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

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[[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.). The color defines a lattice row and the magnitude (large, small, etc.) defines a '''segment''' of that row. Each segment contains 7 ratios. The comma that is tempered out is assumed to be the smallest in cents of those 7~~, excluding any~~ ratio ~~that~~ is a multiple of another comma. For example, the smallest ratio in the central segment of the zozogugu row is 441/440. But since this is (21/20)2, tempering it out would simply result in zgT. Thus ~~zzggT refers to tempering out the next largest ratio, 784/675 = 259¢~~.

[[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.). The color defines a lattice row and the magnitude (large, small, etc.) defines a '''segment''' of that row. Each segment contains 7 ratios. The comma that is tempered out is assumed to be the smallest in cents of those 7. Sometimes the smallest ratio is a multiple of another comma. For example, the smallest ratio in the central segment of the zozogugu row is 441/440. But since this is (21/20)2, tempering it out would simply result in zgT. Thus there is no zozogugu temperament.

If the comma is the 2nd largest ~~valid~~ ratio in the row segment, the temperament name ends with "2". For example, [[Schismatic]] is LyT and [[Mavila]] is LyT2. Likewise, LyT3 would temper out the 3rd largest ratio. Any comma ≤ 90¢ is guaranteed to be the smallest ratio in its segment.

If the comma is the 2nd largest ratio in the row segment, the temperament name ends with "2". For example, [[Schismatic]] is LyT and [[Mavila]] is LyT2. Likewise, LyT3 would temper out the 3rd largest ratio. Any comma ≤ 90¢ is guaranteed to be the smallest ratio in its segment.

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

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

* -bi, -tri, etc. at the end of a name means 2nd/3rd/etc. largest ratio, e.g. Schismatic = Layo and Mavila = Layobi

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

Some 5-limit examples, sorted by color depth. Many more examples can be found on the [[Comma|Commas]] page.

# [[Schismatic]] = Layo = LyT, [[Mavila]] = ~~Layo-two~~ = LyT2, [[Superpyth]] = Sayo = syT. [[Meantone]] = Gu = gT, [[Father]] = ~~Gu-two~~ = gT2.

# [[Schismatic]] = Layo = LyT, [[Mavila]] = Layobi = LyT2, [[Superpyth]] = Sayo = syT. [[Meantone]] = Gu = gT, [[Father]] = Gubi = gT2.

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

# [[Porcupine]] = Triyo = y3T. [[Augmented]] = Trigu = g3T, [[Laconic family|Laconic]] = Latrigu = Lg3T, [[Misty comma|Misty]] = Sasa-trigu = ssg3T.

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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''' for exponent:

* 11-fold = '''le-''' ("leh"), 13-fold = '''the-''' (unvoiced "th"). 17 = '''se-''', 19 = '''ne-''', 23 = '''twenty-the-''', 29 = '''twenty-ne-''', etc.

Even with these abbreviations, temperament names can get quite long~~. To make them quicker to say, and to make the words easier for non-Anglophones, "bee" and "tree" are preferred over "bye" and "try"~~. If the comma's ratio has N digits, the temperament name will usually have N, N-1, N+1 or occasionally N+2 syllables.

Even with these abbreviations, temperament names can get quite long. If the comma's ratio has N digits, the temperament name will usually have N, N-1, N+1 or occasionally N+2 syllables.

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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The temperament name indicates the prime subgroup and the rank of the temperament. For example, ryyT ([[Marvel]]) is rank-3 because it has 2 explicit colors ru and yo and 2 implicit colors wa and clear, and 4 colors minus 1 comma = rank-3. Edos count as commas, but plusses don't. Both 12edo&ryyT and 5edo+yT are rank-2. Primes 2 and 3 are assumed present in the temperament even if they are not present in the comma. Biruyo is rank-3 and biruyo nowa is rank-2.

There are ~~two~~ obvious ways to name multi-comma temperaments. The odd name minimizes the [[Odd limit|double odd limit]] of the comma set~~, and the prime~~ name minimizes the number and size of the primes used by each comma. The odd name for 7-limit [[Pajara]] is rryy&rT, and the prime name is sgg&rT. Often the ~~two~~ names are identical, e.g. y3&rT. The odd name is often shorter, and usually indicates commas more likely to be pumped. The ~~prime~~ name shows relationships between bicolored rank-2 temperaments better. The question of which name to use is not yet fully resolved.

There are three obvious ways to name 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. Thus the 1st comma is ya, the 2nd za, the 3rd ila, etc. The prime-limit name minimizes the prime-limit for each comma, and for each prime limit uses the comma of least double odd limit. Thus the 1st comma is ya, the 2nd yaza, the 3rd yazala, etc. The odd name for 7-limit [[Pajara]] is rryy&rT, and the prime-subgroup name is sgg&rT, and the prime-limit 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.

== Rules for naming remote colors and extreme magnitudes ==

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Gugu is generally preferred over bigu (zogugu not zobigu). But bizo is preferred over zozo sometimes to indicate the GCD, e.g. bizogugu not zozoquadgu. Likewise, tribigu is preferred over trigugu, as is quadbigu over quadgugu, etc.

