Overtone scale: Difference between revisions
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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 and even versions of "non-xenharmonic" scales, even when the corresponding fundamental is too low to be audible. In particular, primodality discards the concept of [[harmonic limit]], which Zhea considers an artificial way to look at JI harmony. Zhea argues that prime family (set of intervals over a small multiple of p) is a more natural way to categorize intervals; intervals from the same prime family (intervals with a common denominator for example, all /2, all /11 or all /13) tend to blend better together. For example, it is preferable to add 21/16 to 4:5:6:7, rather than 4/3. | 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 and even versions of "non-xenharmonic" scales, even when the corresponding fundamental is too low to be audible. In particular, primodality discards the concept of [[harmonic limit]], which Zhea considers an artificial way to look at JI harmony. Zhea argues that prime family (set of intervals over a small multiple of p) is a more natural way to categorize intervals; intervals from the same prime family (intervals with a common denominator for example, all /2, all /11 or all /13) tend to blend better together. For example, it is preferable to add 21/16 to 4:5:6:7, rather than 4/3. | ||
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" ( | 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" (Mode mp of the harmonic series where m is a positive integer) or a subset thereof.. 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.) | ||
Primodality emphasizes unique characters of primes, as opposed to lower-complexity JI identities such as 4:5:6:7:9:11:13. Modes p or 2p (called respectively the ''first'' and ''second octaves of /p'') are considered the most important for the prime's identity: for any prime p, the set of harmonics from p to 2p (called the ''first octave of p'') is unique in the sense that the sets {p/p, ..., 2p/p} and {n/n, ..., 2n/n} only intersect at {1/1, 2/1} for any positive integer n < p. Similarly, the second octaves of p and the second octave of any n < p only intersect at {1/1, 3/2, 2/1}. | |||
Approximations of [[edo]]s in certain primodalities, called ''nejis'' ("near-equal JI"), can be used to explore a prime family, while keeping the transposability, MOS scale structures, rank-2 harmonic theory, etc. associated with that edo. | |||
Zhea Erose's theory also deals with modulations between different prime families, and combining different prime families into one scale. | |||
==== Music ==== | ==== Music ==== | ||
*[https://youtu.be/ZIn6uis5duw Zhea Erose - Novemdeca (in a 12-note 19-primodal scale)] | *[https://youtu.be/ZIn6uis5duw Zhea Erose - Novemdeca (in a 12-note 19-primodal scale)] | ||