A NEW SYSTEM OF HARMONY Based on Four Fundamental Chords EDUARDO GARIEL NEW YORK G. SCHIRMER Southern Branch oftKe University of California s Los Angeles rj This book is DUE on the last date stamped below. MAY 8 1925 OCT 2 9 192ff - JAN 2 8 1935 y 23 1935 MAN MAR 1 2 1947 6 1 5m-8,'21 NOV 2 9 1949 B '59 APfl 1 5 '59 MAY 6 'I? A NEW SYSTEM OF HARMONY BASED ON FOUR FUNDAMENTAL CHORDS BY EDUARDO GARIEL TEACHER OF MUSICAL COMPOSITION AT THE NATIONAL CONSERVATORY OF Music IN THE CITY OF MEXICO ; CHIEF SUPERVISOR OF SCHOOL Music, AND TEACHER OF THE METHODOLOGY OP SCHOOL Music AT THE BOYS' NORMAL SCHOOL, IN THE SAME CITY SECOND EDITION G. SCHIRMER BOSTON .-. NEW YORK .'. LONDON Depositado conforme a la ley de la Republics Mexicana en el afio MCMXVI por G. SCHIRMBR (Inc.), Propieurios, Nueva York y Mexico Copyright, 1915, by EDUARDO GARIEL Copyright, 1916, by G. SCHIRMER MUSIC LIBRARY MT 50 To VENUSTIANO CARRANZA First Chief of the Constitutionalist Army Invested with the Executive Power This is a revolutionary book. To whom should I dedicate it better than to the leader of the greatest and most transcen- dental revolution that ever occurred in Mexico? I beg you to accept it, not only as a token of our old friendship, but as a tribute to the man who has in his hands the reconstruction of our beloved country. THE AUTHOR. City of Mexico, January, 1916. CONTENTS INTRODUCTORY REMARKS . i Explanation of the term " tendency." The real structure of the musical scale. Mathematical ratios between scale-degrees. Greater tone, lesser tone, half-tone. The syntonic comma. Arrangement of the major scale. Tendencies of the ;th, 4th and 6th degrees. The Law of Lesser Effort. The 2d degree also obeys this law. Degrees i, 3 and 5 do not obey it. MUSICAL CHORDS 4 Definition of the term "chord." tj-~ The Science of Harmony. <* HARMONIC SYSTEM BASED ON FOUR FUNDAMENTAL CHORDS. . 5 Tables of these chords and their derivatives. CHORD I : ORDINARILY CALLED THE TONIC CHORD 6 o t CHORD OF THE V DOMINANT NINTH-CHORD 6 ** Its harmonic tendency. ^ Chords V, VII and II derived from it. Their harmonic tendencies and regular progression. These chords, and the Tonic chord, are natural. Irregular progression of natural triads. Free progression of the Tonic triad. o CHORD OF THE II : 10 A mixed chord; its law of movement is duplex. Mixed chords IV and VI derived from it. These chords have two tendencies. Chords IV and VI preceded by chord I. e Irregularly preceded by natural chords derived from the V. Chords IV and VI interconnected regularly and irregularly. vi CONTENTS 8 PAGB THE FUNDAMENTAL MIXED CHORD VI 13 Its law of movement is duplex. Its derivative, the mixed chord III, has two tendencies. Mixed chord III followed by natural chords. Followed by the mixed chords IV and VI. Preceded by natural and mixed chords. FULL FOUR-TONE CHORDS, OR SEVENTH-CHORDS 15 Tables showing derivation from the four great chords. DOMINANT SEVENTH-CHORD V; ITS TENDENCY 16 7 SEVENTH-CHORD ON THE yTH DEGREE, VII; TENDENCY 17 Regular and irregular progression of natural seventh-chords. 7 SEVENTH-CHORD ON THE 20 DEGREE, II ; DOUBLE TENDENCY 18 Preceded by natural seventh-chords. 7 SEVENTH-CHORD ON THE 4TH DEGREE, IV; DOUBLE TENDENCY 20 Regular and irregular progression. SEVENTH-CHORD ON THE 6TH DEGREE, VI; DOUBLE TENDENCY 21 Regular and irregular progression. 7 SEVENTH-CHORD ON THE IST DEGREE, I; DOUBLE TENDENCY 22 Regular and irregular progression. 7 SEVENTH-CHORD ON THE 30 DEGREE, III; DOUBLE TENDENCY 24 Regular and irregular progression. CONNECTIONS OF SEVENTH-CHORDS WITH TRIADS 26 7 Natural V with all Natural Triads; with Mixed Tnads 27 7 Natural VII with all Natural Triads; with Mixed Triads. ... 28 7 Mixed II with Natural Triads; with Mixed Triads 29 7 Mixed IV with Natural Chords; with Mixed Triads 30 7 Mixed VI with Natural Triads ; with Mixed Triads 31 7 Mixed I with Natural Triads ; with Mixed Triads 32 7 Mixed III with Natural Triads; with Mixed Triads 33 TRIADS FOLLOWED BY SEVENTH-CHORDS 34 7 By the Natural Chord V 34 By the Natural Chord VII 35 By the Mixed Chord II 36 By the Mixed Chord IV 37 By the Mixed Chord VI 38 CONTENTS vii 7 PAGE By the Mixed Chord 1 38 By the Mixed Chord III 39 MINOR SCALE AND MINOR KEYS 40 CHROMATICS: EFFECT OF CHROMATIC ALTERATIONS 40 ALTERED OR CHROMATIC CHORDS 41 MODULATION 43 Forty-nine Modulations from C major to G major 44 Thirty-five Modulations from C major to D[? major 51 Six HARMONIZATIONS OF A CANTUS FIRMUS, BY A PUPIL. ... 