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'''. '''Primodality''' is designed to emphasize the identity of the "tonic" as the pth harmonic. Most importantly, primodality sees any overtone is valuable on its own, rather than relative to some fundamental. Taking a specific overtone as a tonic we can get its particular scales and colors, even when the corresponding fundamental is too low to be audible.

[[Zhea Erose]] has considered over-p scales where p is a prime, which she calls '''primodal scales'''. '''Primodality''' is designed to emphasize the identity of the "tonic" as the pth harmonic. Most importantly, primodality sees any overtone as valuable on its own, rather than relative to some fundamental. Taking a specific overtone as a tonic we can get its particular scales and colors, even when the corresponding fundamental is too low to be audible.

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]].

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 === Over-p scales ===
-[[Zhea Erose]] has considered over-p scales where p is a prime, which she calls '''primodal scales'''. '''Primodality''' is designed to emphasize the identity of the "tonic" as the pth harmonic. Most importantly, primodality sees any overtone is valuable on its own, rather than relative to some fundamental. Taking a specific overtone as a tonic we can get its particular scales and colors, even when the corresponding fundamental is too low to be audible.
+[[Zhea Erose]] has considered over-p scales where p is a prime, which she calls '''primodal scales'''. '''Primodality''' is designed to emphasize the identity of the "tonic" as the pth harmonic. Most importantly, primodality sees any overtone as valuable on its own, rather than relative to some fundamental. Taking a specific overtone as a tonic we can get its particular scales and colors, even when the corresponding fundamental is too low to be audible.
 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]].