HARMONY IN PI ANOFORTE- STUDY liflilHltnil THE LIBRARY OF THE UNIVERSITY OF CALIFORNIA LOS ANGELES GIFT OF Benno Rubinyi HARMONY IN PIANOFORTE-STUDY HARMONY IN PIANOFORTE-STUDY A BOOK FOR THE INDIVIDUAL STUDENT BY ERNEST FOWLES FELLOW OF THE ROYAL ACADEMY OF Music; AUTHOR OF "STUDIES IN MUSICAL GRACES," ETC. G. SCHIRMER, INC., NEW YORK British Publishers: J. CURWEN & SONS (LTD.), LONDON, W. COPYRIGHT, 1918, BY G. SCHIRMER, INC. 28036 Printed in the U. S. A. Music Libnn MT TO MRS. CURWEN IN GRATEFUL ACKNOWLEDGMENT OF A HELPFUL FRIENDSHIP OF MANY YEARS THE AUTHOR'S APOLOGY THE following pages contain a digest of principles formulated by the writer for the use of his pianoforte students. In com- mon with his colleagues generally, he has continually to deal with those whose harmonic knowledge and perception are of the slightest; and who, moreover, are unlikely to acquire more than may be af- forded to them in the course of instrumental study. The book is not intended to supplant the work of the expert teacher of harmony; more exactly, it may be regarded as a means of feeling the harmonic pulse of the student at the weekly instrumental lesson. It presents the subject in the most elementary manner. It professes to appeal both to the harmonist, strong in a grasp of part-writing, and to the student whose mind is innocent of such attainment. To the one, it may be a help to bring his theory into touch with the living or- ganisms of actual music; to the other, it may prove a bracing me- dium, stimulating him to the inquiry why these things should be. More than this, indeed, is not attempted; yet it may be confidently asserted that the pianoforte teacher who will yield five minutes of the time of each lesson to the type of study here outlined will reap a considerable reward in the increasing perception of the use, nature, and purpose of harmony, on the part of his students. It is given to all with average intelligence to write a chordal pro- gression in accordance with every rule devised by the wit of harmon- ists; it is given to those only who have received a measure of musical illumination, spontaneously to play such a progression with entire acceptance to the musical sense. The latter achievement is the higher; and when the student has reached the power so to link chords with unpremeditated and yet with aesthetic charm, he has crossed the Rubicon of all harmonic endeavour. 24, BERNERS STREET, LONDON, W. i. vii TO THOSE ABOUT TO USE THIS BOOK A LARGE part of the effect of music is concerned with harmony: since this is so, it behooves every music-lover, listener as well as player, to cultivate the sense which recognizes the harmonic basis upon which virtually every musical progression is founded. The mental necessities which underlie the study of harmony include: (i) A knowledge of the properties of chords and of the sounds generally by which they are accompanied. (2) A keen aural grasp of any possible combination of sounds that may be used in music. (3) The power to conceive harmonic progressions unaided by any other medium than that afforded by the trained inward sense. (4) The ability spontaneously to express these combinations and progressions at the keyboard. (5) The facility to express the same combinations and progressions upon paper. The older methods of teaching the subject now rightly dis- credited laid undue emphasis upon (i) and (5). A perception of the importance of (2) prepared the way for a recognition of the claims of (3), and contributed indirectly to the great advance in the expression of harmonic thought upon paper which followed the adoption of sane aural methods. But however thorough may be the method of (5), it is too cumbrous, too lacking in spontaneity to respond immediately to the conceptions of the inward sense. It is for this reason that (4) assumes a role of infinite importance in dealing with what may be termed the synthetic aspect of harmony. It is the tendency of those whose harmonic discipline has been confined to paper work to regard the chord solely from that par- ticular aspect so aptly described by the French expression, harmonie plaquSe. The tritest of examinations will prove that the presen- tation of harmony in this form is comparatively rare in instrumental music, which inherently demands a large share of that phase of har- monic expression known as harmonie figuree. Yet both types may frequently be observed within the same work. The first movement Vlll To Those About to Use This Book ix of Beethoven's Sonata, Op. 53, contains examples of harmonic plaquee (bar 35 et seq.) and of harmonic figuree (bar 50 et seq.) ; but the great mass of the movement is concerned with the latter rather than with the former. Such being the case, it is evident that the student should endeavour strenuously to cultivate the power of presenting harmony in the florid manner advocated in this book. The fundamental and indispensable condition of success lies in the conquest of Part I. The student who has wholly mastered this Part, who is able, in an interesting manner, to present the harmonic progressions it unfolds, is not likely to encounter any serious barrier to the mental grasp of the principles enunciated in the remaining Parts. The power to present harmonies in simply-embellished form and without the help contributed by the use of auxiliary sounds, a virtual making of bricks without straw, is a preparation indis- pensable to the ultimate expression of musical thought in free ex- temporaneous form. Although the order assigned to the various Steps is the outcome of the author's own experience in the training of students, he would be the first to concede that this order may, and indeed should, be varied in accordance with the needs of the individual. Thus, for a certain type of student, the following schedule may at first be found neces- sary: Steps I, II, VII, VIII, XIII, XV, XVII, XVIII, XIX, etc., the intervening Steps being negotiated after these have been mas- tered. The only objection that can be urged against the course of study advocated here is that it does not make for progress in the art of part-writing. This is by no means the evil that some may think to be the case. Counterpoint is the medium par excellence for acquiring facility in part-writing; harmony is the medium whereby the stu- dent learns to manage the masses of combined sounds in the form of chords unknown to the science of strict counterpoint. The part- writing of the harmonist depends upon the power he has acquired in this respect from contrapuntal study. The niceties of part- management in writing for voices have little to do with the handling of chords intended solely for keyboard expression. If it be disal- lowed to thrust the specialities of harmony upon counterpoint, then the converse must also be true that the rigours of counterpoint should not be permitted to usurp the purely and primarily harmonic function. In those cases where ignorance of the fundamental principles of x To Those About to Use This Book harmony is an unavoidable condition, the teacher of resource will refrain from perplexing the student with a copybook review of rules which, however indispensable to the study of harmony in well-par- ticularized parts, are often a deterrent to the successful portrayal of harmonic shapes upon the pianoforte keyboard. The latter ac- quirement depends upon the capacity to perceive what is or is not radically musical. When a student contrives to present two chords with consecutive octaves between the extreme sounds, or if perchance he alight, let us say, upon consecutive fifths under like conditions, it is easy to point out that, in the one case, he offends upon the ground of monotony, and, in the other, that his crime is against the law of expediency. More than this in the way of precept it is unnecessary to attempt; less than this would negative every impetus towards real advance. The insistence upon self-expression in the major and minor modes alternately is a particular feature of this book. It will be observed that illustration is, in every case, directed to the minor of the same tonic as the foregoing major key, this being in the author's opin- ion the most natural way to emphasize the tonal contrasts. It is open to the teacher, however, to use the minor key of the same signature if he find it more convenient so to do. It will be natural to many a student to be affrighted at the ex- tensive number of "Steps" provided for his delectation. He may, however, be reassured. In many cases, it will be possible to take a number of Steps simultaneously; in other instances, the fact that, at first, one only is advisable at a time, will go far to prove the ur- gency of this type of work, and will, at the same time, act as an in- centive to keen and ever keener studentship. Moreover, it is not the number of Steps mastered which will ultimately count, so much as the accumulative influence of daily effort and the consequent de- velopment of the faculty to think harmonically as well as melodi- cally. It is almost futile to add that a preliminary aural grasp of every harmony presented upon the keyboard should be the consistent aim throughout, so obvious is the fact; yet, the student who desires to obtain every advantage from the study of the following pages will do well continuously and courageously to keep this fact before his mind. Only in this way is it possible to conceive that real and per- manent power will at length become his assured possession. CONTENTS PAGE DEDICATION v THE AUTHOR'S APOLOGY .'. . . vii TO THOSE ABOUT TO USE THIS BOOK viii INDEX TO THE STEPS xii THE PARTS: I. PLAIN HARMONY i II. AUXILIARY SOUNDS 33 III. CADENCES 49 IV. CHORDAL TRANSFERENCE 58 V. SEQUENCES AND PEDALS 66 VI. CHROMATIC HARMONY 72 VII. THE BUILDING OF THE DOMINANT DISCORD 80 VIII. THE ENHARMONIC PRINCIPLE 83 THE AUTHOR'S FINAL NOTE. 87 INDEX TO THE STEPS STEP SUBSTANCE PACK I. Major common chords in root- position I II. The decoration of the same 2 III. First inversions of major common chords 4 IV. The decoration of the same 5 V. Second inversions of major common chords 5 VI. The decoration of the same 6 VII. Minor common chords in root-position 6 VIII. The decoration of the same 6 IX. First inversions of minor common chords 6 X. The decoration of the same 6 XI. Second inversions of minor common chords 6 XII. The decoration of the same 6 XIII. The appreciation of the dominant harmony in the major key . 7 XIV. The dominant and tonic harmonies contrasted 7 XV. The succession of the dominant and tonic harmonies in the major key 7 XVI. The decoration of the same 8 XVII. The intensive treatment of the chords of Step XV 10 XVIII. The improvisation of melodies closing with the progression of Step XV . .--. II XIX. The appreciation of the dominant harmony in the minor key . n XX. The succession of the dominant and tonic harmonies in the minor key 12 XXI. The decoration of the same 12 XXII. The intensive treatment of the chords of Step XX 12 XXIII. The improvisation of melodies closing with the progression of Step XX 12 XXIV. The appreciation of the subdominant harmony in the major key 13 XXV. The succession of the subdominant and tonic harmonies in the major key 13 XXVI. The decoration of the same 13 XXVII. The intensive treatment of the chords of Step XXV 13 XXVIII. The improvisation of melodies closing with the progression of Step XXV 14 XXIX. The appreciation of the subdominant harmony in the minor key 14 XXX. The succession of the subdominant and tonic harmonies in the minor key 14 XXXI. The decoration of the same 14 XXXII. The intensive treatment of the chords of Step XXX 15 XXXIII. The improvisation of melodies closing with the progression of Step XXX 15 XXXIV. The succession of the subdominant, dominant and tonic har- monies in the major key 15 XXXV. The decoration of the same 16 XXXVI. The improvisation of melodies closing with the progression of Step XXXIV 17 xii Index to the Steps Kill STEP SUBSTANCE PAGE XXXVII. The succession of the subdominant, dominant and tonic har- monies in the minor key 17 XXXVIII. The decoration of the same " 17 XXXIX. The improvisation of melodies closing with the progression of Step XXXVII 17 XL. The appreciation of the supertonic harmony in the major key . 