53 CONCLUSION 55 A NEW SYSTEM OF HARMONY BASED ON FOUR FUNDAMENTAL CHORDS A well-known fact in the domain of science is the great im- portance of a good classification. The classification that I shall explain here is based on four fundamental chords, and is marked by a clearness and simplicity not ordinarily found in books treating on this subject. Every well instructed musician knows that the classification now employed groups the musical chords according to their form: and so we have major chords, minor chords, chords of the sixth, of the sixth and fourth, chords of the seventh, of the fifth and sixth, of the third and fourth, of the second, and so forth, according to certain intervals that are found in them. Since Rameau (eighteenth century) this classification has served, it is true, to explain and teach musical Harmony; but surely very many have felt, as I always have, that even after learning to write and play musical chords, it always remains a kind of mystery to employ them in a musical way, and this is especially true of the triads and their inversions. As you will see further on, in my classification the chords are grouped according to their tendencies, making families of chords which obey the same law, irrespective of their form. The books on Harmony teach that chords of the seventh have certain prescribed movements or "resolutions," as they are called but they also teach other movements or resolutions considered as exceptional. Talking about the triads, which are treated first, they say that these are more difficult to handle, being more free in their movements; to guide you they estab- lish certain fixed and almost inflexible rules that leave you in 2 A NEW SYSTEM OF HARMONY the dark as to their origin and reason. What is worse, there are many text-books that do not say anything about the move- ments of these chords. The truth about this and I consider it a real discovery of mine is that the triads also have a tendency, as well as the dissonant chords, and that this tendency is the same when both triads and chords of the seventh have the same fundamental and come from the same origin or great fundamental chord. But now let us leave criticism of the known systems, and speak about the new classification and its results. I hope that my fellow musicians will find it clear, easy and logical, and, above all, practical and useful for the teaching of musical com- position. To make perfectly plain the laws that govern the movements of musical chords, it is necessary to go back to the musical scale itself on which modern music is based. If we consider the real musical scale and not the conventional one ordinarily explained in musical books, we find the following facts: (1) It has eight sounds or degrees, called C, D, E, F, G, A, B, C in the key of C. (2) The mathematical ratios, as given in Acoustics, between each degree and the fundamental, or first one, are as follows: 1 C , D E F-G A B C 1 I II I I 2 Here follows the explanation of this figuring: If we take a C of 240 vibrations, the D or second degree whose ratio is f, will have 9 vibrations in the same time that C has 8, or (com- pleting the computation), 240 X 9 -5- 8 = 270 vibrations for D; and so forth. Now, if we want to know the mathematical ratios between all the contiguous degrees of the scale, we shall find them by dividing the greater one by the lesser. Taking C as i, we aready have ACOUSTICS: LAW OF LESSER EFFORT 3 the ratio of D to C, or f . The ratio between D and E is found by dividing f by f = f = -^-, which is the ratio between the second and third degrees of the scale; and so forth. Below are given the ratios between all contiguous degrees of the scale: 2 CDEFGAB-C ~T IT IF T' ~T TT On inspection we can see at once three different relations and, at the same time, three different kinds of intervals. The one represented by f is called the greater tone; the one represented by ^j- is called the lesser tone. The difference between a greater tone and a lesser tone is found by dividing their respective ratios as follows: f -f- *- = f^. This difference, amounting to f^-, is called in Acoustics a syntonic comma. As not everybody is inclined to mathematical calculations, I will present the scale and its intervals in the following table : 3 CDEFGABC greater lesser half- greater lesser greater half- tone tone tone tone tone tone tone Little by little, as music was changing from the church modes to the modern scale, musicians felt, empirically, the tendency of certain degrees of the scale to proceed to some other degrees. These tendencies are acknowledged in Harmony text-books as follows: The seventh degree tends to the eighth, the fourth degree tends to the third, and the sixth degree tends to the fifth. I must state that many books do not even mention the tendency of the sixth degree. If we study attentively the last example we shall notice that the seventh degree (B) has on the right an interval of a half-tone, while on the left the interval is a greater tone; so when B shows a tendency to C, it tends to where the interval is smaller. 