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

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== Definition ==

[[Color notation]] can name every regular temperament. The name is the same as that of the comma(s) tempered out, but without the degree (unison, 2nd, etc.). For example, Semaphore is the Zozo temperament. The name of the temperament and the comma is always capitalized, to distinguish it from the color. Thus zozo refers to all zozo ratios, whereas Zozo refers to one specific zozo ratio, the zozo 2nd 49/48.

[[Color notation]] can name every regular temperament. The name is the same as that of the comma(s) tempered out, but without the degree (unison, 2nd, etc.). For example, [[Semaphore]] is the Zozo temperament. The name of the temperament and the comma is always capitalized, to distinguish it from the color. Thus zozo refers to all zozo ratios, whereas Zozo refers to one specific zozo ratio, the zozo 2nd 49/48.

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 the smallest in cents of those 7.

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Any comma smaller than 256/243 = 90¢ is guaranteed to be the smallest ratio in its segment, and a -bi or -tri suffix is rarely needed. 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]].

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

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

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

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

# [[Negri]] = Laquadyo, [[Tetracot]] = Saquadyo, [[Vulture]] = Sasa-quadyo, [[Diminished]] = Quadgu.

~~Multipliers~~ like bi-, tri-, etc. can be combined: 6-fold = tribi-, 8-fold = quadbi-, 9-fold = tritri-, 10-fold = quinbi-, 12-fold = quadtri-, 14-fold = sepbi-, 15-fold = quintri-, 16-fold = quadquad-, etc. Higher primes use their color word, but with the suffix '''-e''' ("eh") for exponent:

Exponents like bi-, tri-, etc. can be combined: 6-fold = tribi-, 8-fold = quadbi-, 9-fold = tritri-, 10-fold = quinbi-, 12-fold = quadtri-, 14-fold = sepbi-, 15-fold = quintri-, 16-fold = quadquad-, etc. Higher primes use their color word, but with the suffix '''-e''' ("eh") for exponent:

* 11-fold = '''le-''' (as in "legitimate"), 13-fold = '''the-''' (as in "thesaurus"). 17 = '''se-''', 19 = '''ne-''', 23 = '''twethe-''', 29 = '''twene-''', etc.

Note that sep- means 7-fold, while se- means 17-fold. ~~Multipliers~~ affect all subsequent syllables until the '''-a-''' delimiter occurs: Trizogu = z3g3 and Trizo-agu = z3g. The "a" in la- and sa- acts as a delimiter: Trilayo = L3y, not L3y3, which would be Trila-triyo.

Note that sep- means 7-fold, while se- means 17-fold. Exponents affect all subsequent syllables until the '''-a-''' delimiter occurs: Trizogu = z3g3 and Trizo-agu = z3g. The "a" in la- and sa- acts as a delimiter: Trilayo = L3y, not L3y3, which would be Trila-triyo.

It's theoretically possible for a comma to be larger than an octave and still be tempered out, especially a very complex comma. Such a comma is indicated by the prefix '''co-''', which stands for compound. For example, tempering out (4 -18 11) = 1214¢ makes the Cosa-leyo temperament. There's coco-, trico-, quadco-, etc. ~~Multipliers~~ of co- don't affect the magnitude or color.

It's theoretically possible for a comma to be larger than an octave and still be tempered out, especially a very complex comma. Such a comma is indicated by the prefix '''co-''', which stands for compound. For example, tempering out (4 -18 11) = 1214¢ makes the Cosa-leyo temperament. There's coco-, trico-, quadco-, etc. Exponents of co- don't affect the magnitude or color.

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. Quin is an exception. Quad may optionally be spoken as "kwah", and quin as "kwee". In Spanish and many other languages, "th" would become "tr". See [[Color notation/Translations|Color Notation/Translations]]. ~~Multiplier~~ words like bi or tri are always unaccented. To emphasize the prime limit, the first occurrence of the highest prime is always accented: sasa-'''gu'''gu, bi'''ru'''yo, bi'''zo'''zogu. In longer names, the 1st occurrence of sa/la and/or of lower primes may also be accented: '''sa'''sa-'''gu'''gu, '''zo'''zotri'''gu'''.