18 XLI. The succession of the supertonic, dominant and tonic har- monies in the major key 18 XLI I. The improvisation of melodies, closing with the progression of 19 Step XLI XLIII. The appreciation of the submediant harmony in the major key 19 XLIV. The succession of the submediant, dominant and tonic har- monies in the major key 19 XLV. The improvisation of melodies closing with the progression of Step XLIV 20 XLVI. The appreciation of the mediant harmony in the major key . . 20 XLVII. The succession of the mediant, dominant and tonic harmonies in the major key 21 XLVI 1 1. The improvisation of melodies closing with the progression of Step XLVII 21 XLIX. The appreciation of the chord of the dominant 7th and its in- versions 21 L. The resolution of the chord of the dominant 7th in the root- position ... 22 LI. The resolution of the first inversion of the dominant 7th ... 22 LI I. The resolution of the second inversion of the dominant 7th . . 23 LI 1 1. The resolution of the third inversion of the dominant 7th ... 23 LIV. The improvisation of melodies closing with the progression of Step L 24 LV. The succession of the chords of the supertonic, dominant 7th and tonic in the major key 24 LVI. The same with the chords in inverted form 25 LVII. The improvisation of melodies closing with the progressions of Steps LV and LVI 25 LVI 1 1. The succession of the chords of the submediant, dominant 7th and tonic in the major key 25 LIX. The same with the chords in inverted form 25 LX. The improvisation of melodies closing with the progressions of Steps LVIII and LIX 25 LXI. The succession of the chords of the subdominant, dominant 7th and tonic in the minor key 26 LXII. The succession of the chords of the submediant, dominant 7th and tonic in the minor key 26 LXI 1 1. The improvisation of melodies closing with the progressions of Steps LXI and LXII 27 LXIV. The appreciation of the supertonic harmony formed upon the ascending melodic minor scale 27 LXV. The appreciation of the supertonic harmony formed upon the harmonic minor scale 27 LXVI. The succession of the supertonic, dominant and tonic har- monies in the minor key 28 LXVII. The improvisation of melodies closing with the progression of Step LXVI 28 LXVI II. The appreciation of the mediant harmony formed upon the descending melodic minor scale 28 LXIX. The appreciation of the mediant harmony formed upon the har- monic minor scale 29 LXX. Tonal environment in respect to major common chords ... 30 XIV Index to the Steps STEP SUBSTANCE PAGE LXXI. The same in respect to minor common chords 31 LXXII. The improvisation of progressions exemplifying the less usual resolutions of the chord of the dominant 7th 32 LXXI 1 1. Combinations of the chords treated hitherto 32 LXXIV. The elementary appreciation of auxiliary sounds 34 LXXV. Diatonic auxiliary sounds applied to the single sounds of major common chords 34 LXXVI. The same inverted 35 LXXVII. The same applied to the single sounds of minor common chords 35 LXXVIII. Chromatic auxiliary sounds applied to the single sounds of major common chords 35 LXXIX. The same inverted 35 LXXX. The same applied to the single sounds of minor common chords 36 LXXXI. Diatonic auxiliary sounds exemplified by scale-passages formed upon major common chords 36 LXXXI I. The same applied to minor common chords 36 LXXXIII. Diatonic auxiliary sounds between the various sounds of major common chords 36 LXXXIV. The same inverted . 37 LXXXV. The same applied to minor common chords 37 LXXXVI. Chromatic auxiliary sounds between the various sounds of major common chords 37 LXXXVII. The same inverted . 38 LXXXVIII. The same applied to minor common chords 38 LXXXIX. Diatonic auxiliary sounds applied to the dominant and tonic harmonies of major keys 39 XC. The same in minor keys 39 XCI. Chromatic auxiliary sounds applied to the dominant and tonic harmonies of major and minor keys 39 XCII. Diatonic auxiliary sounds applied to the subdominant, dominant and tonic harmonies of major keys 40 XCIII. The same in minor keys 40 XCIV. Chromatic auxiliary sounds applied to the subdominant, domi- nant and tonic harmonies in major and minor keys ... 40 XCV. Diatonic auxiliary sounds approached by leap 41 XCVI. Basic harmonies for examples of diatonic auxiliary sounds ap- proached by leap 41 XCVII. Chromatic auxiliary sounds approached by leap 42 XCVIII. Basic harmonies for examples of chromatic auxiliary sounds approached by leap 42 XCIX. Accented diatonic auxiliary sounds applied to major com- mon chords 43 C. The same inverted 43 CI. The same applied to minor common chords 43 CII. Accented chromatic auxiliary sounds applied to major common chords _ 43 CII I. The same applied to minor common chords 43 CIV. Basic harmonies for melodies containing accented diatonic auxiliary sounds 44 CV. The same, including chromatic auxiliary sounds 44 CVI. The simultaneous combination of harmonic and auxiliary sounds in connection with single common chords 45 CVII. The same applied to the harmonies of the dominant and tonic. 45 CVIII. Basic harmonies for the further exemplification of the same . 46 CIX. Changing-notes 46 Index to the Steps xv STEP SUBSTANCE PAGE CX. The improvisation of progressions in major keys, ending with a full close 50 CXI. The same in minor keys " 50 CXII. The improvisation of progressions in major keys, ending with the semi-final perfect cadence 51 CXIII. The same in minor keys 51 CXIV. The improvisation of progressions in major keys, ending with the inverted perfect cadence 51 CXV. The same in minor keys * 51 CXVI. The improvisation of progressions in major keys, ending with the subdominant-tonic cadence 51 CXVI I. The same in minor keys 52 CXVIII. The improvisation of progressions in major keys, ending with the subdominant-tonic cadence in inverted form 52 CXIX. The same in minor keys 52 CXX. The improvisation of progressions in major keys, ending with the harmony of the dominant 53 CXXI. The same in minor keys 53 CXXII. The improvisation of progressions in major keys, ending with the second inversion of the tonic and the dominant har- mony 53 CXXIII. The same in minor keys 53 CXXIV. The improvisation of two phrases, the first closing with a domi- nant cadence 54 CXXV. The same in minor keys 54 CXX VI. The improvisation of progressions in major keys, ending with an interrupted cadence 55 CXXVTI. The same in minor keys 55 CXXVIII. The improvisation of two phrases in major keys, the first closing with an interrupted cadence 55 CXXIX. The same in minor keys 55 CXXX. Experiments in the less usual forms of cadence 56 CXXXI. The improvisation of three phrases with diverse cadences ... 57 CXXXII. The improvisation of complete musical thoughts 57 CXXXIII. The linking of a major common chord to another chord without respect to key . * 58 CXXXIV. The decoration of the same 58 CXXXV. The linking of a minor common chord to another chord without respect to key 60 CXXXVI. The decoration of the same 60 CXXXVII. The linking of three chords without respect to key 60 CXXXVIII. The decoration of the same 60 CXXXIX. The linking of three chords with reference to key 62 CXL. The decoration of the same 62 CXLI. Chordal transference from major common chords in reference to change of key 63 CXLI I. The same from minor common chords 64 CXLIII. Chords common to two keys 64 CXLIV. Sequences formed from figures of two chords 66 CXLV. Sequences formed from models of more than two chords ... 67 CXLVI. Non-uniform sequences 67 CXLVII. The sequence as a means of modulation 68 CXLVIII. Pedals 70 XVI Index to the Steps STEP SUBSTANCE PAGE CXLIX. Progressions ending with a chromatic harmony 72 CL. The same in minor keys 72 CLI. Progressions ending with a chromatic chord affiliated to the previous harmony 73 CLI I. The same in minor keys 73 CLIII. Progressions starting with a chromatic harmony 74 CLIV. The same in minor keys 74 CLV. The processes of Steps CXLIX and CLIII combined 74 CLVI. The same in minor keys 74 CLVII. The use of the dominant 7th in closely-related keys 76 CLVIII. The same in minor keys 76 CLIX. The appropriation of the dominant 7th in remote keys .... 76 CLX. The chord of the augmented 6th on the minor 6th of major keys 78 CLXI. The same in minor keys . 79 CLXII. The chord of the augmented 6th on the minor 2nd of major keys 79 CLXIII. The same in minor keys 79 CLXIV. The building of the entire dominant discord 80 CLXV. The combination of the root, 3rd, 7th, and 9th of the dominant discord in major keys 81 CLXVI. The same in minor keys 82 CLXVII. The combination of the root, 5th, 7th, and nth of the dominant discord 82 CLXVIII. The combination of the root, 3rd, 7th, and I3th of the dominant discord in major keys 82 CLXIX. The same in minor keys 82 CLXX. The alternate use of the variable members of the dominant dis- cord 82 ******* CLXXI. Enharmonic change effected by a single sound 83 CLXXII. The succession of chords of the diminished 7th 85 CLXXI II. Modulation by means of the chord of the diminished 7th ... 85 CLXXIV. The enharmonic contrast between the chords of the dominant 7th and augmented 6th 86 HARMONY IN PIANOFORTE-STUDY PART I Plain Harmony STEP I. Play any of the twelve major common chords in the root-position, each chord selected to exhibit several varieties of sound-distribution. (Ex. I.) Ex. A. n . B. c. i D. L/ 1 j*^ 1 S J l o II /L c* 1 1 II KB 1 i 1 S 1 S || \>\) H 1 C (^ H c/ ^ 3. ^v . **^^ |(? 1 " 1 ^ II 1 4f^7 E 1-2 S II ^ ' -^ 5 1 9 1 ^ II Note i. 77^ diatonic scale affords a certain clue to the formation of any common chord. Before proceeding to the chords of Step I, the student should therefore play one octave of the scale belonging to each of the major keys selected. The ist, jrd, and $th degrees of the scale determine the pitch of the sounds which form the common chord of the tonic. Note 2. The common chord contains but three sounds; conse- quently, additional units or parts can be obtained only by repeating or doubling one or more of these sounds. It is in this way that the added sounds in Ex. I are obtained. Note 3. In vocal writing, the number of sounds in a chord is determined by the number of the voice-parts. No limitation of the kind exists in the case of chords intended for instrumental expression. Note 4. All chordal positions, in which the sounds are not indi- vidually perceptible to the ear, should be avoided. Ex. 2, A , is ineffec- tive because of the closeness of position assigned to the three lowest sounds. The elimination of the lower 3rd, as in B, effects an im- mediate improvement. Harmony in Pianoforte-Study Ex.2. Note 5. TVfe sounds of a c^orrf should, under ordinary circum- stances, be distributed at approximately equal distances. If any pronounced interval exist between one sound and another, this should, as a rule, be arranged between the bass sound and the sound next above. Such a separation of the bass sound from the tipper sounds is par- ticularly desirable when a chord is played at a low pitch. Thus, Ex. 2, B, played an octave lower, creates a species of aural confusion; on the other hand, Ex. 2, A , played an octave higher, is perfectly effective. Note 6. In the next Step the student will learn how to present a simple chord in decorated form. It will therefore be interesting and helpful first to play an example of such embellishment by a classic master. (Ex. j.) Ex. 3. Allegro con BEETHOVEN. Sonata, Op. 2, No. 3. STEP n. Treat, decoratively, any of the twelve major common chords in the root-position: (a) By chords presented in the form of figures, (Ex. 4); or (b) by well-defined passages of broken chords (Ex. 5)- Ex.4. Leggiero. Plain Harmony Ex.5. Allegretto. Note 7. In the above examples, it is necessary fully to appreciate the composite nature as well as the entire co-relationship and kinship of the various sounds. It is of equal importance that the ear should realize the influence of the root throughout. Ex. 6 is another version of Ex. 5, and illustrates the importance of the part played by the piano- forte pedal in passages of the kind. In this case the pedal retains the root of the chord throughout. Ex. 6. rj.o , j \ ^11 EZ A h^- 5a X3 X3 ^ 1 Ped. '-I Note 8. r/te ac/ of presenting a chord in decorative form is not completed by the mere succession of the sounds in the shape of figures, chordal or otherwise. Something more is required before such a pas- sage can be said to be invested with musical significance. It is a first condition of success that the grouped figures should be presented in rhythmic form; Ex. 6 is a clearly cut rhythm of four bars. A second and very important condition is that the problems of stress and repose should receive careful consideration; Ex. 6 is represented as demanding a gradually increasing stress. The third condition almost claims priority by insisting upon the expression of each progression in some definite form of time; the examples just given fulfil this condition in each case. In brief, the student must not allow himself to ramble amid an incoherent maze of sounds; on the contrary, before reproducing his conception upon the instrument, he must cultivate the power mentally to conceive the type of progression which he desires to express. It should be his aim to set each example in a thoroughly musical and attractive environment. Note 9. Much can be achieved in the decorative expression of a common chord aided only by the elements of time, accent, and rhythm; Harmony in Pianoforte-Study to which must, of course, be added emotional conception. Ex. 7 is a complete musical thought founded upon a single chord of the kind. Ex.7.