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

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To make the names easier for non-Anglophones, and to make the names quicker to say, the 5 vowels are the basic vowels found in Spanish, ah eh ee oh oo. In Spanish and many other languages, "th" would become "tr". See [[Color notation/Translations|Color Notation/Translations]].

Any comma < 256/243 = 90¢ is guaranteed to be the smallest ratio in its segment. Any comma > 9/8 = 204¢ is guaranteed to not be the smallest, and -bi must be appended to the name. If a comma is 90-204¢, let S = the sum of all the numbers in the monzo except the first one. If and only if S mod 7 is 4 or 5, 256/243 can be subtracted without changing the magnitude, and the comma is the 2nd smallest ratio.

Any comma < 256/243 = 90¢ is guaranteed to be the smallest ratio in its segment. Any comma > 9/8 = 204¢ is guaranteed to not be the smallest, and -bi must be appended to the name. If a comma is 90-204¢, let S = the sum of all the numbers in the monzo except the first one. If and only if S mod 7 is 4 or 5, 256/243 can be subtracted without changing the magnitude, and the comma is the 2nd smallest ratio. Any 204-294¢ comma is -bi, and any 408-498¢ comma is -tri.

Sometimes the smallest ratio in a segment is a multiple of another comma. For example, the smallest ratio in the central segment of the zozogugu row is 441/400. But since this is (21/20)2, tempering it out would simply result in zgT. Thus there is no bizogu temperament, although there is a bizogubi one.

A temperament name will never end with -quin, -tribi or -sep, because it would be named after the octave inverse of the comma instead. Sagusep is actually layo, and sagutribi is actually layobi. Any comma that is 204-294¢ is -bi, and any 408-498¢ comma is -tri.

La means large and also 11-all. The meaning will almost always be clear from context, however "this piece uses la notes" is ambiguous. To clarify, one should say either "large notes" (fifthward notes) or "ila notes" (11-limit notes). Likewise, sa also means 17-all, and "sa notes" should become either "small notes" or "isa notes".

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La is also the La note in solfege, and Sa is the tonic in saregam. The meaning will always be clear from context. Notes are never large or small. In fixed-do countries, the chord ALw (81/64 3rd) is "La lawa".

Multi-comma temperaments are named as a list of commas. For example, 7-limit porcupine is triyo & ru = y3&rT. There are three obvious ways to choose the comma set for multi-comma temperaments. The '''odd name''' minimizes the [[Odd limit|double odd limit]] of the comma set. The '''subgroup name''' minimizes the number and size of the primes used by each comma, but not their depth. Assuming no wa commas, the 1st comma is ya, the 2nd za, the 3rd ila, etc. The '''prime/odd name''' minimizes the prime-limit for each comma, and for each prime limit uses the comma of least double odd limit. The 1st comma is ya, the 2nd yaza, the 3rd yazala, etc. (There is also the '''hermite name''', formed by hermite reduction, which minimizes the prime-limit of each comma, and for each prime limit, tends to minimize the color depth. Finally the '''LLL name''' uses Lenstra–Lenstra–Lovász reduction, and tends to minimize the integer limit of each comma.) ~~See [[User:TallKite/Catalog of seven-limit rank two temperaments with Color names]] for further discussion.~~

Multi-comma temperaments are named as a list of commas. For example, 7-limit porcupine is triyo & ru = y3&rT. There are three obvious ways to choose the comma set for multi-comma temperaments. The '''odd name''' minimizes the [[Odd limit|double odd limit]] of the comma set. The '''subgroup name''' minimizes the number and size of the primes used by each comma, but not their depth. Assuming no wa commas, the 1st comma is ya, the 2nd za, the 3rd ila, etc. The '''prime/odd name''' minimizes the prime-limit for each comma, and for each prime limit uses the comma of least double odd limit. The 1st comma is ya, the 2nd yaza, the 3rd yazala, etc. (There is also the '''hermite name''', formed by hermite reduction, which minimizes the prime-limit of each comma, and for each prime limit, tends to minimize the color depth. Finally the '''LLL name''' uses Lenstra–Lenstra–Lovász reduction, and tends to minimize the integer limit of each comma.)

The odd name for 7-limit [[Pajara]] is rryy&rT, the subgroup name is sgg&rT, and the prime/odd 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.

The odd name for 7-limit [[Pajara]] is rryy&rT, the subgroup name is sgg&rT, and the prime/odd 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. See [[User:TallKite/Catalog of seven-limit rank two temperaments with Color names]] for further discussion.

If the comma is wa, an edo is implied. The temperament is named after the edo, not the wa comma. Tempering out the pythagorean comma and 225/224 makes 12edo&ryyT.

