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

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The color defines a lattice row, and the magnitude (large, small, etc.) defines a '''segment''' of that row. A name without a magnitude, like Zozo, refers to the central segment. Each segment contains 7 ratios. The comma that is tempered out is usually the smallest in cents of those 7. If not, '''-bi''' or '''-tri''' is added to the end of the name to indicate that the comma is the 2nd or 3rd largest ratio in that segment, e.g. [[Mavila]] = Layobi. Any comma smaller than 256/243 = 90¢ is guaranteed to be the smallest ratio in its segment, thus -bi and -tri are only used for very large commas.

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

Some 5-limit examples, sorted by color depth. Many more examples can be found on the comma pages ([[Small comma]], [[Medium comma]], [[Large comma]] and [[Unnoticeable comma]]).

#[[Schismatic]] = Layo, [[Mavila]] = Layobi, [[Superpyth]] = Sayo, [[Meantone]] = Gu, [[Father]] = Gubi.

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

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If the comma is wa, an edo is implied. For the most common cases of 5-edo, 7-edo and 12-edo, the temperament is named after the wa comma. Thus [[Blackwood]] is Sawa + ya, [[Whitewood]] is Lawa + ya, and [[Catler]] is Lalawa + za.

Any other wa comma is named using the Wa-N format. Thus [[~~Counterpyth~~ family|~~Counterpyth~~]] is Wa-41 + ya, not the difficult-to-decipher Tribisawa + ya. Note that multi-ring edos such as 10-edo can't be implied by a wa comma, and Wa-10 is not a valid comma name. However 10-edo can be created by a non-wa comma, or by a wa comma plus a non-wa comma, e.g. Sawa & Yoyo.

Any other wa comma is named using the Wa-N format. Thus [[Countercomp family|Countercomp]] is Wa-41 + ya, not the difficult-to-decipher Tribisawa + ya. Note that multi-ring edos such as 10-edo can't be implied by a wa comma, and Wa-10 is not a valid comma name. However 10-edo can be created by a non-wa comma, or by a wa comma plus a non-wa comma, e.g. Sawa & Yoyo.

Temperaments are abbreviated with "T": Zozo = zzT, Triyo = y<sup>3</sup>T, Gu & Rugu = g&rgT, Layobi = Ly#2T, Sawa + ya = sw+yT, Wa-41 + ya = w-41+yT, Gu + zala = g+z1aT, and Biruyo Nowa = rryy-wT.

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*[[User:TallKite/Catalog of eleven-limit rank three temperaments with Color names]]

*[[Catalog of rank two temperaments]] (under construction)

==Finding the comma from the name and vice versa==

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 The color defines a lattice row, and the magnitude (large, small, etc.) defines a '''segment''' of that row. A name without a magnitude, like Zozo, refers to the central segment. Each segment contains 7 ratios. The comma that is tempered out is usually the smallest in cents of those 7. If not, '''-bi''' or '''-tri''' is added to the end of the name to indicate that the comma is the 2nd or 3rd largest ratio in that segment, e.g. [[Mavila]] = Layobi. Any comma smaller than 256/243 = 90¢ is guaranteed to be the smallest ratio in its segment, thus -bi and -tri are only used for very large commas.
-Some 5-limit examples, sorted by color depth. Many more examples can be found on the comma pages [[Comma|here]], [[Medium commas|here]], [[Large commas|here]] and [[Unnoticeable comma|here]].
+Some 5-limit examples, sorted by color depth. Many more examples can be found on the comma pages ([[Small comma]], [[Medium comma]], [[Large comma]] and [[Unnoticeable comma]]).
 #[[Schismatic]] = Layo, [[Mavila]] = Layobi, [[Superpyth]] = Sayo, [[Meantone]] = Gu, [[Father]] = Gubi.
 #[[Dicot]] = Yoyo, [[Immunity family|Immunity]] = Sasa-yoyo, [[Bug]] = Gugu, [[Diaschismic]] = Sagugu, [[Beatles]] = Sasa-gugu.
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 If the comma is wa, an edo is implied. For the most common cases of 5-edo, 7-edo and 12-edo, the temperament is named after the wa comma. Thus [[Blackwood]] is Sawa + ya, [[Whitewood]] is Lawa + ya, and [[Catler]] is Lalawa + za.
-Any other wa comma is named using the Wa-N format. Thus [[Counterpyth family|Counterpyth]] is Wa-41 + ya, not the difficult-to-decipher Tribisawa + ya. Note that multi-ring edos such as 10-edo can't be implied by a wa comma, and Wa-10 is not a valid comma name. However 10-edo can be created by a non-wa comma, or by a wa comma plus a non-wa comma, e.g. Sawa & Yoyo.
+Any other wa comma is named using the Wa-N format. Thus [[Countercomp family|Countercomp]] is Wa-41 + ya, not the difficult-to-decipher Tribisawa + ya. Note that multi-ring edos such as 10-edo can't be implied by a wa comma, and Wa-10 is not a valid comma name. However 10-edo can be created by a non-wa comma, or by a wa comma plus a non-wa comma, e.g. Sawa & Yoyo.
 Temperaments are abbreviated with "T": Zozo = zzT, Triyo = y<sup>3</sup>T, Gu & Rugu = g&rgT, Layobi = Ly#2T, Sawa + ya = sw+yT, Wa-41 + ya = w-41+yT, Gu + zala = g+z1aT, and Biruyo Nowa = rryy-wT.
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 *[[User:TallKite/Catalog of eleven-limit rank three temperaments with Color names]]
 *[[Catalog of rank two temperaments]] (under construction)
 ==Finding the comma from the name and vice versa==