UC-NRLF 
 
 
u 
 
Harmonic Exercises 
 
 at the 
 
 Fianofbrte 
 
 for 
 
 Beginners and Advanced Pupils. 
 
 Forty-two Exercises 
 
 In 
 
 clear and simple arrangement 
 
 Lu.d.^vrig' ESix^slei", 
 
 New York: G. Schirmer 
 
 Boston: Boston Music Co. 
 Copyright, 1890, by the Publisher, 
 
Af~rt 
 
Table of Contents. 
 
 Prefmoe ••••• ••» VII 
 
 Harmonic Exercises at the Pianoforte. 
 
 I. Major and Minor Chords. 
 
 Page Tf 
 
 § L Omajor Triad .... 1 f S. Circle of Fifths • • . S 
 
 First Exercise. Fifth Exercise. 
 
 § 2. 6^-major Triad . . . • 1 § 6. Constmction of minor 
 
 Second Exercise. Triad « 4 
 
 $ a. F-major Triad. . . • fl Sixth Exercise. 
 
 Third Exercise. | 7. Major and minor Cliordf 
 
 § 4. All the major Triads • 9 in Circle of Fifths . • 5 
 
 Fourth Exercise. Seventh Exercise. 
 
 n. Fisruration. 
 
 I 8. Figurated Chords. • • S § 9. Subordinate ExerdiM • • 
 Eighth Exercise. Ninth Exercise. 
 
 m Varions Positions of the Chorda. 
 
 I to. Fuidamental Chord and 
 
 Inversions • • • • • le 
 Tenth Exercise. 
 
 424838 
 
IV 
 
 IV. Fundamental Triads of the Key. 
 
 I 11. Dominant Triad . 
 
 Eleventh Exercise. 
 
 I 12. Subdominant Triad 
 
 Twelfth Exercise. 
 
 Page Page 
 
 • la % IS. The Minor Key • • • 14 
 
 Thirteenth Exercise. 
 
 13 
 
 Fourteenth Exercise. 
 
 V. The Cadences. 
 
 § 14. The Two -chord and 
 
 Three-chord Cadences. 15 
 
 Fifteenth Exercise. 
 
 § Ifi. The Four- chord Ca- 
 dence 17 
 
 Sixteenth Exercise. 
 
 § 16. The Five-chord Cadence 19 
 Seventeenth Exercise. 
 
 I 17. Figuration of the Ca- 
 dence • 81 
 
 Eighteenth Exercise. 
 
 f 18. Cadences in Minor • • S3 
 Nineteenth Exercise. 
 
 VL The Dissonaneeg. 
 
 I 19. Diminished Triad • • 
 Twentieth Exercise. 
 Twenty-first Exercise. 
 Twenty-second Exercise. 
 
 § 20. Dominant Chord of the 
 
 Seventh 
 
 Twenty-third Exercise. 
 
 $ 21. Besolution of the Chord 
 of the Seventh . . . 
 Twenty-fourth Exercise. 
 
 26 f 22. Positions of the Chord 
 
 of the Seventh ... 80 
 Twenty-fifth Exercise. 
 I 23. Chord of the Seventh 
 
 in Cadence . . . . 80 
 Twenty-sixth Exercise. 
 
 28 § 24. Figuration of Chord of 
 
 the Seventh .... 84 
 Twenty-seventh Exercise. 
 $ 25. Chords of the Seventh 
 
 29 in Circle of Fourths . 84 
 Twenty-eighth Exercise. 
 
 Vn. The Six and Seven-chord Cadences. 
 
 S 26. Chord of the Fourth and 
 
 Sixth 86 
 
 Twenty-ninth Exercise. 
 
 { 27. The Six-chord Cadence 87 
 
 Thirtieth Exercise. 
 
 I 28. In Minor 89 
 
 Thirty-first Exercise. 
 
 I 29. Chord of Seventh on 
 
 Second Degree ... 41 
 Thirty-second Exercise. 
 
 § 80. The Seven - chord Ca- 
 dence 42 
 
 Thirty-third Exercise. 
 
 § 81. In Minor 48 
 
 Thirty-fourth Exercise. 
 
Vni. Chords in Diatonic and Chromatic Progression. 
 
 § 32. Chord of the Sixth . , 
 Thiriy-fifth Exercise. 
 Thirty-sixth Exercise. 
 § 33. The Diminished Triad 
 Tiiirty-seventh Exercise. 
 
 Page 
 45 
 
 47 
 
 Pagt 
 § 34. Diminished Chord of 
 
 the Seventh .... 48 
 Thirty-eighth Exercise. 
 § 85. Chromatic Chords of 
 
 the Sixth 49 
 
 Thirty-ninth Exercise. 
 
 IX. Modulation. 
 
 § 36. Interconnection . • • 
 
 Fortieth Exercise. 
 § 87. Definition of Modulation 
 Forty-first Exercise. 
 Forty-second Exercise. 
 
 51 § 38. Individuality of the Pu- 
 pil, and proper limit of 
 69 instruction* « • • • 66 
 
Preface. 
 
 The following exercises are intended to sup 
 plement and further pianoforte instruction by 
 teaching the elements of harmony through a 
 simple empirical method. Neither musical ter- 
 minology as an essential, nor a systematic school- 
 presentation, has been aimed at. The practical 
 performance of the pupil at the instrument is 
 the sole object of the course, which whenever 
 possible is to rely upon the natural ear, and to 
 be assisted, only where this latter is insufficient, 
 by the merest external pedagogic aids. 
 
 These exercises thus serve to develop the 
 musical sense, which experience proves to be 
 far too easily slighted in piano-teaching. 
 
 Preliminary studies are not presupposed. 
 
 The exercises may be interrupted in any 
 place, whenever the pupU exhibits either dis- 
 inclination or lack of comprehension. Only a few 
 minutes in each lesson should be devoted to them. 
 
vm 
 
 In Music-schools these exercises are suitable 
 for a half-year (summer) piano-course, which may 
 be interpolated between the Primary course and 
 Practical Harmony, and (according to the author's 
 experience) will afford the young musicians Uvely 
 pleasure. 
 
 Thus employed the Exercises form a pre- 
 paratory school, based on simple empiricism, 
 to a practical course in Harmony based on a 
 ; systematic method, 
 
 Ludwig Bussler. 
 
Harmonic Exercises at the Pianoforte. 
 
 I. Major and Minor Chords. 
 
 §1. 
 
 C-MAJOR TRIAD. 
 In the very first piano-lessons the C-major triad 
 1. 
 
 m 
 
 should be struck repeatedly. Derived from the fingering 
 of the five-finger exercises by keys touched with the first, 
 third and fifth fingers. 
 
 Its formation may be attempted simply by ear, after hearing it 
 struck several times. But in the first lessons most pupils are too em- 
 barrassed to make such attempts. 
 
 This triad is called as such the Chord of C-major. 
 The pupil must at all times be able to execute readily the 
 command: Play the chord of O-major! 
 
 First Exercise. 
 
 Chord of C-major. 
 
 §2. 
 . G^MAJOR TRIAD. 
 
 When the pupil can strike the C-major triad with per- 
 fect confidence he may form, at first by ear, the 6?-major triad. 
 
 1 
 
^ 
 
 If he cannot form it easily by ear, the fingering may 
 again be called to his aid, the position of the keys being 
 precisely the same as before. The chord so found is to be 
 called the Chord of 6r-major. 
 
 Second Exercise. 
 Chord of G-major. 
 
 N. B. Where pupils do not readily comprehend, care 
 must be taken — here more than elsewhere — not to push 
 forward. Keep rather to each exercise— all of which are 
 to be treated as comparatively unimportant — until the pupil 
 can master it with perfect ease. 
 
 §3. 
 
 ^-MAJOR TRIAD. 
 The ^-major triad is to be formed like the above: 
 3. 
 
 ^ 
 
 in which, after the ear, positions of the piano-keys are the 
 determining factor. 
 
 Third Exercise. 
 
 Chord of JP-major. 
 
 § 4 
 
 ALL THE MAJOR TRIADS. 
 
 In the following exercise too the ear must first decide, 
 i, •• the pupil should himself seek for the tones forming 
 the Major triad. 
 
3 
 
 Pupils who quickly succeed in this easiest of harmonic 
 exercises, can be taught the further formation of chords 
 before gaining a knowledge of the notes and names of the 
 black keys. Others should acquire this knowledge before 
 advancing. 
 