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. Quin is an exception. Quad may optionally be spoken as "kwah", and quin as "kwee". In Spanish and many other languages, "th" would become "tr". See [[Color notation/Translations|Color Notation/Translations]]. Exponent words like bi or tri are always unaccented. To emphasize the prime limit, the first occurrence of the highest prime is always accented: sasa-'''gu'''gu, bi'''ru'''yo, bi'''zo'''zogu. In longer names, the 1st occurrence of sa/la and/or of lower primes may also be accented: '''sa'''sa-'''gu'''gu, '''zo'''zotri'''gu'''.

Hyphens are used to make the name easier to parse. There are strict rules for hyphenation, to ensure uniformity.

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* Put a hyphen after the magnitude (after the final la- or sa-)

* Put a hyphen after coco-, trico-, etc.

The hyphen after the magnitude is omitted if it would create a subunit of 1 syllable. Thus Layo, Lalagu and Sagugu are all unhyphenated. ~~Likewise~~, ~~there~~ is ~~no hyphen after co~~-.

* Put a hyphen before and after "seventy", "eighty", etc.

The hyphen after the magnitude is omitted if it would create a subunit of 1 syllable. Thus Layo, Lalagu and Sagugu are all unhyphenated. However, the last rule always holds, e.g. 2272/2187 = 32 * 71 / 37 is Sa-seventy-wo.

Sometimes the smallest ratio in a segment is some other comma raised to some power. 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 the Zogu temperament. Thus there is no Bizogu temperament, although there is a Bizogubi one.

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Multi-comma temperaments are named as a list of commas. For example, 7-limit porcupine is Triyo & Ru. See below for further discussion.

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 (Sawa, Lawa and Lalawa respectively). For example, tempering out the pythagorean comma and 225/224 makes Lalawa & Ruyoyo. Every other wa comma is named after the edo it implies, thus [-30 19> is 19-edo, not the difficult-to-decipher Trila-wabi. Note that ~~some~~ edos can't be implied by a wa comma, such as 10-edo. However 10-edo can be created with a non-wa comma, or by a wa comma plus another, e.g. Sawa & Yoyo.

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 (Sawa, Lawa and Lalawa respectively). For example, tempering out the pythagorean comma and 225/224 makes Lalawa & Ruyoyo. Every other wa comma is named after the edo it implies, thus [-30 19> is 19-edo, not the difficult-to-decipher Trila-wabi. Note that multi-ring edos can't be implied by a wa comma, such as 10-edo. However 10-edo can be created with a non-wa comma, or by a wa comma plus another, e.g. Sawa & Yoyo.

If the commas don't include every prime in the subgroup, some primes are untempered. These primes are added with a plus sign: [[Blackwood]] is Sawa + ya. The 2.3.5.7.11 subgroup with 81/80 tempered out is Gu + zala. Primes 2 and 3 are always assumed to be present in the subgroup, even if the commas don't contain them. They are never added, but are sometimes removed. Prime 3 is removed with the term "Nowa", and prime 2 with "Noca" (ca for clear). Thus 2.5.7 with 50/49 is named Biruyo Nowa.

If the commas don't include every prime in the subgroup, some primes are untempered. These primes are added with a plus sign: [[Blackwood]] is Sawa + ya. The 2.3.5.7.11 subgroup with 81/80 tempered out is Gu + zala. Primes 2 and 3 are always assumed to be present in the subgroup, even if the commas don't contain them. They are never added, but are sometimes removed. Prime 3 is removed with the term "Nowa", and prime 2 with "Noca" (ca for clear). Thus 2.5.7 with 50/49 is named Biruyo Nowa. "Nowaca" removes both 2 and 3.

A non-wa comma can also imply an edo, but that edo isn't part of the temperament's name. Tempering out 128/125 from 2.3.5 makes Trigu, not 3-edo + wa. This avoids a non-wa comma having the same name as a wa comma.

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== Rules for naming remote colors ==

There can be more than one way to name a comma. To avoid duplicate names, there are naming rules.

* Adjacent ~~multipliers~~ are always listed largest first: tribi- not bitri-.

* Adjacent exponents are always listed largest first: tribi- not bitri-.

* Bibi- is never used, use quad- instead.

