Sympathetic Vibratory Physics

Ramsay
true. Music is a network of orders, but three notes going to the root of the tonic does not happen to belong to any of them. [Scientific Basis and Build of Music, page 95]

"The notes as they naturally arise from unity have different degrees of development, and according to the degree of development of each note is its specific levity or gravity. The three notes which form the subdominant chord have different degrees of gravity; the three which form the dominant chord have different degrees of levity. The remaining note is the center of the tonic chord -

Tonic

Subdominant - F, A, C E G, B, D - dominant

Center

[Scientific Basis and Build of Music, page 95]

"The three notes of the dominant chord resolve by each note going to the next note upward - G soars to A, B to C, D to E. The three notes of the subdominant resolve by each note going to the next note downward - C sinks to B, A to G, F to E. The two upper notes of the dominant resolve into the tonic chord according to the Laws of Proximity and Specific Levity; and the two lower notes of the subdominant resolve into the tonic chord according to the Laws of Proximity and Specific Gravity. And in this way Nature, in chord-resolution, has two strings to her bow." [Scientific Basis and Build of Music, page 96]

ANOTHER LETTER TO A PUPIL.

The System of Musical Sounds might be sketched as follows:- Three different notes having the simplest relations to each other, when combined, form a chord; and three of these chords, the one built up above the other, form a system. [Scientific Basis and Build of Music, page 96]

Three times three are nine this would give nine notes; but as the top of the first chord serves for the root of the second one, and the top of the second for the root of the third, in this way these three chords of three notes each are formed from seven different notes. [Scientific Basis and Build of Music, page 96]

The middle one of these three chords is called the tonic; the chord above is called the dominant; and the chord below is called the subdominant. The order in which these three chords contribute to form the octave scale is as follows : - The first note of the scale is the root, of the tonic; the second is the top of the dominant; the third is the middle of the tonic; the fourth is the root of the subdominant; the fifth is the top of the tonic; the sixth is the middle of the subdominant; the seventh is the middle of the dominant; and the eighth, like the first, is the root of the tonic.

In the first six chords of the scale the tonic is the first of each two. The tonic chord alternating with the other two produces an order of twos, as - tonic dominant, tonic subdominant, tonic subdominant. The first three notes of the octave scale are derived from the root, the top, and the middle of the tonic dominant and tonic; the second three are derived from the root, top, and middle of the subdominant, tonic, and subdominant. The roots, tops, and middles of the chords occurring as they do produce an order of threes, as - root, top, middle; root, top, middle. The first, third, fifth, and eighth of the scale are from the tonic chord; the second and seventh from the dominant; and the fourth and sixth from the subdominant. In the first two chords of the scale the tonic precedes the dominant; in the second two, the subdominant; and in the third two the tonic again precedes the subdominant; and as the top of the subdominant chord is the root of the tonic, and the top of the tonic the root of the dominant, this links three chords together by their roots and tops. The second chord has the top of the first, the third has the root of the second, the fourth has the root of the third, the fifth has the top of the fourth, and the sixth has the root of the fifth; and in this way these successive chords are woven together. The only place of the octave scale where there are two middles of chords beside each other is at the sixth and seventh. The seventh note of the octave scale is the middle of the dominant, and the sixth is the middle of the subdominant. These two chords, though both united to the tonic, which stands between them, are not united to each other by having a note in common, inasmuch as they stand at the extremities of the system; and since they must be enabled to succeed each other in musical progression, Nature has a beautiful way of giving them a note in common by which to do so - adding the root of the subdominant to the top of the dominant, or the top of the dominant to the root of the subdominant, and this gives natural origin to compound chords. The tonic chord, being the centre one of the three chords, is connected with the other two, and may follow the dominant and subdominant; and either of these chords may also follow the tonic; but when the dominant follows the subdominant, as they have no note in common, the root of the subdominant is added to the dominant chord, and this forms the dominant seventh; and when the subdominant follows the dominant, the top of the dominant is added to the subdominant, and this forms the subdominant sixth. The sixth and seventh of the octave scale is the only place where these two compound chords are positively required; but from their modifying and resolvable character they are very generally used. When the dominant is compounded by having the root of the subdominant, its specific effect is considerably lower; and when the subdominant is compounded by having the top of the dominant, its specific effect is considerably higher. In the octave scale the notes of the subdominant and dominant chords are placed round the notes of the tonic chord in such a way as to give the greatest amount of contrast between their notes and the tonic notes. In the tonic chord the note which has the greatest amount of specific gravity is its root; and in the octave scale it has below it the middle and above it the top of the dominant, the two notes which have the greatest amount of specific levity. Again, in the tonic chord, the top has the greatest amount of specific levity; and in the octave scale it has above it the middle and below it the root of the subdominant - the two notes which have the greatest amount of specific gravity. The third note of the scale, the middle of the tonic chord, is the centre of the system, and is the note which has the least tendency either upwards or downwards, and it has above it the root of the subdominant, the note which has the greatest amount of specific gravity, and it has below it the top of the dominant, the note which has the greatest amount of specific levity. Thus the root of the subdominant is placed above, and the top of the dominant below, the centre of the system; the specific gravity of the one above and in the specific levity of the one below cause them to move in the direction of the centre. [Scientific Basis and Build of Music, pages 96-98]

Hughes
AS an example of the twenty-four, compare A major, developing, in Diagram II., with A minor, Diagram IX., taking the notes in the order which they sound in trinities. The three notes of the primaries sounded by A minor are, first, the same root as the major; the two next are the fourth and seventh higher notes (in the major, the fifth and sixth); the secondaries only vary by the sixth and seventh notes being a tone lower than in their relative major. Observe the order in which the pairs unite; the fourth in depth, sounded seventh, isolated. A and its root do not rise from the chasms. The fundamental key-note C was seen not to be interfered with, neither is the fundamental minor key-note A; G# on the one side, and B? on the other, being the key-notes. The seven of each minor harmony embrace only seventeen tones. C major and A minor are the only two keys which sound the seven white notes of keyed instruments. The minor scale and chords of A are not included in this remark. [Harmonies of Tones and Colours, Diagram IX - The Minor Keynote A and Its Six Notes, page 34a]

Sympathetic Vibratory Physics

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