 Fourth Exercise. 
 
 Construct, first on all white keys and then on all 
 black ones, the Major Triads in the order 
 
 4. F'm&y C-maj. G-maj. 2>-maj. A-m&y i?-maj. ^-maj. 
 
 ^^ 
 
 W='^'=^ 
 
 ^m 
 
 J^tt-maj. Cft-maj. ^ib-maj. J^b-maj. j?l?-inaj. 
 
 S^^E^J^Ei^ 
 
 ^ 
 
 in case the ear should not suffice, according to the con- 
 stant fingering I, 3, 5. 
 
 The key-note (lowest note) is each time to be named 
 or struck by the teacher. 
 
 This exercise is to be continued until the pupil is able 
 at any time, in or out of the order, to strike any chord 
 at once and correctly. 
 
 §5. 
 
 THE CIRCLE OF FIFTHS. 
 
 Let the teacher now call for the chords always in the 
 order of the Circle of Fifths: 
 
 0-maj. G-maj. D-maj. -4-maj. JK-maj. B-maj. -Fjt-maj. Cjt-maj. 
 
 (== i)t>-maj.) 
 Db-maj. -ib-maj. ^b-maj. 5b-maj. J'-maj. C-maj. 
 
 and call the pupil's attention (already accustomed to it by 
 practice) to the interconnection by fifths of the key-notes. 
 
Use to this end the mechanical aid, that the highest tone 
 (fifth finger) of the foregoing chord becomes the lowest tone 
 (first finger) of that following, finally allowing the pupil to 
 construct the succession of chords by himself. 
 
 a^^^^ ^i 
 
 Fifth Exercise. 
 
 Construct the Major Triads of the Circle of Fifths. 
 
 Now show the pupil, that the last chord is the same 
 as the first. 
 
 The series of chords therefore turns back to its source. 
 Thus it is like a Circle. 
 
 We therefore have here a Circle of Chords. 
 
 This is called a Circle of Fifths because the key-notes 
 of the successive chords are five tones (a Fifth) apart. 
 
 The pupil should keep to this exercise until thorough 
 confidence and fluency are attained. 
 
 The exercise should also be played with both hands 
 together. 
 
 ^ .8^. h 
 
 ns^^i^^^ 
 
 *M^ ^m 
 
 §6. 
 
 CONSTRUCTION OF THE MINOR TRIAD. 
 
 The Minor Triad is formed from the Major Triad by 
 lowering the Third— the tone of the third finger. 
 
 (1) Try to construct minor chords by ear. 
 
 (2) Construct the same from major chords by shifting 
 third finder. 
 
Sixth Exercise, 
 Construct, from C-major, c-minor. 
 
 ^=i3*=^t= 
 
 from 
 
 7. jF-major /"-minor ^-major ^-minor -(4b-maj<MP al^-minor 
 
 I 
 
 m = ^i = m 
 
 ^ 
 
 ^i 
 
 -^ 
 
 m 
 
 In like maimer construct minor chord to every major 
 chord. 
 
 MAJOR AND MINOR CHORDS IN THE CIRCLE OF FIFTHS. 
 
 Seyenth Exercise. 
 
 Major and Minor Chords in the Circle of Fifths. 
 
 Let each major chord in the series of the Circle of 
 Fifths be followed by the like-named minor chord. 
 
 8. 
 
 Later let the left hand accompany these chords in the 
 lower octave. This exercise, closing a section, should be 
 practiced by the pupil until he can execute it almost 
 mechanically. 
 
 The minor chords alone must also be performed 
 throughout the Circle of Fifths. 
 
 Advanced scholars, especially in class-teaching, should 
 be made to do all exercises in writing as well, when this 
 does not clash with the plan of instruction. 
 
n. Figuration. 
 
 18. 
 
 A chord is termed figurated, when its toneg are not 
 •ounded together, hut separately in succession. 
 
 Eighth Exercise. 
 
 Figurate the Major Chord ascending (i. «• from 
 below to above). 
 
 9. C-major. 
 
 ^-major. 
 
 Figurate the l^inor Chord in liice manner: 
 
 ¥=t 
 
 10. C-minor. 
 
 fltf-minor. 
 
 ^^ 
 
 ^ 
 
 ^^m 
 
 tzzt 
 
 Always hy heart! Only as shown hy the teacher! 
 Left hand in the lower octave! 
 
 I^ajor and i^linor Chords through the Circle of Fifths 
 In liice manner: 
 
 u. 
 
 W^^-'^S^^=S ^ ^^^f^rfi^ 
 
 mij;S 'JHJF^^^^ 
 
l- g f ; t;rjrT\^^=^ 
 
 ^^^^^i=fe 
 
 -i«-r^L— j L 
 
 ^^ 
 
 ^^^ 
 
 S^^^ 
 
 iji^j 
 
 ia i ^T^ J* 
 
 ^^^^^^^^ 
 
 ^ 
 
 ^ 
 
 g ^c^cj:! 
 
 '<> 'j^ i^ 
 
 •to. 
 
 Left hand in the lower octave. 
 
 Figurate the Chord ascending and descending: 
 
 12. 
 
 In like manner throughout Circle of Fifths. 
 
 Abbreviated Figuration: 
 
 13. C-major ^-minor 
 
 G-major 
 
 ^-mmor 
 
 ^^^g^^^ 
 
 etc. 
 
 In like manner throughout the Circle of Fifths. 
 
 The pupil should practice this exercise too until per- 
 fect confidence is gained. 
 
8 
 
 S9. 
 
 SUBORDINATE EXERCISES 
 
 which may be omitted without disadvantage, should the 
 course of instruction require it. 
 
 Ninth Exercise. 
 
 Figurate descending (from above to below) beginning 
 with the fifth finger: 
 
 14. C-majop 
 
 i =aa-i;j -ijpfi; - 
 
 As above throughout Circle of Fifths. 
 
 15. 
 
 ^^^^^^^^^ 
 
 f^^^^ ^^ 
 
 eta 
 
 Figurate ascending and descending. 
 
 i 
 
 mmf^ ^ 
 
 etc. throughout Circle of Fifths. 
 
 This exercise will not be as easy for the pupils as it 
 may appear at first glance; but like all Subordinate Exer- 
 cises, it is not sufficiently important to hold back pupils 
 who do not readily comprehend. 
 
 Other variations in figuration may here be shown to 
 scholars of quick comprehension. 
 
etc 
 
 ^^gg ^^ ^BTi^L' \3 -^ 
 
 ^ 
 
 ^^^ 
 
 Siz etc. 
 
 fe 
 
 •j-io^iij^i-j^ i if£[i i jij-es= -' 
 
 But these already enter the department of finger-exer- 
 cises to be constructed by the pupil independently, with 
 which we have nothing to do. 
 
 Only a few pupils will easily succeed in reversing the 
 order of the triads by heart, that is, to play them through 
 the Circle of Fourths. The teacher must therefore usually 
 omit this exercise. If it be taken up in rare cases, only 
 Major Chords should be employed at first. 
 18. 
 
 p^^i^^pii^iip 
 
 Here the lowest tone always becomes the highest of the 
 chord next-following, the tone of the first finger becoming 
 the tone of the fifth finger. 
 
 The Minor chords follow in like manner: 
 
 19. 
 
 ^^^^^s^^i 
 
10 
 
 With successive Msgor and Minor chords the Minor 
 ehord comes first: 
 
 20 
 
 i 
 
 etc. 
 
 But this exercise, as before remarked, is seldom so 
 easily to be grasped by the pupils as should always be 
 the case with all exercises here given. 
 
 ni. Various Positions of the Chords. 
 
 § 10. 
 /HE FUNDAMENTAL CHORD AND ITS DIVERSIONS. 
 Strike the Chord of 0-major 
 
 i 
 
 :. Now place the 
 
 first finger on e, the second on gr, and take with the fifth 
 the upper c, omitting the lower c: ^g 
 
 ^ 
 
 We thus 
 
 obtain the second position of the C-major chord, contain- 
 ing the same tones in different order. 
 
 If the teacher needs only to play, let this suffice. 
 
 Now, by beginning the succession of three tones with 
 the third tone, gr, taking it with the first finger, then c and 
 e with the third and fifth fingers in succession, we obtain 
 the third position of the triad: 
 
 21. 
 
