Ramsay
But let us proceed with our development, for we need another fifth, a lower one, a subdominant for our minor scale. Well, let us divide A5 by 3 and we have D1 2/3, the root of the lowest fifth; and if we divide A5 by 5 we have for our middle to this fifth F1, and this is F just as we find it at the major start, and identical in quantity in both major and minor. But let us examine the D1 2/3. It is not easy to compare D1 2/3 with D27 of the major; let us bring it up a few octaves by multiplying by 2. This will not alter its quantity, but simply give us the same quantity in a higher octave, in which we may more easily compare it with the major D1 2/3 multiplied by 2 is 3 1/3; multiplied again by 2 is 6 2/3; once more by 2 it is 13 1/3; and once more by 2 it is 26 2/3. Now we can compare it with D27 of the major, and we find this strange fact, that it is a little lower than the major D. The two D's are at the center of the dual system, but the center of the system is neither in the one D nor in the other, but as an invisible point between them, like the center of gravity in a double star; for the minor D is pushed a little below the center, and the major D is pushed a little above the center of the two modes of the system. [Scientific Basis and Build of Music, page 32]
of the major being upward, and the genesis of the minor being downward. The ascending genesis, beginning with the root of the subdominant major F, produces in the ascent a scale of notes at varying distances, and of increasing levities; the middle note, D27, being carried a little above the center of the system. The descending genesis, beginning with the top of the dominant minor B, produces in the descent a scale of notes with identical variety of distances, but with increasing gravities; the middle note, D26 2/3, being pressed a little below the center of the system, thus giving rise to these two D's - one whose genetic number is 27, the major D, and one whose genetic number is 27 2/3, the minor D - the duality of D is thus residing in itself.1 [Scientific Basis and Build of Music, page 43]
Although the system is composed of only three ratios, which in themselves moreover, are of a very fixed character, yet mobility and variety are chief features among the notes of the system. Great changes are effected by small means. By lowering the second of the major D one comma, the ratio of 80:81, [Scientific Basis and Build of Music, page 61]
Fig. 1. - This figure shows the major and minor measured in commas and placed directly as they stand related, major and relative minor, the minor being set a minor third lower than the major. The interval between C and E in the minor is an 8-and-9-comma interval; between C and E in the major it is a 9-and-8-comma one. This difference arises from the minor D being a comma lower than the major D. In all the other intervals minor and major are the same. [Scientific Basis and Build of Music, page 120]
See Also
major
Ramsay - The Two D's - The Rah and the Ray
Scale
Interval