4 A NEW SYSTEM OF HARMONY Looking now at the fourth degree (F), we notice that it has a greater tone on the right and a half-tone on the left; so, when F shows a tendency to E, it is again where there is a smaller interval. Considering the sixth degree (A), we see that on the right is a greater tone, while to the left is a lesser tone; so, when A tends to G, it tends to the side where there is a smaller interval, just as in the other two cases examined. These three particular cases, in which each degree tends to the side where the interval is smaller, authorize us to deduce a law that may be thus expressed: The degrees of the scale which have a tendency, obey the law of lesser effort. Seeking now for another degree of the scale that may conform to this law, we find the second degree (D), which is placed between unequal intervals, having on the right a lesser tone and on the left a greater torn; therefore, the second degree must obey the established law of lesser effort and have a tendency to the third degree (E). As there is no book, that I know of, assigning any tendency to the second degree, I consider that the tendency now spoken of is a real discovery that must be taken account of in a modern method of musical composition. The law of lesser effort can not be applied to the first (C), third (E) and the fifth (G) degrees of the scale, because the first is the fundamental of the scale and G and E are strong overtones of^C, blending with it so closely as to give almost'the same sen- sation. MUSICAL CHORDS The simultaneous sounding of three, four or five tones at the interval of a third from one another is called a musical chord. The study of chords and their connections is known as the Science of Harmony. According to the new system to be explained here, the whole harmonic structure is based on four fundamental chords of five tones each. These five-tone chords are called in Harmony chords of the ninth; their root-tones are the ist, 5th, 2d and 6th degrees of the scale, respectively. THE FOUR FUNDAMENTAL CHORDS 5 In the following table the fundamental chords are represented in whole notes. The first chord and the fourth have four notes in common (C, E, G, B), as shown by brackets. The chords in quarter-notes are three-tone chords derived from the great chords. HARMONIC SYSTEM BASED ON FOUR FUNDAMENTAL CHORDS vvnii IV VI This form may be better represented by Arabic figures than by notes. And I say better, because the figures stand for de- grees of the scale, irrespective of the tonality or key, and are applicable to all the keys; whereas, the form with notes, in the foregoing tables, applies only to the key of C. We ought to have one form which fits every key. 4 bis Natural Chords f Mixed Chords 7 7 5 /5\ 5 6 6 3 i 6 3 i i 6 6 3 1 6 U ' 4 4 4 4 4 /T\ m ej (2) 2 222 2 (VI) W 1 i ( 7 ) 7 7 7 (II) vi 5 5 5 II IV 3 VII 1 V 9 9 I (V) V VII II IV VI (VI) in 6 A NEW SYSTEM OF HARMONY Playing the first chord C-E-G-B-D on a piano or organ all the tones simultaneously, of course in the key of C, we feel that the chord produced is dissonant and gives the sensation of movement or, in other words, that it has a tendency to move and proceed to another chord. Taking out the second degree (D) marked with the figure 2, we get a chord of four tones (C-E-G-B, in the key of C), which also gives the sensation of movement. CHORD I: ORDINARILY CALLED THE TONIC CHORD Now, leaving out the seventh degree (B), marked in the table with the figure 7, we get a chord of three tones (C-E-G in the key of C) : This chord is called perfect or consonant, and playing it we get a sensation of rest, as G and E are overtones of C, and the three together sound very well, giving a quiet and peaceful sensation. The figuring of this triad formed on the first degree of the scale is with a Roman number I underneath, as it is in the above example. NINTH-CHORD Considering now the second chord of my system, that is, the o chord of the ninth on the fifth degree (5-7-2-4-6), figured V, we notice that it has one degree the fifth in common with the chord I, or tonic chord, and that the remaining degrees (7-2-4-6) are precisely those that, according to the law of lesser effort, have a tendency. It is interesting to observe here that the tendency of the active degrees of the scale is just as urgent when they are alone in the melody, as when they come together THE DOMINANT NINTH-CHORD 7 in musical chords, as you will see later. The strong union of melody and harmony is really noticeable, and it has been a great mistake in the text-books to treat them separately, thus dividing their study. Playing now on the piano the dominant ninth chord, or ninth- Q chord on the fifth degree (which is perhaps more clear) , V, we feel at once a very strong sensation of movement, which is quite natural, as this chord has in it the four degrees of the scale (7, 2, 4, 6) that have a moving tendency. As the tendency of each of these degrees is, individually, toward a degree of the tonic chord or chord I, the natural tendency, or, as we may say, "the e law of movement" of the chord V, is to go to chord I: II ^^^^ 9 ^^^| J ^^^^ J Jj cv \ M J' 1 N '1 ! "** *' ' ' r o V I. 9 3 v 1 i As the V chord has five sounds and chord I only three, it has been necessary, in this example, to double two notes. We may also, and this is more convenient, divide up the great chord into o three chords of three tones each; the great chord V now becomes the father or great fundamental of three smaller chords based, respectively, on the 5th, yth, and 2d degrees of the scale, which give them their names, and which are figured with Roman nu- merals, as follows: 7 , II i \>\J (^ m ! J ^ _ -I . C\' & **S V VII