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semitonic progression

Some of the elements of the Chromatic System were known 200 years ago. The Diatonic scale, being called the "Natural scale," implied that the chromatic chords were consider to be artificial; but the notes of the chromatic chords, from their PROXIMITY to the notes of the tonic chord, fit to them like hand and glove. Nothing in music is more sweetly natural and pleasingly effective than such resolutions; and hence their extensive use in the hands of the Masters. The chromatic chords have close relations to the whole system of music, making the progressions of its harmonies easy and delectable, and producing effects often enchanting and elevating, as well as often subtle and profound; and while they are ever at hand at the call of the Composer, they are ever in loyal obedience to the laws of their own structure and system. When a diatonic chord precedes another diatonic chord belonging to the same scale, it has one note moving in semitonic progression;1 but when a chromatic chord precedes a diatonic chord, it may have three semitonic progressions.2 The primary chromatic chord resolves into 8 of the 24 diatonic tonic chords, with 3 semitonic progressions. These identical notes of the chromatic chord, with only some changes of names, resolve into another 8 of the 24 tonic chords, with 2 semitonic progressions and one note in common; and when they resolve into the third and last 8 of the 24 tonic chords, they move with one semitonic progression and 2 notes in common. So to the chromatic chord there are no foreign keys.3 And as it is with the first chromatic chord, so with the other two. [Scientific Basis and Build of Music, page 51]

The triplet B, D, F, has been called the imperfect triad, because in it the two diatonic semitones, B-C and E-F, and the two minor thirds which they constitute, come together in this so-called imperfect fifth. But instead of deserving any name indicating imperfection, this most interesting triad is the Diatonic germ of the chromatic chord, and of the chromatic system of chords. Place this triad to precede the tonic chord of the key of C major, and there are two semitonic progressions. Place it to precede the tonic chord of the key of F# major, and there are three semitonic progressions. Again, if we place it to precede the tonic chord of the key of A minor, there are two semitonic progressions; but make it precede the tonic chord of E♭ minor, and there are three semitonic progressions. This shows that the chromatic chord has its germ in, and its outgrowth from the so-called "natural notes," that is notes without flats or sharps, notes with white keys; and that these natural notes furnish, with only the addition of either A♭ from the major scale or G# from the minor, a full chromatic chord for one major and one minor chord, and a secondary chromatic chord for one more in each mode. [Scientific Basis and Build of Music, page 52]

The dominant seventh, G, B, D, F, a 4-note chord,1 only requires that the root G be made sharp, which will make G#-B a minor third agreeably with the structure of the other two intervals, B-D and E-F. The chromatic chord only differs from the dominant seventh in that it is wholly of minor thirds. There are four notes in a chromatic chord, but only three of them move by semitonic progression to a tonic chord. When these three notes thus move to a major chord, one is upward to the root, a second downward to the top, and the third downward also to the middle. The relative minor being a minor third below [Scientific Basis and Build of Music, page 52]

the major, the root of the major chord is the middle of the relative minor, and the middle of the major chord is the top of the relative minor; and as the note which has a semitonic progression downward to the top of the major has a semitonic progression upward to the root of the relative minor, so the same three notes which move in semitonic progression to the top, root, and middle of the major chord, likewise move by the semitonic progression to the root, top, and middle of the relative minor. In both cases the progressions are upward to the roots and downward to the tops; but in the major the movement is downward to the middle, while in the minor it is upward. So each one of these three of the four notes of the chromatic chord has two various movements.1 [Scientific Basis and Build of Music, page 53]

The CHROMATIC SYSTEM of chords is developed from these three primitive chromatic chords, and in the course of its development one or two notes are brought in semitonic progression to the middle, one or two to the root, and one or two to the top of all major and minor tonic chords. Likewise, at one time or another in the course of the system, there is one note in common with the middle, one note in common with the root, and one note in common with the top of all the major and minor tonic chords. [Scientific Basis and Build of Music, page 57]

It is the function of the chromatic chord, in the course of its systematic development, to bring two notes, the one above and the other below, in semitonic progression to each of the three notes of the tonic chord; and likewise, without interfering with the imperial character of the tonic chord, it brings two notes in semitonic progression to each note of the other two chords; so that, although at first the subdominant and dominant chords are only like satellites to the tonic chord, they, with their chromatic chords, are now raised to the dignity of planets as it were, having the chromatic chords as their satellites. [Scientific Basis and Build of Music, page 57]

Moreover, it is only from one to five, that is from C to G in ascending, which is its proper direction in the genesis, that the major in being harmonized does not admit of minor chords, but if we descend this same natural major scale of the fifth from five to one, that is from G to C, the first chord is C E G; the next chord is F A C; if this is succeeded by the minor chord A C E, there are two notes in common and one semitonic progression, as very facile step in harmony; and the following two notes are most naturally harmonized as minor chords. So modulation into the minor, even in this major scale, is very easy in descending, which is the proper direction of the minor genesis.2 In a similar way, it is only from five to one, that is from E to A in descending, which is its proper genetic direction, that the minor in being harmonized does not admit of major chords; but if we ascend this same minor scale of the fifth from one to five, the first chord is A C E, the next is E G B, and if this chord be followed by the major C E G, there are here again two notes in common and one semitonic progression; and the two notes following are then most naturally harmonized as major chords. So modulation into the major, even in this minor scale, is very natural and easy in ascending, which is the proper direction of the major genesis.3 The dominant minor and the tonic major are, like the subdominant major and the tonic minor, very intimately related in having two notes in common and one semitonic progression. [Scientific Basis and Build of Music, page 65]

