Overtone scale: Difference between revisions

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Mode 30 in particular is interesting because 30 is the product of the first three primes, so it's a fairly good choice if we want a tonic that isn't a power of two. It contains modes 6 and 10 as subsets. We have the classic minor triad (from 10), the subminor triad (from 6), two major triads in 30:37:45 and 30:38:45, and the Barbados triad of 30:39:45. Chords not based on the tonic include the harmonic seventh chord (32:40:48:56). A good 13-limit subset with 16 notes in it is 30:32:33:35:36:39:40:42:44:45:48:49:50:54:55:56:60.

===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.

==A Solfege System==

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 Mode 30 in particular is interesting because 30 is the product of the first three primes, so it's a fairly good choice if we want a tonic that isn't a power of two. It contains modes 6 and 10 as subsets. We have the classic minor triad (from 10), the subminor triad (from 6), two major triads in 30:37:45 and 30:38:45, and the Barbados triad of 30:39:45. Chords not based on the tonic include the harmonic seventh chord (32:40:48:56). A good 13-limit subset with 16 notes in it is 30:32:33:35:36:39:40:42:44:45:48:49:50:54:55:56:60.
+===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.
 ==A Solfege System==