* Maestoso. _ &- 4 H : f * i-. -4. --. STEP in. Play examples of first inversions of any of the twelve major common chords. Each chord should be presented in various positions, the 3rd being in every case the lowest sound. (Ex. 8.) Ex. 8. II 1 5 1 Z || 5 a 1 1 ; 3 51 1 II o c/ < 1 22. a. r>* r^ EZm& Is | (? ii 1 i 1 II Z " "' ^ E Z - II Note 10. Step III illustrates the importance of listening to the bass sound of a chord. In a very particular sense, the bass is the most virile member of any chordal combination; and it is not too much to add that the harmonic instinct is strong in proportion as the fundamental sounds of harmony are continuously perceptible to the inward sense. . * An approximation of a treatment played to the author by one of his younger students. Plain Harmony $ Note ii. When the 3rd of a major common chord is in the bass as in the case of a first inversion it is usually ineffective to repeat it in another part except as an octave to the bass. Ex. g, A, is unpleas- ing; but this is avoided in B by the alteration in the uppermost part. Ex. 9. A. A B. u If .- 1 E2 A. \\9 1 K ftv . u&> HtH ^K b fz 1 fv.;, -<9- -&- V - *J ^ STEP IV. Apply simple forms of decoration to any of the first inversions of the twelve major common chords. (Ex. 10.) Ex. 1O. Brillante. Note 12. / //fw 5^/>, it is very necessary to ensure that the jrd of the chord be heard throughout the passage as the lowest sound. As a rule, the pedal should be used to retain this sound. (Cf. Notes 7 and /o.) STEP V. Play examples of second inversions of major common chords; each chord to be presented in various positions, the 5th being in every case the lowest sound. (Ex. n.) The substance of Note 10 should be recalled at this point. *="T* D. Harmony in Pianoforte-Study STEP VI. Apply decorative forms to the chords of Step V. (Ex. 12.) Ex. 12. Leggier o. i i i S ic m. Ped ^ * ww. Fed. STEP VII. Play examples of the twelve minor common chords in the root-position. By omitting the sharp, Ex. i may be translated into the tonic minor for illustration. Note 13. The minor common chord should be built up from the 1st, 3rd, and $th sounds of the minor scale. (Cf. Note i.) STEP VIII. Treat, decoratively, any of the twelve minor com- mon chords in the root-position. (Cf. Exs. 4 and 5 translated into the tonic minor by the substitution of a minor 3rd.) ****** STEP IX. Play examples of the first inversions of minor common chords. (Cf. Ex. 8 translated into the minor by the alteration of the 3rd in the bass.) Note 14. The substance of Note n should be remembered in con- nection with the chords of this Step. Regarded generally, however, the indiscriminate doubling of the bass sound is less objectionable in the case of first inversions of minor common chords. STEP X. Apply decorative forms to the chords of Step IX. (Cf. Ex. 10 translated into the tonic minor.) STEP XI. Play examples of second inversions of minor com- mon chords. (Cf. Ex. n translated into the tonic minor.) STEP XII. Apply decorative forms to the chords of Step XL (Cf. Ex. 12 translated into the tonic minor.) Plain Harmony STEP XIII. Having played one octave of any one of the twelve major scales (Ex. 13, A), sound the dominant common chord of that key Ex. 13. A. B. i Y- fc^I g IT TT H -- 2? " ff Note 15. TVze chords treated in Steps I to XII are presumed to be of a tonic, and therefore of a final, nature. The effect of finality is disturbed by playing the scale of the key before sounding the chord of the dominant, and the difference between a chord of completion and one of incompletion becomes clear to the aural sense. A realization of the restless character of the dominant harmony, and the satisfaction it invariably finds in that of the tonic, lies at the root of all harmonic per- ception and endeavour. STEP XIV. Play the common chords of the dominant and tonic in various major keys. The chords should be played individually after the manner of Ex. 14. Note 1 6. Step XIV is a necessary prelude to Step XV. It is not intended that the chords should be regarded as forming one progres- sion, but that the student should be thoroughly well informed as to the tonal position of the harmonies which he will presently be required to play in harmonic combination. N.B. The chords of this Step should not be played in decorative form. STEP XV. Play, in harmonic succession, the dominant and tonic chords of various major keys. (Ex. 15.) The chords should be attempted in as many positions as possible and the strength of the movement of the bass part from dominant to tonic carefully ob- served. (Cf. Note 10.) Ex. 15. A. Harmony in Pianoforte-Study B. C. yK 2 "* ^ H /Tfvo ^1 ~~F H \MJ^5 "* X II O ^ l ^' C"~\ . &) (%} e* M * * ._ Z o ^ 1 25 II Note 17. Experiment will prove that the best effects are produced when the uppermost sounds remain the same in both chords, or move but a 2nd from the first chord to the next. Both types appear in Ex. 15. A is clearly more monotonous than either B or C. B is the strongest or most conclusive progression. The upward movement of the top part of C to the 3rd of the tonic harmony offers more freedom from the commonplace than if it descended to the root. Note 18. The student whose harmonic knowledge has been re- stricted to vocal part-writing will here be inclined to permit any power he may have gained to dominate his presentation of chords upon the pianoforte. When writing for voices, it is not only indispensable that the parts should be clearly individualized, but that the movement of each part should be perceptible to the ear. On the other hand, when writing for, or expressing harmonic progressions upon, the pianoforte, it is the effect of the chord in the mass which usually counts, and no restriction may be held to exist as regards the movement and treatment of the vari- ous members of each chord save those which are imposed by good sense and musicianly effect. Note 19. Extended positions of the chords may be obtained effec- tively by an intelligent use of the pedal. (Ex. 16.) Ex. 16. A. Fed. *Ped.* Fed. #Ped. STEP XVI. Apply simple forms of decoration to the dominant or tonic chords or to both. Ex. 17, A and B, illustrate such em- bellishment by means of a chordal figure; C and D, by the use of the arpeggio. Plain Harmony 9 Note 20. // will be found advisable first to sound the tonic chord of each key before proceeding to the complete progression; and this prac- tice should be adopted generally in all future combinations. Ex. 17. A. B. Lusingando. S \ g Fed. *Ped. Ped. D. Brillante. Ped. * Ped. * 10 Harmony in Pianoforte-Study Note 21. In the act of presenting harmonies in the florid manner above set forth, care should be taken mentally to preserve the original shape of the chord or chords embellished. At this stage, each arpeggio should be formed from a chord which, throughout the process of embel- lishment, is clearly perceived by the inward sense. For example, the original design of each chord embellished in Ex. 18, A, is outlined in B. Ex. 18. A. A llfgretto BEETHOVEN. Sonata, Op. 31, No. 2, 3rd mov. :8: STEP XVII. Repeat the progression of Step XV many times consecutively, exemplifying the chords in a new position at each repetition. (Ex. 19.) Plain Harmony II Ex. 19. Fed.* Ped.^t simile. 8 STEP XVm. Improvise short melodies in the major keys, the last two sounds of which will, in each case, provide a position for the introduction of the progression demonstrated in Step XV. (Exs. 20 and 21.) Ex. 2O. Soavemente. Q -" - ^ ^T Jf u(j f P 9 " P 1 J ,j . ^ N H II CcT) F 1 {. P ^-* 1 *. k j n II * V l P IX ^^"^^ "I B *-===> =r: . ^M w 1 r^v l_ 6"J ^- 1 1 1 17 i! * - 1 1 ^9-\}Q I 5i |J Plain Harmony STEP XXIV. Having played one octave of a major scale (Ex. 24, A), sound the subdominant common chord of the same key (B). Ex. 24. A. V- B. JO.. Note 25. The student is here directed aurally to examine a chord which occasionally supplants the dominant harmony in a final cadence. It will be helpful to alternate Step XIII with Step XXIV; similarly, Step XV with Step XXV. STEP XXV. Connect the common chords of the subdominant and tonic in any of the twelve major keys. (Ex. 25.) Note 26. In the above examples, the strength of the movement of the bass part should be observed experimentally and comparison made with the same feature in the progressions of Ex. 15. Here, also, the best effects will be obtained by the player when the top part remains the same in both chords (B), or moves but a 2nd from one to the other (A and C). (Cf. Note 17.) STEP XXVI. Reproduce the progressions of Step XXV in em- bellished form. STEP XXVII. Repeat the progressions of Step XXV many times consecutively, playing the chords in a new position at each repe- tition. (Ex. 26.) Harmony in Pianoforte-Study Ex. 26. Allegretto. STEP X3CV1II. Improvise short melodies in the major keys, the last two sounds of which will, in each case, provide a position for the chords of the subdominant and tonic. (Ex. 27.) Ex. 27. Placido. (fK"^o b J ^ ** IP -J 1 '-I ^=0 ^ *^F 1 "l II 1 ^~"V I jl _J M .. .1 v ^ ... STEP XXIX. Having played one octave of a minor scale in the harmonic form, sound the subdominant common chord of the same key. (Cf. Ex. 24.) Note 27. .4 grea/ difference between the dominant and subdominant harmonies is observable in the respective modes. Unlike the former, the chord of the subdominant varies with the mode, being a major chord in the major key and a minor chord in the minor key. An (Esthetic vari- ation of this type should be appreciated aurally to the fullest extent, and for this purpose Step XXIX should be alternated with Step XXIV. STEP XXX. Combine the common chords of the subdominant and tonic in various minor keys. (Cf. Ex. 25 translated into the tonic minor by substituting minor thirds in both chords.) STEP XXXI. Reproduce the progressions of Step XXX in deco- rated form. (Ex. 28.) Plain Harmony Ex. 28 Fed. STEP XXXIE. Repeat the progression of Step XXX many times consecutively, playing the chords in a new position at each repeti- tion. (Cf. Step XXVII.) STEP XXXIII. Improvise short melodies in the minor keys, the last two sounds of which will, in each case, introduce the progression referred to in Step XXX. (Ex. 29.) Ex. 2$ j nti 3. btafo. ^ ^ L/tfo /L * fv 1 > s vT) 4- J g i C i wj - . a m J /* ^^ * ^ 1 r~x ft) II I *f f J ^^ m if ^ f>, + II -S 'A B ^ E STEP XXXIV. Combine, in various major keys and in one un- broken progression, the common chords of the subdominant, domi- nant and tonic in the order given. The chords should be played in as many positions as possible. Great variety in melodic movement should also be attempted. Ex. 30 illustrates two of many possibili- ties. Ex. 3O. A. '(?'