II 8 A NEW SYSTEM OF HARMONY Each of these chords, like the great fundamental chord from which they come, has a natural tendency to the tonic chord or chord I; and this is easily explained, as each chord (the V, the VII and the II) has two or three degrees with an individual tendency in conformity with the established law of lesser effort. So the following connections are very good: /r ",. i 53 sa ii (o> _ M 1 J i 1 J^ -1 U J ^ ^ : ^ Jl / _ Bm m i i i i F 1 1 fc ./r r m 1 > II V I, V I vii i VH i, vn L n i, ii i ii i \f I call the first two chords of my system (the I and the V) natural because in them we find all the degrees of the scale, and one or the other may harmonize each and every degree in the scale itself or that may be in any diatonic melody. The chords V, VII and II are also natural, because they are e found, as we have seen, in the great natural V chord, and com- bine between themselves easily, preferably in a contrary direc- tion to that in which they are found; they were derived in this order: V, VII, II, and are interconnected in the reverse order: II-VII-V, or II-V, or VII-V. This is the regular and logical progression of these chords. 11 PROGRESSION OF NATURAL TRIADS Regular progression of natural triads (fh i * f- g* h* * M s r=g H s$ PI* E3 12 i* r E H j r- r n vii v f i n v r t" I VII V I 9* ~-. f-m F 1 1 II It is also possible, though irregular, to combine them in the same order that we found them, giving them a sensation of going away from the tonal centre: V-VII-II, or V-II, or VII-II. 12 Irregular progression of natural triads . a . b . i , yr j | tf 5 E 1 1 irrv p sn ^ r II A r v v ii n r r ' I V II 1 I t-^ * ^ It m 1 __ r r 2_ f The tonic chord (I) can progress freely into any other chord, as it has not any degree with a tendency; so the following con- nections are very good: I-V, I- VII, I-II. 13 I to natural chords V-VII-II /L 1 (?K - J saz z i 8 _ J i r V r VII i n c~\- ft i ) j c S 4 t=E 1 With these four natural triads (I, V, VII and II) we have enough elements to harmonize any melody, and there are nu- merous instances in which the great masters used them exclu- sively. From Bach to Bellini you will be surprised to find them IO A NEW SYSTEM OF HARAfONY harmonizing beautiful melodies; also see the first part of "The Wedding Chorus" from Wagner's Lohengrin, and almost any melody of Bellini, the world-famous master of melody. CHORD OF THE II Let us now consider the third chord of my system, that is, the o ninth-chord on the superlonic or second degree, figured II and com- posed of degrees 2, 4, 6, i, 3. 14 I o II This is a mixed chord, as it has three degrees (2, 4, 6) from the o natural dominant chord V, and two degrees (i, 3) from the tonic chord I. Its law of movement is duplex, for it may go o naturally towards the chord V as well as towards the tonic chord I, because it has notes in common with them both: 15 16 V Dividing up the chord of the ninth on the second degree (II) (2, 4, 6, i, 3) into three triads, we get 2-4-6 4-6-1 6-1-3 (ID TV VI 17 Mixed triads r & it ~/4v ' -f-\- ^ 1 H 1C) g ' ~ &^ H c/ ^ e II W IV VI PROGRESSION OF MIXED CHORDS II One of these chords the II we have already had; but we now get two new chords the IV and VI that are based on the fourth and sixth degrees respectively. These two chords (IV and VI), like the great chord from which they come, are mixed chords; the one on the fourth 9 degree (IV) has two degrees (4 and 6) from the natural chord V, arui one degree (the I) Ijrom the natural chord I. The chord IV, or subdominant chord, as it is generally called, is considered in text-books as a principal chord in Harmony; but it would seem preferable to consider it a mixed chord. The chord VI is also a mixed chord, as it has degree 6 from the 9 natural dominant chord V and degrees i and 3 from the natural tonic chord I. The law of movement of these two mixed chords (IV and VI) is duplex; they may pass easily to the derivatives of the V: 18 Mixed IV in regular recessive progression a , i , , I b i -/k f r~ -J J f B *- - -J ^ -*&? *- ~? r 5 r ' r* ~1 -* r 1 J r r w n, r f r i r n n a iv n tf I i I J vn a i i r i 1 r vn V J J 1 1 /L i m f i j fPK f I J 5 S II IV V V x 19 Mixed chord VI in regular recessive progression * I I J- I J b I J I I* \*\A m\\\ if -iff if i ^^ vi n a n x n vi vn yn a vu z vi v or directly to chord I: 12 A NEW SYSTEM OF HARMONY 20 21 Mixed IV foil, by nat. I : Reg. progression Mixed VI foil, by nat. I : Reg. prog. . 4 J i ! -J- I r The mixed chords IV and VI may, very well, follow the chord I (that is, I-IV and I- VI), not only because they have degrees in common with that chord, but also because the tonic chord can go to any other chord, as it has not any degree with a tendency. 22 Nat. I with mixed IV. Reg. 23 Nat. I with mixed VI. Reg. IV IV, IV r i. r ii Lastly come the connections of the mixed chords IV and VI preceded by natural triads. These connections, though irregular, are possible, and give the sensation of going away from the tonal centre: 24 Irregular . J. j 25 . . progression .... of J J J.. J J J . . . . natural . ~j{~ 9 1_ M~ i 2 j * * M ct) 1 t P 1 '-H-f ( F- p \ U J 1 1 V IV 26 chords 1 p iVj iv a vn iv, 26 bis 1 1 P l_l T IV a IV J 1 J ? 