii"- i 11° .y ^^4^' 4. Diminished triad. with diminished seventh (chord of the diminished seventh) J . .A; / fJ , , a: vn^Y 6. Augmented triad with major seventh In Minor: MA iV UA L 0,F 'IT'4 fiM O A' >r 101 Inversions (Versetzungen) of the Chords of the Seventh, tu Tli6 chord of b. The cliord of tJie o. Th* chord of the sixth and fifth : sixth, fourth and third : the second : 6 6 4 5 3 2 m !?^ -] — ^ F -^ ^=t F IL ALTERED (chkomaticallt changed) CHORDS. a* The augmented triads formed from the major triad : In Major : =^wMmmM= o;¥=*' IV b. The augmented chord of the sixths formed 1. From the minor triad with raised fundamental (so-called double dyuinished triad) : m 1=1^ -y: ■-^t ^ 2. From the chord of the seventh of the second degree in minor. (See the following chords) : C. The augmented chord of the sixth , fourth and third; d. The augmented chord of the sixth and fifth^ — both formed from the chord of the seventh of the second degree in minor : Raising of the third : ^3i=fe|^ fiS= Itwersion : With the ninth from Without Fundamental, the Fundamentxrl aug. chord of the sixth : and wWiout the latter. no> 1 102 '\\': ]''kUi'u^ii^'d>' HA HMO If r. CHAPTER XI. On Modulation of a Passage of Music (eines Tonsatzti). The term modulation has a various signification. Formerly was under- stood thereby the way and manner in which the succession of harmonies is arranged to a vocal part. In the later sense is understood the digres- sion from one key into another. The name, digressive modulation^ which is sometimes found, would be no pleonasm according to the original signi- fication of the word. According to the import of the term, it will next be important, to learn rightly to recognize and determine each occurring modulation (digression into a foreign key) ; farther on, in Chapter XVI., the means for modula- tion will be discussed, whereby the capability of recognizing the latter is more fully supplied. / A modulation arises^ if a harmony foreign to the 'previous hey ap- 'pears. The previous key is then wholly forsaken, and the harmonies must be reckoned to the new key, so long as no harmony, again foreign to it, appears, which effects a new modulation. Thus in the following Example ; 192. or G. is a modulation to D minor in the third measure, because Cj}-E-G-BI?, belongs no longer to C major, but undeniably to D minor, whereas in the fourth measure it is doubtful whether the C triad, which is foreign to the previous key (D minor), is to be reckoned to C major, or to the G major fol- lowing, while the modulation to A minor in the fifth measure is unmis- takable. ^ The dominant chord of the seventh^ as also the chord of the 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 several keys. MANUAL OF UARUONT, 103 Thus the G major triad belongs not exclusively to G major, but is alaa Bub-dominant to D major and sixth degree to B minor. This ambiguity often allows the modulation to be recognized first trom the succeeding chords, as in fact, the decided modulation itself can be formed first through the dominant harmony of the seventh with its derivatives. The musical ear itself proceeds yery simply in the apprehension of s modulation : it always apprehends the foreign haricvw as belonging to ■j^, that key, which is nearest related to the ruling one. J Thus, for example, in 193. :S=Si^ the major triad of D in itself considered, would belong to ♦he key of D major ; in connection, however, with C major, it will be most in:xrediately 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 XV/ Exercises* ^ j 194 ^' 3 6B^5 _ 71) 1 C: IV V 6 5 C: I G: V I d; vu^, C: I 2. m^: -l^-J-, 6 6 4 5 2 6 7 :i^-ii ^^PPiP ^. — ami ^vni ^ ^^ 6 6 66 «26Tb- 5 t • 6-7 , lO^ * 2 6 4-5 5. 5 6 F iipE^ (5 —->- — © ^ «9 — ■•■ — ^- \] - B.^^ _5 6^ ii — ,^ — ■ .1 ^ — I — . ■* ^^ ^ » 104 MANUAL OF HARMONY, J)\ I ^ i[7^~f"-/^/?^^» T-:«^"#"43rv "or 4 3b 4b 4 2 3 6b 6 4 5 6 6 5 5 6 JT^ 3_^ 3 3b^ _ 2 3 4' 5 4 5 5 6_ 8. I 6 6 6 5b iqzzii^zzz- 6 4 7 3 2 6 |g^^ — +~© — ^ f G 3 6b 4 6 2 5 6 6 i The moxiulafcion can be indicated in the same manner as in the first exercises, actt>idiag to which the letters indicate the key and the Koman numbevh, Jwb >i>»\i know, the degrees upon which the chords in quea- iioc rest \.\ ..,. MANUAL OF HARMONT, IQg PAET II. ACCIDENTAL CHORD-FORMATIONS.— TONES FOREIGN TO TIIB HARMONY. CHAPTER XII Suspensions, The simultaneous progression of all voices to the following chord, par- ticularly if, as in our previous examples, it takes place through no metrical variety of the movement, produces a certain measured character and monotony of the musical sentences. A new chaining together and binding of the chords, and a thereby more interesting change of harmonic connections arises, if the voices do not everywhere progress simultaneously ; if one or several of them linger in their places, while others already form the component parts of the next harmony. The most important manner of thus linking harmonies together, and the one to be preferred is the SUSPENSION. This arises through the delaying of a progression of a voice, which is ex- pected at a definite time, or even necessary, and in such a manner, that the voice, which has to progress one degree downwards^ in order to occupy its position in the following chord, lingers still upon the tone of the first chord, wliile the others progress to the second, and this voice does not pasa over into tlie harmony until later. In the toUowing connection of harmony : 1<>5. 106 MANUAL OF HARMONY, the Soprano can linger upon the C during the entrance of the second chord, and pass over later to the B in the following manner : 196. Just so a suspension can be formed from Example No. 195, through the delaying of the Tenor : 197. Z^PS_=lE^Ei — r r ^^^^^. 1 That which is characteristic of the suspensions is, that they form a dis- sonance against the harmony with which they appear, and that they thereby act as a means for harmonic connection, since they render the necessary •relations of two chords more intimate through the resolution expected. In this respect they have a similarity with the sevenths, in common with which, as connecting intervals, they require preparation as well as resolution. The dissonant character of the suspension is, to be sure, not always con- tained in the interval of it which disagrees harmonically with any particular voice ; cases can occur, where the suspension disagrees as interval with no one of the other voices, but where the character of the suspension appears only through situation, position [in the chord] and progression ; as in Ex- ample No. 197, where the tone of suspension forms a chord of the sixth, and where only the unusual appearance, as well as the entire situation O4 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 tho suspensions : A suspension can be formed with a descending progression of o voice hy degrees^ under the following conditions ; it must 1. Be prepared, and 2. Resolve itself There will, therefore, be three things to observe in connection with th« suspension : its preparation ihe suspension itself and its positioL, and its resolution (progression). MANUAL OF HARMON 1. 107 a. The Pi-eparoMon, The preparation of a suspension can take place through either compo- nent part of a triad. The sevenths also are used for preparation although more rarely ; most often the dominant seventh. Preparation through the octave of the Fuadamental ; Through the third: -i_r:: ^ 108. 6 - 4 3 I^^fe BS: 7 6 7 6 C: I |^l£|E|E^|^^^|^=|^^| I a:viio» C: I Through the ^fth : .-ij ^^^^^^mm 9: 9 8 5- -G> — 7 6 4 35 C: I G: V " ' '" f I KIVU^Y VI C: I 17 Through the dominant seventh , I I -ZT-«5>-ci— T— ^ --S— 4— (9- 6 - 4 3 :i^E^ii^^ii 9 8 z g— I — g — C: V-r I =251: ;i^=i^i[i r^ a:V The preparation takes place upon the arsis, the suspension itself enters at the thesis. Besides this, the rule mentioned before (page 71) ap- plies, viz., that the preparation may be of a duration equal with or longer than the suspension, but not shorter. b. The Suspension. The entrance of the suspension at the thesis has just been mentIoiif.<^ ; its position in other respects should be still more particularly explalne**.. The suspension can appear in any voice, before an interval of ih. triad, — before the seventh, only in rare cases. 108 MANUAL OF HARMONY. 199. Suspensions before the Octave of the Fundamental: r\ — ,' ] — g^_ — i — I — T-®- (S-'^p^ — -g<— F-g q ~^^ g'"~r~Q — t — ) — c©- ±i: ;f^s=it 9 8 2 C: V- Before the third : I ^mm^m^ m^^s^r^m=^M ip=^ i 9i; 5 — 4 3 t9- C; IV 5 — 4 3 'g 7 6 4 - 3 - 5 — 2 — :ii^ii^i 1 IV Before the^if^ rarely, only in certain positions: I I ^ 6 5 <2- ;iie^; 2 — id?^ 6 5^ ??: — r— © iilP^ 6 ^4 it^it:: IE F:I 0: I Concernmg the suspensions in case of the fifth, reference may be made to that which was remarked in connection with Example No. 197. Thus the first and third examples will be entirely in the character of the suspension, while the fourth is not to be called a suspension at all. If a seventh is added to the chord, as in the second example, the dissonant character jf the suspension immediately shov/s itself. That the seventh can but seldom have a suspension, appears from the fact, that it [the suspension] would necessarily be formed in most cases by the perfect octave, which in and for itself is only an interval of reduplica- tion, and can never come into a dissonant position (a), except as in the foL lowing Example b^ where the octave is diminished. -I— r ftOO. [==^^^1^-=^ --1— --1— r ^ sn « 8 -Tb 8Q 7b ii^^ E^P^ i^lP^ll^^ MANUAL OF HARMONY. 109 In tlie first case tlie seventh will always be a passing one. C. The Resolution. The resolution of the suspension ensues, as was remarked lefore, in the same voice, hy a step downwards. Remark. — ^Ways of resolution which deviate from tliis will be shown later. Here it is further to be observed that The tone of resolution (the tone which is delayed by a suspension) can he contained in no other voice ; only the Bass or the lowest voice can receive it ivithout disadvantage to the harmony. a. not: b. better: c. not: d. NB. 201. In Example a the Tenor steps from A to C, which last, in the Soprano^ is suspended by D; in Example c the Tenor receives the Gr, which, in the Alto, has the suspension A. Both reduplications are faulty, especially be- cause they concern the third and fifth of the chord. In Example (Z at NB., the reduplication takes place with the fundamental. In this caso the effect is better, especially if the consistency of the leading of the voices necessitates it as in the following movement : Fundamental : Third: 202. Fifth: =F-i II X m -&- i Remark. — It may still be remarked here, that the doubling of the fundamental ahrays assumes the distance of at least an octave, and that the doubling in unison ia faulty, *. g.t The stwpension can indeed appear in such proximity, only between Bass and Tencr, or with the voice which lies next to the lowest. The lowest voice, commonly the Bass, has, however, as the one which determines the chord, the power of counterweight against the dissonance 110 MANUAL OF HARMONY, of the suspension ; reduplications are therefore admissible, if they art based upon a good leading of the voices, e. g, faulty : 203. The faulty progression of the Soprano and Bass in the last example be- comes clear, if the suspension as mere delay of the progression of the voice, is taken away, through which means the open octaves appear : 204. iii^l §i^ i The relation is the same with the fifth-successions, which are covered through the suspension : 205. pi^'^ i==II Here, however, the considerations will rule, which are to be had in view in the case of the covered fifths in general, since position, situation, pro- gression can permit such leading of the voices, without the unpleasantness of the fifths appearing. We condense these remarks into the following rule : The suspension does not remove parallel octaves and fifths ; the follow ing progression will, therefore, be faulty : -A— 206. =£\e^\^M\ Parallel fifths of this kind are not, however, to be unconditionally rejected if through the movement of the other voices a compensation is made for the unpleasant succession, so that they do not appear too plainly. To giv^ positive directions regarding them is impossible; to reject them always would confine us too much. MANVAL OF EARMONT. Ill tX,, suspensions in the Bass, ^hich occur f -««V^/7, '''^/^."^t^d the chord (or, ^hich is the same thing, before the chords of the sixth and ,f the sixth and fifth), allow of no reduplication ^» the other voices. not : 207. 