Kite's color notation: Difference between revisions

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Keys and scales are loosely named after the colors used. Wa is assumed present. In 5-limit JI, the key/scale of A minor is A gu. The Bbh7 - Ebh7 - Bbh7 - Fh9 example in the staff notation section is in Bb yo zo. Like chords, keys can be classified as bicolored (A gu), tricolored (Bb yo zo), etc.

Analogous to the relative and parallel major or minor, one can modulate to relative gu, parallel ru, etc. Modulating from a yo key to the relative gu means using gu chords on yo roots. Modulating from yo to the parallel gu means using gu chords on wa roots. Going from yo zo to the relative gu means using chords with gu and/or ru in them on yo roots. Going to the relative ru means using the same chords on zo roots. Going from yo zo to the parallel gu ru means using the same chords on wa roots. One can also modulate '''fourthward''' or '''fifthward''', abbreviated '''4thwd''' or '''5thwd'''. Modulating from a yo key to the relative gu, then from there to the parallel yo is modulating '''yoward~~''', abbreviated '''yowd~~'''. Likewise, there's '''guward''', '''zoward''', '''iloward''', etc~~. (guwd, zowd, 1owd)~~.

Analogous to the relative and parallel major or minor, one can modulate to relative gu, parallel ru, etc. Modulating from a yo key to the relative gu means using gu chords on yo roots. Modulating from yo to the parallel gu means using gu chords on wa roots. Going from yo zo to the relative gu means using chords with gu and/or ru in them on yo roots. Going to the relative ru means using the same chords on zo roots. Going from yo zo to the parallel gu ru means using the same chords on wa roots. One can also modulate '''fourthward''' or '''fifthward''', abbreviated '''4thwd''' or '''5thwd'''. Modulating from a yo key to the relative gu, then from there to the parallel yo is modulating '''yoward'''. Likewise, there's '''guward''', '''zoward''', '''iloward''', etc.

== Temperament Names ==

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The magnitude is part of the name: [[Schismatic]] is LyT and [[Diaschismic]] is sggT. The degree is too, but only if the comma is not the smallest of the 7 ratios of that magnitude and color: [[Mavila]] is Ly1T and [[Father family|Father]] is g2T. The degree is never needed if the comma is ≤ 90¢.

If the comma is wa, an edo is implied. The temperament is named after the edo, not the comma. 2.3.5.7 and the pyth comma and 225/224 is 12edo&ryyT. If the comma(s) don't include every prime in the subgroup, some primes are untempered. These are added with '''plus''': Blackwood is 5edo+yT = 5-edo plus ya. 2.3.5.7.11 and 81/80 = g+z1aT = gu plus zala.

If the comma is wa, an edo is implied. The temperament is named after the edo, not the comma. 2.3.5.7 and the pyth comma and 225/224 is 12edo&ryyT. If the comma(s) don't include every prime in the subgroup, some primes are untempered. These are added with '''plus''': [[Blackwood]] is 5edo+yT = 5-edo plus ya. 2.3.5.7.11 and 81/80 = g+z1aT = gu plus zala.

The temperament name indicates the prime subgroup and the rank of the temperament. For example, ryyT ([[Marvel]]) is rank-3 because it has 2 explicit colors ru and yo and 2 implicit colors wa and clear, and 4 colors minus 1 comma = rank-3. Edos count as commas, but plusses don't. Both 12edo&ryyT and 5edo+yT are rank-2.

There are two obvious ways to name multi-comma temperaments. The odd name minimizes the [[Odd limit|double odd limit]] of the comma set, and the prime name minimizes the number and size of the primes used by each comma. The odd name for 7-limit [[Pajara]] is rryy&rT, and the prime name is sgg&rT. Often the two names are identical, e.g. y3&rT. The odd name is often shorter, and usually indicates commas more likely to be pumped. The prime name shows relationships between single-comma temperaments better. The question of which name to use is not yet fully resolved.

There are two obvious ways to name multi-comma temperaments. The odd name minimizes the [[Odd limit|double odd limit]] of the comma set, and the prime name minimizes the number and size of the primes used by each comma. The odd name for 7-limit [[Pajara]] is rryy&rT, and the prime name is sgg&rT. Often the two names are identical, e.g. y3&rT. The odd name is often shorter, and usually indicates commas more likely to be pumped. The prime name shows relationships between single-comma rank-2 temperaments better. The question of which name to use is not yet fully resolved.