 ^^1 
 
 The three positions are therefore; 
 22. 
 
 ^E 
 
 1=^ 
 
11 
 
 Tenth Exercise. 
 
 Construct the three positions of the Triad through- 
 out the Circle of Fifths: 
 
 (I) in Major: 
 
 ^ 
 
 JOl Ot- 
 
 ^ 
 
 '^W 
 
 U 
 
 & 
 
 iSi^Sg^Sf^i^sa 
 
 ^st- 
 
 -^?-« 
 
 i=^"^ 
 
 «. 
 
 
 (2) in Major and Minor: 
 
 3 aM 
 
 ^^=^ 
 
 ¥ 
 
 tw 
 
 <5> 1|<9 
 
 If-^ 
 
 
 :l^^— n rJ 
 
 ^^^^^^^%^ 
 
 ^ 
 
 2: 
 
 r-^ " I 'g I' i^ 
 
12 
 
 i 
 
 (3) in Minor: 
 
 ^^£=^ 
 
 t^A 
 
 Q.J1J5. 
 
 lEE 
 
 -^^g=Fg-=l= 
 
 i 
 
 2 
 
 22: 
 
 i 
 
 & 
 
 «: 
 
 :Sf=fe=*F=Ei^ 
 
 ii^i 
 
 2^. 
 
 tt- 
 
 ^^^^ 
 
 |jS||;^ 
 
 (4) out of regular order, when desired. 
 
 Subordinate. The second Position is called the iirst 
 Iiwersion, the third Position the second Inversion. The first 
 inversion is called the Chord of the Sixth; the second, 
 Chord of the Fourth and Sixth. 
 
 IV, Fundamental Triads of the Key. 
 
 §.11. 
 
 DOMINANT TRIAD. 
 
 Three successive major chords in the Circle of Fifths 
 are the Fundamental Triads of the key of the middle triad. 
 
 ^ 
 
 are the fundamental 
 
 For instance 
 
 triads of 0-major. 
 
 The triad on the fifth degree is called, in its relation 
 to the key, the Dominant triad. In the sign-notation it is 
 indicated by a Roman V, and sometimes called "five" for 
 short 
 
13 
 
 Eleventh Exercise. 
 
 Play Dominant Triads of various keys, for example: 
 
 of C-major: 
 
 24. 
 
 m 
 
 :, of il-major: 
 
 ^^1= 
 
 V V 
 
 Dominant triads in all positions, for example: 
 
 of C-major: 
 
 r. 25. 
 
 m 
 
 -^ 
 
 i^z=, of A\^ 
 
 major: 
 
 72zrtia 
 
 ^fezz 
 
 § 12. 
 
 THE SUBDOMINANT TRIAD. 
 
 The ti-iad on the fourth degree is called, in its relation 
 to the key, the Subdominant Triad. 
 
 In musical sign-notation it is indicated by a Roman IV| 
 and sometimes called "four" for short. 
 
 Twelfth Exercise. 
 
 Play Subdominant Triads of various keys, for 
 example: 
 
 26 
 
 of 0-major: |-^y— g — , of il-major: |A_jg=: 
 
 rv IV 
 
 The same in all positions, for example: 
 
 27. ^ ^ ^ ^ 
 
 of Omajor: ^ (S r T~^~^ > ^^ ^-^major: \:M!\iI^^^ 
 
 Play Fundamental Triads of various Major Keys: 
 
 of .4.-major: TO ^ g " ^-^-^ 
 
 IV I V 
 
14 
 
 Likewise in the order I— IV— V or IV— V— I. 
 It will be seen, that these three chords embrace all 
 seven tones of the scale. 
 
 BEMARK (subordinate). The fundamental chords of the Minor keys 
 do not stand next each other in the Circle of Fifths, one of them 
 (the Dominant triad V) being a major triad. A key formed of 
 three minor triads if an impossibility in [modem] musical logic 
 
 §13. 
 THE MINOR KEY .• 
 
 Thirteenth Exercise. 
 
 In Minor the V (Dominant triad) is a Major triad. We 
 know ("Elements of Notation and Harmony", § 40**) that 
 in the harmonic Minor scale the seventh is raised. It thus 
 forms a major third in the dominant triad. 
 
 Play Dominant Triads of Minor Keys, for example: 
 of c -minor: 
 
 28. 
 
 ziz, of a-minorj 
 
 Fourteenth Exercise. 
 
 In Minor the IV (Suhdominant Triad) is a Minor chord. 
 The minor sixth of the harmonic minor scale forms its minor 
 third. 
 
 Play Suhdominant Triads of Minor Keys, for example: 
 
 of c -minor: - frf [ t % ^ of a -minor: 
 
 • Advanced pupils might be told, that key in the abstract sense 
 is called Mode. [Translator's Note.] 
 
 ** By the same author, also published in English by G. Schirmer, 
 New York. [Translator's Note.] 
 
15 
 
 We can now see, that the chords were really not 
 derived from the harmonic minor scale, hut that the latter 
 was formed from the chords. The course of teaching 
 usually shows only the contrary (the key as derived from 
 the scale), because the scales are first learned and practiced- 
 
 V. The Cadences. 
 
 § 14. 
 THE TWO-CHORD CADENCE. 
 With the left hand strike the fundamental note of flie 
 Dominant triad in C-major S" 
 
 :, with the right hand 
 
 the third position of the same -frj — g — ; then both to- 
 gether: 
 
 ^P 
 
 5fc^ 
 
 With the left hand play the fundamental note of tiie 
 
 Tonic triad in C-major 
 
 :, with the right hand 
 
 the second position of the same - gk g ; then both to- 
 
 gether: 
 
 ^ 
 
 P 
 
 zz: 
 
16 
 
 We have thus obtained a four-part Dominant Triad and 
 a four-part Tonic Triad: V-— I, 
 
 The succession of these two triads forms the simplest 
 Cadence, which is called, because consisting of 2 chords, a 
 two-chord Cadence. 
 
 Fifteenth Exercise. 
 Form this Cadence, (I) in C-major: 
 
 32. 
 
 m 
 
 :i=« 
 
 isz 
 
 (2) In all keys of the Circle of Fifths: 
 
 83. 
 
 For learning to form these and the following Cadences 
 many pupils need only to hear them played. Some can form 
 the cadences more easily, when they are preceded by L 
 
 34. 
 
 ^ 
 
 ^ 
 
 IT. 
 
 -■zf: 
 
 «: 
 
 -JSu 
 
 I V I 
 
17 
 
 To prevent misunderstandings we give this formula 
 I— V— I the (not quite appropriate) name of the 
 three-chord Cadence. 
 
 Form this In all keys of the Circle of Fifths: 
 
 35. 
 
 
 "7?" 
 
 
 ^ 
 
 
 
 — 
 
 
 -iW 
 
 -«9— 
 
 
 
 k 
 
 ^~ 
 
 =2Z= 
 
 
 ^ 
 
 
 -«5» — 
 
 tfifc 
 
 -?g 
 
 zfcJ 
 
 h -- 
 
 ^^ \ 
 
 l-^ 
 
 -6l^ 
 
 
 
 -M 
 
 L ^1 
 
 
 
 
 
 ■ 
 
 I-7J 
 
 -77— \ 
 
 
 5«? 6>— t 
 
 b|^^-HS=|,J 
 
 5^^=^ 
 
 %A 
 
 ^ 7 
 
 «9 «5> 
 
 — b<5> 
 
 ^ 
 
 ^^ ^ 
 
 § 15. 
 - THE FOUR-CHORD CADENCE. 
 With the left hand strike the fundamental note of the 
 Dominant triad in C-^major: i-?^^~^' 
 
 with the right the 
 
 first position of the same: i^— g — ^ Then strike both to- 
 gether: 
 
18 
 
 Set this chord hetween two tonic triads as abore 
 (No. 31): 
 
 "I 
 
 37. 
 
 <o fj <d. 
 
 ^ 
 
 i 
 
 ^ 
 
 5 
 
 I IV I 
 
 This formula I— IV— I is called the Subdominant or 
 Plagal Close. 
 
 K we set the Subdominant chord in this form between 
 I and V of the three-chord cadence, we obtain the series 
 
 I-IV-V-I 
 or the four- chord Cadence. 
 38. 
 
