Overtone scale: Difference between revisions

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===Over-p scales===

[[Zhea Erose]] has considered over-p scales where p is a prime, which she calls ''primodal scales''. To construct a 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 range over a certain "lineal segment" (a segment of the harmonic series spanning an octave ~~counting~~ from p) or a subset thereof. If we use all n between p and 2p (inclusive), this would result in a scale 1/1, (p+1)/p, (p+2)/p, .... We may add a 3/2 to the scale root, which corresponds to adding 3p/p.

[[Zhea Erose]] has considered over-p scales where p is a prime, which she calls ''primodal scales''. To construct a 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 range over a certain "lineal segment" (a segment of the harmonic series spanning an octave starting from mp where m is an integer) or a subset thereof. For example, if we use all n between p and 2p (inclusive), this would result in a scale 1/1, (p+1)/p, (p+2)/p, .... We 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 pth 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 where p is a prime, which she calls ''primodal scales''. To construct a 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 range over a certain "lineal segment" (a segment of the harmonic series spanning an octave counting from p) or a subset thereof. If we use all n between p and 2p (inclusive), this would result in a scale 1/1, (p+1)/p, (p+2)/p, .... We may add a 3/2 to the scale root, which corresponds to adding 3p/p.
+[[Zhea Erose]] has considered over-p scales where p is a prime, which she calls ''primodal scales''. To construct a 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 range over a certain "lineal segment" (a segment of the harmonic series spanning an octave starting from mp where m is an integer) or a subset thereof. For example, if we use all n between p and 2p (inclusive), this would result in a scale 1/1, (p+1)/p, (p+2)/p, .... We 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 pth 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.