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 To make the names easier for non-Anglophones, and to make the names quicker to say, the 5 vowels are the basic vowels found in Spanish, ah eh ee oh oo. In Spanish and many other languages, "th" would become "tr". See [[Color notation/Translations|Color Notation/Translations]].
-Any comma < 256/243 = 90¢ is guaranteed to be the smallest ratio in its segment. Any comma > 9/8 = 204¢ is guaranteed to <u>not</u> be the smallest, and -bi must be appended to the name. If a comma is 90-204¢, let S = the sum of all the numbers in the monzo except the first one. If and only if S mod 7 is 4 or 5, 256/243 can be subtracted without changing the magnitude, and the comma is the 2nd smallest ratio.
+Any comma < 256/243 = 90¢ is guaranteed to be the smallest ratio in its segment. Any comma > 9/8 = 204¢ is guaranteed to <u>not</u> be the smallest, and -bi must be appended to the name. If a comma is 90-204¢, let S = the sum of all the numbers in the monzo except the first one. If and only if S mod 7 is 4 or 5, 256/243 can be subtracted without changing the magnitude, and the comma is the 2nd smallest ratio. Any 204-294¢ comma is -bi, and any 408-498¢ comma is -tri.
 Sometimes the smallest ratio in a segment is a multiple of another comma. For example, the smallest ratio in the central segment of the zozogugu row is 441/400. But since this is (21/20)<sup>2</sup>, tempering it out would simply result in zgT. Thus there is no bizogu temperament, although there is a bizogubi one.
-A temperament name will never end with -quin, -tribi or -sep, because it would be named after the octave inverse of the comma instead. Sagusep is actually layo, and sagutribi is actually layobi. Any comma that is 204-294¢ is -bi, and any 408-498¢ comma is -tri.
 La means large and also 11-all. The meaning will almost always be clear from context, however "this piece uses la notes" is ambiguous. To clarify, one should say either "large notes" (fifthward notes) or "ila notes" (11-limit notes). Likewise, sa also means 17-all, and "sa notes" should become either "small notes" or "isa notes".
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 La is also the La note in solfege, and Sa is the tonic in saregam. The meaning will always be clear from context. Notes are never large or small. In fixed-do countries, the chord ALw (81/64 3rd) is "La lawa".
-Multi-comma temperaments are named as a list of commas. For example, 7-limit porcupine is triyo & ru = y<sup>3</sup>&rT. There are three obvious ways to choose the comma set for multi-comma temperaments. The '''odd name''' minimizes the [[Odd limit|double odd limit]] of the comma set. The '''subgroup name''' minimizes the number and size of the primes used by each comma, but not their depth. Assuming no wa commas, the 1st comma is ya, the 2nd za, the 3rd ila, etc. The '''prime/odd name''' minimizes the prime-limit for each comma, and for each prime limit uses the comma of least double odd limit. The 1st comma is ya, the 2nd yaza, the 3rd yazala, etc. (There is also the '''hermite name''', formed by hermite reduction, which minimizes the prime-limit of each comma, and for each prime limit, tends to minimize the color depth. Finally the '''LLL name''' uses Lenstra–Lenstra–Lovász reduction, and tends to minimize the integer limit of each comma.) See [[User:TallKite/Catalog of seven-limit rank two temperaments with Color names]] for further discussion.
+Multi-comma temperaments are named as a list of commas. For example, 7-limit porcupine is triyo & ru = y<sup>3</sup>&rT. There are three obvious ways to choose the comma set for multi-comma temperaments. The '''odd name''' minimizes the [[Odd limit|double odd limit]] of the comma set. The '''subgroup name''' minimizes the number and size of the primes used by each comma, but not their depth. Assuming no wa commas, the 1st comma is ya, the 2nd za, the 3rd ila, etc. The '''prime/odd name''' minimizes the prime-limit for each comma, and for each prime limit uses the comma of least double odd limit. The 1st comma is ya, the 2nd yaza, the 3rd yazala, etc. (There is also the '''hermite name''', formed by hermite reduction, which minimizes the prime-limit of each comma, and for each prime limit, tends to minimize the color depth. Finally the '''LLL name''' uses Lenstra–Lenstra–Lovász reduction, and tends to minimize the integer limit of each comma.)
-The odd name for 7-limit [[Pajara]] is rryy&rT, the subgroup name is sgg&rT, and the prime/odd 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.
+The odd name for 7-limit [[Pajara]] is rryy&rT, the subgroup name is sgg&rT, and the prime/odd 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. See [[User:TallKite/Catalog of seven-limit rank two temperaments with Color names]] for further discussion.
 If the comma is wa, an edo is implied. The temperament is named after the edo, not the wa comma. Tempering out the pythagorean comma and 225/224 makes 12edo&ryyT.