 I 
 
 % 
 
 fr- 
 
 :^ 
 
 I IV V I 
 
 Sixteenth Exercise. 
 Form these, (I) in C-major: 
 (2) in all keys of the Circle of Fifths: 
 
 Q. — ^—^ — a- 
 
 ^m 
 
 ^ 
 
 la: 
 
 :g: 
 
 ^ 
 
 ^^ 
 
 ^ 
 
 -^ 
 
 ■a- o. 
 
 5 
 
 zc 
 
 ■JSL 
 
 yt r. -H-r4?-^+^^-8«^^M1 r-^: =-41 
 
 ¥ 
 
 ffr-'^^-p 
 
 
 ^ 
 
 e, — a. 
 
 1 >v -" ^ f,\ 
 
 . i» ff^ ■ 
 
 
 .lA a-1 
 
 \ \ 
 
 \r-e> *>-n 
 
19 
 
 ,b* V 
 
 g^ll"^^^^ 
 
 5Hi^ 
 
 ^ 
 
 jzazifc 
 
 ^1 
 
 
 ^E ^^^i^^^^gEpi^izi-:^ 
 
 -^_|Za. 
 
 42^ 
 
 ^i=tK 
 
 ztigz: 
 
 T 7^ — ^g=^= 
 
 § 16. 
 
 THE FIVE-CHORD CADENCE. 
 On the sixth degree of every major key there is a 
 
 minor triad 
 
 40. 
 
 m 
 
 22: 
 
 ^ r I * » • ' » 
 
 This minor triad is the tonic chord of the relative 
 minor key. [Relative major and minor keys are those 
 having the same signature.] In the sign-notation it is in- 
 dicated by a Roman VI. 
 
 Seventeenth Exercise. 
 
 Form the triad on the sixth degree of all major keys 
 In the Circle of Fifths: 
 
 41. 
 
 I 
 
 ^ 
 
 P^t^^fe^^^ 
 
 m- 
 
 \± rj 
 
20 
 
 ^ 
 
 s 
 
 * 
 
 ^ 
 
 ^ 
 
 i 
 
 I 
 
 Erect the same triad, in all its positions, in all keys: 
 
 42. C-major. G^-major. ^ i?-major. 
 
 ^ 
 
 ^ 
 
 ■«- 
 
 
 (S*- 
 
 ^ 
 
 =fif=lg=i«2 
 
 9i 
 
 f^ 
 
 iS: 
 
 ^ 
 
 izz: 
 
 
 etc. 
 
 i^ 
 
 ^^^ ^ 
 
 How was the tonic triad formed in our cadences? 
 
 43. 
 
 Answer: 
 
 :g= 
 
 P 
 
 Transpose Bass to the higher octare: 
 
 I 
 
 3s: 
 
 i: 
 
 P 
 
 The above is to be followed by the triad on the sixth 
 
 degree in such a way, that the common tones c—c" shall 
 
 be held by the same fingers. To this end, take with the 
 
 left hand the fundamental of triad VI as near as possible 
 
 to the fundamental of the foregoing triad, i.e. a third lower: 
 ? — 
 . Now with the right hand take the third po- 
 
 1 
 
 •ition of triad VI: 
 
n 
 
 Then strike both together: 
 
 44. 
 
 i 
 
 ig: 
 
 5t 
 
 Set this chord VI between I and IV of the foregoing 
 
 cadences. Thus we have the five-chord cadence: 
 
 45. 
 
 ^ 
 
 1^ 
 
 ^g:= 
 
 9^ 
 
 is: 
 
 I VI IV V I 
 
 Form this cadence in all Iceys of the Circle of Fifths: 
 
 46. 
 
 m. 
 
 %- 
 
 
 |g=r!!S=i^ 
 
 P 
 
 £L etc. 
 
 P 
 
 122: 
 
 ^ 
 
 § 17. 
 FIGURATION OF THE CADENCE. 
 
 The successive striking of the tones of a chord is called 
 an Arpeggio, broken Chord, Figuration. (§ 8.) 
 
 The playing in succession of the tones of a chord is 
 ealled: to figurate, to play arpeggios. 
 
Eighteenth Exercise. 
 
 Figurate (I) the two-chord Cadence in all keys: 
 
 Play the tones from below upward, as eighth-notes. 
 47. 
 
 ^^^ 
 
 iiEl 
 
 As a preparation the chords should first be struck in 
 succession. (No. 32.) 
 
 C2) the three-chord Cadence ditto: 
 
 48. 
 
 f^^^^^ 
 
 P 
 
 i 
 
 (3) the four-chord etc 
 
 49. 
 
 ^^^^^^^ 
 
 ^ 
 
 £ 
 
 --* 
 
 (4) the five-chord etc.: 
 
 60, 
 
 ^ff^= f^ ^^=^=^^m ^^ 
 
 -^- 
 
 ^m 
 
23 
 
 § 18. 
 TWO TO FIVE-CHORD CADENCE IN MINOR. 
 
 This § may be skipped entire, or kept until the last. 
 It supplements § 13. 
 
 In minor the V is a major chord, the I and IV minor 
 chords. 
 
 The positions of the chords, in both chords, are to be 
 taken precisely as in major. 
 
 Nineteenth Exercise, 
 
 Erect accordingly (1) the V in all minor keys: 
 
 61. 
 
 1. c g da e b f^ 
 
 ^ 
 
 T57 
 
 :30i: 
 
 
 i^i^* 
 
 V V V V 
 
 ^tt rftt = e\? 
 
 ^^i ^^^^m 
 
 hv 
 
 V 
 
 f 
 
 ^^^j - ^^ ^^^^^mi 
 
 P 
 
 (2) the IV in all minor keys: 
 
 52. 9 d "«>„,,/■» 
 
 ^-1 
 
 S^ 
 
 S 
 
 ^^.^ 
 
 I: 
 
 i^H 
 
 ^1 
 
 IV 
 
24 
 
 
 gfi _rf8 = «l» 
 
 ^^ ^^^^M^=^W=^ =li 
 
 ^^ ^^^^^ ^=^^= m^=^ 
 
 (3) the two-chord Cadence V I in all minor Iceys: 
 
 53. 
 
 ^^g^p^^i^p^ 
 
 
 m 
 
 igr 
 
 -fit. 
 
 22: 
 
 ^ |i ^' ^l l ^ 
 
 ^£ 
 
 ^^v 
 
 ^^ffi tefe^ft^ 
 
 a^^g^a^^lp ^^ 
 
 jLi, ^ I tr - r 
 
 U ->» 
 
 lei^lg^^^^^^l^^ 
 
 3 ^ " Ig 
 
 fefe 
 
 -«5»- 
 
 la: 
 
 S? 
 
 v^ 
 
 Sl. 
 
 (4) the three-chord cadence I V I: 
 
 ^^^^^m 
 
 £d. 
 
 ^ 
 
 321 
 
 F [r^ 
 
 3C 
 
 i^ 
 
 etc. 
 
 1 
 
+ 
 
 25 
 
 (5) the plagal close I IV I: 
 
 56. 
 
 ^ r g ^ %^Bg^^^ 
 
 m 
 
 3E 
 
 jo: <^- 
 
 -& <5»- 
 
 -& &- 
 
 7g 77 
 
 M 
 
 g=fc=^ 
 
 * < g 
 
 ^ ~~ g ~g^ 
 
 
 ^ 
 
 B 
 
 r.»j 
 
 2z: 
 
 32: 
 
 ?■- 
 
 
 ^ 
 
 :^c 
 
 1^ 
 
 11 
 
 SI"P^ 
 
 :2E^ 
 
 i^ 
 
 
 ^£ 
 
 =g=g=^ 
 
 :g=fc=#: 
 
 I 
 
 a« 
 
 3z: 
 
 te 
 
 ^ 
 
 p^ 
 
 s 
 
 rpa^ 
 
 3C 
 
 I 
 
 (6) the four-chord cadence I IV V I: 
 
 56. 
 
 ^^Ep; 
 
 ;^ 
 
 :a: 
 
 ^^^^^=^ 
 
 ^wt- 
 
 "^ — Z. — ffi2 — 22" 
 
 1^ 
 
 -«> — <5L 
 
 3?: 
 
 -^—^ 
 
 W^ 
 
 ^^Ei^ 
 
 -<5>- 
 
 l^^pl^^^a 
 
 »^ 
 
 -«> <!ii^ 
 
 122: 
 
26 
 
 (7) the five-ohord oadenoe: 
 
 57. 
 