Chords in a harmony are not at liberty to succeed each other in the way that single notes in a melody may. The notes in a melody may succeed in seconds, or they may succeed in larger intervals, any interval in the octave, even sometimes very effectively there may be a leap or fall of a whole octave. Chords cannot follow each other in this free way; they are under law, and must succeed accordingly. Their law is that they must be linked together either by having something in common in their elements, or have small intervals, semitonic progressions, between them. The former way, by notes in common, is the most usual way in diatonic succession of chords, the latter way, by semitonic progression, is a chief feature and charm in chromatic succession; but both in diatonic and chromatic progression of chords in harmony, notes in common and semitonic progression are usually found together. [Scientific Basis and Build of Music, page 68]

"There are three chromatic chords, and each of these three is related to eight particular tonic chords. When one the these chromatic chords goes to any one of its eight tonic chords, three of its notes move in semitonic progression, and the other note moves by the small tone, the ratio of 9:10. There is exception to this rule, whether the key be major or minor. But when the chromatic chord which should resolve to the tonic of C is followed by the subdominant, or the tonic of F (the example in Mr. Green's book), only two of its notes move in semitonic progress. Your friend describes the chord as if it had gone to the tonic of B; and what he said about it, and about D going to C, is what is supposed to be [Scientific Basis and Build of Music, page 94]

DIATONIC RESOLUTIONS, SIMPLE AND COMPOUND.


In the major system, when the tonic chord follows the subdominant one, there is one semitonic progression to the middle of the tonic, and one note in common with the root, so these two chords are linked together in different ways. When the tonic chord follows the dominant one, there is one semitonic progression to the root of the tonic, and one note in common with its top, so these two chords also are linked together in two different ways. When the tonic chord follows the compound dominant, i.e., the dominant seventh, there are two semitonic progressions, one to the middle and one to the root, and one note in common with its top, so these two are linked together in the same two ways; but the semitonic progression being double gives this resolution great urgency. And now we come to the two chords, the subdominant and dominant, which have no note in common, and must, when they succeed each other, be helped to come together. Nature teaches us how this is to be done by a process of borrowing and lending which will establish between them a similar relationship to that which keeps the continuity of the other chords in succession. We have seen that the top of the subdominant and the root of the tonic are a note in common to these chords, and so the top of the tonic and the root of the dominant also are a note possessed in common by these two chords. In like manner in this disjunct part, when the dominant follows the subdominant, the root of the subdominant is lent to the top of the dominant, and thus they come to have a note in common. The top of the [Scientific Basis and Build of Music, page 111]

subdominant also moves by semitonic progression to the middle of the dominant, and so, like the simple chords, they are brought into continuity. When the subdominant follows the dominant, the top of the dominant is lent to the root of the subdominant, and they come to have also a note in common; and the middle of the dominant moves by semitonic progression to the top of the subdominant; and thus resolving continuity is established between them. [Scientific Basis and Build of Music, page 112]

With perfect duality of response does resolution of chords go on in the minors. When the tonic chord follows the subdominant one, they have for their note in common A, i.e., in the key of A; and the middle of the subdominant moves by semitonic progression to the top of the tonic. When the tonic chord follows the dominant one, the top of the tonic and the root of dominant E is a note in common, and the top of the dominant goes by semitonic progression to the middle of the tonic. These simple chords are thus linked together exactly with the same degree of continuity as the simple chords of the major. When the tonic chord follows the compound subdominant, this compound chord, like the compound dominant in the major, has two semitonic progressions - one to the top and one to the middle of the tonic - and they have one note in common. When the compound dominant follows the subdominant, the root of the subdominant is lent to the top of the dominant, and thus a note in common is created, and the middle of the subdominant moves by semitonic progression to the root of the dominant. When the compound subdominant follows the dominant, the top is lent to the root of the subdominant, creating a note in common between them, and the root of the dominant goes to the middle of the subdominant in semitonic progression. This is the way of Nature. The unbroken continuity of her ways is perfectly illustrated in the linked sweetness and kinship of chords in a key; or when one key passes by modulation to another key; and that through all the chords and all the keys. We shall see wondrously more of this when we come to the study and contemplation of the Chromatic System of Chords. [Scientific Basis and Build of Music, page 112]

THE CHROMATIC CHORD IN TWO-SEMITONIC PROGRESSION.


This is an illustration of the chromatic chord resolving by two semitonic progressions and one note in common into four key-notes, which are shown in different positions and inversions; for example F A C F, A C F A, C F A C. Like a universal joint, the chromatic chord turns to each in a suitable form for resolution. [Scientific Basis and Build of Music, page 116]


This plate illustrates how the chromatic chord resolves into four key-notes, in different positions, by one semitonic progression and two notes in common; for example, G B D G, B D G B, D G B D. In a pianissimo and slow passage this resolution has a subtle, soft effect; like a snake in the grass. [Scientific Basis and Build of Music, page 116]

Fig. 4 is a setting of the minor and the major chord-scales, showing how they stand linked by notes in common in their direct sequence from dominant minor to dominant major. To each of the six chords is placed the first chromatic chord, showing how it resolves in its three-fold manner by 1, 2, and 3 semitonic progressions in each mode, and by 1 and 2 notes in common variously in each mode; and here again the law of duality is seen in its always symmetrical adjustments. Duality, when once clearly and familiarly come into possession of musicians, will be sure to become an operative rule and test-agent in composition. [Scientific Basis and Build of Music, page 121]

See Also


Delta
evolution
progression
semitone
semitonic
step

Created by Dale Pond. Last Modification: Thursday January 7, 2021 03:18:49 MST by Dale Pond.