* Avoid using the -a- delimiter if possible: z4gg = bizozogu, not quadzo-agugu.

Therefore if the color (the name minus the magnitude) starts with ~~a multiplier~~ word, and there's no -a- delimiter, that first ~~multiplier~~ word usually indicates the color GCD and thus the [[Pergen|pergen's]] split(s). e.g. bizozogu = (P8, P5/2, /1). In the list of colors below, an asterisk marks cases where this isn't possible, and the GCD is not obvious.

Therefore if the color (the temperament name minus the magnitude) starts with an exponent word, and there's no -a- delimiter, that first exponent word usually indicates the color GCD and thus the [[Pergen|pergen's]] split(s). e.g. bizozogu = (P8, P5/2, /1). In the list of colors below, an asterisk marks cases where this isn't possible, and the GCD is not obvious.

Bi- is not used with primary colors (zogugu not zobigu, and zozotrigu not bizo-atrigu), unless preceded by another ~~multiplier~~ (tribigu not trigugu). Bi- is always used with compound colors, to indicate the GCD: bizogugu not zozoquadgu.

Bi- is not used with primary colors (zogugu not zobigu, and zozotrigu not bizo-atrigu), unless preceded by another exponent (tribigu not trigugu). However bi- is always used with primary colors of two or more syllables (bitwetho not twethotwetho). Bi- is always used with compound colors, to indicate the GCD: bizogugu not zozoquadgu.

There follows examples of remote colors, for illustration. These examples don't all correspond to musically useful temperaments.

