Kite's color notation: Difference between revisions

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Yo and ru intervals tend to be major, and gu and zo ones tend to be minor. But interval quality is redundant (if a third is yo, it must be major), it's not unique (there are other major thirds available), and quality isn't used with color names (see "Higher Primes" below for why). Instead of augmented and diminished, remote intervals are '''large''' (fifthward) and '''small''' (fourthward), abbreviated L and s. '''Central''', the default, means neither large nor small. The '''magnitude''' is the sum all the monzo exponents except the first one, divided by 7, and rounded off. 0 = central, 1 = large, 2 = double large, etc. 81/64 = Lw3, 135/128 = Ly1. Unfortunately, magnitudes do not add up predictably like colors and degrees do: w2 + w2 = Lw3.

Colors can be doubled or tripled: 25/16 = yoyo 5th = yy5 and 128/125 = triple gu 2nd = g32. Double and triple are often abbreviated '''bi-''' and '''tri-''', especially in temperament names such as biruyo and trigu. Quadruple and quintuple are abbreviated '''quad-''' and '''quin-''', as in quadyo or quinlarge. ~~Higher multipliers: 6 = tribi-~~, ~~7 = '''sep-'''~~, ~~8 =~~ ~~quabi-, 9 = tritri- and 10 = quinbi-.~~

Colors can be doubled or tripled: 25/16 = yoyo 5th = yy5 and 128/125 = triple gu 2nd = g32. Double and triple are often abbreviated '''bi-''' and '''tri-''', especially in temperament names such as biruyo and trigu. Quadruple and quintuple are abbreviated '''quad-''' and '''quin-''', as in quadyo or quinlarge. For sextuple, etc., see "Temperament Names" below.

[[File:Lattice41a.png|833x833px]]

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Temperaments are named after the color of the comma(s) they temper out. [[Meantone]] = the gu temperament = gT. [[Porcupine]] = triple yo temperament = y3T. [[Porcupine family|7-limit Porcupine]] = triple yo and ru = y3&rT. Each variety of porcupine has a different name, thus color names provide more information than standard temperament names. Both porcupines have the same [[pergen]], (P8, P4/3), thus pergens group together similar temperaments.

The magnitude is part of the name: [[Schismatic]] is LyT and [[Diaschismic]] is sggT. The degree is ~~too~~, ~~but only if the comma is not the smallest of the 7 ratios of that magnitude and color: [[Mavila]] is Ly1T~~ and ~~[[Father family|Father]] is g2T. The degree~~ is ~~never needed~~ if the comma is ≤ 90¢.

The magnitude is part of the name: [[Schismatic]] is LyT and [[Diaschismic]] is sggT. The degree is usually omitted, and is always omitted if the comma is ≤ 90¢.

~~For the sake of brevity, many~~ words are abbreviated. Large becomes '''la''' and small becomes '''sa'''. Double, triple, etc, become bi-, tri-, quad- and quin-. Higher primes use their color word, but with the suffix '''-e''' for exponent. Thus 11-fold becomes '''le-''' ("leh"), 13-fold becomes '''the-''' (unvoiced "th"),17 = '''se-''' (not to be confused with sep- ~~for 7~~), 19 = '''ne-''', 23 = '''twenty-the-''', etc. See the [[Comma]] ~~page~~ for examples.

Many words are abbreviated. Large becomes '''la''' and small becomes '''sa'''. Double, triple, etc, become bi-, tri-, quad- and quin-. Higher multipliers: 6 = tribi-, 7 = '''sep-''', 8 = quabi-, 9 = tritri- and 10 = quinbi-. Higher primes use their color word, but with the suffix '''-e''' for exponent. Thus 11-fold becomes '''le-''' ("leh"), 13-fold becomes '''the-''' (unvoiced "th"),17 = '''se-''' (not to be confused with sep-), 19 = '''ne-''', 23 = '''twenty-the-''', etc. See the [[Comma]] lists for examples.

If the comma is wa, an edo is implied. The temperament is named after the edo, not the wa comma. 2.3.5.7 and the pyth comma and 225/224 is 12edo&ryyT. If the comma(s) don't include every prime in the subgroup, some primes are untempered. These primes are added with '''plus''': [[Blackwood]] is 5edo+yT = 5-edo plus ya. The 2.3.5.7.11 subgroup with 81/80 tempered out is g+z1aT = gu plus zala.

