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 using an alternate format designed for commas. This format omits the degree (unison, 2nd, etc.). For example, [[Semaphore]] tempers out the zozo 2nd and is called the Zozo temperament. The name of the comma and the temperament is always capitalized, to distinguish it from the color. Thus zozo refers to all zozo ratios, whereas Zozo refers to one specific zozo ratio, 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.

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.

~~Words like large, small, double, etc. are abbreviated, to make the names a reasonable length.~~

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]].

* Double = '''bi-''' ("bee"), triple = '''tri-''' ("tree"), quadruple = '''quad-''', quintuple = '''quin-''', septuple = '''sep-'''

* '''-bi''' or '''-tri''' at the end of a name indicates that the comma is the 2nd or 3rd largest ratio in that segment, e.g. [[Mavila]] = Layobi

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

~~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, [[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.

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:

Exponent syllables like bi or tri are always unaccented. To emphasize the prime limit, the first occurrence of the highest prime is always accented: 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'''.

* 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. 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. 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]]. 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.~~

* Put a hyphen before every -a- delimiter

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

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

* 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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Tempering out 128/125 from 2.3.5 makes Trigu. Since 128/125 is a two-prime comma, it implies an edo, and Trigu can unofficially be thought of as 3-edo plus wa.

Temperaments ~~can be~~ abbreviated ~~using~~ "T": Zozo = zzT, Triyo = y3T, 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.

Temperaments are abbreviated with "T": Zozo = zzT, Triyo = y3T, 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.

More examples of 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 using an alternate format designed for commas. This format omits the degree (unison, 2nd, etc.). For example, [[Semaphore]] tempers out the zozo 2nd and is called the Zozo temperament. The name of the comma and the temperament is always capitalized, to distinguish it from the color. Thus zozo refers to all zozo ratios, whereas Zozo refers to one specific zozo ratio, 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.
+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.
-Words like large, small, double, etc. are abbreviated, to make the names a reasonable length.
+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]].
-* Double = '''bi-''' ("bee"), triple = '''tri-''' ("tree"), quadruple = '''quad-''', quintuple = '''quin-''', septuple = '''sep-'''
-* '''-bi''' or '''-tri''' at the end of a name indicates that the comma is the 2nd or 3rd largest ratio in that segment, e.g. [[Mavila]] = Layobi
-* Large = '''la-''', small = '''sa-''', double large = lala-, triple small = trisa-, etc.
-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, [[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.
-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:
+Exponent syllables like bi or tri are always unaccented. To emphasize the prime limit, the first occurrence of the highest prime is always accented: 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'''.
-* 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 <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. 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]]. 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.
-* Put a hyphen before every -a- delimiter
-* Put a hyphen after the magnitude (after the final la- or sa-)
-* Put a hyphen after coco-, trico-, etc.
-* 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.
@@ Line 42: / Line 25: @@
 Tempering out 128/125 from 2.3.5 makes Trigu. Since 128/125 is a two-prime comma, it implies an edo, and Trigu can unofficially be thought of as 3-edo plus wa.
-Temperaments can be abbreviated using "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.
+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.
 More examples of temperaments: