Ramsay - Symmetry an Expression of Duality



The Greeks most probably constructed their musical tetrachords in a symmetrical order in analogy with their sculpture, and showed the ear identical with the eye in its love of symmetry. With them, therefore, the Dorian mode would have a certain pre-eminence. Beginning this mode on D, without knowing the musical mystery that resides in D, they had two tetrachords with the semitones symmetrically in the middle in one mode; it was next possible for them to arrange in pairs, symmetrically, the other tetrachords.

D8 E5 F9 G8 A9 B5 C9 D
E5 F9 G8 A9 B5 C9 D8 E — C9 D8 E5 F9 G8 A9 B5 C
F9 G8 A9 B5 C9 D8 F5 F — B5 C9 D8 E5 F9 G8 A9 B
C9 D8 E5 F9 G8 A9 B5 C — E5 F9 G8 A9 B5 C9 D8 E
B5 C9 D8 E5 F9 G8 A9 B — F9 G8 A9 B5 C9 D8 E5 F
A9 B5 C9 D8 E5 F9 G8 A — G8 A9 B5 C9 D8 E5 F9 G
G8 A9 B5 C9 D8 E5 F9 G — A9 B5 C8 D9 E5 F9 G8 A

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

1 Pole's researches led him to conclude that the Diatonic Scale has remained essentially unchanged; as the series of notes was when Euclid described it, so it is now; and as it formed the basis of the melodies of the Greeks 2,000 years ago, so it forms the basis of the tunes of the present day." - Philosophy of Music. [Scientific Basis and Build of Music, page 45]

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Created by Dale Pond. Last Modification: Sunday October 18, 2020 04:08:20 MDT by Dale Pond.