* 1 L/ . !/ o j II / I/ 1 O (^ ^j H /^\P b^ /v ^ I =^=1 (foP|?g ^ =g= ~^ H w 1 ! 1 ,5) II ) "**" ^ ^ rti.O _, ^=\\ ^=n i6 Harmony in Pianoforte-Study Note 28. // may be pointed out that, in progressing from the sub- dominant to the dominant chords, the best results are obtained when the upper parts proceed in contrary movement to the bass part. This is the case in each of the above examples. Note 29. The chords of the subdominant, dominant and tonic should also be treated intensively after the manner of Exs. 19 and 26; and this procedure may be followed with advantage in the remaining Steps of this Part. STEP XXXV. Treat, decoratively, the progressions of Step XXXIV. The embellishment may be in chordal form (Ex. 31) or in arpeggio-form. (Ex. 32.) In all cases the tonic chord should first be sounded. (Cf. Note 20.) Ex. 31. Leggiero. ^ % Ex. 32. Con moto. Plain Harmony 17 STEP XXXVI. Improvise short melodies in various major keys, the last three sounds of which will, in each case, provide a position for the chords of the subdominant, dominant and tonic. (Ex. 33.) Ex. 33. /kt>tT}| -* q ~fe~~: L/ i/ 1 j^^Jj N rgi-i- J. -&- rv iS rfr.Btr EESS -* f~ * 3E STEP XXXVII. Combine, in various minor keys and in one un- broken progression, the common chords of the subdominant, domi- nant and tonic. (Cf. Ex. 30 translated into the tonic minor by substituting a minor 3rd in the first and last chords.) The chords should be presented in as many positions as possible and great variety of melodic movement attempted. Note 30. The combination given in this Step should be compared carefully and experimentally with the same combination in the major mode. (Step XXXIV.) In the major key, the chord of the dominant stands between two major chords; in the minor, it is between two minor chords. Nevertheless, it must be clear aurally that the bass part IV, V, I is the same in either case. The tonic, dominant and subdomi- nant, or the three primary members of tonality, are invariable both in the major and in the minor. STEP XXXVIII. Treat, decoratively, the progressions of Step XXXVII. (Cf. Exs. 31 and 32.) ****** STEP XXXIX. Improvise short melodies in various minor keys, the last three sounds of which will, in each case, provide a position for the chords of the subdominant, dominant and tonic. (Ex. 34.) Ex. 34. Grazioso. tfTTf^^ ^=^\ \ ' r rf * - ' m* *-*? * P^- t=t^ i: Tf?!~ ucr ; ' ^ i8 Harmony in Pianoforte-Study STEP XL. Having played one octave of a major scale (Ex. 35, A), sound the common chord of the supertonic (B). Ex. 35. A. a Note 31. In the chord of the supertonic a minor chord, as will be observed the student is introduced to one of the tonal harmonies which, while highly important as members of the key, are lacking in the direct and positive effect peculiar to those of the dominant and sub- dominant. The latter chords, sounded in conjunction with the tonic harmony, provide the most perfect means of tonal satisfaction. The elementary student should therefore regard the remaining common chords of the scale as requiring the cooperation of the dominant chord for their clear expression in relation to key. The point involved may be expressed by a simple but helpful rule: When in doubt, proceed to the dominant harmony. STEP XLI. Form progressions in various major keys, introduc- ing the following chords in the order given: supertonic, dominant, tonic: (a) In plain form (Ex. 36, A); (b) in embellished form (B). B. Leggier o. Plain Harmony 19 Note 32. The movement of the bass part in the above example //, V, I should be observed and compared aurally with the same feature of Ex. 30, viz., IV, V, I. (Cf. Note 10.) The substitution of the chord of the supertonic for that of the subdominant necessarily 'widens the choice in melodic progression. The examples should not only be presented in as many chordal positions as possible, but each progression should contain a different melodic outline. STEP XLII. Improvise short melodies in major keys, closing with the chords of the supertonic, dominant and tonic. (Ex. 37.) Ex. 37. Largamente. ^ * X JT / ' r F 1 ^K t I LJ r r P * fT\ / 1 r * J 3 \>v/ V 25? < mf -== I =- -= kc :^~ ^ ^ = p -JP O-^v. r^ ^> fs II til* ^* ^^* , z / & STEP XLIII. Having played one octave of a major scale (Ex. 38, A), sound the submediant chord of the same key (B). Ex. 38. A. *=# Note 33. >l5 a secondary harmony of the key and, like that of the supertonic, a minor chord, the chord of the submediant is referred to in Note ji, g_.v. STEP XLIV. Proceed as in Step XLI, substituting the chord of the submediant for that of the supertonic. (Ex. 39.) To ensure correct tonal appreciation, begin, in each case, by sounding the harmony of the tonic. Ex. 39. A. fe- ^ -&- Harmony in Pianoforte-Study Note 34. The growing responsibility attending the use of new chords and of new chordal progressions renders it the more imperative that the student should be familiar, not only with the characteristic effect of each progression as a whole, but, in particular, with the individual movements of the respective bass parts. The bass movements of Ex. 30, IV, V, I; of Ex. 36, II, V, I; of Ex. 39, VI, V, I, should all be individualized clearly by the inward sense. STEP XLV. Improvise short melodies in major keys, closing with the chords of the submediant, dominant and tonic. (Ex. 40.) Ex. 40. Grazioso. njf ^ . ^"** "^ fi 1 tr^ " J^ ffffi r f t* n ' -1 -A * (JT) 4 r -\ \ _^_-f,^_ _ g * 1 */ ^^ ^"^^ P* -=- f"\ *fO ^? * ^? * <2 II B *if* J ^^* ^^* Hill ^ * ^* S | ^ vl V 'I * II STEP XLVI. Having played one octave of a major scale (Ex. 41, .4), sound the common chord on the mediant of the same key Ex. 41. A. Note 3$. The chord of the mediant, like those of the submediant and supertonic, is a minor chord. It is another of the secondary har- monies referred to in Note 31, q.v. Plain Harmony 21 STEP XLVII. Proceed as in Step XLI, substituting the chord of the mediant for that of the supertonic. (Ex. 42.) In each case, begin by sounding the chord of the tonic. STEP XLV1I1. Improvise short melodies in various major keys, closing with the chords of the mediant, dominant and tonic. (Ex. 43-) Ex. 43. Lento. n v * i ^ mf dim. m - *- STEP XLIX. Play the chord of the dominant 7th and its inver- sions in various keys, major and minor. (Ex. 44.) Care must be taken to ensure an effective presentation of each chord. Ex. 44. A. Root-position. 1st inversion. 2nd inversion. ^9- -OL. 3rd inversion. 3rd in bass. 5th in bass. 7th in bass. 22 Harmony in Pianoforte- Study B. Root-position. ist inversion. 2nd inversion. 3rd inversion. ^==i=FI :tirs=u== &-fo 3rd in bass. 5th in bass. 7th in bass. 1 Note 36. The student is here called upon to appreciate the mental effect of essential dissonance, or that type of dissonance which is an in- tegral and essential part of a prevailing harmony. The chords treated hitherto are in every case concordant; but the introduction of a dis- cordant interval, such as the ?th of Ex. 44, brings into existence a chord which requires the succession of another harmony to satisfy, to complete or resolve the dissonance created. The process of satisfaction, comple- tion, or to give the term usually applied to it resolution, is one of entire naturalness; and it should be particularly observed that the movement of the sound which forms the ?th is towards the jrd of the tonic harmony, and that this feature is operative in every position or inversion of the chord. STEP L. Combine in one progression the root-position of the chord of the dominant 7th and the common chord of the tonic : (a) In simple chordal form (Ex. 45, .4); (b) in decorated form (B). Fed. cresc. a 1 *Ped, STEP LI. Resolve upon the tonic harmony, in various keys, major and minor, the first inversion of the chord of the dominant 7th: (a) In plain form (Ex. 46, ^4); (6) in embellished form (B). Note 37. It must be particularly observed that the quality of dis- cordance is not impaired by the inversion of a chord which contains an essential dissonance. The aural necessity properly to resolve the 7th in Exs. 46, 47, and 48 is not less perceptible than in Ex. 45. Ex. 46. Plain Harmony Scmplice. i f*? * * -& STEP LII. Resolve upon the tonic harmony, in various keys, major and minor, the second inversion of the dominant yth: (a) In simple form (Ex. 47, A); (b) in decorated form (B). Ex. 47. A. Hr-yg- fcfc B. Leggieramente. Ped. * /'^ STEP LO. Resolve upon the tonic harmony, in various keys, major and minor, the third inversion of the dominant 7th : (a) In simple form (Ex. 48, .4); (b) in decorated form (B). Ex. 48. A. B. Pesante. ^ ^ - 1 24 Harmony in Pianoforte-Study Note 38. It will be remarked that attention to the natural resolu- tion of the 7th requires the last inversion of the chord to be followed by a first inversion of the tonic harmony. (Cf. Note 36.} Note 39. The last inversion brings into particular prominence the fact that the original dissonance of the chord is of a dual character. Not only is it the outcome of the fundamental and characteristic inter- val between the root and the 7th, but an additional dissonance is created between the 3rd and 7th in the form of a diminished $th or its inversion, an augmented 4th. The individual effect of these two discordant inter- vals may be appraised by playing in two ways the chord given in Ex. 48: (a) Omitting the 3rd, leaving thus the dissonance of the root and 7th only (Ex. 49, A); (b) omitting the root, the dissonance of the 3rd and 7th alone remaining (Ex. 49, B}. If Ex. 48 be subsequently played, the greater richness of the effect obtained from the union of the two dissonances will be clearly demonstrated. Ex. 49. A. rQ : 1 B. JZ. & l_fl ~~^ M fl\ ^^ II STEP LIV. Improvise short melodies in major and minor keys alternately, the last two sounds of which will in each case afford an opportunity for the introduction of the dominant 7th and its resolu- tion. (Ex. 50.) Ex. 5O. Con gusto. STEP LV. Play, in various major keys, harmonic progressions composed of the supertonic common chord, chord of the dominant 7th and tonic chord, each in the root-position: (a) In chordal form; (6) in decorated form. Plain Harmony 25 STEP LVI. Repeat the progressions of Step LV, introducing various inversions of the chords concerned: (a) In chordal form; (6) in decorated form. (Ex. 51.) Ex.51. Delicate. /TN r\ -i + 9 i p - U yf f--s 1 1 (S>4 *-"- f i ' =i=b ^' i r ' O ^e^ 3 ^ U S S Id 1 -&- f"\* i Z ' Fed. # A*/. Ped. * STEP LVII. Improvise short melodies in various major keys, closing with the progression referred to in Steps LV and LVI. STEP LVIII. Play, in various major keys, progressions composed of the submediant common chord, chord of the dominant 7th and tonic chord, each being in the root-position: (a) In chordal form; (6) in decorated form. ****** STEP LIX. Repeat the progressions of Step LVIII, introducing inversions of the chords concerned: (a) In chordal form; (6) in decorated form. STEP LX. Improvise short melodies in various major keys, closing with the progression referred to in Steps LVIII and LIX. (Ex. 52.) Ex.52. Piacevole. ^K J ff !I A^ -f 8 -f ' ^ ^ h-h- -s> -^-f| (ft *4 "^ 1 r ' ^ d f* r ^.^.j ( 2 ^ >> -^* ~~ -^t -s-: nttA H -F H \r if3 _l Ml ****** Note 40. The two forms of the minor scale known as the harmonic and melodic illustrate collectively the harmonic peculiarities of the minor key. Fundamentally, the harmonic form provides the framework for 26 Harmony in Pianoforte-Study the tonal harmony; but the variable degrees of the melodic form are suggestive of further concords which enrich greatly the harmonic possi- bilities of the minor mode. STEP LXI. Having played one octave of a harmonic minor scale (Ex. 53, ^4), sound the subdominant common chord of the same key (B). Add the harmonies of the dominant 7th and tonic, playing the whole progression: (a) In chordal form (C) ; (b) in embellished form (>). Ex. 53. C. B. ^- -<9- D. Brillante. 