5 - 2 - 5 — 4 - 2 - 5 4 - 2 - 1^1^^; ^^-^j^Ml The suspensions before the fundamental and the fifth rarely show them- selves practicable. t — «i-i— « -■ not: 208. The indication of the suspensions in the Thorough-Bass notation is, in nart, 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., 4 3, 9 g, T6, the remaining figures determine the chord where it becomes necessary. e g the chord of the sixth g £, the chord of the sixth and fourth g 4 or f 6 I*f the suspension lies in the lower voice, the chance intervals of the remaining voices are likewise indicated by numbers, e. g., 2_, or in case of the chord of the seventh |=; 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 diagona stroke above it, »nd the corresponding chord set over the tone of resolution, which I3 plainer as concerns the latter, e. g. 209. i In the succeeding examples the first manner is chosen, as the most common. 112 MANUAL OF HARMONY. Exercises, 6- 4 3 7 6 210 §!; •il^^: 7 6 5 7 5- 4 3 :at—'. _-<2; 2. 3 6 9 8 C: I IV iigzfzig^ 6 7 4 « 6 - 4 - 2 - 9 8 il £Ef^ 3=33: 5- 4 3» s^i 3 6 - 2 - 7 6 6 7 6 sPIesJIe^I ^ 6-7- 6 31; 6 J( 5 4 4 3 1 §L%^; 6 - 4 - 2 - f^ tp: IE 9 8. 2 6 :a— s-- 6 2 _5 6 ii=l=£^^fe^=^pi: 7 6J] 4 - 7 7 6 9 8 3 - 6 5b t 5 -t© Etef* 6- 6 4 3 5 7j8r 4- 6 3-4 6 6 5 9 8 7 5 6^ _44 — (i-fi.. h^=^ 7 6 6 EE^E^: 1 6 5 — 4 4 3# 8 6 4 3 2 6 5 — 25- ::l=l 5«- ^ 3 - 3b 6 2 — 6 4 3- ;iiii^liEi?^l^l 9 8 7 ^s^^pip^iBimi^^ 5-6 4 3 4 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, and is iu general a useful preparatory exercise in score reading. Here, however, it becomes necessary to write the voices, which, in the 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 of which is indispensable to every musician. The knowledge of these clefa can be very soon attained by attentive practice, and through comparison with those already known. Kemark. — The knowledge of the Alto and Tenor clefs is requisite Cur the understand tog and reading of soores. since manv voices and instruments are exclusively or partialiy written in these clefs, and the Soprano clef itself, which occurs more rarely, afForos with various instruments, which are tuned in a particular way, an esv^ecial facility in reading. The clef which is used for the upper three voices. Soprano, Alt.o, 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 is found upon the lowest^ for the Alto upon the third, and for the Tenor upon the fourth line, e. g, ■ . Soprano-clefs. Alto-clefs. Tenor-clefs. it3="=Wf=- The most common compass of the voices exhibits itself in these clefa . ■ ^"?i"-fT7"^'^^M"lT^ Soprano-clef — ^-j-;— ^"f —[—(-— ^ 1 ' ' l_ I _ I I I I M _^_i-_#- ^ . I I I I I I 11 ~'"rrrr"i~iTx^ I I I I I ■ .#. ^ 4- 4- -^ -m—w—\ — \ — I — \ gr^E=^ E^E^;EEE^;EEgEE -^■=t 114 MANUAL OF HARMONY. RE>iA iK, — ^The orig'a of these various clefs from the mostsimplo foundation, from th« so-called Tablature (eommouly a system of ten lines, upon -which all the voices were written, with especial designation of the lines upon which the principal tones, F, C, O, came to stand) is interesting, its farther explanation would here, however, lead us too fa;-. The easiest method of impressing these clefs upon the memory, is probably, to observe accurately the position of the triad in the various voicefa, whereby the tones which lie between and on each side are easily found out. Thus the position of the complete C-triad, with doubling of the funda- mental, will be : In the Soprano : WZC — €-r.G \w=i~-^o In the Alto : n-E^ C In the Tenor, best in tlie position ij]"?- — #-c of the chord of the sixth and fourth : y #~ g i^= m. The carrying out of the first exercise of No. 210 in these clefs follows here : 211. _ Bops AND, Alto. rsKOB. Bass. ±z=:t: i m t==^-^^ 5 - 4 3 fn^mri" 6 5 6 5 — 4 -©- C: G, ^7 "7 7 II The worl 1/ Suspensions from Below Upward* Suspensions from below are only in a few isolated cases to be regarded 86 such ; most progressions of this kind arise out of the suspensions from above, before treated of, through contraction (abbreviation) of the sam«^ with a farther succession in a upward direction, e. g. from . 213. The suspension from below can take place in connection with the pro gression of the leading tone : 214. J sm^t —G> o _.'^!2— ] L i— II I also with several intervals, which progress a half-step upwards, especially with those altered chords, which receive augmented intervals through elevation, e. g. 315. -5-« 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 itseif before (page 64) as chord of the seventh of the first degree in nuDor, and which was explained as unfit for use as fundamental harmony. (See pago 74). That, in the above application, it is to be couBidered as suspension of the leading iooe, requires no farther explanation. MANUAL OF HARMONY. 117 Of other suspensions, especially those which progress a whole step upwards: U some show, of themselves, the unnaturalness of their progression ; and some the theory must pronounce not genuine, and unfit for use for the pure harmonic structure, however often they may find place in the practice. IfHhese false suspensions should be carried out after the manner pre- viously shown (No. 213), faulty progressions would show themselves, upon which they are based : 'a I J — I — I , -&^>g;#-^- — f-^-T ii?l^^i^^^-H[|l Here would also belong that unison passage from the overture to Leonore " (No. 3) of Beethoven : :M^-=l.^-l^- I u! cresc. . [1^ V tK ± h t te t ti_ ■F=5F i!*- ifl^f^g^^igglf; "fife £ £^£ ^-*„ , '^ MANUAL OF HARMONY 123 CHAPTER XIII. TJie Organ Point, Stationary Voices, An especial manifold character of the harmonies, and a mingling of them, arises by means of one or even more than one of the voices remaining stationary upon one tone, and by means of the chords thereby accidentally formed. We frequently meet (particularly in the Bass) as well at the beginning of a composition, as in the middle and at the conclusion, at the point where the cadence should begin, with a long sustained tone, during the continuance of which the remaining voices, apparently without reference to it, continue their harmonic movement. If this tone lies in the Bass, it is called ORGAN-POINT [Pedal Point] ; f such prolonged tones occur in the other voices, the lattei are called STATIONARY VOICES oa STATIONARY TONES. Remark. — Many give these last also the name Organ-Point, but incorrectly. The tones, which are adapted for remaining stationary are the tonic and dominant ; they also occur together. Remark. — Attempts with the third of the triad, which in later times have been instituted by many composers, betray too plainly to the ear the unnatural and far sought. The harmonic connection, as well as the progression of the remaining voices takes place, always, during the organ-point, according to the known rules, so that the next lower voice assumes the conduct of the harmony, and in general without regard to the stationary tone. Before we enter more particularly into the manner of treating the organ- point, some examples may follow. S3' Organpoint upon the tonic: ^1 I J. I I * . * .§:Ee 124 MANUAL OF HARM. NY. Upon the dominant: ! I U -A— A -1—1- -ij — ^—r-0 ^- -M—r — ' n 1 iiEE -*: iii^ff= -0- 'rffj-^ US: ^:^I^-S1 Upon both at the same time; II I I r I I ^lEEETEgiE^zzziEz i^i 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 Hme ; 2. By means of a chord to ivhich the Bass tone harmonically belongs ; 3. The last chord of the organ-point must likewise he in harmony with 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 commonly by mean? of the fundamental of a triad, as in Example No. 234 a, Cj d^ or at &, 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 order to avoid digressions violating the character of the organ-point which is only to be found in the holding firmly together of various ohord-combi nations. MANUAL OF HARMONY. 125 I Thus the following organ-point would be faulty in this regard : 235. ^mw^m^mmm isr: 1_« 1. m^ 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 the remaining voices, and not by the circumstance that it is seventh to the Bass. If the organ-point stands upon the dominant, as is often the case at the close, no plagal close can be formed upon it, as appears already from the third of the above adduced rules, e. g. I I . 336. :==d^j^; I I V NB. »;e The plagal close can, however, ensue with the organ-point of the tonic 837. ^IdEEL^E^ I 1^ n I r I I J. ^ ^ ^ * ». ^ \-^~ — -- g" I I The end of the organ-point is indeed to be just as carefully treated ai^ its entrance. In the examples brought forward above, this always takes place through a cadence. In this case it presents no difl&culty, 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 carifully •bserved, e. g. 126 23S. MANUAL OF HARMONY, ._-4_._J_^- I I I ' I I I &C. 9;Ee=-:5^:^|: Breaking off in the following manner would not, however, be good : 239. &c. S;be; :j=ii:ippiiiiiei iSf « tionit ry Voi ces. Upper or middle voices remaining stationary upon one tone, in the man- ner 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 thein 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 : 240. e r \ I ' i I ^ I ' ' '11 Q:^^i^E^S-i-i-f-.—.-*-Y-i~s- ?L=^t=EEElE^EEtEtEkEE': r while the following tone, prolonged as dominant, is better because the last chords of the example belong to it : 241, T-ifl: 1 ,_..._:r-^xJ_.-J-J,J- m^^^^^^^mmm^ ^-=x- MANUAL OF HARMONY. Ii7 As example of effective use of stationary voices and prolonged tones und for their treatment, a place can be adduced in the " Gloria " of Che- rubini's Mass in C-major, where the violins hold Ky for a length of time, while the choir and instruments taking 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 gllickliche Fahrt " of Mendelssohn Bartholdy. In both cases but few chords can be found, 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 upper 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. 242. NB. I ! I ' I I ^-feE^EEl^L-^l^pZ.-^^ Remark. — As completion of what was said of the chorda of the ninth, the following may here still find place : In the foregoing Example h, if the stationary voice be included [in the reckoning], a 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- tances, as above, furnishes no ground for regarding them as independent chords, since they occur only in the relations there found, viz., in connection with a stationary tone, the character of which is, however, also to bear harmonies foreign to it, as, for example^ ia the case with the following ninth, which certainly forms no chf rd of the ninth. 243. 12R MAN" UAL OF HARMON 1 If we wish to mark by numbers the harmonic progression abova ths organ-point, they must always have reference to the stationary tone in the Bass, whereby in many cases the otherwise general marking of the ch( rds is altered. Thus the organ-point found under No. 234 h, could be marked thus ; 6-76 4 - 5 3b 844. 9L— ?=iz 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. V 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 betwee,n, of greater or smaller harmonic voice-steps, e. g. 345. m^^^^m^^w^m ,_^_,^ — M-i^ ^;g^^fe|! gigggEij^gg^ ^ag^ tf The notes marked by a cross x form the passj 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. HAN UAL OF HARMONY. 1^9 ^%^. The passing notes found under a of Example No. 245 are called diet- tonic^ those under h chromatic passes. The passing notes go from, one harmonic note over to another har- monic note ; they appear, therefore, not with the entrance of the chord, but after it, upon smaller divisions of the measure, and can be introduced only in progression hy degrees. Changing noteSj on the contrary, are those tones foreign to the har- mony, which either appear in the character of a suspension or appog- giatura at the time of the entrance of the harmony (thus in this sense upon the accented part of the measure), and attach themselves to the harmonic note (No. 247 a), or, after the manner of the passing notes upon the unac- cented part, serve for the melodic adornment of two like notes. (No. 247 b). a. ¥: ¥^ ^-^ 247. I J I mmi ^ ^^ ■-^- rn^^ ITXl-j J J I 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 chan^^Ing Dotes can be formed by the note which lies immediately below thf> 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 -^ * " d-^r^ -I— T — -- — ^-*ri—r-rr 248. £— zi=zf-^ji gi=| ==^^ji gz:^g I This applies particularly to the changing notes introduced by skipa It is otherwise if they appear in a progressing series, whereby they take on the character of the passing notes. Thus the following series of chang- ing notes at d would not, of necessity, be so formed as at h» a. ^ 249. --f- ^ I 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 h^ while c is not so good as fZ. 6. .. c. I ^ I <«. I ^ 1 250. ■»• i=iiiiiii!?iii: f i 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. Rem irk. — The third of the triad bears the changing note as whole step better than lU' fifth and octave. Since -with the latter the changing note can appear at the same fsiive AS seventh, so that the succession only can determine in respect to it. Ohvi.iging notes above the harmonic note, whether they enter free (by «&if>g), or in the manner of No. 250, can form major or minor seconds to •tiae <3hord-tone because they are always formed diatonically, and govern tbemselvcs according to the key and modulation. 