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

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Temperaments can be abbreviated much as colors are: zzT = Zozo, y<sup>3</sup>T = Triyo, g&rgT = Gu & Rugu, Ly#2T = Layobi, and g+z1aT = Gu + zala.

Every ratio can be named either as a standard interval or as a comma/temperament, e.g. 128/125 is both the trigu 2nd and the Trigu comma. The latter is awkward for low-odd-limit ratios: 5/4 would be Yobi and 6/5 would be Gutri. But the former is awkward for high odd-limit ratios, because there will be many 2nds and 3rds and even 4ths, and many of them will be negative.

It's fairly easy to find the color name for a temperament. If the comma is < 90¢, the name can be found directly from the monzo. The color is obvious. The magnitude is the sum of all the exponents except the 2-exponent, divided by 7 and rounded off.

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4thward commas sharpen the 5th and 5thward ones flatten it. This indicates where in the scale tree compatible edos are likely to be. Thus temperaments that start with sa-, e.g. Sayo, tend to be compatible with sharp-5th edos 15, 17, 22, etc. And la- temperaments, e.g. Laru, tend to be compatible with edos 19, 21, 26, etc. Several caveats: central comma names like Triyo don't indicate 4thwd vs. 5thwd. Also, it's possible for a la- comma to be 4thwd if the color depth is >= 5 and the color is over, e.g. Laquinyo = Magic = (-10 -1 5). Sasa- or lala- commas are safe up to color depth 11. Furthermore, Layo, while quite 5thwd, is compatible only with accurate-5th edos like 12, 24, etc.

Color names are easier than conventional temperament names for non-Anglophones. No need to learn to spell and pronounce obscure English words like porcupine, hedgehog and opossum. Color names are based on only those words that a first-year student of English would know, and spelling and pronunciation are greatly simplified.

Color names are easier than [[Tour of Regular Temperaments|conventional temperament names]] for non-Anglophones. No need to learn to spell and pronounce obscure English words like porcupine, hedgehog and opossum. Color names are based on only those words that a first-year student of English would know, and spelling and pronunciation are greatly simplified.

Color names don't use mnemonics that rely on obscure facts, many with an implicit cultural bias, such as:

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* Sensis/Sensus

* Wurschmidt/Worschmidt/Whirrschmidt

Temperaments have the same name as commas, reducing memorization, unlike conventional names, in which:

* The diaschisma creates Srutal

* The semicomma creates Orson

* The gamelisma creates Slendric

* The schisma creates Helmholtz

One last advantage: Color names are very flowing, and fun to say out loud. :)

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 Temperaments can be abbreviated much as colors are: zzT = Zozo, y<sup>3</sup>T = Triyo, g&rgT = Gu & Rugu, Ly#2T = Layobi, and g+z1aT = Gu + zala.
+Every ratio can be named either as a standard interval or as a comma/temperament, e.g. 128/125 is both the trigu 2nd and the Trigu comma. The latter is awkward for low-odd-limit ratios: 5/4 would be Yobi and 6/5 would be Gutri. But the former is awkward for high odd-limit ratios, because there will be many 2nds and 3rds and even 4ths, and many of them will be negative.
 It's fairly easy to find the color name for a temperament. If the comma is < 90¢, the name can be found directly from the monzo. The color is obvious. The magnitude is the sum of all the exponents except the 2-exponent, divided by 7 and rounded off.
@@ Line 118: / Line 120: @@
 thward commas sharpen the 5th and 5thward ones flatten it. This indicates where in the scale tree compatible edos are likely to be. Thus temperaments that start with sa-, e.g. Sayo, tend to be compatible with sharp-5th edos 15, 17, 22, etc. And la- temperaments, e.g. Laru, tend to be compatible with edos 19, 21, 26, etc. Several caveats: central comma names like Triyo don't indicate 4thwd vs. 5thwd. Also, it's possible for a la- comma to be 4thwd if the color depth is >= 5 and the color is over, e.g. Laquinyo = Magic = (-10 -1 5). Sasa- or lala- commas are safe up to color depth 11. Furthermore, Layo, while quite 5thwd, is compatible only with accurate-5th edos like 12, 24, etc.
-Color names are easier than conventional temperament names for non-Anglophones. No need to learn to spell and pronounce obscure English words like porcupine, hedgehog and opossum. Color names are based on only those words that a first-year student of English would know, and spelling and pronunciation are greatly simplified.
+Color names are easier than [[Tour of Regular Temperaments|conventional temperament names]] for non-Anglophones. No need to learn to spell and pronounce obscure English words like porcupine, hedgehog and opossum. Color names are based on only those words that a first-year student of English would know, and spelling and pronunciation are greatly simplified.
 Color names don't use mnemonics that rely on obscure facts, many with an implicit cultural bias, such as:
@@ Line 133: / Line 135: @@
 * Sensis/Sensus
 * Wurschmidt/Worschmidt/Whirrschmidt
+Temperaments have the same name as commas, reducing memorization, unlike conventional names, in which:
+* The diaschisma creates Srutal
+* The semicomma creates Orson
+* The gamelisma creates Slendric
+* The schisma creates Helmholtz
 One last advantage: Color names are very flowing, and fun to say out loud. :)