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

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

== Bicolored examples ==

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-[[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.). The color defines a lattice row and the magnitude (large, small, etc.) defines a '''segment''' of that row. Each segment contains 7 ratios. The comma that is tempered out is assumed to be the smallest in cents of those 7, excluding any ratio that is a multiple of another comma. For example, the smallest ratio in the central segment of the zozogugu row is 441/440. But since this is (21/20)<sup>2</sup>, tempering it out would simply result in zgT. Thus zzggT refers to tempering out the next largest ratio, 784/675 = 259¢.
+[[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.). The color defines a lattice row and the magnitude (large, small, etc.) defines a '''segment''' of that row. Each segment contains 7 ratios. The comma that is tempered out is assumed to be the smallest in cents of those 7. Sometimes the smallest ratio is a multiple of another comma. For example, the smallest ratio in the central segment of the zozogugu row is 441/440. But since this is (21/20)<sup>2</sup>, tempering it out would simply result in zgT. Thus there is no zozogugu temperament.
-If the comma is the 2nd largest valid ratio in the row segment, the temperament name ends with "2". For example, [[Schismatic]] is LyT and [[Mavila]] is LyT2. Likewise, LyT3 would temper out the 3rd largest ratio. Any comma ≤ 90¢ is guaranteed to be the smallest ratio in its segment.
+If the comma is the 2nd largest ratio in the row segment, the temperament name ends with "2". For example, [[Schismatic]] is LyT and [[Mavila]] is LyT2. Likewise, LyT3 would temper out the 3rd largest ratio. Any comma ≤ 90¢ is guaranteed to be the smallest ratio in its segment.
 Words like large, small, double, etc. are abbreviated, to make the names a reasonable length.
 * Double = '''bi-''' ("bee"), triple = '''tri-''' ("tree"), quadruple = '''quad-''', quintuple = '''quin-''', septuple = '''sep-'''
+* -bi, -tri, etc. at the end of a name means 2nd/3rd/etc. largest ratio, e.g. Schismatic = Layo and Mavila = Layobi
 * Large = '''la-''', small = '''sa-''', double large = lala-, triple small = trisa-, etc.
 Some 5-limit examples, sorted by color depth. Many more examples can be found on the [[Comma|Commas]] page.
-# [[Schismatic]] = Layo = LyT, [[Mavila]] = Layo-two = LyT2, [[Superpyth]] = Sayo = syT. [[Meantone]] = Gu = gT, [[Father]] = Gu-two = gT2.
+# [[Schismatic]] = Layo = LyT, [[Mavila]] = Layobi = LyT2, [[Superpyth]] = Sayo = syT. [[Meantone]] = Gu = gT, [[Father]] = Gubi = gT2.
 # [[Dicot]] = Yoyo = yyT, [[Immunity family|Immunity]] = Sasa-yoyo = ssyyT.  [[Bug]] = Gugu = ggT, [[Diaschismic]] = Sagugu = sggT, [[Beatles]] = Sasa-gugu = ssggT.
 # [[Porcupine]] = Triyo = y<sup>3</sup>T. [[Augmented]] = Trigu = g<sup>3</sup>T, [[Laconic family|Laconic]] = Latrigu = Lg<sup>3</sup>T, [[Misty comma|Misty]] = Sasa-trigu = ssg<sup>3</sup>T.
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 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''' for exponent:
 * 11-fold = '''le-''' ("leh"), 13-fold = '''the-''' (unvoiced "th"). 17 = '''se-''', 19 = '''ne-''', 23 = '''twenty-the-''', 29 = '''twenty-ne-''', etc.
-Even with these abbreviations, temperament names can get quite long. To make them quicker to say, and to make the words easier for non-Anglophones, "bee" and "tree" are preferred over "bye" and "try". If the comma's ratio has N digits, the temperament name will usually have N, N-1, N+1 or occasionally N+2 syllables.
+Even with these abbreviations, temperament names can get quite long. If the comma's ratio has N digits, the temperament name will usually have N, N-1, N+1 or occasionally N+2 syllables.
 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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 The temperament name indicates the prime subgroup and the rank of the temperament. For example, ryyT ([[Marvel]]) is rank-3 because it has 2 explicit colors ru and yo and 2 implicit colors wa and clear, and 4 colors minus 1 comma = rank-3. <u>Edos count as commas, but plusses don't</u>. Both 12edo&ryyT and 5edo+yT are rank-2. Primes 2 and 3 are assumed present in the temperament even if they are not present in the comma. Biruyo is rank-3 and biruyo nowa is rank-2.
-There are two obvious ways to name multi-comma temperaments. The odd name minimizes the [[Odd limit|double odd limit]] of the comma set, and the prime name minimizes the number and size of the primes used by each comma. The odd name for 7-limit [[Pajara]] is rryy&rT, and the prime name is sgg&rT. Often the two 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 prime name shows relationships between bicolored rank-2 temperaments better. The question of which name to use is not yet fully resolved.
+There are three obvious ways to name 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. Thus the 1st comma is ya, the 2nd za, the 3rd ila, etc. The prime-limit name minimizes the prime-limit for each comma, and for each prime limit uses the comma of least double odd limit. Thus the 1st comma is ya, the 2nd yaza, the 3rd yazala, etc. The odd name for 7-limit [[Pajara]] is rryy&rT, and the prime-subgroup name is sgg&rT, and the prime-limit 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.
 == Rules for naming remote colors and extreme magnitudes ==
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 Gugu is generally preferred over bigu (zogugu not zobigu). But bizo is preferred over zozo sometimes to indicate the GCD, e.g. bizogugu not zozoquadgu. Likewise, tribigu is preferred over trigugu, as is quadbigu over quadgugu, etc.
-There follows examples of remote colors, for illustration. These examples don't all correspond to musically useful temperaments!
+There follows examples of remote colors, for illustration. These examples don't all correspond to actual temperaments.
 == Bicolored examples ==