251. • -^ — f — - • w-^^ - F-i^- I I I t 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. W=%.=. =-ja?zzz:==:h§zz===f!:=iz=i~s-?===--=^--—U MANUAL OF HARMONJ n\ Upon this 13 founded also the following often occurritg manner of em- bellishment : s^ 253. ^^^^i5^:^d: 0- ^ J0- -^ I I I i Passing and changing notes can occur in all voices. If this takes place, by preference, in one voice alone, this one will become prominent in com- parison with the others, and receive a concerting character, while the remaining voices serve for accompaniment. If this should not be the case, all the voices can be made prominent, interchangeably, by such by- tones, and gain thereby in significance. Wherever the position and progression of a voice adapts it for the introduction of such by-tones, it will by this means admit of more significant melodic development ; but here also the proper mean must be found, since, otherwise, over fullness and a lack of clearness can easily arise. Tho following simply harmonic movement, 254. I ^ r I p^ ^^ fEm^E^m^ ■^-^J-.,^=J-M^ ^: —&- might, by the use of the above by- tones, assume the following form 255. m=*. ■i^K:d--j=:d--1=i=^q:--:^ : ^ g, ^c m^^mMiM^M^E ;i 1 ) The passing and changing notes are here marked by crosses X- That through such copious use of tones foreign to the harmony, the pas- sage can easily suffer from overloading, is to be seen in the above example if it is executed in a somewhat rapid tempo ; a slow movement is better adapted to this manner of writing. In the introduction of the changing notes, care is to be taken, as wa& before remarked in connection with the suspensions, that no voice receiver the harmonic tone which in another is introduced through a changing note, e. g. 256. w This can only occur if the distance of the harmonic tone from the tone oreign to the harmony is at least one octave, e. g. 257. This reduplication, according to the principles of reduplication in gen- eral, will take place better with the fundamental or fifth, than with the third of the fundamental chord. In a rapid movement, however, and more extended carrying out of such figures formed through changing notes, other considerations arise, as the following passage shows ; this to be sure, cannot be conceived of as a four- voiced vocal movement : SI5§. Iflit "S^ r In the case of the regular passing notes, like regard is to be had to theii approximation to harmonic tones, and figures such as No. 259 a, &, de not appear so pure as c^ df €• MANUAL OF HARMON T. b. c d. 139 More rapid figures allow this approximation more readily, e. g. 260. :^^ -s- n pee; ^r-# ,,_«. ;[| i=g J/'aulty Progressions in Connection with Passing and Clianging 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 : a. , Si' 261. -iJ~T \ 1_ Open octaves formed with passing tones cannot occur, because the first of them will be harmonic as much as the second. 262. :^~^r-^ On the other hand, in the following instances, the passing notes will not ©over the open octaves, and consequently will be considered as faulty * 263. eteziz==z=z:z zJz^,=n^: -I ,' Bemark. — The last kind of octaves -would find application in instrumental mcvementtg Qoder the conditiou of intended strengthening and reduplication. 134 MANUAL OF HARMONY. In like manner the entrance or progression of the changing note id parallel movement is to be called faulty if it takes place in the following manner • 864 w^^^^^m^^mm^i The last example is better because the octave progression appears covered. Passing and Changing Notes in more than one Voice at the same time. The movement of the passing notes in more than one voice at the same time is best adapted, in parallel motion, to the successions of thirds and ixths, e. g. 265. S ^ ;[ii 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 favoi-able position. Progressions in fourths are good if a third voice is added as third below ; 266. Single fifth-successions arising from passing notes are occasionally mei with in good compositions, which, however, is no reason for recommending MANUAL OF HARMONY, 135 them as faultless. (See that which is said concerning fifth -suv cessions page 27 and what follows). Just so the harshness of the seventh-successions can only be alleriated through favorable position and good leading of the voices throughout ; indeed, through tempo, movement, etc. In contro.ry 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 n^umerously and in too many voices at the same time. fc 267, !fes= 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 (pass^ing) 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. r 36§. -#-€-*-^ — i — h #-« 0-i In all such places everything depends upon the question, whether at the hange of the harmony the voices are in a position which allows them o form their progression regularly. Changing notes can occur in various voices ; a. In tivo voices : 186 MANUAL OF HARMOyr, in pa allel motion : 209. ^-l^J^tzt^^^^ 270. in contrary motion: '^ ' 1 i . J VJ I I fjj ! i, I its:: 1 b. In three voices 2T1. C, In four voices : m-tt i '^.j^i I I f^ Remark. — ^The most of the above examples can also have the force ot harmonic pro gressions with the organ-point. It becomes evident from these examples, that also in the parallel move- ment of two voices in changing notes, the progression in thirds and sixths appeaTs most natural, while the parallel seconds, fourths, fifths and sevenths always produce a very disagreeable effect. Thus no one ATOuld be likely to pronounce changing notes of the following sort, good : 273. ^^^^rii=m ^^ Changing notes can also be of longer duration, than the harmonic not to which they are joined, e, g. I 274. I 1 i I ' I r- MANUAL OF HARMONY. 137 The 9»gnificaiice, in composition, of the subjects explained in Chapters XII. 5 XIII. and XIV., is great enough to subject them to a careful inves- tigation ; as a thorough knowledge of them contributes materially to th understanding of the inner harmonic structure. We have still to speak concerning their relation to the pure harmonic structure — the object of our immediate studies. Since on page 24 the term " pure harmonic structure " was only spoken of in a general way, it becomes necessary to consider the question more narrowly, and to present it something in this manner : What application of these means for composition does our immediate purpose^ (the exercises in the pure harmonic structure)^ allow ? It is undeniable that these means are particularly adapted for develop- ing and adorning the voices. If, however, our most immediate work is the recognition and carrying out of simple harmonic formations^ then, to be sure, everything which is adapted to develop the voices will be appropriately used ; but anything else, serving only for embellishment, will be excluded ; in brief, the essential must be separate from the unessential. As belonging to the unessential will always be reckoned, firstly : All harmonic artificialities (Kiinsteleien) in general^ in so far as they are founded upon no inner necessity ; unnatural introduction of little' used harmonies. They easily produce over-fullness, swollen over-loading of the passage, and bear witness rather to a morbid or mentally weak condi- tion, than to originality and fresh, free, powerfully secure movement ; Then: Irregular introduction of the suspensions ; the use of stationary voices, and of the anticipated and after-struck tones ; Especially, however : The changing notes which are struck free and the figures formed 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 in the use of the harmonies, and for the learning of a good and pure leading of the voices, the elaboration of chorals or simple movements in the manner of chorals is directly suggested as most to the purpose, this also will iiot exclude the use of those means in so far as they serve not merely for embellishment but for the development of the lead* ing of the voices. 138 MANUAL OF HARM. NT. Among these is especially to be reckoned the use of the susponsions and of the regular passing and changing notes. In accordance with the foregoing, the strictness of the pure harmonic struc ture in connection with the first study of harmony, and later contrapuntal labors may now be judged, which forbids many things the practice likes to use in appropriate places, as not to the purpose, immaterial, and as causing deviation from the chief object. The thorough study of good compositions will serve for the complete understanding of all subjects thus far discussed. Chapter XIX. in Part III of this book, in which we return to this subject, will afford opportu- nity for attempts of our own. CHAPTER XV. Passing Chords, Those are called passing chords, which in smaller parts of measures, after the manner of the passing notes in several voices, appear as actual chord-formations, in the entrance and treatment of which, however, a manner is sometimes found deviating from the general rules of chord- connection. Of these, one kind has appeared already in such passing and changing notes in three voices, as take on the chord form, e. g.^ in Nos. 271 and 272. Just so, the most of the chords which are formed over an organ-point can in a certain sense be called passing chords. There are, however, still other phenomena of the kind, which are to be here explained. As, in general, passing and changing notes depend principally upon the relations of measure, it becomes necessary for the explanation of the passing chords to cast a glance at the various division of measure. It is known, that in the simple, even varieties of measure, the natural accent rests upon the first measural-division, while the second receives a less weight. If now the harmonic progression be based simply upon the two measural- divisions, then the harmonies, which come upon the accented division (Thesis) will always appear as the more weighty, and must always be conceived of as the goal to which the chords of the second divison (Arsis) lead : MANUAL OF HARMONY. 