Ramsay
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]
among the Greeks on account of having symmetry in itself. The primitive scale was doubtless that which is the model of all major music; and our minor model is its dual, as Ramsay has shown, which in its genesis indicates the duality of all the rest of the notes, although it is not probable that the Greeks saw the musical elements in this light. It is remarkable and significant that in their modes the Greeks did not lift up the scale of Nature into different pitches, preserving its model form as we do in our twelve major scales, but keeping the model form at one pitch they built up their symmetrical tetrachords, allowing the larger and lesser tones of the primitive scale to arrange themselves in every variety of place, as we have shown in the table of tetrachord modes above. Without seeing the genetic origin of music's duality they were led to arrange the modes by symmetry, which is one of the phases of duality. Symmetry is duality in practice. It may not always be apparent how symmetry originates in Nature; but in music, the art of the ear, duality emerges in the genesis of the minor scale; in the true mathematical build of the major on the root of the major subdominant F, and the true relation of the minor to it in the inverse genesis descending from the top of the minor dominant B. [Scientific Basis and Build of Music, page 46]
See Also