1 STEP LXH. Proceed as in Step LXI, substituting the chord of the submediant for that of the subdominant. (Ex. 54). Ex. 54. C. A. B. m BizH2 gZ ^^= = = D. Grazioso. Plain Harmony 27 STEP LXIII. Improvise short melodies in various minor keys, closing with either of the progressions referred to in Steps LXI and LXII. (Ex.55.) Ex. rf#- 55. Giocoso. 0- f 9 1 ^3 bpf ^g 1 f~ -f^% * J. j J 1 i ^ I i ^ M \~ t ' lL -Vn k - >* I*- * ^ ^- ^ P^H = Fed. * Fed. * Fed. STEP LXTV. Play one octave of various melodic minor scales, harmonizing the last three sounds as in Ex. 56. Ex. 56. i i P Note 41. The chord of the supertonic is represented in Ex. 56 as formed upon the melodic form of the scale. In this phase the chord is a common chord, and may be used with the absolute freedom usual in all harmonies of the kind. STEP LXV. Play an octave of the ascending form of various minor scales, harmonizing, in each case, the last three sounds as in Ex. 57. Harmony in Pianoforte- Study Ex. 57. fc^F 1 ] H ~g taH ^ x f] 1F ^ *- L -^ * ' r^ j_ o s II V'uvV ...j? . -4 * H Note 42. The chord of the supertonic is represented in Ex. 57 05 formed upon the harmonic form of the scale. In this phase it is not a common chord, and requires to be used with some discretion. STEP LXVI. Connect the chords of the supertonic, dominant and tonic in various minor keys. (Ex. 58.) Sound the tonic chord first in all cases. (Cf. Note 20.} Ex. 58. Leggiero. *dT i STEP LXVil. Improvise short melodies in various minor keys, closing with the progression referred to in Step LXVI. (Ex. 59.) Ex. 59. Espressivo. r \ Jf \\P fi ^^ N rj J i \ i U^ * ~^ ?1*\ [r bO K 1 DT /htJ ui 51 i v^l-f "lS P - ' * |H (H/l . 11 . rf II < *y r* * I H3 HI r Si in II J i P b * n * II Z b hi C A " b^ & . * * * * * * STEP LXVin. Having played one octave of a descending mel- odic minor scale (Ex. 60, A), sound that form of the chord of the mediant which is constructed upon the same scale (B). Follow the chord by suitable harmony and conclude with the tonic chord (Q. Plain Harmony STEP LXIX. Having played one octave of an ascending har- monic minor scale (Ex. 61, .4), sound that form of the chord of the mediant which is constructed upon the same scale (B). Follow the chord by suitable harmony and conclude with the chord of the tonic (C). B. 1 -z- Note 43. // w important to remark the nature of the difference between the two types of chord peculiar both to the supertonic and to the mediant. As exemplified in Steps LXIV and L XVII I, these chords are concordant; in Steps LXV and LXIX they are discordant. In the latter phase, they call for that particular form of harmonic treatment known as resolution. (Cf. Note 36.) The most elementary resolution is, in both cases, effected by the succession of the chord a 4th above. Therefore, the student will do well to resolve the supertonic chord with the diminished 5th upon the chord of the dominant; the mediant chord with the augmented 5th upon that of the submediant. Note 44. The student will now be called upon to appreciate the various mental effects obtained from one common chord by change of tonal environment. Thus, the major common chord in Ex. 62, A, is that of the tonic; in B, that of the dominant; in C, that of the sub- dominant; in D, it appears as the dominant harmony of a minor key; in E, as that of the submediant, also of a minor key. Harmony in Pianoforte-Study B. -&- c. -7p*jf |J> ^ cS _^ 1 -g <5 ~0 1 -jr : ^ t " D. A u <5 V i " , IO -^j <&* h^ J <5* (fo <5? ? ^ ^ ^ li rt J -& " ^ /^ -3T3 -^; u - E. ntt ^ - J2- l/Jfu. 12 <5 % II ^ s ^ J rHi or : ^- z? * &! j^ > II -rr STEP LXX. Select various major common chords, trace them through the five keys in which they occur individually, and treat them in the manner exemplified by Ex. 62. In each case the mental grasp should first be stimulated by playing one octave of the scale concerned or by sounding the chord of the tonic. Note 45. The same process may be continued in connection with minor common chords. Thus, the chord in Ex. 63, A, is that of the tonic; in B, that of the subdominant; in C, it is transferred to the major key and appears as the chord of the supertonic; in D, as that of the submediant; in E, as that of the mediant. Ex. 63. A. *== B. \JjLb - ZP * 1^ ^ j-tt m S | L^T 23 S> ^~ c. -z; -- 4 j & |o ^ ~& i ~TL^ & & ~ ~ --* ^=1 -&- Plain Harmony D - J -^ I/ [/ I*J /o ~fir& ^ 73 (5> - a i < ^ \A) o <^ & 1^1 ^ I E - J Q k < ^ IO /^i ^ a | ^K,b|> . 25 S> ^ - g a 5? W Kq? p g> *"- ^ : S H STEP LXXI. Select various minor common chords, trace them through the five keys in which they occur individually, and treat them in the manner suggested by Ex. 63. Begin, in each case, by playing one octave of the scale involved. Note 46. It is impossible to exaggerate the importance of the tonal appreciation connected with Steps LXX and LXXI. The positive and negative elements of tonality whether major or minor are symbolized by the admixture of major and minor chords con- tained within every form of key; and the mental discrimination which realises the perpetual presence of these two forms of chordal expression in music of every type is the gateway to an understanding of harmony in its most occult forms. Note 47. The discords referred to in this Part are, in all cases, exemplified with their most natural form of resolution. If a resolu- tion of this nature were invariably applied to every discord, the expres- sion of harmony would sink to the level of mere conventionalism. As soon as the student has grasped the elements of the idea embodied within the act of resolution and has proved his grasp by illuminative exempli- fication, he should proceed to experiment with the less general, if less natural, phases of resolution; bearing in mind that the thought which underlies the process is that of the absorption of dissonance in another harmony, and that, provided that the absorption be complete, any reso- lution of a discord is acceptable to the musical sense. We append a few resolutions of the chord of the dominant 7th. In Ex. 64, A, the chord is resolved upon the harmony of the submediant; in B, upon that of the subdominant; in C, upon that of the super tonic. Harmony in Pianoforte-Study B. Ca f\ u jf ntabile. , 1 * < "~~N If O/. -*-= 4 H- P-4- =r^ k&L&L f- rf ^~ )*- --; J ^-h ^3F i r 1 ^ .* F C 1 p_ ^f .*- *^ *-^- . * -- -- p-T- p p' rv * t-V Kfi | -J tz -- -f H F-- -! M _ 1 ^SH ***"" ***" ' ^& ^^ &* -f JJ r i^a >^-U ^ C. Vivo. M U ^-A-- /fcpfe f * M *T r-7 fff* s 1 ! -^-Tf-l ^ l -^^ * u* rn /TN 1 11_, 1_| * "| i ; ! . ^> stacc. rr r ^ LLi^ TiH*-i-f-- ^ fi-^- ***J ff * ff ^= -^-l c r H 1 1 1 1 m i * 1 1 Jf jl TJ 1 - J g , - i . * F ^ F ! r 1 ICn 'I J_ 5 |ZKjl z f- 1 f * II iv|/ *r_ *rsr^3 - -6*- ^.7 STEP LXXII. Improvise progressions in major and minor keys, introducing examples of various resolutions of the dominant yth: (a) In chordal form; (&) in decorated form. (Ex. 64.) STEP LXXIII. Combine any of the chords inverted or un- inverted referred to in this Part. The following combinations should be regarded merely as suggestive. Each progression should be presented both in simple chordal form and in florid or decorated form. (^4) Major Keys. (1) Tonic subdominant dominant (yth) tonic. (2) Tonic mediant submediant dominant (yth) tonic. (3) Tonic submediant supertonic dominant (yth) tonic. (4) Tonic dominant supertonic subdominant domi- nant tonic. (B) Minor Keys. (1) Tonic subdominant dominant (yth) tonic. (2) Tonic submediant -subdominant tonic. (3) Tonic submediant harmonic supertonic domi- nant (yth) tonic. (4) Tonic dominant harmonic mediant submediant subdominant tonic. End of Part I. PART II Auxiliary Sounds Note 48. Music is composed of two species of sounds: (a) Those which form a part of the prevailing chord or harmony, (b) those which are foreign to the harmony. All the sounds referred to or de- scribed in Part I are of the former species; those indicated by asterisks in Ex. 65 belong to the latter. Ex. 65. ^-J$tl ,5) x -0 ^ in =: r Fed. * Fed. * Fed. Note 49. An introductory experiment is necessary to explain the operation and nature of auxiliary sounds. A series of repeated sounds may be played during the continuance of a chord of which the repeated sounds do not form a part. (Ex. 66, A.) No explanation will be necessary to indicate the unmusical character of the effect produced. If, however, the same sounds are followed immediately by sounds of the harmony (IS), the process satisfies the musical sense. This process is analogous to the act of resolution referred to in Note 36. 34 Harmony in Pianoforte-Study ' _^__^ __~__ ____^_ . i , j. j. . j. j. j. j. v -j^J 5*5^?^i STEP LXXEV. Play examples oi single major and minor com- mon chords. In each case, introduce auxiliary sounds as in Ex. 66, B, repeating them several times before the act of resolution. N. B. Each auxiliary must be one scale-degree above any one sound of the chord selected. Note 50. An auxiliary sound stands in the place of the harmonic sound which it displaces temporarily. The characteristic dissonance of such a sound arises from the fact that the sound of resolution is mentally inferred at the moment when the auxiliary is heard. Hence, the sounds indicated by asterisks in Ex. 67, A , are not auxiliary sounds, because the ear expects them to be followed by the harmonic sounds which they have displaced. In B, on the contrary, the sounds similarly marked are in each case resolved upon the neighboring harmonic sounds, and the ear is satisfied. Ex. 67. B. ^=^^ STEP LXXV. With the left hand play the tonic chord of any major key; with the right hand play successively: (a) A sound of the harmony, (6) an auxiliary sound one scale-degree above, (c) the original harmonic sound. Repeat in various major keys. The process is illustrated by Ex. 68, and may be adapted to different times and figurations. Ex. 68. Auxiliary Sounds 35 Step LXXVI. Proceed as in Step LXXV, playing the moving part below the chord. (Ex. 69.) Ex. 69. CD" fi S^T 55 " - - - V " <.'* -C*T ' -f~* ^ * J r~ ~i H ^T-bH ^ , ^ ' J r J r 1 "* 1 1 s H ****** STEP LXXVH. Transfer Steps LXXV and LXXVI to minor keys. Note 51. Auxiliary sounds may consist of the scale-degree of the prevailing key or of sounds which belong specifically to the chromatic scale of the same key. Those treated hitherto are of the former kind; those now to be considered include the latter. STEP LXXVIH. With the left hand, play the tonic chord of any major key; with the right hand, play in succession: (a) A sound of the harmony, (6) an auxiliary sound one semitone below, (c) the original harmonic sound. (Ex. 70.) Repeat in several major keys, employing various time-groupings and figurations. Ex. 7O. (4^f PS s V -ihid j" r r r- H * 5 *- g"V'^ f^ -P 5S ^ ii 5 ^ ^% r ^ II * 1 1 1 II ***** STEP LXXIX. Proceed as in Step LXXVIII, playing the mov- ing part below the chord. (Ex. 71.) Ex. 71. Sfi: 36 Harmony in Pianoforte-Study STEP LXXX. Transfer Steps LXXVIII and LXXIX to minor keys. ****** Note 52. The auxiliary sounds considered hitherto have been cen- tred round the individual members of a single chord. No provision has yet been made for progressing from one sound of a chord to another. In a broad sense, this may be illustrated by a passage passing through every sound of the scale during the prevalence of the tonic harmony. (Ex. 72.) Ex. 72. I STEP LXXXI. Play scale-passages above or below the tonic harmony of various major keys after the manner of Ex. 73. Ex. 73. 