139 275. I. ifllilfflllil^ll^il ^ -^—G— i ^-^-^ r^zz- '-m^: In this sense, the chords of the second measural-division can be called passing chords, although in the regular movement this character of theirs does not appear so plainly. That this has been so understood in the theory, even if seldom plainly expressed, is shown by the fact that, at their entrance, more care has ever been bestowed upon the chords upon the thesis ; and in case of those upon the arsis, much has been allowed which was not conceded to the former. The character of the passing chords appears, however, more plainly with such harmonies as are assigned to smaller divisions of the measure, as in the following examples : lil^iipii^^i^liSii «T6. ^ee: -0 — ^- I 7b I 2 7b ms 6 ' 8 4 7 iliiiii; ipplgUi 277. The peculiar manner of appearance of the chord of the sixth and fourth in Example No. 276 a and c, as well as of the chord of the seventh in d is only to be explained through the ensuing progression {in the characief 140 MANUAL OF HARMONY, of the passing notes) of all voices, hy degrees, to tJieii nearest goal — the chord of the thesis in the following measure. These voices can be still more easily recognized in the^^ character as passing, if one voice is allowed to remain stationary, for example, the Bass of No. 277 a^ or the upper voices h, (See above, No. 277). The leading of the voices in No. 276 a^ has arisen from the application of both modes. If this condition (the progression of the voices by degrees) is fulfilled, then all chords can enter free ; they will find explanation in the principal chord which immediately succeeds them. NB NB. 278. i — q ^ :^1^>5 1^ llEMARK. — In this explanation of the passing chords, the free treatment of the seventh, meationed 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 ot less weight. Passing chords will show themselves in the following manner : 279. I I 6 6 4 I 6 7 5h 9 8 7 2 4 J8^ 7 5 6 ^^m^i^smfi^^^sEii --'=f=^- 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 wll either progress according to the known rules of the connection of harmony, or deviate from them. In the first case, whiok is more frequent, no farther remark is necessary ; in the last, it will depend upon a flowing melodic leading of the voices, as well in them* MANUAL OF HARMONY, 141 selves, as also in relation to each other, whether formations of this kind are to be called correct. It can only be remarked in general, that the progression of the voices hy degrees will also here determine the character of the passing chords^ and that all such passages are to be judged after taking into account the rjthm, tempo and character of the composition. CHAPTER XVI. On the Means for Modulation* The term modulation has already been explained in Chapter XI. There the object was to determine each modulation correctly ; now we are to treat of the best means for effecting a modulation. The art of modulation consists in finding out those harmonies which stand in connection with two or more keys, in order, by means of these to pass from one key into the other. Every modulation can be effected in various ways, and will serve various purposes. It can, Firstly : begin abruptly^ be quicMy completed and pass by^ or Secondly : be more gradually prepared jor^ seek out the new hey as a qoal^ and take it for a length of time as basis. In the first case it will avail itself of the simplest means, make its ap- pearance with decision, but soon leave the new key, and perhaps, indeed not allow it to attain to a definite development of itself; in the second case it is commonly prepared and worked out gradually by various means, and endeavoring to impress the new key upon the ear, will probably also lead to a close. Thus, in the following example : 2S0. iize \- 1— ^— r — \—i — I--I-, — J--I — J--I-I rr —p — f-r-^-^ — ."-ti-— r-|— ?-*-.s— " — B t 7 1 I I the modulation will be transient and frequently charging, without forsak- ing materially the principal key, C-maicr. 142 MANUAL OF HARMOj\ r. This kind of modulation is only adapted for the nearest related keys, and although more distant ones can be reached by especial and decided meanSj still in their development very natural and organic combinations mu.«t prevail, if they are not to appear unintelligible. In the next example, however, the more distant key becomes the goal, which is gradually reached ; the original key is entirely forsaken, and the new one takes its place : 2§1. i 'IH , 7b 6 6b 6 C: I Bb: viio-y Bb:I f: V^ Eb: Vy This example shows plainly, how the extended modulation, which sets for itself the new key as goal, makes use of the passing modulation, in crder to reach it, and this the rather, as it was not the object to reach El? major quickly. Unless we wish to use such short passages as i':/terlude 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 fche 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 woik — ^^ Die Grand' zuge der musikalischen Formen und ihre Analysed — (Leipsic, G. Wigand.) We make use at present of the formation of such modulations as exer- cises, in order thereby to promote skill in the use of the harmonies and their appropriate connection. While the means for modulation are being searched out, no immediate attention will be paid to the hind of modulation used, since the same can serve for both the above designated kinds. The first and simplest means will be THE TONIC TRIAD OF THE NEW KEY itself. If, however, this triad is already a component part of the nrst key, then what succeeds only, and particularly the subsequent dominant harmony of the new key, will really determine the intended modulation. Thus, in tha MANUAL OF HARMONY. 143 folio wi'^g example at a^ no modulation will be felt, wliile at& we bear tbe key of G-major plainly only wben we come to the tbird barraony : 2§2. J=:|=±zzi:Ed=:| 6- i mi f#J In case of more distant keys tbe minor triad can, to be sure, as tonic triad, have a more decided effect, still for tbe sake of definiteness tbe dom- inant harmony will succeed it (at a) ,* tbe major triad, however, will incliu'?* to make itself understood as dominant (&). 2S3. Hii^hid^i^l^-l^Eh^k^^ ::zzzq: C: I C: in x: I V7 C: I .r~v 6 C: I 6 k: V ~t — G- 1: i As ansatisfying as tbe tonic triad shows itself to be, for modulation, in tbe way used above, in as great degree has one of its inversions (tbe chord of the sixth and fourth) the quality of rendering such modulation particularly decided. For just as it naturally takes part in the closing cadence (see pages 49 and 53), so it produces at its entrance the feeling of a modulation, if it is not used in tbe manner of the passing chords, but enters at the thesis. However, in this case also, it is naturally followed by the dominant, which first completes the modulation. »S4. '^i^ii^i^ltM- ^m^wM^mr^mimmi^^ I V. C: 144 MANUAL Oil JfARMONT. Upon the arsis it will not indicate the key so definitely 3§5. ^Jiiii=il[ili:^l^{ill 7 6 t 4 All examples given above, however, point to a still more potent means of modulation, viz., THE DOMINANT HARMONY. The triad, as well as the chord of the seventh of the dominant, shows itself as the most natural and best means of digression, since, through it, (which applies especially to the dominant harmony of the seventh) the key is most unmistakably determined : The modulation through the chord of the seventh of the dominant can be effected without intermediate chord in the following manner. According to the principle that that connection of harmony will be most easily comprehended, which is effected through like or stationary tones (preparation), modulations can be effected through the dominant chord of the seventh, from the tonic major triad into all remaining keys, except the keys of the minor and major third, and that of the augmented fourth. From C-major we can reach all keys, except El?, E-and Fj{, (it can remain undetermined for the present whether major or minor) thus : From C to d: F: G — 2S6. — B: C Db: or: C C— !?«_«_« ; Ab: ^^k^^B^mm-m^^ c — ^* V-sr ^5: Everywhere in these examples the like tones, which are connected with eaxjh other by a tie, mediate the transition to the dominant of the next key ; thus, from C major to D minor, the tones G and E, which become fifth and seventh of the dominant harmony, &c. i MANUAL OF HARMONT. 145 Remark. — It only need be mentioned, that these modulation? ouh also be reached through other positions of the chords, e. g. C — d: or: ««' fei%:E£=i^iilSlME I ^=|:-^ If wc wish to modulate in the same manner into the three keys which are wanting above, it can be done by means of an inserted chord (in the pimplest manner, by a triad), which then supplies the missing conneo- . tion e. g. P ''-om to Ety: — E: C — FJ: The modulation from the minor can be formed thus : From AtoB: a — d: a — e: a — F: — G: ^ 3r - Bb: 77 -^—2.- To the remaining keys C, Di?, Ej?, Fj| and Ab, by means of a connecting chord : From A to C: a — D^: A — EJ^: 290. lil^i^JiffB^^ i^'jf: ^i^pfe^^^ " O — ^ '-"ill It is self evident that this manner of modulation is only exhibited as the simplest principle^ and that it is by no means necessary that a modu- lation should always take place in this way ; likewise, that as simple con- nections of harmony can be produced without a stationary tone^ so also can modulations ; as, for example, the following modulations can be accomplishinJ without intermediate chord : 146 MANUAL OF HARMONY. From O to Efe: C — k: a 291. \ jz:c rti-i ii !;zr 77" "*^ for the connection of harmonies and especially of the keys, it will, how* iver, 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 ftll 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- .aiony, will frequently be more adapted for modulation than the latter, jince its entrance is much milder, particularly in those cases in which deverth and fundamental of the dominant harmony would be obliged tv^ rt:'itei tree at the same time. The following examples present the use of this chord : Piom to 1%: C — B: C — d: a — k: Beside this application, this chord shows, by means of its enharmonic liature, a farther, peculiar capability. Thp following chords, entirely like as to sound, but variously written : .03. h^^i^^iM^ \ long to four different keys, viz. : in the first form to F minor, m thi second to D minor, in the third to B minor, in the fourth to Aj? ramor. Through this circumstance a fourfold modulation is possible : C — 1) : C — k: C — Afr: 891, ^**' — ^ ■' '^'' ^ — ^-'-^r^ ~r - I -^ -r-|t=f=it?^^I=' Sinv.0 now all the chords of the diminished seventh can appear in the foUowiiV^* three positions, as the piano-forte shows most plainly, MANUAL OF HARMON T.' 147 295. tnd cacli of them, through enharmonic interchange, will belong to four keys, modulations present themselves for all twelve keys in minor, to which in many cases we can add the twelve in major, since this chord can often be used instead of the dominant harmony in major. Here also the industrious writing down of this manner of modulation will tend greatly to advancement in the comprehension of the inner connection of all keys, as well as of the multiplicity of harmonic con- nection. Although this manner of modulation shows itself to be adapted to mani- fold uses in actual composition, still it must be remarked that it should not be used too often, since, being applied lightly, its artistic worth becomes less. ,, A similar application, though not in so comprehensive a manner,^ is exhibited by THE AUGMENTED CHORD OF THE SIXTH AND FIFTH. Its similarity as regards sound, to the dominant chord of the seventh' 296. g=|=-ir==lE with enharmonic change, adapts it, in connection with the latter, for mod* nlation into certain keys, e. g. F->m C to b: E|j -- d: 2»7. ;t— g . I C: V^ B. iio.y I V 1 EijrV-j. »: iio.^ 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 (he following manner : From, one key into the other hy rneans of the triads of various degrem. From C to D through the triad of the third degree : / r_ «_ _J[ T L_ From C to 1) through the triad m MANUAL OF HARMONY, Of ill* fourth degree. 8»9. Of the fifth degree,. Oflht sixth degre^e Z7 Of Vie seventh degree %. From C major to E through the triad Of the second degree : ^0 300. Of the fo urtJixtfgree : Of the fifth degree: Of the sixth degree : -V* — ^ . Of the seventhdegree ; ^0 -y i These indications may suffice for learning to form other modulations according to the same principles. Extension of Modulation ami its Completion through the Cadence, "The process shown above, for passing from one key into the other, W^' based upon the simplest and most natural means. If. we wish to carry out more at length a digression into a new key, the aboye means must, to be sure, serve to this end, they are not however applied 80 suddenly and directly, but the before mentioned passing modulation ia used, and the new key introduced only gradually. The use of the cadence- formulae will, however, establish the ultimate key in the best manner. To this end we can form for ourselves the following kind of problems, e. g. Let a modulation be made from C major through d minor, a minor, and G major to e minor. ■This problem would be solved something in this manner : 301. Kei^i^i^ililtlilprel^liilf C: I d: viiOi. O.V- «:V, MANUAL OF HARMONY m! In connection with the addition of the cadence, the foil 3wing is to be Observed : If the modulation takes place through the chord of the sixth and fourth of the tonic triad of the new key (see page 143), then the succession- of the dominant chord with its natural progression will be sufficient f«>T effecting the cadence, e. g, 302. *--i:=:|=^=:?|z:|iig==z[^ In other cases the extended cadence^ or the known closing formulae witt be requisite (see page 40) in order to determine the final key. As thd simplest of such closing formulae the following are commonly used : In other positions : 30;t. Q i 1-, 1- -a— 1 ^i mmm In other positiont : 6 5 11 :t=ZT-i\: :j=^-t=i5? ppn I -F— -c=f -t. ^m^^mmi If these 3adence- formulae 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 E|7, No. 288, closes with the fifth in the Bpprano. To this is added the cadence in the position which smswerspte this last chord, e. g. 150 From C to Eh : i- MANUAL OF HARMONY, Cadence : -A- 804. =?~i:z=±:^_zi£S-|:Piz::i?