 (8) Figurate the cadences in minor. 
 
 Example with the five-chord cadence in minor: 
 
 
 =f# 
 
 — rj-#- 
 
 ■nr— 
 
 =f1^ 
 
 — ^-1 
 
 -TJ ^^- 
 
 a 
 
 
 :U= 
 
 -I ' # 
 
 r — 1 
 
 -<9- 
 
 fit. 
 
 "• ' 
 
 7 J J* 
 
 1 1 
 
 a 
 
 \f^-^ — 
 
 
 
 -1— 
 
 1__ 
 
 
 r^ 
 
 JJ 
 
 The close lacking in these and other figurations can 
 he added by a repeated (not figurated) striking of the last 
 ehord. 
 
 VI. The Dissonances. 
 
 § 19. 
 
 THE DIMINISHED TRIAD. 
 
 On the seventh degree of the key is situated the 
 diminished Triad. — In C-major: 
 
 59. 
 
 i 
 
 It will be struck, for the purpose in hand, in all 
 keys with the same fingers as the other triads, namely 
 1,3,6. 
 
27 
 
 Twentieth Exercise. 
 
 Erect the diminished triad in all keys of the Cirote 
 of Fifths: 
 
 The diminished triad is a dissonant chord, t. c. it must 
 be resolved. The resolution takes place, in the fingering 
 with the 'two free fingers 2 and 4. 
 
 i 
 
 ^^fc^ 
 
 Twenty-first Exercise. 
 
 Form the Diminished Triad, with resolution, in all 
 major Iceys of the Circle of Fifths, taking the same 
 fingering in all cases: 
 
 61. 
 
 i^ 
 
 fe 
 
 p^ 
 
 ^ 
 
 I^-gEj^i^ 
 
 :^ 
 
 In minor keys the diminished ti-iad is the same as in 
 the like-named major keys, in 0-minor as in C-major, in 
 il-minor as in ^-major, etc. The fingering is consequently 
 the same. But in the resolution the higher tone progresses 
 a half-tone further down, the major third of the major key 
 being replaced by the minor third of the minor key. E, g. 
 
28 
 
 62. c-minoT fl'-minor 
 
 /"D-minor 
 
 P^^^^jig^ 
 
 Twenty-second Exercise. 
 
 Play the diminished triad, like the others, in three 
 positions. 
 
 Form the three positions of the diminished triad in 
 all keys: 
 
 ii 
 
 W=^ 
 
 22: 
 
 k=^ 
 
 w^w=^ 
 
 ■m 
 
 1^^- 
 
 etc. 
 
 20. 
 
 DOMINANT CHORD OF THE SEVENTH. 
 
 By adding above another Third to the dominant triad V 
 we obtain a chord of the seventh, also called Dominant 
 Chord of the Seventh. 
 
 64. 
 
 ^ 
 
 Twenty-third Exercise. 
 
 Form this chord of the seventh in all keys. Finger- 
 ing: 1, 2, 3, 5. Here it is better (musically more reasonable) 
 to progress through the Circle of Fourths rather than of 
 Fifths. At first it is easier to name the key and fundamental 
 of each chord of the seventh. 
 
 Thus: 0-major, O: 
 
 65. 
 
 F-major, C; 
 
 m 
 
29 
 
 Here too the formation of the chords should he assisted, 
 as far as possible, by the ear, especially when seeking the 
 fourth tone which completes the chord of the seventh. Below 
 are the 
 
 Chords of the Seventh in the Circle of Fourths. 
 
 fe^^ 
 
 =S»J|= 
 
 Figurate the chord of the seventh throughout the 
 Circle of Fourths, upward and downwards. (Compare 
 Example No. 12, p. 7.) 
 
 § 21. 
 
 RESOLUTION OF THE CHORD OF THE SEVENTH. 
 
 The three highest tones in the chord of the seventh 
 form the diminished triad. 
 
 The right hand takes the diminished triad, and resolves 
 it as above: 
 
 67. 
 
 I 
 
 ;l^ 
 
 The left hand takes with the thumb the fundamental 
 of the chord, and repeats it in the second chord with the 
 addition of the fundamental of the triad, taken by the little 
 finger: 
 
 Together: 
 
 68. 
 
 I 
 I 
 
 T 
 
 i 
 
30 
 
 Twenty-fourth Exercise. 
 
 Form accordingly Dominant chords of the seventh 
 in all keys, with resolution. 
 
 The fingering, which here serves as a guide, must al- 
 ways remain the same, whatever keys are to be struck. 
 
 69! 
 
 ^mr^i^^^^m^^ 
 
 1=^ 
 
 i=Pi 
 
 22Z32: 
 
 -<S> — <5»- 
 
 I2ZZ5?: 
 
 7J 
 
 j^_x_^_^_ 
 
 H-\^ 
 
 ^^^sarjg gga^ 
 
 5i3=^i2£* 
 
 ^^i^ 
 
 •»• i9- 
 
 Pt 
 
 >&—& 
 
 % 
 
 l&HIZ. 
 
 ^17 
 
 § 22. 
 POSITIONS OF THE CHORD OF THE SEVENTH. 
 
 This chord having four tones, it has likewise four 
 positions: 
 
 figurated: 
 
 Twenty-flfth Exercise. 
 
 Play the Dominant chord of the seventh in all keys 
 and positions. 
 
81 
 
 The first position is called the fundamental chord; the 
 rollowing are the first, second, and third iuversion*. 
 71. 
 
 f: 
 
 I: 
 
 1^ 
 
 S: 
 
 S^ 
 
 t- 
 
 ^i 
 
 
 ^^ 
 
 c 
 
 ^te 
 
 ^i^^ 
 
 
 ^^a^^^^MffSSSp^^Efe^ 
 
 igrns: 
 
 ^ 
 
 i3 
 
 -6iL_ ^._. 
 
 =!^ 
 
 ^ 
 
 i5i=5 
 
 .€t 
 
 ^^ 
 
 ^1^^ 
 
 i^^iS^l^fe^^ 
 
 g: 
 
 3:;r5^ 
 
 
 Play these positions also with two hands, and figurate them. 
 §23. 
 THE CHORD OF THE SEVENTH IN THE CADENCE. 
 
 In the cadence the dominant seventh precedes the tonie 
 triad, thus replacing V. The right takes the third position 
 
 of the chord of the seventh: 
 
 g^::, the left hand the 
 
 fundamental: 9' ; together: 
 
 72. 
 
 g^ 
 
 ^EE 
 
32 
 
 Twenty-sixth Exercise. 
 
 (I) Erect dominant chord of the seventh in above 
 position in all iceys. 
 
 This position is followed in the cadence by the tonic 
 triad, as the latter before followed the Dominant Triad V. 
 
 73. 
 
 ZZL 
 
 g^g: 
 
 (2) Form this two-chord close in all keys. 
 
 In all more complicated cadences the chord of the 
 leventh takes the place of the V (dominant triad). 
 
 (3) Form, with the chord of the seventh instead of 
 the dominant triad, and in all keys 
 
 three-chord cadences: 
 
 74. 
 
 ^ 
 
 :§: 
 
 \k 
 
 S^ffe^ 
 
 -eh—£±- 
 
 f=g^^ 
 
 f »i^^ 
 
 -^ — g — I 
 
 i 
 
 -«5»- 
 
 U 
 
 etc 
 
 lEE 
 
 la: 
 
 four-chord cadences 
 
 75. 
 
 ^^^^ ^^^^^ ^^ 
 
 jQ-. 
 
 -<5> ^ 
 
 [> O ^ 
 
 -c^--^ 
 
 
 I 
 
 ^ 
 
33 
 
 five-chord cadences: 
 
 76. „ 
 bt 7^- i^ 7^ •;^ /> — \ ff— 
 
 
 
 JJ 
 
 1 ^ ^ ^_^_g=:r|_ 
 
 -6»— 
 
 77 
 
 =i-^r^ 
 
 ( I. ii_ [JL 
 
 
 
 
 
 1 «5>-J^ 
 
 tiF=^'^=«=«==-';;==^=^i»? 
 
 'J— g=:gz=; 
 -js. 
 
 rg^ 
 
 1^ 
 
 ^- 
 
 -0^^ 
 
 ■s?-«- 
 
 ^ 
 
 .^- 
 
 n——^ 
 
 nA 
 
 ZBT. 
 