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 == Definition ==
-[[Color notation]] can name every regular temperament. The name is the same as that of the comma(s) tempered out, but without the degree (unison, 2nd, etc.). For example, Semaphore is the Zozo temperament. The name of the temperament and the comma is always capitalized, to distinguish it from the color. Thus zozo refers to all zozo ratios, whereas Zozo refers to one specific zozo ratio, the zozo 2nd 49/48.
+[[Color notation]] can name every regular temperament. The name is the same as that of the comma(s) tempered out, but without the degree (unison, 2nd, etc.). For example, [[Semaphore]] is the Zozo temperament. The name of the temperament and the comma is always capitalized, to distinguish it from the color. Thus zozo refers to all zozo ratios, whereas Zozo refers to one specific zozo ratio, the zozo 2nd 49/48.
 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 the smallest in cents of those 7.
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 Any comma smaller than 256/243 = 90¢ is guaranteed to be the smallest ratio in its segment, and a -bi or -tri suffix is rarely needed. 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]].
 # [[Schismatic]] = Layo, [[Mavila]] = Layobi, [[Superpyth]] = Sayo, [[Meantone]] = Gu, [[Father]] = Gubi.
-# [[Dicot]] = Yoyo, [[Immunity family|Immunity]] = Sasa-yoyo, [[Bug]] = Gugu, [[Diaschismic]] = Sagugu = sggT, [[Beatles]] = Sasa-gugu.
+# [[Dicot]] = Yoyo, [[Immunity family|Immunity]] = Sasa-yoyo, [[Bug]] = Gugu, [[Diaschismic]] = Sagugu, [[Beatles]] = Sasa-gugu.
 # [[Porcupine]] = Triyo, [[Augmented]] = Trigu, [[Laconic family|Laconic]] = Latrigu, [[Misty comma|Misty]] = Sasa-trigu.
 # [[Negri]] = Laquadyo, [[Tetracot]] = Saquadyo, [[Vulture]] = Sasa-quadyo, [[Diminished]] = Quadgu.
-Multipliers like bi-, tri-, etc. can be combined: 6-fold = tribi-, 8-fold = quadbi-, 9-fold = tritri-, 10-fold = quinbi-, 12-fold = quadtri-, 14-fold = sepbi-, 15-fold = quintri-, 16-fold = quadquad-, etc. Higher primes use their color word, but with the suffix '''-e''' ("eh") for exponent:
+Exponents like bi-, tri-, etc. can be combined: 6-fold = tribi-, 8-fold = quadbi-, 9-fold = tritri-, 10-fold = quinbi-, 12-fold = quadtri-, 14-fold = sepbi-, 15-fold = quintri-, 16-fold = quadquad-, etc. Higher primes use their color word, but with the suffix '''-e''' ("eh") for exponent:
 * 11-fold = '''le-''' (as in "<u>le</u>gitimate"), 13-fold = '''the-''' (as in "<u>the</u>saurus"). 17 = '''se-''', 19 = '''ne-''', 23 = '''twethe-''', 29 = '''twene-''', etc.
-Note that sep- means 7-fold, while se- means 17-fold. Multipliers affect all subsequent syllables until the '''-a-''' delimiter occurs: Trizogu = z<sup>3</sup>g<sup>3</sup> and Trizo-agu = z<sup>3</sup>g. The "a" in la- and sa- acts as a delimiter: Trilayo = L<sup>3</sup>y, not L<sup>3</sup>y<sup>3</sup>, which would be Trila-triyo.
+Note that <u>sep- means 7-fold, while se- means 17-fold</u>. Exponents affect all subsequent syllables until the '''-a-''' delimiter occurs: Trizogu = z<sup>3</sup>g<sup>3</sup> and Trizo-agu = z<sup>3</sup>g. The "a" in la- and sa- acts as a delimiter: Trilayo = L<sup>3</sup>y, not L<sup>3</sup>y<sup>3</sup>, which would be Trila-triyo.
-It's theoretically possible for a comma to be larger than an octave and still be tempered out, especially a very complex comma. Such a comma is indicated by the prefix '''co-''', which stands for compound. For example, tempering out (4 -18 11) = 1214¢ makes the Cosa-leyo temperament. There's coco-, trico-, quadco-, etc. Multipliers of co- don't affect the magnitude or color.
+It's theoretically possible for a comma to be larger than an octave and still be tempered out, especially a very complex comma. Such a comma is indicated by the prefix '''co-''', which stands for compound. For example, tempering out (4 -18 11) = 1214¢ makes the Cosa-leyo temperament. There's coco-, trico-, quadco-, etc. Exponents of co- don't affect the magnitude or color.
-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. Quin is an exception. Quad may optionally be spoken as "kwah", and quin as "kwee". In Spanish and many other languages, "th" would become "tr". See [[Color notation/Translations|Color Notation/Translations]]. Multiplier words like bi or tri are always unaccented. To emphasize the prime limit, the first occurrence of the highest prime is always accented: sasa-'''<u>gu</u>'''gu, bi'''r<u>u</u>'''yo, bi'''<u>zo</u>'''zogu. In longer names, the 1st occurrence of sa/la and/or of lower primes may also be accented: '''sa'''sa-'''gu'''gu, '''zo'''zotri'''gu'''.
+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. Quin is an exception. Quad may optionally be spoken as "kwah", and quin as "kwee". In Spanish and many other languages, "th" would become "tr". See [[Color notation/Translations|Color Notation/Translations]]. Exponent words like bi or tri are always unaccented. To emphasize the prime limit, the first occurrence of the highest prime is always accented: sasa-'''<u>gu</u>'''gu, bi'''r<u>u</u>'''yo, bi'''<u>zo</u>'''zogu. In longer names, the 1st occurrence of sa/la and/or of lower primes may also be accented: '''sa'''sa-'''gu'''gu, '''zo'''zotri'''gu'''.