1 . J V : J 1 ~^f ! - m . II _L 1 * nma i ^n. , -X"**. ! j 112 f* I-S i - |(j) -m -1 9 _^ ^_ H-l *-M g i i * i r"T f r ' r IV IV V VI VI NINTH-CHORD OF THE SUPERDOMINANT VII m f - r VI VI f VI VI The mixed chords IV and VI may be interconnected in any order, as their fundamentals are separated by an interval of a third and give the impression of being a single chord of four tones: IV- VI is good, but VI-IV is better and more used for its regular recessive progression: 27 Reg. progression of mixed chords I _J I J- 1? 28 Irreg. progression of mixed chords CHORD OF THE VI, ALSO CALLED NINTH-CHORD OF THE SUPERDOMINANT 29 _ I w e VI This is the fourth chord of my system. It has two degrees o (the 6 and 7) from the natural dominant chord V, and three degrees (1,3 and 5) from the natural tonic chord I. This, then, is a mixed chord, and being a mixed chord, its law of movement e is duplex; it can go equally well either to V or to I: 30 31 J J J -1 9 9 VI V 9 VI i A NEW SYSTEM OF HARMONY Dividing up the chord VI (6, i, 3, 5, 7) into three triads we have: 6-1-3 1-3-5 3-5-7 (VI) (I) (HI) 32 Mixed chord III (t)=t o VI III Here are two chords that we have already had (VI and I), and a new triad, the III. This triad III has one degree the 7 B from the natural V, and two degrees the i and 3 from the natural chord I. Thus it is a mixed chord, like the great 9 chord VI from which it conies, and its law of movement is duplex; o it can pass easily to the derivatives of the chord V (that is, III-II, III-VII, III-V): 33 Mixed III with nat. 1 1- VI I- V and I : Reg. prog. tarn 34 i 35 J ti^l*)M ' /T ' - r m vn or directly to I (III-I) : in v m iid * I in i FULL FOUR-TONE CHORDS, OR SEVENTH-CHORDS 15 The connections of the mixed chord III with the other mixed chords VI and IV, in regular regressive order, are also good and much recommended in the usual text-books: 37 38 Mixed III with mixed VI : Reg. progr. Mixed III with mixed IV : Reg. progr. ^m a T-T-T f III VI VI In In fact, these last two connections are the only ones recom- mended by some writers, but the great composers also employ triad III with the connections given in Examples 33, 34, 35 and 36. This is quite logical, as triad III is a mixed one, and has 9 notes in common with the natural chords I and V. Hence, the relation of triad III to both chords, as well as to their deriva- tives, is evident. There is, therefore, no reason to limit the connections of this triad with IV and VI, as is done in most text-books on Harmony. The mixed triad III may follow, in irregular order, every natural three-tone chord, and also every other mixed chord: 39 Mixed III preceded by nat. triads. 40 Mixed III preceded "by other mixed triads. yr i m 1 m m i m 1 II * m f\\ 1 r - P * 1 f 9 II \JJ a ' -" 1 '"^ 1 II i II I V V 11 ] 1 . I ^ n i V r-\ II 1 m II Iz T. r t * f ^r i 9 FULL FOUR-TONE CHORDS, OR SEVENTH-CHORDS The full four-tone chords, or "chords of the seventh," as they are called, are also found in the four great chords of my system, as may be seen here: 16 A NEW SYSTEM OF HARMONY 41 Chords of the seventh (four-tone chords) derived from the four fundamental chords n Natural chords 11 Mixed chords 1 ! i i -- J t v Iff J fl 1 /5> tit /T _ & I 1 |(TV K> & I * 1 /5 i II \,J & E i 9 I _/' 9 m & '0 POO IV II VI ^^,I 7 7 V V r f~^\ ^-1 1 i g -33 JJ z or directly to I: 53 4 r r^rn This IV may, very well, be followed, in regular regressive order, by the other mixed chord II: 54 reg. /K % -r. rh= A ^T~T 'f f- 7 7 iv n P H 2^-F- H -^ or preceded by it in irregular progression: SEVENTH-CHORD ON THE SIXTH DEGREE 21 55 irreg 55 bis SCHUMANN: Romanza Ich grolle nicht," meas. 7 You will notice that these two chords constitute the great 8 fundamental chord II from which they are derived. SEVENTH-CHORD ON THE SIXTH DEGREE, FIGURED VI Like the great fundamental chord VI from which it is derived, 7 the chord VI is a mixed one, because it has degree 6 from the 9 natural dominant ninth-chord V, and degrees i, 3 and 5 from the natural tonic chord I. Its law of movement is therefore dual or 9 77 duplex; it may go either to the derivatives of V (that is, V or VII) : 56 Mixed VI 3C * - ET |(TV ^' ^ safe 2 ^*^ ~**m J C VI 7 7 V VI i 7 VII pv- * 1 1 T. I 1 or directly to I: 57 reg. 22 A NEW SYSTEM OF HARMONY In regular regressive order to the tonal centre the chord VI, which we are now considering, passes very easily through the e 77 mixed chords that come from II (that is, IV and II) : 58 59 reg. I t/ - .-. II j j 1 J , j/T" I fl J J ^ II n ^ ^ | f J xQ}^ =-^*-: 1 i* a ^ BE 2 ii ; t * 1 l-^f 1 1 ' C i j 77 777 VI IV VI(IV)II ^"^ vi(iv)n- -*- 1 l i v vu n m i 1 1 1 1 1 1T~i 1 1 1 *-J 4 1 1 # (a) I-I. No progression; seventh goes up a second. 7 (b) I-V. Regular progression; seventh keeps in the same part. (c) I- VII. Regular progression; seventh keeps in the same part. 7 (d) I-II. Regular progression; seventh goes down a second. CONNECTED WITH MIXED TRIADS 85 foil, by mixed triads a b c IV i U J H VI i-J. in i (a) I-IV. Regular progression; seventh goes down a second. 7 (b) I-VI. Regular progression; seventh goes up a second. 7 (c) I-III. Irregular progression; seventh goes down a third. PROGRESSIONS OF THE MIXED CHORD III 33 MIXED CHORD III CONNECTED WITH NATURAL TRIADS 86 Mixed III foil, by natural triads a b c d EH 1 01 I 1 5 -IS *ll ^K ' p to | II 33 ' ' C * ^P 1 VII P II cv \ 1 1 1 1 1 I II j' P \i P f H 2? # r J (a) III-I. Regular progression; seventh goes up a second. 7 (6) III-V. Regular progression; seventh keeps in the same part but vanishes as a dissonance. 7 (c) III-VIL Regular progression; seventh changes part and vanishes as a dissonance. 7 (d) III-II. Regular progression; seventh keeps in the same part. CONNECTED WITH MIXED TRIADS 87 foil, by mixed triads a b c L, , / | , M F ^^f -F- f IV VI III S H^_ I (a) III-IV. Regular progression; seventh goes down a second. 7 (6) III-VI. Regular progression; seventh goes down a second. 7 (c) Ill-Ill. No progression; seventh goes up a second. 34 A NEW SYSTEM OF HARMONY TRIADS FOLLOWED BY SEVENTH-CHORDS We have seen seventh-chords connected with triads. We are now going to see triads connected with chords of the seventh. Besides the laws of movement that we are familiar with, we must keep in mind another important condition. The practice of the great masters was, from the beginning, to prepare the dissonance in the chords of the seventh, that is, to make the same sound appear as a consonance in the preceding chord. Mon- teverde, a great Italian composer (1567-1643), was the first to let the seventh enter free, that is, not prepared, in the dominant 7 seventh-chord (V), and from that time this usage has been respected; nevertheless, all the remaining seventh-chords were kept under the primitive rule and had to prepare the seventh. 7 7 In my system, the chords V and VII, being natural chords, may have the seventh free; but the remaining four- tone mixed 77777 chords II, IV, VI, I, III, must enter with the seventh prepared. A modern practice is to consider as sufficient preparation coming down a degree when both chords have the same fundamental, as you will see in the examples below. All these precautions are to be strictly observed in vocal part-music, but in instrumental or free style music, modern composers take many liberties in the handling of the seventh- chords. The attentive reading of works by good masters, and a musically educated ear, are a sure guide to the young composer. THE NATURAL CHORD V May follow any natural or mixed triad; e.g. : 88 Nat. V nat. triads TRIADS FOLLOIVED BY SEVENTH-CHORDS 35 (a) I-V. Seventh free. (b) V-V. Seventh free. 7 (c) VII-V. Seventh prepared. 7 (d) II-V. Seventh of the second chord heard in another part of the first chord. 89 mixed triads . Vl J_ 6 w IV VI III (a) IV-V. (6) VI-V. Seventh prepared. Seventh free. (c) III-V. Seventh free. i NATURAL CHORD VII May follow any triad. 90 Nat. VII natural triads a \ \ b c d n n ' ' ' 1 y 1! 1 IA 1 1 /L _i * II fm * J Q \^V m < 1 | 4 p> i| | f ' V VI * ^ * i n 1 1* 1 i in 1 . K 1 * J (a) I-VII. Seventh free. (b) V-VII. Seventh free. (c) VII-VII. Seventh free. 7 (d) II-VII. Seventh prepared. A NEW SYSTEM OF HARMONY 91 mixed a triads b e \j <* ">- | III S( r m , fn\ f * 1 if ^K f ' f n Er r - - IV VI -J- J * J -?- in i r"V A r I M * * 1 r II (a) IV-VII. Seventh prepared. 7 (b) VI-VII. Seventh prepared. (c) III-VII. Seventh free. MIXED CHORD II Cannot follow V, VII, or III because the seventh cannot be prepared. 92 Mixed II natural triads a ^_ ^ 1 * * 1 * * 1 p \% -f -^ 'y^ VII \ ii f r~v- 1 m 1 *-J. r m m ^S r . *.. r 40 A NEW SYSTEM OF HARMONY (a) I-III. Bad. (b) V-III. Good. (c) VII-III. Good. (d) II-III. Good. 101 a b ! | / 1 1 "1'--^ H / 1 3' M c\ 1 1 l ll V ) 1 1 ii IV ty VI & I II C\* | | T* I 1 P ^^^^ ^ 1 1 (a) TV-Ill. Bad. (b) VL-lll. Bad. 7 (c) Ill-Ill. Seventh prepared by a second down; permitted, because both chords have the same fundamental. MINOR SCALE AND MINOR KEYS The laws that have been established for major keys are appli- cable in every case to the minor keys. CHROMATICS Chromatic alterations to single degrees of the scale produce the following results: (i) When applied to a tranquil scale-degree (i, 2, or 5), chro- matic alteration gives it a tendency to go in the same direction that the alteration points; that is, if the alteration is a sharp (or a natural, in the flat keys), the tendency imparted is to continue upward: ALTERED OR CHROMATIC CHORDS 102 T When the alteration is aflat (or a natural, in the sharp keys), it gives tranquil degrees a tendency to go down: 103 3 I (2) In case the chromatic alteration is applied to an active scale-degree (7, 4, 5, or 2), it will intensify the tendency of the said degree if it is in the same direction as the tendency: 104 pN^d=fl -*=-#* Or it will change the said tendency when the alteration is in a contrary direction. 105 4 ALTERED OR CHROMATIC CHORDS All that has been said here of chromatic alterations, when applied melodically to single notes, is also good when we come to altered chords. The natural chord I, that has no particular tendency, acquires one when it becomes an altered chord: 106 107 108 ii i i r e I i Ij 7 VII 42 A NEW SYSTEM OF HARMONY 7 7 The natural chords V, VII, II, V and VII, which have a ten- dency to proceed to the natural tonic chord I, intensify this tendency when they become altered chords: 109 I 110 111 112 / "fe ^ It* ffi F II ir F H 9 a9 2 II \ m ~~? ~^ H ft l_lZjK V [ js a Je a fa r r M _ i* 11^ ! 1 1 ^ Ill i* M r _i ii 1 * I m III III II ' M V I IIj VII 3 I II H! I 113 114 115 1 1 J J J 7 7 v v 3 yl 7. J II m ru II 1 1 In? ^ & H-? VZ H f fc H InzS -&* f H-jr f H i p s r i r r LJ J 5 J- r r I I^-V 1 B. H VBl p ^ ' 1( y 77 7 7 v a v 3 i v vn i vn a The chromatic alterations employed in the mixed chords IV, 7 7 II and IV make them lose the faculty that they had, at the o choice of the composer, to go to the derivatives of the V, and give them a decided tendency to the tonic chord I: 116 117 118 J> d . 3 ii 3 fe= 3 i J^J -j-n |p ' v * * H . II 'i T r r ba a a - b a $ bf * 5 ft 1 ^-f-H e t i^ ^ H P 1 H ' ' 1 H 5 IV IV Ij IV JIV! I 1 7 i! I a 119 MODULA TION 120 121 43 I ir I 9 A J I I 7 7 II II I On the contrary, the chromatic alterations in the mixed 7 chords VI, VI and I, make them lose the ability to go to the tonic chord, and give them a decided tendency to the derivatives of the dominant ninth-chord: 122 123 124 125 t bi I 77 VI V 777 I }VI a V a V MODULATION In musical Harmony, modulation means a change of key or tonality; by extension, the change of mode is also considered as a modulation. Therefore, we may say that MODULATION is a change of key, or of mode, or of key and mode at the same time. The change of key brings a change in the function of the tones (or notes) in the scale and, therefore, a change in the function of chords, as a natural Ionic chord may become a natural domi- nant, or a mixed chord, and so forth. The principle that rules modulation is very simple and may be stated thus: A key may be abandoned at ANY CHORD (natural, mixed or altered), entering the new key through ANY CHORD (nat- 44 A NEW SYSTEM OF HARMONY ural, mixed or altered). The last chord of the old key escapes, of course, the laws previously established; but the first chord of the new key is governed by the said laws, and must obey them. The author believes that the place to treat thoroughly of modulation is in a method of Harmony based on his system; nevertheless, it may not be out of place here to give a sample of the almost unlimited resources that the principle just stated about modulation puts in the hands of the composer. There are more than two thousand ways of leaving a key. It is not im- possible that some of the extravagances of the ultra-modern composers in striving after novelty is due, in good part, to the many restrictions of the accepted books on Harmony. Here follow, as a sample, forty-nine different ways of effecting a modulation from C major to G major, employing only chords of three tones. If we choose to use four-tone chords (chords of the seventh), we shall have another forty-nine different ways of effecting the same modulation. There will be some fifteen or twenty more new ways if we employ altered chords! What a wealth of resources for a single modulation like this! Leaving the Key of C major at I and entering G major, suc- cessively, through I, V, VII, II, W, VI, III. 1 234 J*M *FF 3P^ r T r mRF^a 1 VII n VI in MODULATION 45 Leaving the Key of C major at V and entering G major, successively, through I, V, VII, II, IV, VI, III. i *p V G I V G V 10 11 1 1 r ^L i i J &- ^ yX "* ~*/5 4 ' % 1 ~^~ 1?T\ A ^ n ~ f \ \>L/ II ^ \\ 1 1T __ p r~ -f ^^ ^"T 1 _j^ 1 ^ H i 1 - r ' ~? H 3 1 1 ! i II V GVII V Gil 12 V GIV 13 tfo ^ " , T~sr= iS> -*tir 3 VvJ f A p . p u t^-r r -r -- T?- i "i i r f i i! i ft- 1 Oil ! M i u ^J- * i HE _ p ^ E3 H V G VI 14 r V GUI 4 6 A NEW SYSTEAf OF HARMONY Leaving the Key of C major at VII and entering G major, successively, through I, V, VII, II, IV, VI, III. 15 16 i II - p i r f * - T ^P C VII G I c VUG v 17 18 *= T=3E i - p r P ' I I I 1K C VII G VII c vn GH 19 20 . A i ! ^ ol | | -# 9 1 -J i T? || J I ^T^ ~~ - K jg II * - -0 m. " t ' A j r i i 1 r r ^ i T a* T- J f m *-. . 4 c VTIG iv C VTIGVI 21 XL a __* 2 ft\ 3 ^^ H 3 H TO - Bi ftr J r T -P- "T" 1" c\- i r J S ii as I ' r II c vn G m MODULATION 47 Leaving the Key of C major at II and entering the Key of G major through I, V, VII, II, IV, VI, III. 22 23 xL I t J- f i il * : -* H BEE2 - -^ *-d -* ^E r - J tiS -f H j J- J r ' I "! i r -- P 1 "T" . * r c\. z H fl <. j 1 F f* 1 ! J ., _. C II G I C II G V 24 25 XL * C & \\ 2 g II ft> m * f i M i* r 1 II II J | i 1 a* \>zm P * 11 m tt /9 II T' i <^ II -i fl Z * II i II 2( r~9 a \ \ i- ! 