 M 
 
 S 
 
 ^g^^l^s^^^i^ 
 
 -^L 
 
 *; 
 
 .^- 
 
 fif «fi,TL*. 
 
 ■*ifL' 
 
 a 
 
 -g? ^> -?; 
 
 ^ 
 
 1==?— ^ 
 
 r ^ 
 
 tj f-^, g « f! TV — cs>- 
 
 ^i^l 
 
 -fit. 
 
 is: 
 
 s 
 
 l±i£^ 
 
 -^-^ 
 
 ^ 
 
 :S^=:S 
 
 yy ?5^- 
 
 :7=r22z=:a=^ 
 
 ±:t?=:g=g=^=gg=g- 
 
 3^^^=^ 
 
 -<5> ^ 
 
 ^SQi 
 
 31 
 
 ^^i^^^ 
 
 ^- 
 
 ^ 
 
 
 s^ « 
 
 ^ 
 
 -«> — ^~ 
 
 i 
 
 / 
 
§ 24. 
 
 FIGURATION OF THE CHORD OF THE SEVENTH. 
 
 In figurating the cadences the repetition of the funda- 
 mental in the chord of the seventh (right hand) is omitted, 
 that the rhythm may be equal, and we therefore play, not: 
 
 ^^m 
 
 Twenty-seventh Exercise. 
 
 Form as above the flgurated five-chord cadence in 
 all keys. Example: 
 
 78. 
 
 I 
 
 ^ 
 
 '-f~i-^-^f^ -if-C4^ 
 
 ^zijrjz^i: 
 
 mi 
 
 p 
 
 £ 
 
 -!(5>- 
 
 §25. 
 
 ^ CHORDS OF THE SEVENTH IN CIRCLE OF FOURTHS. 
 
 Alternate, while progressing through the Circle of 
 Fourths, between the first and third positions of the chord 
 of the seventh in the right hand: 
 
 Circle of Fourths: C-maj. ^-maj. i?l>-inaj. ^b-maj. ^b-maj. i)|?-maj. 
 Position: I. in I. m. I. in. 
 
 79. 
 
 1^^^^^^^^ 
 
 Circle of Fourths : i^jj-maj. ^-maj. J^-maj. ^-maj. i>-maj. G-m&j. C-m&y 
 Position: I. III. I. HI. I. IH. I. 
 
 4i 
 
 %=tH 
 
 "ft^ 
 
Twenty-eighth Exercise. 
 
 Play above series by heart with the right hand. 
 
 The left hand plays the fundamental to each chord. 
 
 Play the series with both hands: 
 
 80. 
 
 =S^&^ 
 
 ^^^^ 
 
 5^ 
 
 ■fa. 
 
 -^ ^ I'"- ^ 
 
 ia: 
 
 ¥^^^r^^=f 
 
 —49- 
 
 The same figurated: (See No. 70.) 
 
 81. 
 
 $^^^^^^^ 
 
 ^ 
 
 ^ 
 
 j? r> n - 
 
 (fii- 
 
 p^r^^^^^^^^^^^^^ 
 
 5H|p 
 
 -6*- 
 
 -fS^- 
 
 or: 
 
36 
 
 Vn. The six and seven-chord Cadences. 
 
 § 26. 
 
 CHORD OF THE FOURTH AND SIXTH. 
 
 The second inversion (third position) of the tonie triad 
 is called the Chord of the Fourth and- Sixth. 
 
 82. 
 
 m 
 
 Take this with the right hand, douhling the lowest 
 note with the left: 
 
 83. 
 
 ^: 
 
 ^EE^ 
 
 giving chord of the fourth and sixth in four parts. 
 
 This chord retains it significance as chord of the fourth 
 and sixth, when the right hand takes another position of 
 the triad, as long as the hass is the same. 
 
 84. 
 
 I 
 
 -<5»- 
 
 «=^ 
 
 9i 
 
 -ZL 
 
 la: 
 
 Of these three chords of the fourth and sixth we use 
 the second in cadence, i. e* the one having the tonic of the 
 key as highest note. 
 
87 
 
 Twenty-ninth Exercise. 
 
 Form the chord of the fourth and sixth as above in 
 all keys. 
 
 85. 
 
 ^ 
 
 i& 
 
 P 
 
 W 
 
 ^^ 
 
 }<9- 
 
 =^1= 
 
 31=1^ 
 
 i 
 
 ^w^. 
 
 ^ 
 
 i: 
 
 g 
 
 « 
 
 ^ 
 
 9^=^ 
 
 §27. 
 THE SIX-CHORD CADENCE. 
 
 Play the chord of the fourth and sixth given in the 
 foregoing § between the third and fourth chords of the 
 fiye-chord cadence. 
 
 ^^ 
 
 -Kf- 
 
 
 ^ 
 
 ^ 
 
 3 
 
 I VI IV I T 
 1 ' 
 
 We thus obtain the six-chord cadence. 
 
 Thirtieth Exercise. 
 
 (I) Form the six-chord cadence in all major keys. 
 
 C-migor as aboTe. (No. 86.) 
 
38 
 
 87. C-major, 
 
 i>-major. 
 
 13^^^^^ 
 
 «=f 
 
 ^ 
 
 ^-^-^-^ 
 
 ^ 
 
 a 
 
 li 
 
 & — &- 
 
 zzr. 
 
 U- 
 
 ^-major. 
 
 ^^^i 
 
 
 etc. 
 
 m^ 
 
 1^: 
 
 •g — a: 
 
 i?t>-inajor. 
 
 ^b-major. 
 
 ^ 
 
 r:g=g=fn:T^=g; 
 
 5EgE5^?EiE|?Eg 
 
 i^r 
 
 ^ 
 
 i^izgz m n 
 
 •6>- iS>- 
 
 ^^^^P' 
 
 Tz: 
 
 -G—&- 
 
 §s?a 
 
 e^ 
 
 ^ 
 
 :^-g> <g- 
 
 ^i>-major. 
 
 =g 
 
 -^ — fi^- 
 
 g^ggzzgzzH 
 
 etc. 
 
 .<s, fi ^- 
 
 S 
 
 Figurate 
 
 88. ^ 
 
 the six- 
 
 chord C2 
 
 idence. 
 
 
 
 
 'J * ^ J J -H"^-^ 
 
 ps — ^ r1 n 
 
 J -^ — H \ 
 
 -^EB 
 
 ^ 
 
 g 
 
f 28. 
 
 m MINOR. 
 
 Thirty-first Exercise. 
 
 (I) Form in like manner the tonic chord of the fourth 
 and sixth in all minor keys. 
 
 89. 
 
 fei= 
 
 * 
 
 ^^ 
 
 W 
 
 =^ 
 
 ZSti 
 
 ^ 
 
 ^ 
 
 -^^ 
 
 ^^- 
 
 !iE 
 
 izs: 
 
 -OL 
 
 m 
 
 ^ 
 
 # 
 
 w^^ 
 
 ?^ 
 
 teS 
 
 I 
 
 (2) Form the six-chord cadence in minor. 
 
 90. <;-niinor. (^-minor. 
 
 ig^g-rgz^^^^ 
 
 ^f#g=!^2=^i=r-^g±|^^=|3j^ 
 
 i< 
 
 ^ 
 
 -6/ <& 
 
 pa: 
 
 -<5> ^- 
 
 3E 
 
 I VI IV 1 f I 
 
 ^-minor. 
 
 <g fog — ^ 
 
 zc 
 
 eta 
 
 i 
 
40 
 
 (3) FIgurated: 
 
 91. c-minor. 
 
 ^^E^i^^^^^ 
 
 m 
 
 ISl 
 
 X r 
 
 JZ. 
 
 m 
 
 ^-minor. 
 
 ^P 
 
 i^^^i^^^^^ 
 
 ^ 
 
 ^i=t 
 
 -&- 
 
 3 
 
 BEMAEK. The brightest pupils, but only these, may be told here, 
 that, instead of the subdominant triad, the chord of the sixth on the 
 subdominant (first inversion of the subordinate triad on the Second) 
 may be played. 
 
 Major: 
 
 
 0^- 
 
 jf~ Ti 7^ ^ 25 -::. V2 
 
 ■ 
 
 iy. " a » 
 
 \ 
 
 ^ ... , * , 
 
 _ c 
 
 Figurated 
 
 rrrS^l^^fei^fag^Jrfg 
 
 ^ 
 
 s 
 
 -za 
 
 1Z. 
 