1 ^ \\A STEP LXXXIL Transfer Step LXXXI to minor keys, using (a) the harmonic scale, (b) the melodic scale. STEP LXXXIQ. Introduce diatonic auxiliary sounds between the various members of major common chords. This should be done in various times, with diverse figurations and at various oc- taves. It will be noted (Ex. 74) that a single auxiliary suffices be- tween the root and 3rd or between the 3rd and 5th; while, between the 5th and octave, two such sounds are necessary. Ex. 74. Auxiliary Sounds 37 STEP LXXXIV. Proceed as in Step LXXXIII, playing the moving part below the chord. (Cf. Exs. 69 and 71.) STEP LXXXV. Transfer Steps LXXXIII and LXXXIV to minor keys, using (a) the harmonic scale, (6) the melodic scale. (Ex. 75-) Ex, 75. Moderate. Note 53. TTie use o/ the melodic minor scale enjoined here will demonstrate the origin of the name and the purpose of the scale in the most effective manner. Speaking broadly, the major 6th and major ?th are employed in ascending passages, the minor 6th and minor ?th in those which move downwards. STEP LXXXVI. Introduce chromatic auxiliary sounds between the various sounds of major common chords. As before, different times and figurations should be attempted. Ex. 76 is a chromatic version of Ex. 74. Ex. 76. 38 Harmony in Pianoforte-Study STEP LXXXvlI. Proceed as in Step LXXXVI, playing the moving part below the chord. STEP LXXXVni. Transfer Steps LXXXVI and LXXXVII to minor keys. Ex. 77 is a chromatic version of Ex. 75. Ex. 77. Moderate. Note 54. The student has now demonstrated his power to form an independent melody upon one harmony. It is extremely rare, however, to find a melody constructed upon so limited a basis. Variety in melodic formation calls for the use of many harmonies, and the facility with which an auxiliary sound joins two members of the same chord is but a faint indication of its power to connect sounds belonging to differ- ent harmonies. The continuity of the melody of Ex. 78 is the outcome of the use of the auxiliary sounds indicated by the asterisks. Ex. 78. Andante. Fed. Auxiliary Sounds 39 Fed. STEP LXXXIX. Combine the dominant and tonic chords in various major keys. Add a diatonic melody, using auxiliary sounds in the process. (Ex. 79.) Sound the tonic harmony before each example. (Cf. Note 20.) Ex. 79. i STEP XC. Transfer Step LXXXIX to minor keys. STEP XCI. Repeat Steps LXXXIX and XC, employing oc- casional chromatic auxiliary sounds. Ex. 80 is a chromatic version of Ex. 79. Ex. 8O. 4 o Harmony in Pianoforte-Study STEP XCII. Combine the chords of the subdominant, dominant and tonic in various major keys. Add a diatonic melody, employing auxiliary sounds in the process. Sound the tonic harmony before playing each example. (Cf. Note 20.) ******. STEP XCIII. Transfer Step XCII to minor keys. (Ex. 81.) Ex. 81. STEP XCIV. Repeat Steps XCII and XCIII, employing oc- casional chromatic auxiliary sounds. Ex. 82 is a chromatic version of Ex. 81. Ex. 82. -= n'lLal ^1^ ~l 3 b! g j ! | => fe ****** Auxiliary Sounds Note 55. // is an essential characteristic of all auxiliary sounds that they should proceed to their sounds of resolution by the step of a second; but it is not necessary that they should be approached in the same manner. Any auxiliary sound may be approached by leap. The auxiliaries in Ex. 83 are thus treated in every instance. Ex. 83. Moderate. Fed. STEP XCV. Add to various tonic chords, major and minor, melodic passages containing diatonic auxiliary sounds approached by leap. (Ex. 84.) Ex. 84. Teneramente. W^ 1 > H ^ ] Bi = ^ ^H Jn f\ ^ K - jj X i X ^..[j -^r-^-ld 9 H: J rinf. STEP XCVI. Form, upon the following harmonic bases, melo- dies containing diatonic auxiliary sounds approached by leap. (A) Major Keys. (1) Tonic, dominant, tonic. (2) Tonic, subdominant, dominant, tonic. (3) Tonic, submediant, supertonic, dominant, tonic. i Harmony in Pianoforte-Study (B) Minor Keys. (1) Tonic, dominant, tonic. (2) Tonic, subdominant, dominant, tonic. (3) Tonic, subdominant, submediant, dominant, tonic. STEP XCVII. Add to various tonic chords, major and minor, melodic passages containing chromatic auxiliary sounds approached by leap. Note 56. The direction to add chromatic auxiliary sounds must not be interpreted as meaning that every sound of the kind is to be chro- matic. Ex. 85 is a chromatic version of Ex. 83; and the student will remark that auxiliary sounds of both types, diatonic and chromatic, are included. Ex. 85. Moderate. Fed. * STEP XCVin. Form, upon the harmonic bases given in Step XCVI, melodies containing chromatic auxiliary sounds approached by leap. Note 57. Auxiliary sounds may occur upon a non-accented beat or upon the weaker part of an accented beat; or they may be introduced upon an accented beat or upon the stronger part of any beat, accented or unaccented. The appoggiatura furnishes a familiar example of the latter kind. The auxiliaries treated hitherto fall upon the weaker parts of the bars or beats; in Ex. 86 they occur throughout upon the stronger. Ex. 86. Allegretto. Auxiliary Sounds 43 STEP XCIX. With the left hand, play the tonic chord of any major key and in any position or inversion; with the right hand, add a melody containing accented diatonic auxiliary sounds after the manner of Ex. 86. STEP C. Proceed as in Step XCIX, playing the moving part in the bass. (Ex. 87.) Ex. 87. Allegrttto. STEP CI. Transfer Steps XCIX and C to minor keys. (Ex. 87.) ****** STEP OH. Proceed as in Steps XCIX and C, playing each auxil- iary sound at the distance of a semitone below the harmonic sound. This will entail the use of chromatic auxiliary sounds. (Ex. 88.) Ex. 88. Esfressivo. STEP Cffl. Transfer Step CII to minor keys. ****** 44 Harmony in Pianoforte-Study STEP CIV. Form, upon the harmonic bases given in Step XCVI, melodies containing examples of diatonic accented auxiliary sounds. (Ex. 89.) Ex. 89. Generoso. STEP CV. Proceed as in Step CIV; but introduce auxiliary sounds of both types, diatonic and chromatic. Note 58. One of the most striking evidences of the value of the auxiliary sound in respect to musical effect is obtained by sounding the auxiliary together with the chord upon which it is superimposed; and, it may be added, no slight difficulty is often experienced by the student who, in such cases, is inclined to confuse the foreign sounds with those belonging to the prevailing harmony. The auxiliary sounds in Ex. 90 are all easily recognisable as such, but the charm which accompanies their dissonance against the respective chords may not be immediately perceptible. The harmonic education of the ear is rarely of greater importance than in this particular phase of aural appreciation. Ex. 9O. Sonore. ^- * cresc. r/'T & -\ \ ^ \ ~^\ 3 3 1 -& ** -& & #- 1 Auxiliary Sounds 45 STEP CVI. Incorporate auxiliary sounds, diatonic or chromatic, with the members of the tonic harmony in various keys, major and minor: (a) In plain form (Ex. 91, .4); (6) in decorated form (B).* Ex. 9 1 . 4 J i B. Grazioso. STEP CVII. Proceed as in Step CVI, taking the dominant and tonic chords as the basic harmony. (Ex. 92.) Ex. 92. Grazioso. This may appear to be an unnecessary repetition of Steps XCIX, etc. It must be ob- served, however, that the attention of the student is here directed to the chordal aspect of the auxiliary sound as compared with that phase of the sound which is more particularly concerned with pairing from one melodic sound to another. 46 Harmony in Pianoforte-Study STEP CVin. Improvise phrases containing chords treated as in Ex. 90. The harmonic bases given in Step XCVI may be regarded as suggestive. Note 59. The law which directs the resolution of an auxiliary sound by the step of a 2nd is apparently broken in Ex. pj. This, how- ever, is not the case. The auxiliary sounds above and below the har- Ex. 93. manic sounds A and F are both brought into play and the resolution is therefore only postponed. This most useful device is known as a 11 changing-note" and the term implies the obvious changing of one auxiliary for another. One of the most familiar examples of the use of changing-notes may be found in the first subject of Weber's "Rondo Brillante " in E flat, of which we quote the first bars. (Ex. 94.} Ex. 94. Moderate e con grazia. B:.b2 a A ^ 9 b4 H I E E STEP CIX. Form changing-notes upon various chords, major and minor; or upon various combinations of chords. (Ex. 95.) Auxiliary Sounds 47 Ex. 05. Allegro. Note 60. We have seen that the use of auxiliary sounds below the members of a chord entails the introduction of chromatic sounds on those foreign to the key-signature. Sounds of this nature may be freely employed in passing from chord to chord, provided that the one con- dition common to the use of all auxiliary sounds be observed that resolution be effected strictly by conjunct means or, in other words, by the step of a 2nd. (Cf. Note 55.) Ex. 96 contains sounds of this kind. Ex. 96. i Note 61. rAe student is now in a position to improvise progres- sions formed upon the tonal harmonies generally, and it should be his ambition steadily to increase the number of chords used. The chordal 48 Harmony in Pianoforte-Study successions outlined in Step XCVI have been frequently used as ex- amples of basic harmonies, and they possess, at least, the merits of simplicity and directness. But the student must no longer be content to limit his exemplification to harmonic conventions; on the contrary, he must begin to experiment in the broadest possible manner. The com- binations opened up by the accented auxiliary sound are practically inexhaustible; and, at the present stage, there is no better way of cul- tivating aural discernment and facility in musical self-expression. End of Part H. PART III Cadences Note 62. Before proceeding to the substance of this Part, the student is counselled to make a careful examination of Lussy-Dutoit' s " Short Treatise on Musical Rhythm. 11 * It is impossible to progress to any extent in harmonic facility until the connection between harmony and the musical cadence, as the defining medium of rhythm, is per- fectly clear to the musical sense. Note 63. In musical parlance and regarded broadly the cadence is the close of a musical thought. The following thoughts from Beethoven's Sonatas may be played at this point to illustrate the function of the final cadence, the attention being confined in each case to the effect of the last two harmonies: Op. 2, No. i: second mov., bars 23 to 27. Op. 2, No. 3: first mov., bars Q to ij. Op. 2, No. 3: third mov., bars 8 to 16. Op. 7: fourth mov., bars I to 8. Op. 10, No. 2: second mov., bars i to 8. Op. 14, No. i: third mov., bars i to 8. Note 64. Two chordal combinations of a cadential nature were referred to in the course of Part I (Steps XV, XX, XXV, XXX). Since these are generally used at the close of musical thoughts, they form examples of the final cadence or the full stop of the musical lan- guage. Note 65. Scarcely less important than the cadence itself is the harmony by which it is approached. The many Steps of Part I which call for the combination of three chords will have prepared the student to approach the dominant harmony in various effective ways; but since it is not possible to conceive a cadence in the absence of an idea to be cadenced, he should strive to gain the utmost facility in the expression of the harmonies which form the main part of each thought. The tran- sition to the closing harmonies will then be natural and free from arti- ficiality. The elementary combinations suggested in Step XCVI may first be used as basic models for the expression of properly cadenced progressions. * English translation by the author (Winthrop Rogers, Ltd.). 