Kite's color notation/Temperament names: Difference between revisions
in advantages, added a paragraph about splitting colors other than wa |
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Color names are fairly concise. 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. | Color names are fairly concise. 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. | ||
The color name indicates the prime subgroup. For example, Ruyoyo ([[Marvel]]) is yaza (2.3.5.7) because it contains 2 explicit colors ru and yo and 2 implicit colors wa and clear. For explicit colors, each color pair (yo/gu, zo/ru, ilo/lu etc.) indicates a single prime. For example, Sagugu & Biruyo has only 2 explicit color pairs, and is yaza. | The color name indicates the prime subgroup. For example, Ruyoyo (225/224, [[Marvel]]) is yaza (2.3.5.7) because it contains 2 explicit colors ru and yo and 2 implicit colors wa and clear. For explicit colors, each color pair (yo/gu, zo/ru, ilo/lu etc.) indicates a single prime. For example, Sagugu & Biruyo has only 2 explicit color pairs, and is yaza. | ||
The color name also indicates the rank of the temperament. Ruyoyo is rank-3 because 4 colors minus 1 comma = rank-3. Sagugu & Biruyo is 4 color pairs minus 2 commas = rank-2. <u>Subtract edos, but not plusses</u>. Both 12edo&ryyT (4 colors minus 1 edo and 1 comma) and 5edo+yT (3 colors minus 1 edo) are rank-2. Primes 2 and 3 are assumed present in the temperament even if they are not present in the comma. Biruyo is yaza and rank-3, and Biruyo Nowa is yaza nowa and rank-2. | The color name also indicates the rank of the temperament. Ruyoyo is rank-3 because 4 colors minus 1 comma = rank-3. Sagugu & Biruyo is 4 color pairs minus 2 commas = rank-2. <u>Subtract edos, but not plusses</u>. Both 12edo&ryyT (4 colors minus 1 edo and 1 comma) and 5edo+yT (3 colors minus 1 edo) are rank-2. Primes 2 and 3 are assumed present in the temperament even if they are not present in the comma. Biruyo is yaza and rank-3, and Biruyo Nowa is yaza nowa and rank-2. | ||
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The color name also hints at the [[pergen]]. The name only indicates the amount of splitting, not which wa interval is split. Because Sagugu has gu twice, it halves something, in this case the 8ve. Zozo halves the 4th, Bizozogu halves the 5th, and Latrizo splits the 5th into three parts. A name with a tribi color either splits something into six parts, or splits something into two and something else into three. (This is the rationale for using tribi and not hexa, to show the possibilities.) A strong extension of a temperament has the same pergen, and a weak extension has a different one. Thus Gu & Biruyo must be a weak extension of Gu, and a strong extension of Biruyo. The commas in a multi-comma temperament are chosen to indicate strong & weak extensions. | The color name also hints at the [[pergen]]. The name only indicates the amount of splitting, not which wa interval is split. Because Sagugu has gu twice, it halves something, in this case the 8ve. Zozo halves the 4th, Bizozogu halves the 5th, and Latrizo splits the 5th into three parts. A name with a tribi color either splits something into six parts, or splits something into two and something else into three. (This is the rationale for using tribi and not hexa, to show the possibilities.) A strong extension of a temperament has the same pergen, and a weak extension has a different one. Thus Gu & Biruyo must be a weak extension of Gu, and a strong extension of Biruyo. The commas in a multi-comma temperament are chosen to indicate strong & weak extensions. | ||
The color name also indicates splitting of other | The color name also indicates splitting of colors other than wa. For example, Ruyoyo equates every zo ratio with a yoyo ratio. Every other yoyo ratio is some yo ratio doubled, so every other zo ratio is halved. The zo ratio may need to be widened by an 8ve, so actually every other voicing of every other zo ratio is halved. Likewise every other ru ratio equals two gu ratios. For example, two yo 3rds equals a zo 6th, and two gu 2nds equals a ru 2nd. | ||
The length of the color name is a rough indication of the comma's [[Commas by taxicab distance|taxicab distance]] in the lattice. Each la- or sa- adds on average 7 steps on the three-axis. Each yo or gu adds a step on the five-axis, each zo/ru adds a seven-axis step, etc. If [[Commas by taxicab distance|triangularized]] taxicab distance is desired, let over-colors (yo, zo, ilo, etc.) cancel under-colors of smaller primes (gu, ru, etc.), and let under-colors cancel smaller over-colors. | The length of the color name is a rough indication of the comma's [[Commas by taxicab distance|taxicab distance]] in the lattice. Each la- or sa- adds on average 7 steps on the three-axis. Each yo or gu adds a step on the five-axis, each zo/ru adds a seven-axis step, etc. If [[Commas by taxicab distance|triangularized]] taxicab distance is desired, let over-colors (yo, zo, ilo, etc.) cancel under-colors of smaller primes (gu, ru, etc.), and let under-colors cancel smaller over-colors. | ||