Overtone scale: Difference between revisions

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===Over-p scales===

[[Zhea Erose]] has considered over-p scales, which she calls ''primodal scales''. To construct a p-primodal scale, we fix a prime ''p'' to be the denominator and take intervals of the form n/p, where n ≥ p. Zhea often takes n ~~to be~~ from a certain "lineal segment" (a segment of the harmonic series spanning an octave) counting from p~~, say~~ p ≤ n ≤ 2p, ~~resulting~~ in 1/1, (p+1)/p, (p+2)/p, ...~~; she then adds~~ a 3/2 to the scale root, which corresponds to adding 3p/p.

[[Zhea Erose]] has considered over-p scales, which she calls ''primodal scales''. To construct a p-primodal scale, we fix a prime ''p'' to be the denominator and take intervals of the form n/p, where n ≥ p. Zhea often takes n from a certain "lineal segment" (a segment of the harmonic series spanning an octave counting from p) or a subset thereof. If we use p ≤ n ≤ 2p, this would result in a scale 1/1, (p+1)/p, (p+2)/p, .... Zhea may add a 3/2 to the scale root, which corresponds to adding 3p/p.

Primodality seems designed to emphasize the identity of the "tonic" as the ''p''th harmonic; this may help in hearing higher primes such as 17, 19, and 23 which may be difficult to hear otherwise as the overtone of some fundamental.

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 ===Over-p scales===
-[[Zhea Erose]] has considered over-p scales, which she calls ''primodal scales''. To construct a p-primodal scale, we fix a prime ''p'' to be the denominator and take intervals of the form n/p, where n ≥ p. Zhea often takes n to be from a certain "lineal segment" (a segment of the harmonic series spanning an octave) counting from p, say p ≤ n ≤ 2p, resulting in 1/1, (p+1)/p, (p+2)/p, ...; she then adds a 3/2 to the scale root, which corresponds to adding 3p/p.
+[[Zhea Erose]] has considered over-p scales, which she calls ''primodal scales''. To construct a p-primodal scale, we fix a prime ''p'' to be the denominator and take intervals of the form n/p, where n ≥ p. Zhea often takes n from a certain "lineal segment" (a segment of the harmonic series spanning an octave counting from p) or a subset thereof. If we use p ≤ n ≤ 2p, this would result in a scale 1/1, (p+1)/p, (p+2)/p, .... Zhea may add a 3/2 to the scale root, which corresponds to adding 3p/p.
 Primodality seems designed to emphasize the identity of the "tonic" as the ''p''th harmonic; this may help in hearing higher primes such as 17, 19, and 23 which may be difficult to hear otherwise as the overtone of some fundamental.