1 ' 2 !7 | J j J t- tff t r 3tZ BSE -j ^~ i=t irH 1 t ut I* f Saz r fl r J 1 ^1 -j : f r 1 ' i 1 1 i i_ i aj * t f J ~~r1"h~ -f i* ^ ~H H z 1 9 c xJ C II G IV C II GVI 28 X i II fits 1 ig f? SB >l H d i "1 J r i 1 1 i ~\ M* Z. 1 ] II GUI 4 8 A NEW SYSTEM OF HARMONY Leaving the Key of C at IV and entering the Key of G through I, V, VII, II, IV, VI, III. 29 30 1 II; C IV G I C IV GV 31 32 i* 5c 1 C IV GVII C IV Gil 33 34 1 *t C IV GIV C IV G VI 35 fo p j - -i-^- ^= gz=| i I '> *\ p\* i -* \ P *7 , 1 1 T i Ck* 1 f 3 II y. I f ' 2: < m * II c in GUI The composer has the same liberty in the so-called "extra- neous modulations." Let us take, as an example, a modulation a minor second upward; some books teach one way only of effect- ing this modulation, namely, "to leave the old key at the tonic chord (I) and to enter the new key through its dominant seventh- 7 chord (V)." Here follow thirty-five different ways of effecting MODULATION 51 the said modulation, leaving the old key at the tonic chord. Imagine how many more ways there are if we apply the principle of "leaving the key at any chord!" THIRTY-FIVE MODULATIONS FROM C MAJOR TO Db MAJOR (that is, a minor second upward), starting with the tonic triad 123 4 VII, II J_ J , J_fe*: I jJfc*: ^J I 16 A NEW SYSTEM OF HARMONY 17 18 ff&- ^ rff^rh^B 19 20 btW 21 jj tJt^g uii TT iu ^=n"~T~l L'.u! ETt-ti Ib> 1 1 . a |bw n f^-gb ^r^^^U-^M LJ?-L ^ + vnij 22 23 24 i ivb 25 26 27 !.bJ J b< I, W -I h ;ftri ^ "!KZ ' V ^~- f iT r^T -M> ^J-JJ^-H^W-L 1 Hi? ivb MODULATION' 53 32 Pf , ^ r ~S g ~H * \S 33 J J tj ^^ jj r P-M- SI :n ^ jtit 7 34 In order to show the rapid progress which is possible when applying my system of Harmony and the laws and principles derived from it, I append a melody (given subject) harmonized in six different ways by a pupil of mine after he had taken thirteen lessons! I must say, to be exact, that this exercise re- quired three or four corrections. 54 A NEW SYSTEM OF HARMONY Given Subject ! s m : V w w m 52 II 1 (.([) ^ ' !, . t 2 m * m M t 1 f p ^ 1 \ r r " * i 1 '-^*li ff/i ' p -f h H \ ~^~^^r^r] * p ~ f " "* D~T H H 1 H \ *T IX ' 1 u 2 . S J \J JPILTT . (V , i X S /* fry n {j { * * 9 ' ^ J- t s 1 r ' f 9 a -* -- U J J * ^^]$r?~[ --P < J r~? * H -S fi * / ' "jf o Tl ix p II 3 G .s 1 1 1 L/ ^*uiT ; B I I J^JL U / * m ! j I?T\ * \ y < * c * f ^5/ VM_y ^ S f 1 1 * - * I s r f r^v Jr C |t IV J * tfy f * m -P I m j i* ft ^ / 1 -j^ 4 1 / .L' Trifr B !| _, II v Ir * J f m & /?r\ ff I. j - m J m 2 a V^L/ ' i P M h J - 1 I J ' t? r > r R.$Jrrr - =PEZ =P= j i H ^ / \ ' h ^ ^ -z? H G. S. 1 5 \ \ --I -i hn -jJ^typT-j j EE -0 - J H _j 4- "s^ H (Cn ' f i ^ f * * 4 ^ 9 ^ H ii U -f r r X r P r r r -<9- ' J rxiS-jI^- rj-#j*ff/>. ^ f - J G. S. CONCLUSION 55 m This concludes the exposition of my system. I call it a new one because I do not know of any author who has explained the whole system of harmony based on these four fundamental chords. It is not a mere trifle, or an object of mere curiosity, for the laws that rule melody as well as chords have been deduced by a rigorously scientific method, as you have seen. Further- more, these rules are very few, eminently practical, and easy of application. I have read many times, and I was inclined to believe so my- self, that the true method of musical composition ought to be deduced from the practice of the great masters. I confess here that after much thinking on the subject there came to my mind, as a revelation, the group of four fundamental chords that make up my system; the laws that I have explained here are the result of long study and a strict application of scientific prin- ciples. Having discovered the laws, the next step was to see if the great composers had observed them in their handling of musical material; and I was soon convinced that they had, guided surely by the fine sense and marvelous intuition peculiar to great artists. I could quote innumerable examples that prove what I have said here, but the proper place for these will be in a Method of musical composition still to be written, based on this new classification of chords. 56 A NEW SYSTEM OF HARMONY In handling the musical chords under the laws stated here, you are conscious of what you are doing; this (if I may speak from my own experience) is not the case when you are studying the ordinary text-books on the subject. For many years I have devoted myself to the study of Pedagogy, trying assiduously to apply its principles in all branches of music-teaching. Viewing my system* from the pedagogical standpoint, a new path is in sight, which reveals the most im- portant facts for writing a true pedagogical method of compo- sition a method in which melody, harmony and counterpoint will go simultaneously hand in hand, as the real friends that they are, and not disconnected one from the other as it has been the custom to present them heretofore. I hope that the foregoing exposition will be considered by the musical world with the attention that I think it deserves; and I shall be glad to read and take account of all the criticisms that my fellow musicians may have to make about this important subject. EDUARDO GARIEL Tacubaya, D. F., suburb of the City of Mexico October, 1915 UNIVERSITY OF CALIFORNIA LIBRARY Los Angeles - This book is DUE on the last ., STACK OCT 5 RECEIVED JUL28 1987 STACK ANNEX UC SOUTHERN REGIONAL LIBRARY FACILITY A 000146218 3 SOUTHERN BFr UNIVERSITY' OF CALIFORNIA LIBRARY, ANGELES, CALIF. U ary