 Hyphens are used to make the name easier to parse. There are strict rules for hyphenation, to ensure uniformity.
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 * Put a hyphen after the magnitude (after the final la- or sa-)
 * Put a hyphen after coco-, trico-, etc.
-The hyphen after the magnitude is omitted if it would create a subunit of 1 syllable. Thus Layo, Lalagu and Sagugu are all unhyphenated. Likewise, there is no hyphen after co-.
+* Put a hyphen before and after "seventy", "eighty", etc.
+The hyphen after the magnitude is omitted if it would create a subunit of 1 syllable. Thus Layo, Lalagu and Sagugu are all unhyphenated. However, the last rule always holds, e.g. 2272/2187 = 32 * 71 / 3<sup>7</sup> is Sa-seventy-wo.
 Sometimes the smallest ratio in a segment is some other comma raised to some power. 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 the Zogu temperament. Thus there is no Bizogu temperament, although there is a Bizogubi one.
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 Multi-comma temperaments are named as a list of commas. For example, 7-limit porcupine is Triyo & Ru. See below for further discussion.
-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 (Sawa, Lawa and Lalawa respectively). For example, tempering out the pythagorean comma and 225/224 makes Lalawa & Ruyoyo. Every other wa comma is named after the edo it implies, thus [-30 19> is 19-edo, not the difficult-to-decipher Trila-wabi. Note that some edos can't be implied by a wa comma, such as 10-edo. However 10-edo can be created with a non-wa comma, or by a wa comma plus another, e.g. Sawa & Yoyo.
+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 (Sawa, Lawa and Lalawa respectively). For example, tempering out the pythagorean comma and 225/224 makes Lalawa & Ruyoyo. Every other wa comma is named after the edo it implies, thus [-30 19> is 19-edo, not the difficult-to-decipher Trila-wabi. Note that multi-ring edos can't be implied by a wa comma, such as 10-edo. However 10-edo can be created with a non-wa comma, or by a wa comma plus another, e.g. Sawa & Yoyo.
-If the commas don't include every prime in the subgroup, some primes are untempered. These primes are added with a plus sign: [[Blackwood]] is Sawa + ya. The 2.3.5.7.11 subgroup with 81/80 tempered out is Gu + zala. Primes 2 and 3 are always assumed to be present in the subgroup, even if the commas don't contain them. They are never added, but are sometimes removed. Prime 3 is removed with the term "Nowa", and prime 2 with "Noca" (ca for clear). Thus 2.5.7 with 50/49 is named Biruyo Nowa.
+If the commas don't include every prime in the subgroup, some primes are untempered. These primes are added with a plus sign: [[Blackwood]] is Sawa + ya. The 2.3.5.7.11 subgroup with 81/80 tempered out is Gu + zala. Primes 2 and 3 are always assumed to be present in the subgroup, even if the commas don't contain them. They are never added, but are sometimes removed. Prime 3 is removed with the term "Nowa", and prime 2 with "Noca" (ca for clear). Thus 2.5.7 with 50/49 is named Biruyo Nowa. "Nowaca" removes both 2 and 3.
 A non-wa comma can also imply an edo, but that edo isn't part of the temperament's name. Tempering out 128/125 from 2.3.5 makes Trigu, not 3-edo + wa. This avoids a non-wa comma having the same name as a wa comma.
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 == Rules for naming remote colors ==
 There can be more than one way to name a comma. To avoid duplicate names, there are naming rules.
-* Adjacent multipliers are always listed largest first: tribi- not bitri-.
+* Adjacent exponents are always listed largest first: tribi- not bitri-.
 * Bibi- is never used, use quad- instead.
 * Avoid using the -a- delimiter if possible: z<sup>4</sup>gg = bizozogu, not quadzo-agugu.
-Therefore if the color (the name minus the magnitude) starts with a multiplier word, and there's no -a- delimiter, that first multiplier word usually indicates the color GCD and thus the [[Pergen|pergen's]] split(s). e.g. bizozogu = (P8, P5/2, /1). In the list of colors below, an asterisk marks cases where this isn't possible, and the GCD is not obvious.
+Therefore if the color (the temperament name minus the magnitude) starts with an exponent word, and there's no -a- delimiter, that first exponent word usually indicates the color GCD and thus the [[Pergen|pergen's]] split(s). e.g. bizozogu = (P8, P5/2, /1). In the list of colors below, an asterisk marks cases where this isn't possible, and the GCD is not obvious.
-Bi- is not used with primary colors (zogugu not zobigu, and zozotrigu not bizo-atrigu), unless preceded by another multiplier (tribigu not trigugu). Bi- is always used with compound colors, to indicate the GCD: bizogugu not zozoquadgu.
+Bi- is not used with primary colors (zogugu not zobigu, and zozotrigu not bizo-atrigu), unless preceded by another exponent (tribigu not trigugu). However bi- is always used with primary colors of two or more syllables (bitwetho not twethotwetho). Bi- is always used with compound colors, to indicate the GCD: bizogugu not zozoquadgu.
 There follows examples of remote colors, for illustration. These examples don't all correspond to musically useful temperaments.