|-J_^^ - ^r ^- ^^ b 6b 5b 6 4b 7b 91=2 =b. The following modulation from C to a in No* 286, would require s cadence in this position : From C to A : Cadence : z g — ^^_i_. G C G i^^m :c_: :i=iiif The addition of the middle voices will now present no dijficulties; c G c » o c 313. 80PBAN0. Alto. Tknoh. Bass. im^m r— ©—- r— s>— T— ^ nniiiiriiEiiiiiKi SiieEiii^iiiiii Let this working out of the exercise serve, for the present, for the expU nation of the exercises themselves. The next exercises will give opportunity for becoming acquainted with the principles of a good leading of the Bass, as well as of melodic voices in general so far as the simplest harmonic progression requires. Examples worked out in a faulty manner can best serve this end. Exercise with indication of the fundamentals : ■ ^3 T T — « T ^5 T ® 311. pll=lilliiitlilliiii[l RniARK. — In the treatment of this and the following examples we use the violin elef for the sake of saving room, and write the voices together on two staves ; for the personal work of the pupil, however, we recommend, most earnestly, the manner of no tation used in No. 313. The working out of this exercise may be as follows : MANUAL OF HARMONY, 158 315. i^^lliElEilEfeg^ks^l^llI ^m~: 6 mm i\ There appears nowhere in this example a transgression of any rule ol progression and chord-connection thus far known, and still, on account ol 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 ths 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 formationsy 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^ (/ominantj or sub-dominant triad, under the following conditions : a. If the fourth is prepared ; b. If the Bass progresses by degrees to the following new chordy or remains stationary The following examples show the application : 816. 154 MANUAL OF HARMONY. '-I — G G- 1— :f-:f izS|z!^l[^==^: ^mm^mmmwmm F=*-*- In the Examples at a, it appears most naturally, because it rests upon tonic, dominant and sub-dominant, while upon other degrees {h) it easily produces the feeling of a modulation. Used upon the arsis (beside appearing under the above conditions), it can also appear with preparation of the Bass. 317. '83 :=r-1- 1 -T=— r=:i— ; } — (g — (g- G 4 l=Ei^fei[iililiiil^ m G — o Tr G G 4 m. (9— w The chord of the sixth and fourth shows itself in all these examples, either as passing chord (upon the arsis), or, as above, in the character of the suspension upon the thesis ; with preparation of the Bass upon the thesis, it appears much weaker. r==i:3=feEE3EEiE:Tg=|EFS=FE 31 S. -G-X-G- I ^ G 4 4 3 lUiii EEEE -Si: i Not unfrequently it will appear as itself a suspension, whereby the preparation of the fourth is perfectly justified. 319. ^l^^ W:^ E^^J^-^-^^^E=^\^^^ 6 4 3 6 G 4 5 MANUAL OF HARMONY, 156 In tbe second case still more decidedly, because it arises with a rarelj DCcurriKg chord (that of the third degree). That the chord of the sixth and fourth, however, caii also enter free in connection with a leading, by degrees, of the voices of smaller measural* divisions, in passing, as : d: 320. mmmm 6 4 — mmwm^^m E^t^EE}=i^ will require no farther explanation after what was said in Chapter XV., of the passing chords, and after the examples, Nos. 276, 279. Remark. — Tbe often necessary preparation of the perfect fourth in the chord of ine •izth and fourth, has led many theorists to reckon it among the dissonances. In the introduction to this system of harmony, in the division of the intervals (page 16), it is introduced among the consonances ; and also (page 20) the reason of this view is given. The doubtful relation of the perfect fourth, and tbe necessity of its preparation occurs only over against the Bass, or the lowest voice, and, in fact, in the chor'^ of the sixth and fourth only, since in the chord of the sixth, fourth and third, itself, th»^ 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»ra.?t^r every- where, whether they appear above, below, or in the middle. The chord of the sixth and fourth of the diminished triad will seldom be appropriate for use four-voiced, because it appears too incompleto. 321. On the other hand, it will occur in three-voiced composition, when? it often takes the place of the chord of the second. (See later, the thr<^e- voiued movement). Besides the condition of a good harmonic progression, viz., that the Bt « itself should form a good and intelligible foundation for it, the sccoi I requirement is, THAT THE PROGRESSION SHOULD ALSO BE MELODIC. 156 MANUAL OF HARMONY, Among the unmelodic progressions have always beei nghtly rtckoned certain skips. The succession of two fourths and fifths in the same direction, e. g. These skips are improved thus 323. glLZz::=Jr '—^ — I G- i=i=i3=L5=E=: iiilt Even 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 : hetter : better : 1 li^^^i^iPE^ Augmented interval-steps and skips are to he avoided as unmelodic; diminishe(\ are, however, good. not: better: not: better: 325. l^li^^li^rE^^i^lipi better: better: iiiii^[i^g=ii ii§^r==| 11 '¥ II Deviations from this rule are often found ; they find their explanation in A formation of melody, or in the especial character of the composition as a whole. The observance of the rule in theoretical labors will always be very improving. The skip into the major seventh is to he entirely avoided; that into the minor seventh can he used, hut only in case of an inversion of the same chord. not: 826. ^ not: C- ,-!?«- :a~ I The last, perhaps, with the following progression of harmony : not very good : not : not : 897. s; bl_ ' m^m^m^mii MANUAL OF HARMONY. w\ These few observations contain the principal features of a good melodic leading of the voices, and especially for the next (simply harmonic) exercises, prove themselves sufficient. It should still be remarked, that these rules apply, not alone for the leading of the Bass, but in general for all voices. The exercise given under No. 814 can, with an improved progression of the Bass, be worked out something in this manner : i^£Elri=liiEl=iiif=iEl^i:-=f 328. &5£^liE^i=lE^I: 5-^ 8 7 mi Exercises, 32S5. P m -ffl_..: :: ^_©-_^G i -S"— T m ^lE^I !?-= C G o- c — ^Mlli ?=:Ti^TT??:zTi^-Tr^ F D7 4. xSJSr- w--- mm^i c — -«— T-©— T-O— T^ "7 G^ G J>^ r=llliill 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 D^ O 7 "7 329. e: l^i; w The following faulty work may serve for illustration 830. (feiE^lEiElElElEiE^lil^^^^^ pE^jE^I TV •S^ --[ ■[ r " 6 6 6 7 158 MANUAL OF HARMON r. The faults of this treatment of the exercise consist, firstly, in tlie doubling of the third of the Fecond chord through the Bass, which, with- out occasion, gives to this and the following harmony an awkward position; secondly, in the indicated covered fifth (from the fourth to the fifth measure), and lastly, in the introduction of the seventh by a skip, in the next to the last measure. As concerns the last, this can take place with the dominant seventh only — the fundamental being already present (prepared). (See page 70). 3:11, More tolerable and less har:^h is the free entrance of the seventh, and of the fundamental in contrary motion ; 332. in parallel motion. \\QVfQ\eY, 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. fo — -^ : jiiiSi.^=ii 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. iw^m^^m ^^f^^m MANUAL OF HARMONY. 159 These fifths and octaves becorae open, if the skip which one or "both I voices make, be filled out by the tones which lie between, as is indicated above by the points. Since in every four-voiced movement certain covered fifths and octaves can occur, withcut which the choice of chords, as well as the leading of the voices, would be very much limited, and also, since others are to be avoided, it becomes necessary to take a somewhat nearer view of the manner of their appearance. An attempt to give positive rules for their use, which would be sufficient for all cases, has not yet been success- ful, and would probably with great difiiculty succeed ; there are, therefore, only general observations to be made, which, however, will furnish a stan- dard of criticism for especial cases. Covered fifths and octaves between two voices can occur : 1. If one voice moves hy a step and the other skips ; ^ 2. If both voices skip. i In the first case : a* By a step in the upper ^ and a skip in the lower voice; !>• By a skip in the tipper^ and a step in the lower voice. In regard to both cases as concerns the kind of voices ; a* Between the outer voices^ l>. Between the middle voices, and C. Between a): outer and a middle voice. Covered Fifths and Octaves in the Oitter Voices,* A. They are to be allowed, if the upper voice progresses hy a step, a. Fifths ' b, c, Octdvex : d. e. / 335. \\ - ^ ^ ^ Here it is well, if one voice be at the same time led in the contrary movement or remain stationary, as in Example No. 335 a^ by C, It is not so well, if all voices go in parallel motion [d). Remark. — Although the above rule will sufiiee iu so many cases, still it cannot always 4pply, as the al)ove Example, No. 335 d, shows, which is not to be reckoned among those which exhibit a first rate leading of the voices, since the progression from the chord of the sixtl), c, is a very forced one. We must remember also, what has been said before concerning the cadencing pro- gression of the Bass, pages 35 and 36, viz., that covered octaves which pass over the Uading tone, or iu general, over the half-step, are always more tolerable than thoa« which pass over the whole-stop. 160 MA NUAL OF IIARMOVr. In the exercises exhibited above, the octave always shows itself as fundamental of the chord ; cases in which it forms the third of the chord are much more questionable, and therefore to be used more cautiously. not: 336 not: i=y Even as fifth of the chord it is not to be called good, 337. ^^§£^'^i^[f Remark. — Witli the covered fifth, the lower voice will always be the fundamenud o the chord. Covered fifths in the outer voices are to he rejected if the upper voic€ skips. a, b. e, d. e. (t3§. w V^-^ ^- .?— . i^!fiieie^iii^E^i^^=[^ Wherever a seventh makes the connection of the harmony firmer, as at h, (l, €f the progression of fifths appears more covered and less harsh. Covered octaves in the ovier voices are not to he unconditionally rejected if the upper voice skips. 339. b. not: d. not . e. ill^-^-Pirir=filio^iiil Here also those cases in which tlie Bass progresses a half-step (a) show themselves to be most tolerable. What was said in connection with Nos 83G and 337 applies for d and e* Covered fifths and octaves in the outer voices are to he rejected if both voices skip. MANUAL OF HARMONY. ICl S40. Siiii^^^JlSilieiiB If, however, ihey only form inversions of the same chords they are not to be considered as faults, since in that case they are not progressing fifths and octaves at all. 341. Piesiil iii^ll^illi^lf^ I Covered Fifths and Octaves in the 3Iiddle Voices, Although the leading of the middle voices must be just as pure u that of the outer, still their situation, which is much covered by the latter, allows them occasionally a greater freedom ; this particularly applies to the covered fifths. Covered octaves are, here, if only for the sake of the good relation of the voices, not to be called good ; with respect to the covered fifths, aside from the above observations, all will immediately depend upon an otherwise good connection of harmony. A few cases may have place here : not: iiPiilJfJll^ilJiS:: - not : ^ G^ mt^miimm^^: Covered Fifths and Octaves between the Outer and Middle Voices, The considerations which are to be taken into account in connection with these progrc^isions of the voices, are to be sought in a good and natural 162 MANUAL OF HARMONY, connoction of Larmony, rather than established through merely mechani oal rules. Here are some examples : W^^l^W^^^^I^M^zl 343. 7— "^T-g— .— ^^— yl^^=^ T-f^ -(2 . j^i^jMiH^i^liiiiiE not good: not: ^l^^E!EL^]i&i=tL^= g=3=«f ^^f^ ^ ^^^^ ^mw^Mm 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. 