 Minor: 
 
 fe r^-^^-r-^ 
 
 W- 
 
 ize: 
 
 2E 
 
41 
 
 I 
 
 Figurated: 
 
 ^a. 
 
 tn^zj:; 
 
 ^^^^ 
 
 -«?- 
 
 ^ 
 
 g 
 
 -<2- 
 
 ^ 
 
 2^ 
 
 §29. 
 
 CHORD OF THE SEVENTH ON THE SECOND DEGREE. 
 By adding to the subdominant triad (IV) a tUrdi below, 
 
 g we obtain this chord. Its fundamental is 
 
 the Second (second degree) of the key. 
 
 Thirty-second Exercise. 
 
 (I) Form the chord of the seventh on the Second 
 in all major keys. 
 
 93. 
 
 ^ 
 
 ^:'-- 
 
 3B2 
 
 ^- 
 
 fe 
 
 H- 
 
 
 =1^ 
 
 i??.- 
 
 ianpi 
 
 ^b E^ 
 
 B)f 
 
 (2) Form the same chord so, that its fundamental 
 is taken an octave lower by the left hand, the right 
 taking only the subdominant triad. 
 
 n 
 
 pt 
 
 
 g= 
 
 
 5? 
 
 i — <5>. 
 
 S 
 
 £ 
 
 B 
 
 f=f^ 
 
 :es 
 
 #« 
 
 Of 
 
42 
 
 17<^- 
 
 \ ^rr- -y^ ,-^g 
 
 ^^ 
 
 1 
 
 3±=5i= 
 
 1 
 
 iiii ^1? 
 
 ^b 
 
 § 30. 
 
 THE SEVEN-CHORD CADENCE. 
 
 Introduce the chord of the seventh just explained be- 
 tween the third and fourth chords of the last cadence, i. «. 
 between the chords of the subdominant and of the fourth 
 and sixth. 
 
 95. 
 
 <Z u a Oi ej. <5) Cl 
 
 ^ 
 
 ^ 
 
 -ISi^II^. 
 
 IV II7 It 
 We thus obtain the seven-chord cadence. 
 
 Thirty-third Exercise. 
 (I) Form the seven-chord cadence in all major keys. 
 
 96. u 
 
 gzzg=:g=:gz=:giz^^fiiE=ig=^: 
 
 
 -.KH <a iL|_g. 
 
 s: 
 
 is: 
 
 -G—G- 
 
43 
 
 (2) FIgurated. 
 
 97 
 
 |zi: ^ 5Jim1x^ ^pp^ 
 
 ■^ 
 
 .T3t 
 
 ^i 
 
 m 
 
 ^=1=:^ 
 
 ^^^g^^^^^ 
 
 ^^t'F^ 
 
 3£& 
 
 ::r: 
 
 :3c 
 
 § 31. 
 IN MINOR. 
 
 Thirty-fourth Exercise. 
 
 (I) Form chord of the seventh on the Second, as 
 above, in minor. Only singly, because their regular suc- 
 cession sounds disagreeably. 
 
 98. 
 
 ^S; 
 
 Jt^ 
 
 ^ 
 
 it 
 
 ■^i^ 
 
 -^ 
 
 u 
 
 ^ 
 
 n «« 
 
 ipi^^B^i^ 
 
 teszitt: 
 
 
 g 
 
44 
 
 (2) Form the seven-chord cadence in minor. 
 
 99. c-minoT. 
 
 d-mmor. 
 
 -^ 
 
 jO—e^. 
 
 ^ 
 
 m 
 
 ~cu 
 
 ^^^1 L\- 
 
 /9- 
 
 7? 7S 
 
 Si 
 
 ^ 
 
 g a^J" i r— g — ^f J - 1^ ^ 
 
 In forming these chords of the seventh in minor, strike with the 
 right hand, as previously in major, the subdominant chord (IV), then 
 adding with the left the lower third (Second of the key) an octave below. 
 
 EEMARK. As a subordinate exercise the minor chord of 
 the seventh on the seventh degree of the major scale 
 may be taken up here. It is resolved to the tonic 
 triad, and with this resolution exhibits a very clear 
 picture of the key, and the mutual relations of its 
 seven tones. 
 
 ^Di A^ g9 B)^ F 
 
45 
 
 Without this resolution the chord does not present the 
 major key so clearly, as it may then easily be mistaken 
 for the chord of the seventh on the Second in minor. 
 
 VIII. Chords in Diatonic and Chromatic 
 Progression. 
 
 § 32. 
 CHORD OF THE SIXTH. 
 
 The chord of the sixth ^ g — ; can process dia- 
 
 tonically in all parts, and thus form a scale of chords of 
 the sixth either ascending or descending. 
 
 Thirty-fifth Exercise. 
 
 Form scales of chords of the sixth, with each hand 
 alone, in a1 major Iceys. 
 
 100. -a. iSd ^ za -a. 
 
 ai 
 
 g-» s' " -^^-^ ^ ^-jg -g^ 
 
 u 
 
 ^^^^^^^^ 
 
 
 We can proceed in like manner with the chord of the 
 sixth and fourth; hut this series is far less pleasing in effect, 
 and requires in composition a special harmonic actuation. 
 
46 
 
 Thirty-sixth Exercise. 
 
 Chords of the fourth and sixth in diatonic pro* 
 gression. 
 
 101. 
 
 i 
 
 g^^ 
 
 ww^^=^^ 
 
 SElElElEiEE^^ 
 
 ■e>—z, 
 
 t^^f^=:«= 
 
 77 ■» 
 
 * ^ * S^ 
 
 i^-i^f: 
 
 «: 
 
 =S=g=i=^=S 
 
 ^^JEgEJEp^ 
 
 77 -^^ 
 
 'S'— zr 
 
 ^ 
 
 ^ 77 
 
 #=#=1=?=^ 
 
 Ppaa ^^^E ^P^g^ 
 
 Here the best opportunity offers for a subordinate exer- 
 cise — that of practically showing the pupil the nature of the 
 suspension. In C-major let him strike, hefore the highest 
 tone of each chord of the sixth, that of the chord next 
 above, together with the two lowest tones. 
 
 , I 1 J I i J J i 
 
 i 
 
 dz^- 
 
 E 
 
 ii: 
 
 :§ 
 
 ^^^^ 
 
 I 
 
 ? ^ ^ i i J 
 
 % 
 
 -^ 
 
 ^ 
 
 I I 
 
 
 •to. 
 
 Variation. 
 
 i 
 
 3 < g g 
 
 i-. -i- ^ ■ ^ ' J -» ■ ' ^ 
 
 ±=ii 
 
 3z: 
 
 :|!^ 
 
 3= 
 
 <nr with tie: 
 
 
 In other keys the signature must be carefully obserred*. 
 
47 
 
 § 33. 
 
 THE DIMINISHED TRIAD. 
 
 The diminished triad may progress chromatically, each 
 part of the same moving hy a semitone either ascending or^ 
 descending. 
 
 Thirty-seventh Exercise. 
 
 102. 
 
 ^^^^i^^^Bi^^ 
 
 ^^S^^^i^^^ 
 
 This progression can of course also occur in Figuration: 
 
 ^^ 
 
 1 
 
 ^P 
 
 etc. 
 
 i^^ p^^^ 
 
 Both inversions should also he worked out: 
 First (chord of the Sixth). 
 
 etc. 
 
 ^ J^ ^^ z^ 
 
 c^^-^UB-f^f±§. 
 
 In Figuration: 
 
 ete. 
 
 9r:^r-^ ejJ--t^^ ^ 
 
48 
 
 Second (chord of the fourth and sixths 
 
 I 
 
 * 
 
 ? 
 
 etc. 
 
 In Figuration; 
 
 ''^ ^ , eta 
 
 ^iz ^j^pd^zt;^ ^^ 
 
 § 34. 
 
 DIMINISHED CHORD OF THE SEVENTH. 
 
 For a long period this chord has occurred more fre- 
 quently than any other with the above chromatic pro- 
 gression. 
 
 The diminished chord of the seventh consists of a 
 diminished triad with added minor third. It therefore com- 
 prises in all three minor thirds. 
 
 Thirty-eighth Exercise. 
 
 (I) Form the diminished chord of the seventh on 
 all degrees of the chromatic scale, with each hand alone. 
 