== Ups and Downs, Lifts and Drops, Plain and Mid ==

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 Keys and scales are loosely named after the colors used. Wa is assumed present. In 5-limit JI, the key/scale of A minor is A gu. The Bbh7 - Ebh7 - Bbh7 - Fh9 example in the staff notation section is in Bb yo zo. Like chords, keys can be classified as bicolored (A gu), tricolored (Bb yo zo), etc.
-Analogous to the relative and parallel major or minor, one can modulate to relative gu, parallel ru, etc. Modulating from a yo key to the relative gu means using gu chords on yo roots. Modulating from yo to the parallel gu means using gu chords on <u>wa</u> roots. Going from yo zo to the relative gu means using chords with gu and/or ru in them on yo roots. Going to the relative ru means using the same chords on zo roots. Going from yo zo to the parallel gu ru means using the same chords on wa roots. One can also modulate '''fourthward''' or '''fifthward''', abbreviated '''4thwd''' or '''5thwd'''. Modulating from a yo key to the relative gu, then from there to the parallel yo is modulating '''yoward''', abbreviated '''yowd'''. Likewise, there's '''guward''', '''zoward''', '''iloward''', etc. (guwd, zowd, 1owd).
+Analogous to the relative and parallel major or minor, one can modulate to relative gu, parallel ru, etc. Modulating from a yo key to the relative gu means using gu chords on yo roots. Modulating from yo to the parallel gu means using gu chords on <u>wa</u> roots. Going from yo zo to the relative gu means using chords with gu and/or ru in them on yo roots. Going to the relative ru means using the same chords on zo roots. Going from yo zo to the parallel gu ru means using the same chords on wa roots. One can also modulate '''fourthward''' or '''fifthward''', abbreviated '''4thwd''' or '''5thwd'''. Modulating from a yo key to the relative gu, then from there to the parallel yo is modulating '''yoward'''. Likewise, there's '''guward''', '''zoward''', '''iloward''', etc.
 == Temperament Names ==
@@ Line 262: / Line 262: @@
 The magnitude is part of the name: [[Schismatic]] is LyT and [[Diaschismic]] is sggT. The degree is too, but only if the comma is not the smallest of the 7 ratios of that magnitude and color: [[Mavila]] is Ly1T and [[Father family|Father]] is g2T. The degree is never needed if the comma is ≤ 90¢.
-If the comma is wa, an edo is implied. The temperament is named after the edo, not the comma. 2.3.5.7 and the pyth comma and 225/224 is 12edo&ryyT. If the comma(s) don't include every prime in the subgroup, some primes are untempered. These are added with '''plus''': Blackwood is 5edo+yT = 5-edo plus ya. 2.3.5.7.11 and 81/80 = g+z1aT = gu plus zala.
+If the comma is wa, an edo is implied. The temperament is named after the edo, not the comma. 2.3.5.7 and the pyth comma and 225/224 is 12edo&ryyT. If the comma(s) don't include every prime in the subgroup, some primes are untempered. These are added with '''plus''': [[Blackwood]] is 5edo+yT = 5-edo plus ya. 2.3.5.7.11 and 81/80 = g+z1aT = gu plus zala.
 The temperament name indicates the prime subgroup and the rank of the temperament. For example, ryyT ([[Marvel]]) is rank-3 because it has 2 explicit colors ru and yo and 2 implicit colors wa and clear, and 4 colors minus 1 comma = rank-3. Edos count as commas, but plusses don't. Both 12edo&ryyT and 5edo+yT are rank-2.
-There are two obvious ways to name multi-comma temperaments. The odd name minimizes the [[Odd limit|double odd limit]] of the comma set, and the prime name minimizes the number and size of the primes used by each comma. The odd name for 7-limit [[Pajara]] is rryy&rT, and the prime name is sgg&rT. Often the two names are identical, e.g. y<sup>3</sup>&rT. The odd name is often shorter, and usually indicates commas more likely to be pumped. The prime name shows relationships between single-comma temperaments better. The question of which name to use is not yet fully resolved.
+There are two obvious ways to name multi-comma temperaments. The odd name minimizes the [[Odd limit|double odd limit]] of the comma set, and the prime name minimizes the number and size of the primes used by each comma. The odd name for 7-limit [[Pajara]] is rryy&rT, and the prime name is sgg&rT. Often the two names are identical, e.g. y<sup>3</sup>&rT. The odd name is often shorter, and usually indicates commas more likely to be pumped. The prime name shows relationships between single-comma rank-2 temperaments better. The question of which name to use is not yet fully resolved.
 == Ups and Downs, Lifts and Drops, Plain and Mid ==