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 starting from mp where m is a positive integer) or a subset thereof. For example, if we use p = 13 and and take all n between 13 and 26 (inclusive), this would result in the scale 13:14:15:16:17:18:19:20:21:22:23:24:25:26. 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 a positive integer) or a subset thereof. For example, if we use p = 13 and and take all n between 13 and 26 (inclusive), this would result in the scale 13:14:15:16:17:18:19:20:21:22:23:24:25:26. 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.

'''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.

== A Solfege System ==

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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 starting from mp where m is a positive integer) or a subset thereof. For example, if we use p = 13 and and take all n between 13 and 26 (inclusive), this would result in the scale 13:14:15:16:17:18:19:20:21:22:23:24:25:26. 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 a positive integer) or a subset thereof. For example, if we use p = 13 and and take all n between 13 and 26 (inclusive), this would result in the scale 13:14:15:16:17:18:19:20:21:22:23:24:25:26. 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.
+'''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.
 == A Solfege System ==