3f4. ^^B^^^t^^^^^^^^ -b -|2^5^ '^^mmmk^^^mmmi'^mm (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, l)etween Tenor and Bass, however, they are to be regarded as covered octaves — according to the postion of the chord and of the voices themselves. The cases, in which covered fifths and octaves can appear, are so man- ifold, that it would be superfluous, if it were, in fact, possible, to adduce them all. The above observations may suffice, if we add the following maxim, which, to be sure, is not written for those beginners who still have to do with the technical, or the properly mechanically-harmonic structure, without regarding the higher requirements of art : Avoid, indeed, covered fifths and octaves as much as possible ; consider them, however, as safe if on the one hand, an otherwise natural, good con* nection of harmony takes place, or on the other, considerations of a higher Kort prevail ; such as melodic voice-movement, application of definite motives, etc. k MANUAL OF HARMONY, 16S After this digression, we return to No. 330, in order to correct the before. mentioned fault. A correction of the covered tifth found there, which belongs in that category where both voices skip, will be hardly possible in this case, because, even if the Bass-progression proceed in the contrary movement, the evil presents itself again in another place, e. g. 345. S:=iE;s 1 Thus it only remains to alter, in this case, the harmony itself, and seled another marking of the fundameatal tones. The following alteration can take place : S46. or: 347. bO 1,7 :$; 1; 3^=i ■'=^*ii 6 6 5 8 7 -^- s 9Je^e; -&- EE ^ bO •i- ^r F ^^ 8 7 1(2 = :t== ^i 347 A. P \ t i_. Exercises, :^=^: P Bb F «o P 2. pe^ 5^ «7 C7 P :a=:T ^ 104 MANiAL OF HARMONY. rffi-=iimiiiii: i=i^i^i[ |3- :^e: mmwm . C- J t--^: -« -G— ■ .1 C7 F G, C7 ...<2 — ^ -G -G 11 The following exercise : o c G D7 G c G --G- we will work out in this manner : 4. 5. 349. i|il3=li^pLiP|iSi^1^E §ib; 6 6 4 5 8 7 IQIII ipB The faults of this work are indicated by figures. The movement of all the upper three voices, by skips in parallel motion, at No. 1, is not good, since it offends against the first principles of all har- monic connection and is by no means necessary. A leading of one or two voices^ by skips, can take place only if through a third voice (by a tone remaining stationary or by a contrary motion), ^Ae harmonic connection is preserved. No. 2 also contains the same fault, which here becomes still harsher because seventh and fundamental enter free and come thereby into an awkward position, so that one is crowded by the other. It has already been mentioned (pages 72 and 158), that the free entrance of the seventh can take only place without harshness, if the fundamental IS already present, and can remain stationary in the same voice. Thus, none of the following examples exhibit a superior leading of the roices. 850. X G—r-6> SLlSS^I^^E^SSli MANUAL OF HARMONY. 165 H| Probably few of these and similar instances would be excusable for more important melodic reasons. The following examples may still serve as completion of the free intro- duction of the fundamental and the seventh in contrary motion, mentioned on page 158. 351 smw^mm^m^i wmmiM^iMm=Mmm The instance No. 2, of Example No. 349, contains besides this, another fault, contrary to the rule laid down above (page 153), in connection with the chord of the sixth and fourth, viz., that the Bass should not skip from the chord of the sixth and fourt^i. The third fault of Example No. 349 consists in the covered fifth, which is the more prominent in connection with the skip of the Soprano in the same direction, as well as in the general scattered leading of the voices. The covered fifth in No. 4 is to be condemned, on the ground that it was 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. 852. =g=--6>— - y^^feni^ * £. ^^ — — — -rr" „ 8 7 JEocercises, P^ GO 2 -fl-__._<5,- 352. 6. -^^E^i=ii|z=|^=|=|z=|=|=| G r — G — D — The next exercise^ DOG D-T ~0 853. ^zE^e: rr? B7 (5> — - r"c: ..C 5, with the following treatment : I: 354. xJSL ;:=sr- 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 tone immediately follows the same tone in another voice, hhromatically raised or dep7'essedy as here upon the G of the Alto the Gjf 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 progressioD, 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 o<;cur in a per- fectly natural manner, without examining the reason why they do not sound faulty. Some of them will be here adduced : I I 855. s/--®- IZ^l—Z^ZfL dzzJ^Dzdz. .-I-J- ■i-y: t-f fc ^^ IT £L MANUAL OF HARMONY. 167 I I ^- I u I ! u I ' I < |s=g¥ ^P^g^^^=piPfg^PP •/». i='t^i§EEp[E^=E^^[^=E^===^= 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 ci^ b^ f/^ or through contraction (drawing together) of natural, but for the metrical construction, too cir- cumstantial harmonic connections, at c, cZ, e, /*, It, The first needs no proof, and there is only the observation to be added, that this kind of cross-relations would probably occur mostly with smallei divisions of the measure, and the above notation in half notes is rare and therefore unsuitable, because through it the simple harmonic foundation is expressed, and not those tonic elements, which serve for embellishment. The original progression of the voices with the above cross-relations, which are the result of contraction, is the following : * 356. 1 iH^il^^liiiia^l h. liiPmiEl ^i^g^i Let these examples be compared with those under No. 35 5j at c*, f?, e, 1u 168 MANUAL OF HARMONY, All these conditions, through which cross-relations are most enduralle are wanting in the following and similar cases, which are therefore faulty »57. 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§ •I It is held to be unmelodic and unvocal because each of its tones requires an especial progression, which tones properly appear assigned to two dif- ferent voices': 359. ^^""^ f-f— "• of which the one must remain disregarded in its progression, if the step is transferred to one voice : :t=p=t:=t=zf:=:^=J— EE , 360. ^ KBless the melodic su3cession be formed thus »««• §=^='^=S I MANUAL OF HARMONY. 169 That this, however, is not the only reason of the unpleasant effect of this interval-step, is shown by the very often used inversion of the same, which would likewise require a two- voiced progression, »62. f and is just as intelligible and easy of performance, as the tritonus appears difficult and refractory. Remark. — It may still be remarked, in this connection, that the tritonus depends upon the diminished triad and its progression, as becomes plain from Example No. 362 above. (See page 38). That this step was formerly especially held up as faulty, lay in the circumstance, that, in connection with the otherwise customary simple harmonic formation of tone-compositions, it formed the only augmented progression which diatonically exhibited itself. At this day, with the extended use of all artistic means, it is simply reckoned among the aug- mented progressions, which, in a pure harmonic leading of the voices, are to be avoided as unmelodic, or at least, lised~wttirt?a:tition. The things to which reference is to be had in the use of the tritonus, are its situation and its manner of appearance. It can occur, based either Upon one chord (a) or Upon two chords (&), e. g. 363. ±1 1 (^Mmi^imm^m^^i ^^^ Ct- i If it occurs upon one chord, its entrance is not unexpected, and the ear is prepared; in connection with two chords, however, the feeling of a forced progression is easily produced. Formerly the prohibition of the tritonus was extended to the two majo' thirds^ which follow each other at the distance of a whole step, e. g.^ not however : 364. " ' " tE3^^^^i=E=i and it is not to be denied, that this progression produces, iwo-voiced^ th« 170 MANUAL OF HARMONY same unpleasant effect, whereas the same three and four-AOiced, espcciallj if it does not appear in the outer voices, is rendered much milder. 365. 9i=.-£= mm 1 i That formerly the step from the fourth *to the seventh degree of the minor scale, e. g., D to Grjf, 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. 363, and attempt a better treat- ment. 366. Ao. mmmmmwm Exercises. 366 A. i-^ -JO — ::zs: wmi !3^ :i£: -^m^m\ ¥ m^ ■^rm E ;riii: DjO B' -^^- r^- ^== ^^\^L=^^^m 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 the fundamentals. MANUAL OF HARMOJtT. 17J Alto C t67. Exercise. CFG 0.y G C G- i^i^^ir=iiiiei^i"e[| In the treatment of this exercise, the first and most important thing will, I again, be the sketching of the Bass. At the same time, however, the Soprano, as the most prominent voice, can be added, e. g. 368. m c \ (2 m tj M^[^ D^ G |l^^|E^|E.^i=|=i-|^E^^fE 6 6 The foregoing can answer as a three-voiced movement ; through the addi- tion of the Tenor it will assume this form : 869. lligigi^iej^Ull^ J I i;^jligi^l=ilii=iiOi^^ Exercises with given Alto, 1. f O Cy D Giy F F Bb li=iEill}l^ mm ^ mmmmm m^^i o C F 6. PE^: . i:s:r 1 §:g Z I-g- ± 1^ ^ ^l Four-voiced : 372. W- ;iE ife^ JO. © <2. -fi> -L 372 l>. — s>- JEkJcercises with given Tenor, _G. |3= O G 7 *- Gy iHil^ li izsizzTi^: G- 4. iiir=i^iii^^i^=i^riii.^i^-i[E 4^ — bO These exercises are to be continued, until tie sketching of the Bass, as well as the leading of the voices in general, is perfectly pure and certain. At the close of this chapter it should be remarked, that to a good car- rying out of these four-voiced movements, a good position of the voices ii MANUAL OF HARMONY, 173 especially necessary ; the boundaries of the voices theuidelves 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. Tn this relation let the following rule be noted : Of the upper three voices^ the distance from one to the next must not he 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, since they would appear exactly in the former manner, as figured Basses. They ean only be set for free harmonic treatment. CHAPTER XVIII. Extension of the Harmonic Accoinpanirnent, 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. Exercisem F— ^ bo g 3T3. E^E^JEJEEpE^: ZZTHq ?— == ;[i The Bass can be sketched in this manner : 374. (I^fe^- V.ZZSl (^ £ 6 7 2 6 -« ^ £=t 8 7 . :p In the second and fourth measures, sevenths of secondary chords of th« seventh show themselves wi+hout preparation. 174 MANUAL CF HARMONY, Ti *d kind are called passing sevenths. They start from the fundameiitjii of th J chord, and always appear upon the arsis. In such a manner they can occur in all voices. The addition of the middle voices to the above sketch of a Bass, gives the following four-voiced movement . i 375, ^m^\m^^^^. 6 7 6 8 7 The same exercise with a richer change of harmony can be given in this manner : Ff^o^ GGjfo.j- ACyb dD G— .j- C 376. " -^: M\ Treatment : 877. m^l I I r-^ m. I * ^ i ^ 6 7b 7 4 6-87 3b ^ The next exercise Tfill exhibit the use of the suspensions. 878. 879. J-iZ^--! .^ -g ef- 6 - r MANUAL OF HARMONY, 17£ > We pass over the exercises in the middle voices. The using of the simply melodic progression in whole notes, as exercises, (cantus firmus) took place for this purpose, viz., in order to exhibit the simple harmonic content of a measure, or, as takes place in Alla-breve measure, to exhibit it in its principal divisions (half-notes). If the exer- cise is given in half-notes, then chorals can be selected for the purpose. For personal practice the fundamental tones of existing good har- monic treatments of chorals can be very easily drawn off, and the treatment attempted. In the next exercise the process will be be shown. Choral: O Ilaupt voll Bliit und Wanden. DA Dij- B^iy E E — E -, 380. fei^— :3^ ifSE^^E^teliii F=P G C F bO C P O C "tb A AFfO ^t^l^i-^m^^lE^^l^^fa^i C G G C ^3^ g ^ \ r — ^ T ^ r=EEEF£f3E^3^3H r:j=::=::|=q; -a-a- Tbe treatment of this choral can, according to the above exercise, be khe f blowing : 38y =iEi3=3; ;e^=e -^-^- 1-4 I ; I I ^"'¥ -^ — © I— « « 3 I I ri^—-r — g— T -g — g— p- g — g— T g y hsi — ;s^— T — g — g — t 176 MANUAL OF HAllMONT. d=I= g^miE I „ I M l^ilii BgEy^te Si^ :i f=r---±-F=^ i:==.=EEf~?£E;3=E: I I I r— r— ^-1 — r— A J -&<5- -r #= I I mm I -(5»— It::: 9^ I ;e^^i^ 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 devei 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, tc know and use what in them is essentially harmonic. All will here depend upoi. the recognition and comprehension of the following principles : MANUAL OF HARMONY. Hi Every melody^ however extended and developed it may be, hat, a founda Hon just as simple as those we have used, as exercises, in our last examples Every harmonic leading of the voices, however complicated, admits^ therefore, of reduction to a simple connection of harmony. In order to recognize this, it is necessary to learn to distinguish th» essential notes from the subordinate and accessory work. We select to this end the analytic method, and endeavor to develop tho following melody, which we will write down in the simplest manner according to the above mode with indication of the fundamental tones. Both melody and harmony are, as selected, simple, and the latter may be carried out, four-voiced, in the following manner : i{§3. :^kzlf3^fefelzfEl^felESElE^I ^ ^ i m^^^^l=l ±—Q—i- 'i^^lr2i\m\^^il 1_^_-«_^_5,- 6 7 4 Before we proceed to a farther development of this movement, it becomes necesary to premise what is to be mentioned concerning the rythmical for* mation of a melody. A melody can be either a musical movement without definite boundary* containing more or less measures, as it is often found as theme (motive of a composition), or it can be a whole, separated and bounded by means 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 " thosis and anti thesis" (Vordersatz und Nachsatz). 