49 5 Harmony in Pianoforte-Study STEP CX. Improvise short harmonic progressions in various major keys, ending with a full close in the tonic. Place the 3rd in the uppermost part of the penultimate or dominant chord, so that it may proceed naturally to the octave of the tonic in the final chord. STEP CXI. Transfer Step CX to minor keys. Note 66. A perfect cadence is often presented in such a manner that the effect of finality is modified considerably. Thus, the tonic chord may contain the jrd or $th in the top part; in either case, the final force will be greatly lessened. In Ex. 97 both types are illustrated; the cadence at * is but semi-final; that at ** is absolute. Ex. 97. BEETHOVEN. Sonata, Op. 90. [/**,, 8*9 1 m w ^ H y ~ * "* 1 1 -* - I . , r ^ * f M * P f P f i^TTfr * + 3 \ 4 Cadences $ i STEP CXII. Improvise short harmonic progressions in various major keys, ending, in each case, with a perfect cadence in the tonic of the non-absolute type. STEP CXm. Transfer Step CXII to minor keys. ****** Note 67. Like their prototypes, the stop-points of literature, the cadences of music are definitely final, semi-final, or distinctly non- final; further, an infinity of shade significances lie between the ex- tremes of absolute finality and absolute non-finality. Thus, the semi- finality of the dominant-tonic cadence just illustrated may, as in Ex. Q8, be made still less final by the use of inversions. Ex. 98. Maestoso. i j=i . r x l **=>, Harmony in Pianoforte-Study Note 68. This cadence is comparatively seldom used to indicate finality in instrumental music, but it is of frequent occurrence in choral and particularly in church music. The student should, however, be familiar with its use at the keyboard. STEP CXVH. Transfer Step CXVI to minor keys. STEP C XVIII. Proceed as in Step CXVI, but present each ca- dence in inverted form. Ex. 1OO. Deciso. STEP CXIX. Transfer Step CXVI 1 1 to minor keys. (Ex. IOO.) Note 69. Many varieties exist of the cadence used to produce an effect of non-finality, of incompleteness and abeyance of idea. The most usual form is that in which the harmony of the dominant is the last heard. (Ex. 101.) Cadences 53 Ex. 101. Allegro vivace. BEETHOVEN. Sonata, Op. 31, Nr t * * " ' r; 1 . / *-& j; i C x x I ~x x j ^J 3 =r: .. &^j P ^ =i 3 (5* ^ 1 ^~ i J-^ -J ^-i i ri ii m^ 1- ^ J If 8 |b *" 1 * * 1 1 i i-i -&T T~x Tl '-^i.' 11 frw^r. | r-y9 z&9 n ~> ^~* ^s^cfe-wfa--^ Cug |~U^ g g* ^J> ^g=Rg=j. ' ^ fe~ U STEP C XXXIV. Apply simple forms of decoration to the pro- gressions of the previous Step. Three phases of embellishment should be attempted: (a) With plain chordal or arpeggio treat- ment (Ex. 112); (6) with unaccented auxiliary sounds (Ex. 113); (c) with accented auxiliary sounds (Ex. 114). 58 Chordal Transference 59 Ex. 1 12. n f f f |f p ' f fan. rfTt^Jt^llb^-H ^S ^ ^ ^5 ^rfT^ :fac adgl: S5 ^ i M^ Ex. 1 13. Volante Ex. 1 14. y? ndante. I""" ^ ^ i i H i fe- 3-| /ffci ^ fc 1 * '-H 1 1 " -fri i ^ i P m * t __^- _^ "*f 4 J 4- i i #***** 6o Harmony in Pianoforte-Study STEP CXXXV. Proceed as in Step CXXXIII, taking any minor common chord as the antecedent harmony. A few examples are appended. C. D. E. -19- l~ I g fry I g V' STEP CXXXVI. Apply forms of embellishment to the progres- sions of Step CXXXV, after the manner of Exs. 112, 113 and 114. Note 78. Three chords, all having one sound in common, may now be linked together; but, as heretofore, without reference to key. In Ex. 116 the common sound proceeds from the 5th of the antecedent chord; in Ex. 117, from the root. Ex. 1 16. Ex. 1 17. STEP CXXXVTI. Starting from any major common chord, link together three common chords, all having one sound in common. The root, 3rd, and 5th of the antecedent chord should be taken in succession as the link-sound. STEP CXXXVin. in embellished form. Present the progressions of Step CXXXVI I Note 79. In the process of embellishment, it is not necessary that the link-sound should remain throughout in one individual part. It is sufficient that the student realize mentally the source of the cohesion between the respective harmonies. The chords of Ex. 117 are here presented in varied form (Ex. 118). Chordal Transference 6i Ex. 1 18. Allegro. ^- i - tfe- ^ ifmi J" r~k J -t S -* \ VUJ4 B I ' _ * < /^" ^ fr (W== ^T-F?F^- -^r^f- t bm , m r T 1 1^4 * r Fed. * b ' # /vI x= - * S^Z __^___i p0 1 1_ ^*-bfe. +- F H>. t-. ^^ RT 1 1 1 1 * 1 Kf i ^b * P 1 1 [ H ^n n ^. ^^ I i T bJ. ~~i r~H II K? # /v * Note 80. ^4 series o/ /Aree chords, linked together in the manner iemonstrated, may be brought within the range of declared tonality by adding a perfect cadence suggested a by the progression as a whole or (b) by the effect of the third chord. The entire progression of Ex. IIQ, for instance, prepares the mind naturally for the key in which the final Ex. 1 19. Ex. 1 19. Lento. !% s i I; -F P- S E3^^ i ^r~* JL iAa rr ^ IP p ^ i cadence is cast. In Ex. 120, on the contrary, the mind waits instinc- tively until the third chord determines the tonal trend of the passage. Ex. 12O. Vivace. 62 Harmony in Pianoforte-Study STEP CXXXIX. Starting from any major common chord, link together three common chords, all having one sound in common. Add a perfect cadence in accordance with the tonal suggestiveness of each passage. In Exs. 121 and 122 the 3rd of the first chord, and in Ex. 123 the 5th, is the link-sound. Ex. 121. ~^~- Ex. 122. -$*- Ex. 123. z. 1 V '-^ I/TV _ \/^ vjj & S lm.i^ \\ K \j & ka -&- 9" t U f~\' ^G> LT & ~^f- P-i9 (>2? UL^ STEP CXL. Present the progressions of Step CXXXIX in em- bellished form. Note 81. Many varieties of the type of harmonic movement out- lined in Note 79 may be discovered by the enterprising student. The link-sound to name but one example may be placed in the bass, entailing thereby the use of chordal inversions. (Ex. 124.) Chordal Transference Ex. 124. Largamente Note 82. Chordal transference occurs in passing from one key to another, a harmonic function of great importance. Thus, any one sound of a common chord may be regarded, prospectively, as root, jrd, or 5th of a common chord, major or minor; or as root, jrd, 5th, or Jth of 'the chord of the dominant 7th. The 5th of the chord of F major may, in this manner, provide a means of transference to many keys. (Ex. 125 .) Ex. 125. A. B. As root. C. As minor 3rd. _g & Tyyg ;fg D. As major 3rd. E. As 5th. F. As root of dom. 7th. G. As 3rd of dom. 7th. H. As 5th of dom. 7th. I. As 7th of dom. 7th. STEP CXLI. Regard the root, 3rd or 5th of any major common chord as providing a means of transition to other chords, forming the several progressions upon the models given in Ex. 125. Complete each progression by a final cadence in the new key. The examples should be played: (a) In plain chordal form; (6) in embellished form. Ex. 126 is an embellishment of Ex. 125, G. Harmony in Pianoforte-Study Ex. 126. STEP CXLII. Proceed as in the previous Step, taking, in each case, a different minor common chord as the antecedent harmony. Note 83. Chordal transference of a more subtle nature may take place when a chord is conceived as possessing a dual individuality; or, in other words, as related directly to two keys, to the antecedent key and to a new key remaining to be established. In Ex. 127 the third or tonic chord, of the first key is quitted as the submediant harmony of the new key. Ex. 127. STEP CXLin. Establish one key by combining not less than three chords; regard the last chord as belonging both to the first and to another key, adding two or three chords to confirm the new tonality. Note 84. Step CXLIII opens up a mine of possibility to the student. It is only necessary to add that the examples should also be played in decorated form. Ex. 128 is an embellished reproduction of Ex. 127 and is illustrative of the type of passage now to be attempted. Chordal Transference Ex. 128. Grastioso. End of Part IV. Sequences and Pedals Note 85. Continuity of musical thought is obtained in many ways; in some cases, by the use of devices of a purely decorative origin. The simple harmonic progression at A in Ex. 129 is subsequently re- peated on successive degrees of the same key, and a complete musical thought is the result. Ex. 129. STEP CXLIV. Play a simple harmonic figure of two chords Form a sequence by reproducing this figure on successive degrees of the same key until a perfect cadence is reached. Note 86. No limit may be assigned to the number of chords con- tained within the model progression, save only that which is necessarily imposed by an accurate perception of rhythmic proportion. In Ex. jjo the model contains four chords. Ex. 13O. Giocoso. "^j J J H * ' m J_g 3_ / ~^d^ ' ^ h d 4~. i - i fn\jt ^ J m m ' * | Vl/1- ] *1 d ^i r "1 8 . ^ ^ ^ L/ *" ' f^W 1* *~=j i F^ ^s F a ^ : P ** =1 - =? U y 66 Sequences and Pedals i dim. e rail. ^T ^-fi r | ,t t t * .f^fr f i * c=c^ ^ i \j -^T r~^ ^ i v * j -p-* 1 ^ i : ^i i 3f STEP CXLV. Form models consisting of more than two chords and proceed as in Step CXLIV. Note 87. // w wo/ aw essential feature of the sequence that the reproductions of the model should occur upon the consecutive degrees of the scale. Any degrees may be selected by the player to form the basis of the thought he desires to express^ In Ex. 131 one degree is missed between each reproduction of the model. Ex. 131. Andante, STEP CXLVI. Form sequences of varied extent, omitting re- productions upon some of the scale-degrees of each key chosen. Note 88. The sequences treated hitherto occur throughout within the key of the model. Progressions of this nature may, however, provide an excellent medium for modulation. The model of Ex. 132 is trans- ferred through keys which correspond in number to the reproductions. 68 Harmony in Pianoforte-Study Ex. 132. Ben marcato. pfa -&-_ _22 m Note 89. // mW &e observed, that the major and minor modes are used interchangeably in the above sequence. This is due to the neces- sities which underlie the employment of several keys in close succession. The successful formation of sequences of this nature demands a large amount of harmonic experience and a keen sense of tonal effect. STEP CXLVII. Having formed a strongly tonal model, repro- duce it in sequential form in three or four keys. The final cadence may be in the original key or in that of the last reproduction. Note 90. A sound, entirely independent of the harmony, is fre- quently sustained throughout a series of chords. A sound of this kind appears in instrumental music under various forms. In Ex. Jjj the pedal or pedal-point, as it is sometimes called is observed in its simplest form; in Ex. 134 it is decorated by octave repetitions; in Ex. 135 it is embellished by a shake. Ex. 133 So 0r0. l 1 i JltfJ** ^ J fl 1 1 1 i <=== i 1 1 2 -3 * -J 4 J f-i H J J J J 1-1 {(T) v tte Sr-J -i *^* -! 9 ai i 5 1 ."I H _ .. J I I ! ! J I 1 * 3^3. J -,-U, C^-J ft'U t!^. ^ s Jd * 9 = PJ ~^ H b|> u4 jy xv -- ?y ~M M Sequences and Pedals Ex. 135. Con brio. /K*f i 3 q ., t9>4 T * **^ ^ n h" . u * ^ L/rt J ^ "JS p 1 i 1 i 1 i pv V M i r f- 1 r-J- J J9- t E F ^-M^ 1 ' =1 J n^ F r\- 1 i n ^^-U 1 ^ -5^ ^Ml /r. 70 Harmony in Pianoforte-Study Note 91 . The scale-degrees usually employed as pedal-sounds are the tonic and dominant. The dominant is used in Ex. 133; the tonic in Ex. 134; while in Ex. 135 both degrees are introduced. Note 92. A pedal may occur above, below, or actually within the accompanying harmony. Ex. 136 illustrates the employment of three inner dominant pedals in the keys of F, D minor, and C, respectively. Ex. 136. Vivo. * I>- * * * SCHUMANN. Papillons. & (*> = H - *? * ^~ t>- Z ffi FJi L H 1 Note 97. // must be specifically understood that any common chord, major or minor, may be introduced into any key, major or minor. That some chromatic chords are difficult to treat successfully is the natural result of the differences between close, comparatively close, and remote key-relationship. A wide field for experiment lies here for the re- sourceful student, who should not be satisfied until he is able, spon- taneously, to employ such chords with entirely musical effect. STEP CLIV. Transfer Step CLIII to the minor mode. STEP CLV. Combine the processes outlined in Steps CXLIX and CLIII. Complete harmonic progressions will result, in each of which the chromatic chord will occupy a central position. Ex. 142 may be regarded as a simple model. STEP CLVI. Transfer Step CLV to minor keys. (Ex. 144.) Chromatic Harmony 75 Ex/ 1 44. Graziosd, Note 98. When used in its native key, the chord of the dominant 7th is strictly diatonic; when used as it may be in other keys, it becomes chromatic. The successful appropriation of this chord for use in other keys depends to some extent upon the comparative nearness or remoteness of the tonal relationship of those keys to its original key. It is, for example, possible to introduce the dominant jih of G (Ex. 145} or of F (Ex. 146} into the key of C with but little difficulty, since both keys are related tetrachordally to the central key; but the problem is ac- Ex. 145. Ex. 146. centuated in proportion as the scale-relationship becomes more remote. In Ex. 147, for