Overtone scale: Difference between revisions

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== Primodality==

[[Zhea Erose]] has considered over-p scales and chords where p is a prime, which she calls '''primodal scales'''. '''Primodality''' is an approach to JI designed to emphasize the identity of the "tonic" as the pth harmonic. Scales and ~~structures~~ having the identity of the prime p as the tonic are collectively called a '''prime family''', and can be denoted simply by ''/p''. Zhea also uses various adjectives for specific primodalities, such as ''septimal, undecimal, tridecimal, septendecimal, novem(decimal)'' for /7, /11, /13, /17, /19, which are not to be confused with the use of these adjectives to denote prime limits.

[[Zhea Erose]] has considered over-p scales and chords where p is a prime, which she calls '''primodal scales'''. '''Primodality''' is an approach to JI designed to emphasize the identity of the "tonic" as the pth harmonic. Scales and chords having the identity of the prime p as the tonic are collectively called a '''prime family''', and can be denoted simply by ''/p''. Zhea also uses various adjectives for specific primodalities, such as ''septimal, undecimal, tridecimal, septendecimal, novem(decimal)'' for /7, /11, /13, /17, /19, which are not to be confused with the use of these adjectives to denote prime limits.

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.

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 == Primodality==
-[[Zhea Erose]] has considered over-p scales and chords where p is a prime, which she calls '''primodal scales'''. '''Primodality''' is an approach to JI designed to emphasize the identity of the "tonic" as the pth harmonic. Scales and structures having the identity of the prime p as the tonic are collectively called a '''prime family''', and can be denoted simply by ''/p''. Zhea also uses various adjectives for specific primodalities, such as ''septimal, undecimal, tridecimal, septendecimal, novem(decimal)'' for /7, /11, /13, /17, /19, which are not to be confused with the use of these adjectives to denote prime limits.
+[[Zhea Erose]] has considered over-p scales and chords where p is a prime, which she calls '''primodal scales'''. '''Primodality''' is an approach to JI designed to emphasize the identity of the "tonic" as the pth harmonic. Scales and chords having the identity of the prime p as the tonic are collectively called a '''prime family''', and can be denoted simply by ''/p''. Zhea also uses various adjectives for specific primodalities, such as ''septimal, undecimal, tridecimal, septendecimal, novem(decimal)'' for /7, /11, /13, /17, /19, which are not to be confused with the use of these adjectives to denote prime limits.
 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.