178 MANUAL OF HARMONY. The more complete treatment of this subject belongs to the doctrine ol J Form.* \ That the above movement will form a period, is seen in the close of the whole, and it will be necessary, above all, to seek out the separatin, point of the divisions. This point of separation is very often discovered in the cadences, which either as imperfect whole or as half-cadences, show themselves as plagal in the middle of the movement. Such a half-cadence (in general, a close in the dominant) is found in our exercise in the sixth and seventh measures, and the separating point of the divisions of the periods may be assumed to be at the place where the sign t stands. The first division, the thesis, would accordingly receive seven, the antithesis six measures, each of which can be rythmically altered so as to contain four measures. This may take place in the following manner : 3S4. iPl^^tegE^J^rM^liiL^g If we add the harmonic accompaniment selected above, we obtain a com plete musical period. It needs, also, only a glance, to enable us to see that all farthei transformations into various kinds of measure, e. g., into ^ » 9 » o or § measure, admit of easy accomplishment, e. g. 395. S: 3^S^ Sl^i :^ ^^ E^IE^^^^EEtE^^EiiE^ &c. — Q ~i * t I ti rm" -O- H _.t5L — I 1_(: — ^_it ^ — 35: — 1=— m &c We proceed now to the tonic variations of the melody, and add to it passing and changing notes, e. g. 3§6. ^WMl^f^^^^^i^. * See the work of this author — " Die Orundzuae der musik tUschen Formen^ — (Leip8i<\ O. Wifijand.) Sif^S-h.i^ OJB j^j^KMOjVT, 179 Still riebe.' »^e of all by-tores couM give the folloving lormation : Adagio. 38r. Originally : .^ ,.f2__ :F-_=c==U -•*! 0- t—T' i&J: ^SgHgilE-l^i t;** iEElE^H^^I TJhe 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 : _Adagio. 38§. I^^g^l^lfeg^g^^^p 180 MANUAL OF HARMONY, V I b=E=EgEEiE[E=EE: We may remark concerning the octave parallels in the middle voices, lo be found in the third measure of this example, that they are to be regarded as faultless if they do not occur singly, but appear only as a means of additional strength, in a more extended succession, for the inten- sification of a harmonic and melodic progression. The movement is, in this case, to be regarded as three-voiced. As little independent worth as this example has, it still served, here, to show of what development the simplest melodic and harmonic movement is capable. The advantage of the contemplation and recognition of these melodic and harmonic relations is too great to allow us to forbear to furnish another example in the following interesting movement. The fundamental harmonic progression is just as simple as that shown efore. \g2 ^ — 1_^ — 1. — i_o — 1_^ — i_fi, — i_g — i_g, — j^^ ai«o. © — \ mmi ■I^\^:^ -G&- This movement forms a period; the middle close is easily found in the fealf-cadence of the seventh measure. We omit here the various kinds of measure, and select the following division : toa li.A .=5 wmMm^m^^s^^^ MANUAL OF HARMON/, 18i The dev^elopment of the upper voice may take place in the following CLanner, reference being had to the harmonic progression : 391 • I^^Eg^^gEjIgE^gi^Si^ll What part the other voices can take in melodic development, the follow- ing movement from the E^ major quartette of Beethoven will show : I 392. YlOLlNO L TlOUKO II. VlOLONCVXLO. -#• — C — f '-^ -0- —T -V Viola. J M ^j} h^ ^T~ ^ ' -=] ' -"f-^]^-- E?Il3=f ZI^ZZZZlB Wfe^l iEiE=3=*:=iE=L^-*_-=L:d=b^^ fc^=tTt-C3T:^i-^^i=,i-^-= -^-^ ^^^: m^^Em^=\\ ^iipi^ilH^iip^i ii^i^i^pg^iSiii=eis ite=lE=-^l^gip£^=y: A comparison with No. 390 will show the melodic and harmonic variations. There now follows still another alteration of the original melodj^ out of the same composition : 182 MANUAL OF HARMONY. 393. 8 ^ -F= -1/ — ' t^B U'^EEiE-^^^f^ ^-'r--A-=^- be— T" ^ F-» ^"" L_^_; Si^lfP The other voices show themselves in the following alteration : mm^^m^^ -»-? :eeSe &a 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 ; for just so certain as it is that in composition one does not always proceed in the way 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, and showed themselves, even if subordinate, still not on that account insig- nificant. It yet remains to speak concerning other kinds of accompaniment, whiob will be done in the next chapter. MANUAL OF HARMONY 183 CHAPTER XX. On Development of the Accompanying Voices, The l.'ist examples of the foregoing chapter have already shown in what manner the accompanying voices take part in harmonic, metrical and melodic development. There are, however, still other kinds of accompaniment, which are known tinder the name of THE FIGURATED 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, 1 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. b. U^^ 4-1^ > ^ i::S3== =25:^ i^ ^"^^53 =^r#-t, 7^~^^ ^* a *^ tt- 1 — I — ff^-l — 1^ — ' — ^-| — * 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 some kinds of accompaniment. This may be preceded by the following remarks : If the figures repeat themselves uniformly {e. g. in broken chords), then 184 MANUAL OF HARMONY, all the rules of the harmonic leading of the voices are to he ol served ai the CHANGE OF THE CHORDS, as Well as in the reduplication. We must not. write : !_ : ' 0_ _j tf 396. but somewhat in this manner 397. or .■ —^^ II ■■mill I — 1 i-^ #-«-T a-* • ri- ■=J: At the change of the harmony, the last note of one figure and the first note of the next must not form a false progression with any other voice, e.g. not: better : not. —0 39S. ;t^ not better : i=|J=^E=i .^% 1 The harmonic figuration also affords the means for forming one-voiced movements in greater perfection. The examples will begin with this : 399. One 'soiced MANUAL OF HARMONY. 186 i That these movements are calculated for an instrument, probably sucb I as a violin or clarionet, is easy to be seen. 400. Tico voiced : ?^ -^ j— — ^ »^z=^— j:|zp : ;; - JTi;:z:z=# .-K J^0. JL ^ h-# Three voiced: In the middle voices: in tlie lower voice: i!t?^E==^i^==?=fe :il=: -0- -^ 9-r* ^-»^ -&-i ?4-h - in the upper voice: r=E #-#-#-#-— I — I ^^ ^f ^T-« i!i^^.T3=J ;f^ in two voices: #. z: i^l^^^^^H lJ i; The figuration in the four-voiced movement^ after thefe attempts witi the above example, will be equally easy of acoomplishmer t. 186 MANUAL OF HARMOXT Instead of this we prefer to select, as an example of manifold figuratioji, the following passage from the above quoted quartette movement of Beethoven. 401. ^m ,l^r> n :^:4id^iz^t^irzT=^j£?--p?*Tf_-.-_^r_?-z*: §ife^-^-^=f ^^-EfEE^| Ef =^^f=?iFf^^_ ^^ I S?£^ E^SIJ m A 1 • 1 1 1, 9Jitel m=g^^E#^f^-El^=^=!^SH!=^; b=z j"i^..'»= ^^::^:-!=T= ESLg=£-^7 :- f- g^-gi^==3 w^. I^EE^.Ei' ■0 — ft. '^^^^^^^^^=m^~^f^ MANUAL OF HARMONY. 187 ■mW^^W^^^^^^i m Sl^fep=ili^==lE5Eg=l^^~fe?i This whole rich development rests upon the foundation given IB Nos. 390, 391 and 392, and wherever the harmonic change enters, the leading of the voices is carefully observed. If we wish to obtain a clear insight into such elaborated compositions, and arrive at an understanding of their inner harmonic structure, it will be very useful to reduce compositions of this kind back to their simple foundation ; industry in this will reward itself by enrichment of knowl- edge of many kinds, and by our being rendered capable of formations of our own. CHAPTER XXI. The .Exercises in the Three-voiced Movement, With few exceptions, the four-voiced form of writing has been used for our exercises hitherto, and although it affords greater completeness, and appears most adapted for the harmonic connections, the three-voiced movements are also of much advantage, since they are especially calcu- lated to make the leading of the voices more skillful and many-sided. We begin, as before, with the problems with figured Basses. 402. ^^ 8 7 :r— [_ (s: TVMttTne^if: 1^ :^=^ :|^li 410. i^^^ii 1^; m ^1 -_(2 l^l^iEli^l ^m^= 6 il fundamental. This treatment needs no explanation. The choice of the middle and lower voices will depend upon the position •of the chords in general. Thus, in a low position, the Tenor as middle voice, will be more suitable than the Alto, just so the Tenor can be selected as lower voice instead of the Bass. For the following example the Tenor is selected as middle voice, since its movement attaches itself more to the Bass, while on the other hand the simple song of the Soprano appears, of itself, isolated. The previous Exercise in more extended harmonic treatment : Ca DpyG Ea GC DGjfO^ AB 1>D Giy C 411, -^. 413. Treatment. ._C_ :iE; 1 &==EfeB^g^ii^lEEy^E£il^ ^^ -F- --SL-. 6 ^ .^ .^ 7 ,66,-57 liiii^iiiiiiiifii^i^ NB. In the fifth measure at NB. appears the real ninth-suspension (through *jhe position of the voices), as second, which occurs very seldom, and only *>etween Tenor and Bass. In this connection it is to be remarked, that a second-suspension cannot exist, because the second depends upon the inver- sion of the seventh, and governs itself according to the progression of the latter, e, g. 192 MANUAL OF HARMONY, I I Tnversion : 413. i=:^^^E&:E'zA ^ f ■ f n Exercise in a middle voice. Tenor. d A Bfe C o rfl A 9 mmimmw As npper voice, the selection of the Alto is here most to the purpose. 415. m^mM^i 3 G E!E=J^-felE?=-L>:S The same Exercise with the following determination of chords : DO A— 7 Bb G C F Bb C^ D BbF oeO D A » 416 Si^ij^i^ll^liilii^lii^ifll Treatment: 417. ^-© :^:;3C iiJ — (©- 6 _6 6_ EizE^El^-Eim^ElgaE _^„^_c^ il^il 4 6 7 If 6 l^^llEll^f^El|E^^lE^[E MANUAL OF HARMONY. iViZ The next to the last measure aflfords the proof, that even the sixth can be suspension. For farther practice, former exercises, which were given for the four* roiced movement, may 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 b« admitted in a few cases where the chord of the sixth and fourth can regularly stand, or if it occurs instead of the chord of the second. (See page 188). Example : bO 4.8. p^y^^: p ■» ;l^: G O -& T— ?5- l\ 419. ^ Treatment: i=i^i=r^o P:^: _-<2- — ^ G- mi 6 3 P 194 MANUAL OF HARMON Y. Tho omission of intervals is plain through a comparison of the fun^ damental tones of Example No. 418. Want of clearness of the harmony will be rare in connection with this, since each chord explains itself through •ts situation, i. e., through the preceding and following harmony. The same, exercise with the following marking : G «•• pfe ZjS^. C C A - m laiiL'^liz.'^iz :s?T3 •6^ — -^ 1 -voiced : Ifi^^^^i^^^E MANUAL OF HARMONY, Progression to the third degree : A-voiced: b-voiced : 207 l-vmced : 8-voietd: i ^~^t^^- iis^^l^^l; ^ — 4 — -j9_- — S- — -a" ^= Progression to the fourth degree : 4-t)oiced: 6-voiced: G-voiced: 1 -voiced : ^-voiced: § r— , i- — F-a — r p^gB pgi^g=^g:^ l^p Progression to the ,^i^^ degree : ^-voiced : 5-vofced: ^voiced: 7-voiced: 8-voiced fe^:dEfe€di -OS — ^- [-fii-] — c o 1 — s L — Q L g, re 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. BOPBANO I. & II. ALTa Tbrob I. & IL V^ d — ^— T-s" — ^- u 6 6 6 6 7 P i!S=Ei^a;3fElEL=F=^l.#33 208 MANUAL OF HARMONY im=^ :dz^d3Tzd=:d 4— « — S>— +— ^ »— Fl f^ — f ST. \ 51^- & ;fes -6? (©- -fi* G— =:f:: fE E=?^iE E|E^|E EfeSE: -G t:=bz=z: 6 6 4 2 6 .-L — « f 3 4 1-1— J l—r-J -l-T-a' 1 -r— 1 i'— T-H — h — 1 i^=Fa^ ^ (9 S> O- EHEEaEES^ES -^ G- 1 :Jz: iLwapM: 4_,_J__J. ;E g G -—f^ — G t5^ isfzro. 1 7 4 3 ?=iiEl=^E|3EESEkJ=^=?^"^i=J=?= Lf^f^^^P 11-^ g {gs<— :r^ si—i—d d — t-h — -c?^t-sI — -g— y-^^^-g--. f 6 I £ 3 - 6 zizd: 7 BE niiq ^=3 MANUAL OF HARMONY. 209 ^^^■ E g^|E ^EE^|; 4 — X -A-. -*3 m^^- -^*- T— r- eB r^^^i^^E^^i i^[^ Hi; -I J r— H 5i -I— J 4 i:??: :gli :t== 6 7 - 4 3 -^^^mm^mi Since in polyphonic chorus-movements, all the voices do not always work at the same time, as in a choral-treatment, the movement often appears only three and four-voiced, and receives an increase of intensity through the accession of a number of voices. The following examples will explain this kind of chorus-movement and especially serve to show, that in polyphonic work also, suspensions and passing notes can very well be introduced, without detriment to the clear ess and intelligibility. 