Kite's color notation/Temperament names: Difference between revisions

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The odd name for 7-limit [[Pajara]] is rryy&rT, the subgroup name is sgg&rT, and the prime name is sgg&rryyT. Often the three names are identical, e.g. y3&rT. The odd name is often shorter, and usually indicates commas more likely to be pumped. The subgroup name shows relationships between bicolored rank-2 temperaments better. The question of which name to use is not yet fully resolved.

If the comma is wa, an edo is implied. The temperament is named after the edo, not the wa 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 primes are added with '''plus''': [[Blackwood]] is 5edo+yT = 5-edo plus ya. The 2.3.5.7.11 subgroup with 81/80 tempered out is g+z1aT = gu plus zala.

If the comma is wa, an edo is implied. The temperament is named after the edo, not the wa comma. Tempering out the pyth comma and 225/224 makes 12edo&ryyT. If the comma(s) don't include every prime in the subgroup, some primes are untempered. These primes are added with '''plus''': [[Blackwood]] is 5edo+yT = 5-edo plus ya. The 2.3.5.7.11 subgroup with 81/80 tempered out is 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. Primes 2 and 3 are assumed present in the temperament even if they are not present in the comma. Biruyo is rank-3 and biruyo nowa is rank-2.

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. When counting explicit colors, count each color pair as one -- yo/gu, zo/ru, etc. When counting commas, edos count as commas, but plusses don't. Both 12edo&ryyT and 5edo+yT are rank-2. Primes 2 and 3 are assumed present in the temperament even if they are not present in the comma. Biruyo is rank-3 and biruyo nowa is rank-2.

If the comma's numerator has N digits, the temperament name will usually have N, N-1, N+1 or occasionally N+2 syllables. Thus the spoken color name is generally much shorter than the spoken ratio.

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 The odd name for 7-limit [[Pajara]] is rryy&rT, the subgroup name is sgg&rT, and the prime name is sgg&rryyT. Often the three 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 subgroup name shows relationships between bicolored rank-2 temperaments better. The question of which name to use is not yet fully resolved.
-If the comma is wa, an edo is implied. The temperament is named after the edo, not the wa 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 primes are added with '''plus''': [[Blackwood]] is 5edo+yT = 5-edo plus ya. The 2.3.5.7.11 subgroup with 81/80 tempered out is g+z1aT = gu plus zala.
+If the comma is wa, an edo is implied. The temperament is named after the edo, not the wa comma. Tempering out the pyth comma and 225/224 makes 12edo&ryyT. If the comma(s) don't include every prime in the subgroup, some primes are untempered. These primes are added with '''plus''': [[Blackwood]] is 5edo+yT = 5-edo plus ya. The 2.3.5.7.11 subgroup with 81/80 tempered out is 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. <u>Edos count as commas, but plusses don't</u>. Both 12edo&ryyT and 5edo+yT are rank-2. Primes 2 and 3 are assumed present in the temperament even if they are not present in the comma. Biruyo is rank-3 and biruyo nowa is rank-2.
+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. When counting explicit colors, count each color pair as one -- yo/gu, zo/ru, etc. When counting commas, <u>edos count as commas, but plusses don't</u>. Both 12edo&ryyT and 5edo+yT are rank-2. Primes 2 and 3 are assumed present in the temperament even if they are not present in the comma. Biruyo is rank-3 and biruyo nowa is rank-2.
 If the comma's numerator has N digits, the temperament name will usually have N, N-1, N+1 or occasionally N+2 syllables. Thus the spoken color name is generally much shorter than the spoken ratio.