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. This corresponds to taking Mode mp of the harmonic series. For example, if we use p = 13 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. (3/2 is a natural "halfway point" for harmonic scales, since if N is even, Mode N has a 3/2 as its N/2-th note.) Zhea considers the intervals in the first octave over p of the harmonic series to be the most ~~consonant~~ intervals in p-primodality. In particular, primodality discards the concept of [[harmonic limit]].

[[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. This corresponds to taking Mode mp of the harmonic series. For example, if we use p = 13 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. (3/2 is a natural "halfway point" for harmonic scales, since if N is even, Mode N has a 3/2 as its N/2-th note.) Zhea considers the intervals in the first octave over p of the harmonic series to be the most "natural" intervals in p-primodality. In particular, primodality discards the concept of [[harmonic limit]].

'''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 otherwise be difficult to hear 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 starting from mp where m is a positive integer) or a subset thereof. This corresponds to taking Mode mp of the harmonic series. For example, if we use p = 13 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. (3/2 is a natural "halfway point" for harmonic scales, since if N is even, Mode N has a 3/2 as its N/2-th note.) Zhea considers the intervals in the first octave over p of the harmonic series to be the most consonant intervals in p-primodality. In particular, primodality discards the concept of [[harmonic limit]].
+[[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. This corresponds to taking Mode mp of the harmonic series. For example, if we use p = 13 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. (3/2 is a natural "halfway point" for harmonic scales, since if N is even, Mode N has a 3/2 as its N/2-th note.) Zhea considers the intervals in the first octave over p of the harmonic series to be the most "natural" intervals in p-primodality. In particular, primodality discards the concept of [[harmonic limit]].
 '''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 otherwise be difficult to hear as the overtone of some fundamental.