447. ^ Soprano I&II. Alto. Tbnor I&ll. 1^ :fei=i=i ::rc= mr^^^ eeIeee ;l; <5»- 1^1 I !gEgE|g^^p:^ g= |^ : 9r =i? ^$=l=fel ts: ;liEE= ¥- il=^rE!^l^l=-=l^i£ii^=I^E[^ --J-.-^ i --I- SI — aJZcti 4~^\zz^.z^ f=f= (S5> :iE3iil I--1 I J 4f^ \-?^t'^—^t-;^ r-« l-T— i l-T ! h==^ ^t r- rr f^^^^^^==^^\ 210 ftOPSANO I. BOFKANO II. U- Alto. t. Alto II, Tenor. Babs. MANUAL OF HARUONT :^=" EEEEtEfE?EEEE:?E^E; JEEE Eg^g F-^^ " i h-j — -f—^—0— — y — »— ;g — j sje^ee: -m^^ iiEE^E==: -r-t— = 1^— r-»-» \ / r ;=E: •-# ?q::«: m EEi iiE^^ipE w- ^E5E^=SE^E5i; •(2 ^^^lii=lEiiiil _^ ^- MANUAL OF HARMONY, 2U iif^ll^i^ii^il^iillE ^-;^^.^- i-s^lfe^illi-32=li=[[ 5; 0-m- EEEEiEfEEE^Q^: tq: ?E^t #-r-#-^j iif^J^I-^l^l^iilii^m^l 9^=; g z±±: ^01= In eight-voiced chorus-movements, for which, as a rule, the customary four voices are used twice, the latter are not always found employed as eight independent voices, which would easily cause too great fullness, but frequently two voices of like kind are employed in unison (for example, two Sopranos, two Altos, or two Tenors and two Basses in unison), so that the movement often appears four, five and six-voiced. We find also the eight voices divided into two different choirs, which work each for itself, and only in single passages together. As an example of the particular progression which many of these voices must make, the beginning of the choral given above may follow here for eight voices : Tmob I. & II. — t — h=^-i — F— ^— r naag^pgEi^igggpaggg 212 MANUAL OF HARMONY 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 where two or more choirs work together, it is not altogether the tonical difference, but often the metrical, which separates the voices ; it is alway * to be presumed, however, that the harmonic succession takes place in th simplest manner, and never in rapid changes. The above is generally to be understood when we speak of twelve or six teen-Toiced choruses, movements, etc., and single pieces of Bach only are found, where eight and more voices (among which, however, instru mental voices are to be reckoned), are treated obligate. 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 of so manj instruments of varioug kinds allows us to suppose) in the compass adduced , for this last, in the majority of cases, the four-voiced movement will be 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), mnst still be subject to other principles. MANUAL OF HARMONY. 2ia CHAPTER XXVI. On the Musical Forms of Close. Several kinds of close have already been mentioned (pages 32 and 33) , in relation to the authentic close, farther remarks followed on pages 40 and 53 ; in the course of the whole treatise, however, no farther opportu- nity has been given to take up the subject, so that a fuller explanation of these and other kinds of close may here follow : The forms of close are immediately divided into The authentic close and The 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. 450. plagal elofte m^m II In the last case, as in the above example, it is introduced by means of a modulation. The closes (cadences) are also divided into whole and half closes 'cadences). By the first is imderstood the same which is comprehended under tha authentic cadences. In the case of the whole cadences a farther distinction i8 again made between perfect and imperfect ones. The perfect whole cadences are those in which the Bass receives the 214 MANUAL OF HARMONY fundamentals of the dominant and tonic, and the Soprano the fundamental of the tonic, e» g. 451. If this is not the case, they are called imperfect^ e. g. ^^1,^:^=::^ |-H-go-|-^H -i-4--S- 1-— T^^J-g--T-i-- 452. i^i^-l^l I 1^ &0 __c — —G ._C__ 1 If the Bass progresses from the dominant to another degree, they are called deceptive cadences. 453. a G 6 —(5 ^^^^^ — G See the examples, pages 82 to 85. The half-cadences have the formula I-V, e. g. 454. fei:E|^§-:=l 75- V They consist therefore in this ; that the dominant triad completes the movement. Besides the tonic triad, other chords of other degrees can precede the dominant in the formation of a half-close, e. g. 455 _g_j_; iifl IV VI V Among the half-cadences are also counted those closes in the key of th4 MANUAL OF HARMONY. 215 dominant whicli are formed by a modulation into the same ; with which, however, the modulation itself is not, in a definite manner, effected tlirough the fundamental position of the dominant harmony of the seventh, but either through its inversions or through the chord of the seventh of the seventh degree, e, g, G: viio^ I g: viio^ C: V o: u^<-j V This is, however, the case only in relation to the ruling key, which has immediately before been made use of. For the farther understanding of these kinds of cadences, compare those which are found in the examples of this book. In No. 388 is found in the third and fourth measures a half cadence formed through ii-V, which effects the close of the first division of the whole period ; in the seventh and eighth measures, however, we find a perfect whole or authentic cadence. In Example No. 392 is found a half cadence, in the third and fourth measures, formed through I-V, and a perfect ivhole or authentic cadence in the key of the dominant at the conclusion. (Thus this is no half cadence, sicce the dominant harmony of the seventh renders the modula- tion decided). In the choral treated under No. 446, the first strophe ends with an imperfect whole cadence, the second with a perfect whole cadence, the third with a ^aZ/^-cadence to e minor (iv-V), the fourth with a perfect whole cadence in G major, the fifth with 2i, perfect whole cadence in a minor, the sixth with a half cadence in e minor (iv-V), and the seventh with 2k perfect whole cadence in Gr major. The application of the various cadences is easily found in chorals; for more extended pieces they form the means of boundary and connection of the smallest, as well as of the more extended movements, and are therefore to be used with much care, because upon them depends a great part of the Form-construction of a piece. INDEX OF SUBJECTS. A^emnpaniment, figurated, 183; harmonic accompaniment to a given Toice, 161 ; 17tj 195. After-striking of hafmonic tones, 121. , Alto, 23 ; alto notes, alto clef, 113. Anticipation, 1^1. Arsis, 107, 138, 174. Bass, 23; movement, progression of the same, 34, 36, 153, 205. By-tones, harmonic, 128. Cadence, 55, 81; whole, half, 178, 213; perfect, imperfect, 62, 213; in connection witll modulation, 148. Cadence formulce, 149, 150. Cantus Jirmus, 195. C-clef, 113. Chorals, as exercises, 175, 205. Chord, 21. Ch-crd formations, accidental, 105. Ohords, 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 ooO' nection with modulation, 143 •, as passing chord, 139 ; use of the same, 153. of the augmented triad, 92, 198; of the diminished triad, 155, 188. Chord of the sixth and fifth, 59, 60, 62; the same as suspension, 189 ; augmented, 97; in connection with modulation, 147. Chord of the second, 59, 61, 63. Chord of the sixth, fourth and second (see Chord of the second). Chord of the seventh, 21, 64; dominant chord of the seventh, 54, 67, 61, 82, 144; es- sential, 64; the same m passing, 138. of the seventh degree in major, 68, 78, 90, 200. s^ diminished, 76, 79, b7, 90; in connection with modulation, 146; in the poly- phonic movement, 204. Chords of the seventh, connection of the same among themselves, 73 ; in connection with chords of other tone degrees, 81, 86 ; view of the same, 100. Chord of the sixth, 47 ; augmented, 94. Chord of the thirteenth, 88, 90. Chord of the fourth and third, chord of the sixth, fourth and third, 69, 60, 62. Chord of the eleventh, 88, 90. Chord of four tones, 54 (see chord of the seventh). Chromatic alteration, 91. Consonance, 17; complete, incomplete, 17. - Contrary motion, 26, 135. MANUAL OF HAKMONT. 217 Cv^ntction of chords, 25, 73, 81 ; local, inner, 36. Close, 82 ; authentic, plagal, 32, 33. .- see also cadence, whole close, half close, deceptive cadenoe. Closing cadence, 55, 81. Closing formuUe, 40, 41, 149. Cross-relation, unharmonic, 16fe, Deceptive cadence, 81. Degrees, diatonic, 13. 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^ 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, 73 ; of the connection of the chords of the seventh among themselves, 74 ; of the secondary chords of the seventh in minor, 77 ; of the inversions of ths same, 80 ; of the deceptive cadences, 85 ; of the secondary chords of the seventh in connection with chords of other tone degrees or keys, 87 ; of the augmented triad, 94 ; of other altered chords, 98 ; in searching out modulation, 103 ; of the suspen- sions, 112, 119; of the harmonic accompaniment to a given voice, 151, 152, 157, 163, 164, 165, 170, 171, 172, 173; in the development of melody, 177 ; in the three- voiced movement, 187, 191, 192; of the two-voiced movement, 193; in the harmo- nic accompaniment to a given voice in melodic development, 195, 200 ; in the five- voiced movement, 202, 206 Fifteenth, 14. Fifth, 13, 22 ; perfect, 15, 16 ; augmented, 16, 16, 75 ; diminished, 15, 16, 38, 60; fiifbh in the chord of the seventh, 57, 70. Fifth-progressions (parallel fifths), 26, 28, 51,79, 97; open, 30, 78; covered, 80,37, 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 fourth, 155; the same as chord, 189, 196. Fourth-progressions (fourth parallels) in passing, 134, 136. Formation of the close, 39, 53, 55. Fundamental harmotiies, 21 ; chromatic alterations of the same, 9L Fundamental, 21 ; in the chord of the seventh, 67. Half close (half cadence), 178, 213. Harmony, 21. Harmony, tones foreign to the, 105. Intervals, division of, 17 ; view of the same, 16, 18 ; inversion of the same, 1& see also omission, reduplication. Intervals, doctrine of, 13. Interval, 1 3 ; major, perfect, 14 ; minor, augmented, diminished, 1ft. Interval steps and $kip8, augmented and diminished, 166. Intervals above, 18. Intervals be^cw, 18. 218 MAITUAL )F HARMONY. Inversion, 47; of the triads. 47 ; of the chords of the seventh, 59, 62, 78 (see also In tervals). Leading tone, S 7, 39, 56, 76, 116, 159, 203. Major triad, 22, 65. Melody, its development, 176; its rhythmical formation, 177. Middle voices, 23. Minor triad, 22, 33, 65. Modulation, 102 ; means for the same, 141 ; its extension and completion, lt8. Movement, one-voiced, 184; two-voiced, 193; three-voiced, 187; four-voiced, 28; fiT»« 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, 1 1 8. Oblique movement, 26. Octave, 13 ; perfect, augmented, diminished, 16, 16. Octave-progressions (octave parallels), 26, 28; open, 30, 110, 133; covered, 80, 86, U, 84, 158, 208; in contrary motion, 201. Omission of intervals, 57, 73, 188, 193. Organ-point, 123. Outer voices, 11. Pass; passing notes, 128, 134. Fussing chords, 138. Period, 177. Flagal close, 33, 41, 213. Position of the chord, close, open, dispersed, 31, 82, 114. Preparation, of the seventh, 70; of the suspension, 107. Prime, 13; perfect, augmented, 15, 16. Primary chord of the seventh, 54, 64. Primary triads, in major, 23, 33 ; in minor, 40. Progression, melodic, unmelodic, 155, 156. of the secondary chords of the seventh, 66, 73, 81; see also resolution, bftM. unison, octave, fifth progressions &c. ; connection of the chords. Reduplication, 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 secondaiy chords of the seventh (in major) 65; (in minor) 74; of the suspension, 106, 109, 116, 120. Scale (see Triads). Secondary triads, in major, 33 ; in minor, 42. Secondary chords of the seventh, 64, 78, 86. Second, 13 ; major, minor, augmented, 15, 16. Second-progressions (second parallels), in passing, 134; "with changing notes, 18^ Second, step of the augmented, 44. Sequence, 37. Seventh-progressions (seventh parallels), in passing, 134; with changing notes, 136. Seventh, 13; major, minor, diminished, 15, 16; passing, 72, 176; preparation, 70; the same vfithout preparation, 72, 77, 158, 164. Sixth, 13; major, minor, augmented, 15, 16. Signatures, 53. Soprano, 23* soprano notes, soprano cle£| 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 several Tcices, 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, 156, 67 70 (see Leading tone). Thirteenth, 14. TJiorough-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 ; subdominant triad, 28. double-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 oi 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). Fbu-es, compass of the, 113. Voices, relation of the, 113. Voices, outer, 23 ; middle voices, 23 ; development of the accompanying voices, 146. Vordersatz, 174. 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