Ramsay
Now we come to a remarkable arrangement of Nature. The minor does not grow in the same way out of this third chord's top. Two features come before us: first the minor chord grows out of the major, but it is taken not from the top but from the middle, from a rib out of his side. B, the middle of the major dominant chord; B, the last-born of the major genesis; B is the point of departure in the outgrowth of the minor mode. The feminine is a lateral growth from the masculine. Another feature: it grows downward, like a drooping ash or willow. Its first generated chord is its dominant, and its last is its subdominant. Its middle chord, like the middle one of the major, is its tonic. Still further, it is generated by division, not multiplication; B45 is divided by 3 and by 5 for the root and middle of this highest chord, E and G. E15 is divided by 3 and 5 for the root and middle of the tonic chord, A and C. A5 is divided by 3 and 5 for the root and middle of the lowest chord, D and F. Thus we have the whole generation of the elements of music, six generations of harmony, like the six days of creation. Up to this point the whole process and aspect is inverse; growing from a middle; growing downward; growing by division;- while the major is growing from the top; growing upward; growing by multiplication. But here the inverse aspect ends. The generating primes of the major are 3 and 5; 3 and 5 are also the generating primes of the minor. In this essential phase of their creation their comparison is direct, not inverse. [Scientific Basis and Build of Music, page 67]
"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 -
[Scientific Basis and Build of Music, page 95]
- and it is balanced between the two forces. If the effects of notes or chords depended solely on their ratios, then the effect of the subdominant, tonic, and dominant would have been alike, for these chords have exactly the same ratios. The centrifugal force of the notes of the dominant chord would take if away from the tonic chord; but Nature, in her skill to build and mix, has in the octave scale placed the middle of the dominant B under the root of the tonic C, and the top of the dominant D under the middle of the tonic E; so that these two rising notes are inevitably resolved into the tonic chord. The gravitating tendencies of the notes of the subdominant would take it also away from the tonic; but in the octave scale Nature has placed the middle of the subdominant A above the top of the tonic G, and the root of the subdominant F above the middle of the tonic E; so that these two falling notes also are inevitably resolved into the tonic chord. In this way two notes resolve to the center of the tonic, D upwards and F downwards; one to the top, A to G, and one to the root, B to C. Nature has thus placed the notes which have upward tendencies under the notes having downward tendencies; she has also related them by proximity, the distance from the one to the other being always either a semitone or the small tone of the ratio 9:10. [Scientific Basis and Build of Music, page 95]
dominant; 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 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 was 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; and in the octave scale it has above it the middle and below it the root of the subdominant - the two notes which the greatest amount of specific gravity. The third note of the scale, the middle of the tonic chord, is the center 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 center of the system; the specific gravity of the one above and the specific levity of the one below cause them to move in the direction of the center. [Scientific Basis and Build of Music, page 98]
See Also