 103. 
 
 1^^^*!= 
 
4» 
 
 (2) Practice this succession, till thoroughly fluent, 
 In both Chords and Figuration, f^rst with either hand 
 alone, then with both together. (Incidentally, with figu- 
 ration in one hand and chords in the other.) 
 
 I 
 
 ife 
 
 m 
 
 eto. 
 
 ^^^P 
 
 5*^==^^ 
 
 § 35. 
 
 CHROMATIC CHORDS OF THE SIXTH. 
 
 These chords, and likewise those of the fourth and 
 fdxth, may progress chromatically as above, but with lesi 
 agreeable effect than the preceding. 
 
 (a) Chord of the Sixth, major triad: 
 105. 
 
 ^If ^W i-^i ^ 
 
50 
 
 f ^^^ ^ 
 
 et«u 
 
 
 etai 
 
 eto. 
 
 52 
 
 (b) C^orc? o/" Fourth and Sixth of same: 
 106. . . «_ ^«,_ z^ >#,kfebf „i;it^ « 
 
 «*g*^^^^ 
 
 ^^^^ 
 
 ^^^s 
 
 eto. 
 
 eto. 
 
 (o) Chord of the Siocth, minor triadi 
 
 107. . . 
 
 ^^|^^5p^ 
 
 eta 
 
 (d) C%or({ 0/* JFVmrfA am2 <Sfia?fA, minor ^rtod; 
 
 108. 
 
51 
 
 ^ ^ ^^ 
 
 ete. 
 
 Thirty-ninth Exercise. 
 Form such progressions. 
 
 IX. Modulation. 
 
 §36. 
 
 INTERCONNECTION. 
 
 Those chords which stand next each other in the Circle 
 of Fifths or Fourths are termed interconnected (related). 
 
 Major and minor chords, whose keys have like signatures, 
 are called relative. 
 
 Fortieth Exercise. 
 
 (I) Play major triads, with their relative minor triads, 
 throughout the Circle of Fourths. 
 
 c F B\f e:\^ A\^ J)> i^S 
 
 ^&^g^ p^p3i^pto^ 
 
 • i g t f V} d% 
 
 B E A V—^ e C 
 
 
 ^m 
 
 Major and minor chords having the same fundamental 
 are called like-named. The exercise, to play the like-named 
 triads, haa already been given. (Seventh Exercise.) 
 
 4* 
 
52 
 
 ^ (2) Pass from a major triad to the like-named minor 
 
 triad, from this to its relative major triad, which is then 
 to he treated similarly. 
 
 '^^. 
 
 ^S^S^igp^tj^ 
 
 w^ 
 
 \w% W^ ^- 
 
 ^%- 
 
 a-pjyg^' 
 
 a 
 
 ^ 
 
 equal to 
 
 $^ ^^^ ^^^^"^^i^^P 
 
 Application: 
 
 
 etc. 
 
 like-named \ interconnected \ 
 
 relative 
 
 N^^#^^ 
 
 f77 >^ 
 
 2 
 
 
 etc. 
 
 § 37. 
 
 DEFINITION OF MODULATION. 
 
 The transition (passing over) to another key is called 
 Modulation. 
 
 The series of chords of the seventh in Nos. 79—81 
 modulates with each progression; t. e. each chord of the 
 series helongs to a different key. ' 
 
 Rules for modulation can he presented only in a sys- 
 tematic and methodic course of Harmony. Here all must 
 be left, after a mere passing suggestion, to the talent and 
 inclination of the pupil. More serious endeavors should be 
 based on the exercise of practical harmony* 
 
ftS 
 
 A Modulation is effected by the introduction and reg- 
 ular resolution of the dominant chord of the seventh be- 
 longing to that key, into which we wish to pass. 
 
 111. 
 
 From C-major to 6?-inajor. 
 
 =f-|^l^ 
 
 ^: 
 
 -O 
 
 i. «. by the two-chord caden<}e 6f tne new key. The two- 
 chord cadence forms, as we know, the two last chords 
 (and the most essential part) of all cadences. 
 
 Also, the three last chords of the seven-chord cadence 
 may be used for modulation; of course we always mean the 
 cadence of that key, into which we wish to pasa. 
 
 112. 
 From C'-major to 6?-major. 
 
 w 
 
 w 
 
 Also, the four last chbri 
 113 
 
 xbrds: 
 
 ? ^ 
 
 i 
 
 t=t 
 
 ■^—^-. 
 
 'W^^'^^ 
 
 ^ 
 
 -G- 
 
 Also, the five last chords 
 
 L V 
 
 i 
 
 7 X • 
 114. From ^-minor to C-major. 
 
 f - f - i-g- ^^ 
 
 ^. 
 
 IV 1 
 
 >'\r^ V-] i 
 
64 
 
 Also, the six last chords: 
 
 115. From ^-major to (7-major. 
 
 L ^—G <^ 
 
 
 g=g=g^g=: 
 
 «: 
 
 ^i 
 
 <9- 
 
 la: 
 
 «9- 
 
 Forty-flrst Exercise. 
 
 Modulate by the two-chord cadence from any key 
 into any other. 
 
 Here no heed should be given to the progression and 
 leading of the individual parts, unless the pupil's talent 
 fairly demands it. 
 
 Should the chord of the seventh in the new key not 
 follow harmoniously upon the first chord, a related triad 
 may he introduced between the two. 
 
 116. 
 
 ^^J^I^PHig^i^ 
 
 95 
 
 -12^ 
 
 iza: 
 
 Instead of a triad we may introduce a dominant or 
 diminished chord of the seventh, or one on the second de- 
 gree, whereby the pupil however, from his present stand- 
 point, can not be guided by rules, but exclusively by his 
 ear and taste. 
 
 117. 
 
 -t2^ 
 
 ^ 
 
 Xi. 
 
55 
 
 Forty-second Exercise. 
 
 Modulate with the two-chord cadence and a chord 
 previously introduced. 
 
 § 38. 
 
 UPON THE INDIVIDUALITY 
 
 of tlie pupil it will depend whether, or at what stage, the 
 teacher shall begin with the systematic exercise of prac- 
 tical harmony. Upon this only it also depends, how far 
 the teacher shall let him work out the exercises here pre- 
 sented, and whether any or many may be skipped or no. 
 More especially the exercises in minor are often repugnant 
 to less gifted or zealous pupils, in which case they may 
 be left out. On the other hand, the teacher may pay more 
 attention to the minor keys than has been done above, 
 whenever a pupil exhibits the necessary intelligence and 
 interest. For instance, the resolution of the diminished triad 
 and dominant chord of the seventh may also be carried 
 out in minor; the key of the diminished chord of the seventh 
 may be determined, the chord followed through its in- 
 versions, and resolved to major and minor. Peculiarly tal- 
 ented pupils may also attempt to follow up and vary the 
 cadences through inversions. 
 
 Still, with such gifted pupils, it is always better to 
 proceed to systematic instruction. 
 
 We must again repeat, that the foregoing exercises 
 have no further purpose than to awaken and increase in- 
 terest in the harmonic foundation of modern music; that 
 they hereby purposely avoid systematic completeness, ap- 
 pealing only to the musical power of perception, to the ear, 
 and aiding the latter, wherever necessary, by helps of a 
 quite external nature. They thus form, in a degree, an 
 
 harmonic Kindergarten, 
 a preliminary course, based simply on empiricism, to the 
 
56 '^e. .<:..;... -.,:;.«,. ^; 
 
 jsystematic method of harmony, but quite self-dependent, 
 and independent of the latter, forming a supplement to the 
 practical course of music, which is especially useful in 
 piano-teaching. With most other instruments, the player's 
 own production of the tones is beneficial to the musical 
 perception. Yet they too, although perhaps in a less de- 
 gree, require this supplementary course, an application of 
 which to other instruments, or in singing-lessoniSi, offers no 
 difficulty. 
 
 -ogSo- 
 
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 j 
 
 
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 / 
 
 
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 7 : tt7 
 
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 1;0V2 9 1979 
 
 
 APR 17 1980 . 
 
 
 NOV 12 1982 
 
 
 MAY 2 1985 
 
 
 REC'D MUSIC 
 
 
 fMY 2 1 1986 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 T rk oi A in^ r: 'Rf: General Library 
 
I MT50.B83 
 
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 Music Library 
 
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