instance, the dominant fth of E is employed as a chro- matic discord in the key of C. Ex. 147. Note 99. However tonally remote may be a chord of this type, it is always possible to recover, as it were, the key of the tonic by the simple expedient of following the order of tetrachordal alliance. For instance, Ex. 147 may be continued as in Ex. 148 without loss as regards the antecedent tonality; but a progression of this kind is avowedly clumsy and should be resorted to only for the purpose of demonstration. In all cases, it should be the aim of the player to annul as soon as possible Harmony in Pianoforte-Study Ex. 148. the disturbing element which threatens the tonality; and this can usually be effected by the immediate interposition of some chord specially indica- tive of the original key. STEP CLVII. Improvise passages in various major keys, in the course of each of which may be introduced the chord of the domi- nant 7th of one of the keys allied tetrachordally with the key se- lected. Follow the chromatic chord of the 7th by the dominant 7th, inverted or uninverted, in the manner illustrated by Exs. 145 and 146. STEP CLVHI. Transfer Step CLVII to minor keys. STEP CLIX. Proceed as in Steps CLVII and CLVIII, but in- troduce dominant 7ths of keys more remote than those directly con- nected tetrachordally with the central key. A few examples are appended. Ex. 149. Piacevole. Ex. 1 50. Deciso. -^. i! r i jn gyVj_f r r~i ^KftVJ x- =^=h 3 J *= LJ i Chromatic Harmony 77 Ex. 151. Largo. * * * * * Note loo. A chromatic chord, of great usefulness to the player may be found in that known as the augmented 6th, from the interval between its extreme sounds. It is generally observed in three distinct forms: Ex. 152, A, accompanied by the major jrd, its simplest form; B, by the major jrd and augmented 4th; C, by the major jrd and perfect $th. Ex. 152. A. C. iv b I b i b-% U Note 101. The chord of the augmented 6th is usually taken upon the minor 6th and minor 2nd in both modes, major and minor. The for- mer is illustrated by Ex. 153, the latter by Ex. 154. Harmony in Pianoforte-Study Ex. 153. Ben marcato. Ex. 154. Dolente. Note 102. As a rule, the chord of the augmented 6th is most effec- tively resolved when the sounds which constitute the interval of the 6th proceed in contrary motion, or progress a semitone upwards or down- wards, or when one remains to be a sound of the following harmony. The chord is, however, susceptible of great variety in respect to harmonic resolution. The following are examples: B. Ex. 1 A. 55. Lf f\ vf ^3 ^^ , V |\ ( \ ^~ it 1 ^^ T'ir ^5 tf~ oBxEk2 H^/ . -f -s>- a' (- t/C' ^ f 2 -^ o H f\ l * S. <5> 1 ifno ^ I ij | 1^1 r*f[ \!^L>^s U ^3 22 S 1 r^v t"i ? ^^ /*^) I'M J[ C. D. -2- Jjljj -- 1 ^% nr^^ STEP CLX. Having established a major key, introduce the chord of the augmented 6th on the minor 6th, and complete the progres- sion by further harmonies in the original key. The chord should be exemplified in the three forms. (Ex. 156.) Chromatic Harmony 79 Ex. 156. Pastorale. f^-f M- Jz*. STEP CLXI. Transfer Step CLX to minor keys. Begin by playing Ex. 156 in the tonic minor. STEP CLXII. Proceed as in Step CLX, introducing the aug- mented 6th on the minor 2nd of the key. The chord should be exemplified in the three forms. (Ex. 157.) Ex. 157. Alia tnarcia funebre. frT-4- i i -T r^ J S *: i i i J: "-IT- sonoro. ^' nTT - ^' g^j ^ ^filS fS 1 ' > -- -9- r\ *___^__ ~M a i Ylm <** ~ Ifti'fft II u h ^ 1 W? M , P P* |-?i * rteb~ -T^~ -f 8 46 8 7 -^- &- STEP CLXIV. Build up the entire dominant discord (a) in vari- ous major keys; (b) in various minor keys. Note 104. // is manifest that the chords built up in Step CLXIV are so extensive as to be unmanageable for ordinary use; they are, in fact, heard but seldom in complete form. As a rule, the dominant discord is most effective when it occurs in parts or sections. The following illustrate some of the many possible combinations. The figures correspond with the numbered members of the chord in Ex. 158. Ex. 159. A. B. |, c. 1 J J 1 1 If. A IK^jl 1 a^y J J /f-u4- . ! j h-i m o. (foPj. 7&b J_ _JZd_J2* g & IA 1-&- * J &&_ \-4. l-Op! lr-4- 80 The Building of the Dominant Discord 81 J I -^.' J. -49- -6S>- r r Note 105. A great difference exists between the four lowest mem- bers of the dominant discord (or those which form the chord of the domi- nant 7th) and the three added sounds. The latter often partake of the nature of accented auxiliary sounds and are then followed immediately by the concordant sounds one degree above or below, while the rest of the chord remains. In Ex. 160, A , the first added sound (otherwise called the pth) falls to the octave, the rest of the chord remaining for subsequent resolution; in B and C, the second added sound (otherwise known as the nth) and the third added sound (or ijth) are similarly treated. Ex. 16O. B. ^ N 1 U i f B i* ' /Lb r J c* Im C . * ik\) r 1 ~T ^~ )f- -fc 1 3E 33 i j=i i r STEP CLXV. Combine the root, 3rd, 7th and 9th of the domi- nant discord in various major keys. Resolve the 9th upon the 8th, and complete the progression by a perfect cadence in the tonic. (Ex. 161.) Ex. 161. Deciso. tf+ f:i|;i i i m frsemfre P E* wvm I ^e -POL Harmony in Pianoforte-Study STEP CLXVL Transfer Step CLXV to minor keys. Begin by playing Ex. 161 in the tonic minor and with the minor 9th. STEP CLXVII. Combine the root, 5th, yth and nth of the dominant discord in various keys, major and minor. Resolve the nth upon the 3rd, and complete each progression by a perfect ca- dence in the tonic. (Ex. 162.) Ex. 162. Piangevole. STEP CLXVIII. Combine the root, 3rd, 7th and I3th of the dominant discord in various major keys. Resolve the I3th upon the 5th, and complete each progression by a perfect cadence in the tonic. (Ex. 163.) Ex. 163. Andantino. ii J: m $ *- F* m -9 STEP CLXIX. Transfer Step CLXVIII to minor keys. Begin by playing Ex. 163 in the tonic minor, substituting the minor I3th. ****** Note 106. Although the major Qth and jj th and the minor gfh and ijth belong naturally to the major and minor modes respectively, they are nevertheless used interchangeably in either. STEP CLXX. Repeat the combinations of Steps CLXV and CLXVIII, proceeding to the minor in the final cadence. Note 107. The varied resolutions of the chord of the dominant 7th exemplified in Note 47 are obviously applicable to the dominant discord considered as a whole, and this fact should stimulate the student in the direction of fruitful investigation and experiment. End of Part VH. PART VIII The Enharmonic Principle Note 1 08. The enharmonic principle permeates every form of musical expression. Its most objective phase is that concerned with change of key. Modulation, for example, may be easily effected by prolonging one sound of a chord and at the same time referring it men- tally to a key indicated by one of its enharmonic counterparts. (Ex. 164.) Ex. 164- Animate. , n i r r v J J M- H ^-W-HW Jj . --{?, -'^M g ^ -^ 'ftf f - h ^Si X X STEP CLXXI. Having established a major or a minor key, re- peat one of the sounds of the last chord after the manner of Ex. 164; then, by enharmonic change, proceed to the new key. Note 109. The enharmonic transition of Ex. 164 is effected by the simplest of means: by the mere mental reference of a sound to an- other tonic. The principle, however, is illustrated in a fuller measure by its adaptation to a complete chord. The most striking of the chords 83 Harmony in Pianoforte-Study adapted specially to enharmonic treatment is that known as the chord of the diminished 7th, a chord formed by the 3rd, 4th, 7th and minor gth of the dominant discord. (Ex. 165.} The versatility of this chord is unequalled by any other harmonic combination. The chord given Ex. 165. in Ex. 165 is shown in Ex. 166 as providing a means of passing into all the twelve keys, major and minor; from which it will appear that the player has but to adjust the dominant chord of the new key to the part-distribution of the chord of the diminished 7th to effect at once the desired modulation. Ex. 166. G. H. ?- kg I L i a - e J. K. The Enharmonic Principle 85 STEP CLXXII. Play the twelve chords of the diminished 7th in unbroken succession. Harmonize the chromatic scale by a series of the same chords. Note no. Certain composers of pianoforte music have particu- larly favoured the form of progression directed in Step CLXXII, (Ex. 167.} Ex. 167. CHOPIN. Study, Op. 25, No. 6. STEP CLXXni. Pass into each of the twelve keys, major and minor, from any one of the twelve chords of the diminished 7th. In each case, contrive the modulation by playing the dominant harmony of the new key immediately after the chord of the di- minished yth. (Ex. 1 68.) Ex. 168. Tranquillo. ^ I A- Jt?l 86 Harmony in Pianoforte-Study Note in. It will not have escaped the notice of the observant stu- dent that the chords of the dominant 7th and the augmented 6th, accom- panied by the 3rd and 5th, are represented by the same keys upon the pianoforte. This is but another instance of the working of the enhar- monic principle; yet nothing can be more different in effect than the two chords in their respective tonal environments. Cf. the chords marked by the asterisk in Exs. 169 and 170. Ex. 169. c^ Ex. 1 4 Ott 7 O. * VffQ /L ' 1 f(T\ /i f J \J *t ^ '6 * "t "' * * -t r ^j ^J *t? ^ -P STEP CLXXIV. Contrive examples of modulation through the medium of the dominant yth changed enharmonically into the chord of the augmented 6th; or vice versa, by the enharmonic change of the augmented 6th to the dominant yth. Note 112. Like all other chords, that of the augmented 6th is susceptible of inversion, and the student will do well to discover the several inversions for himself, making use of each in the course of modulatory and non-modulatory progressions. End of Part VIH. THE AUTHOR'S FINAL NOTE It is to be hoped that the student who has diligently pursued his way through the foregoing pages will have discovered himself pos- sessed of a new power that of musical self-expression founded upon knowledge. The act of extemporization as it is called is not to be regarded as an exotic in respect to musical study; as something which comes to the musician, as it were, by stealth; as merely a desirable but inessential section of musicianship. On the contrary, the power to extemporize, to give musical expression to thought and mood, should be held to be the aim of the student as well as the joy of the cultivated artist. Although it is true that not a few lovers of music are able with more or less success to give spontaneous expres- sion to their personal thoughts, yet it should ever be remembered that every power called into activity by the workings of the art- instinct is not only intended to be cultivated, but is, moreover, infinitely worth the cultivating. However apparently skilful the art of the extemporaneous player, there can be for him no real progress unless the power he displays be the offspring of fundamental knowl- edge; and, to such a player, one of the most essential of all forms of musical knowledge is that comprehended by the term harmony. It is the harmonic substratum which provides a lodgment for his fleet- ing thoughts; it is the harmonic chain which helps to bind them in a close unity; it is the harmonic divisions which point the way to a true rhythmic alignment, the harmonic colouring which reflects mood and contributes its wealth of effect to the portrayal of climax and repose. In no respect, indeed, is it possible to underrate the im- portance of a clear grasp of the harmonic principles of music. And if it should come to pass that those readers who have hitherto floun- dered hopelessly in their struggles to attain the power of instrumental self-expression become conscious of receiving help and inspiration from the teaching of these pages, this little book will have abun- dantly achieved the purpose for which it was written. University of California SOUTHERN REGIONAL LIBRARY FACILITY 405 Hilgard Avenue, Los Angeles, CA 90024-1388 Return this material to the library from which It was borrowed. " LIBRA MT 224 F69