# duality of D

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]

It is according to the Law of Duality that the keys on the piano have the same order above and below D, and above and below G# and A♭, which is one note. In these two places the dual notes are given by the same key; but in every other case in which the notes are dual, the order above the one and below the other is the same. The black keys conform to the scale, and the fingering conforms to the black keys. On that account in the major scale with flats, for the right hand the thumb is always on F and C; and as the duals of F and C are B and E in the minor scale with sharps, for the left hand thumb is always on B and E. [Scientific Basis and Build of Music, page 44]

Here, then, we have an order of modes entirely symmetical in pairs placed thus; the only mode that can stand alone being the Dorian, built on D, whose duality has been discovered to reside in itself. All this build of symmetry, which was the watchword of Greek art, as it is also one of the watchwords of Nature, presupposes that the tones of the scale, with lesser and larger intervals lying between them, were resting in their ears exactly as they are in ours,1 and as they are in all humanity, save where it has sunk down into the savage condition, benighted in the evil that is in the world. It is not to be concluded that the Dorian mode is Nature's primitive scale, although it might have a certain pre-eminence [Scientific Basis and Build of Music, page 45]

In going round the circuit of the common chords of the major and its relative minor, and beginning our circuit with the minor, we encounter a triplet,2 differing from all the rest in its constituents, thus -

DF A, AC E; EG B; BDF; F AC; C EG; G BD.

Here we have passed through minor and major from D to D, and seem to have come to the point from which we started; but we know that these two D's are [Scientific Basis and Build of Music, page 53]

By taking four minor thirds upward from G# or downward from A♭, we have the first chromatic chord in its twofold form. Its central note is D, the top of the dominant major, and the root of the subdominant minor, being its own dual, that is to say, its minor birth being dual to its major birth.1 On the keyboard it has the same order of keys above it and below it; this dual D [Scientific Basis and Build of Music, page 56]