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

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* Large = '''la-''', small = '''sa-''', double large = lala-, triple small = trisa-, etc.

Some 5-limit examples, sorted by color depth. Many more examples can be found on the comma pages [[Comma|here]], [[Large commas|here]] and [[Unnoticeable comma|here]].

# [[Schismatic]] = Layo = LyT, [[Mavila]] = Layobi = ~~Ly2T~~, [[Superpyth]] = Sayo = syT. [[Meantone]] = Gu = gT, [[Father]] = Gubi = ~~g2T~~.

# [[Schismatic]] = Layo = LyT, [[Mavila]] = Layobi = Ly2T, [[Superpyth]] = Sayo = syT. [[Meantone]] = Gu = gT, [[Father]] = Gubi = g2T.

# [[Dicot]] = Yoyo = yyT, [[Immunity family|Immunity]] = Sasa-yoyo = ssyyT. [[Bug]] = Gugu = ggT, [[Diaschismic]] = Sagugu = sggT, [[Beatles]] = Sasa-gugu = ssggT.

# [[Porcupine]] = Triyo = y3T. [[Augmented]] = Trigu = g3T, [[Laconic family|Laconic]] = Latrigu = Lg3T, [[Misty comma|Misty]] = Sasa-trigu = ssg3T.

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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. Subtract edos, but not plusses. 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 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. However, it's not obvious that Sagugu & Biruyo is a strong extension, nor that Sagugu & Zozo isn't.

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. However, it's not obvious that Sagugu & Biruyo is a strong extension of Sagugu, nor that Sagugu & Zozo isn't.

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.

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 * Large = '''la-''', small = '''sa-''', double large = lala-, triple small = trisa-, etc.
 Some 5-limit examples, sorted by color depth. Many more examples can be found on the comma pages [[Comma|here]], [[Large commas|here]] and [[Unnoticeable comma|here]].
-# [[Schismatic]] = Layo = LyT, [[Mavila]] = Layobi = Ly2T, [[Superpyth]] = Sayo = syT. [[Meantone]] = Gu = gT, [[Father]] = Gubi = g2T.
+# [[Schismatic]] = Layo = LyT, [[Mavila]] = Layobi = Ly<sub>2</sub>T, [[Superpyth]] = Sayo = syT. [[Meantone]] = Gu = gT, [[Father]] = Gubi = g<sub>2</sub>T.
 # [[Dicot]] = Yoyo = yyT, [[Immunity family|Immunity]] = Sasa-yoyo = ssyyT.  [[Bug]] = Gugu = ggT, [[Diaschismic]] = Sagugu = sggT, [[Beatles]] = Sasa-gugu = ssggT.
 # [[Porcupine]] = Triyo = y<sup>3</sup>T. [[Augmented]] = Trigu = g<sup>3</sup>T, [[Laconic family|Laconic]] = Latrigu = Lg<sup>3</sup>T, [[Misty comma|Misty]] = Sasa-trigu = ssg<sup>3</sup>T.
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 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 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. However, it's not obvious that Sagugu & Biruyo is a strong extension, nor that Sagugu & Zozo isn't.
+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. However, it's not obvious that Sagugu & Biruyo is a strong extension of Sagugu, nor that Sagugu & Zozo isn't.
 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.