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.

Temperament names are further explained here: [[Color notation/Temperament Names]].

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Rank-2 temperaments can be notated with ups and downs as well. Plain and mid are also used in this context. Some temperaments require an additional pair of virtual colors, '''lifts''' and '''drops''' (/ and \). Notes are named lift C = /C, downdrop F sharp = v\F#, etc. Intervals are named drop 4th = \4, uplift major 3rd = ^/M3, etc. Plain means neither up nor down nor lifted nor dropped. There may be upmid or liftmid intervals. Chords are named C-up lift-seven = C^,/7 = C ^E G /Bb, C uplift-seven = C^/7 = C ^/E G ^/Bb, etc. See [[Pergen|pergens]].

==Translations==

:''For translations of color notation terms into other languages, see [[Color notation/Translations]].'' [[Category:color_notation]] [[Category:ji]] [[Category:notation]]

@@ Line 158: / Line 158: @@
 Yo and ru intervals tend to be major, and gu and zo ones tend to be minor. But interval quality is redundant (if a third is yo, it must be major), it's not unique (there are other major thirds available), and quality isn't used with color names (see "Higher Primes" below for why). Instead of augmented and diminished, remote intervals are '''large''' (fifthward) and '''small''' (fourthward), abbreviated L and s. '''Central''', the default, means neither large nor small. The '''magnitude''' is the sum all the monzo exponents except the first one, divided by 7, and rounded off. 0 = central, 1 = large, 2 = double large, etc. 81/64 = Lw3, 135/128 = Ly1. Unfortunately, magnitudes do not add up predictably like colors and degrees do: w2 + w2 = Lw3.
-Colors can be doubled or tripled: 25/16 = yoyo 5th = yy5 and 128/125 = triple gu 2nd = g<sup>3</sup>2. Double and triple are often abbreviated '''bi-''' and '''tri-''', especially in temperament names such as biruyo and trigu. Quadruple and quintuple are abbreviated '''quad-''' and '''quin-''', as in quadyo or quinlarge. Higher multipliers: 6 = tribi-, 7 = '''sep-''', 8 =  quabi-, 9 = tritri- and 10 = quinbi-.
+Colors can be doubled or tripled: 25/16 = yoyo 5th = yy5 and 128/125 = triple gu 2nd = g<sup>3</sup>2. Double and triple are often abbreviated '''bi-''' and '''tri-''', especially in temperament names such as biruyo and trigu. Quadruple and quintuple are abbreviated '''quad-''' and '''quin-''', as in quadyo or quinlarge. For sextuple, etc., see "Temperament Names" below.
 [[File:Lattice41a.png|833x833px]]
@@ Line 261: / Line 261: @@
 Temperaments are named after the color of the comma(s) they temper out. [[Meantone]] = the gu temperament = gT. [[Porcupine]] = triple yo temperament = y<sup>3</sup>T. [[Porcupine family|7-limit Porcupine]] = triple yo and ru = y<sup>3</sup>&rT. Each variety of porcupine has a different name, thus color names provide more information than standard temperament names. Both porcupines have the same [[pergen]], (P8, P4/3), thus pergens group together similar temperaments.
-The magnitude is part of the name: [[Schismatic]] is LyT and [[Diaschismic]] is sggT. The degree is too, but only if the comma is not the smallest of the 7 ratios of that magnitude and color: [[Mavila]] is Ly1T and [[Father family|Father]] is g2T. The degree is never needed if the comma is ≤ 90¢.
+The magnitude is part of the name: [[Schismatic]] is LyT and [[Diaschismic]] is sggT. The degree is usually omitted, and is always omitted if the comma is ≤ 90¢.
-For the sake of brevity, many words are abbreviated. Large becomes '''la''' and small becomes '''sa'''. Double, triple, etc, become bi-, tri-, quad- and quin-. Higher primes use their color word, but with the suffix '''-e''' for exponent. Thus 11-fold becomes '''le-''' ("leh"), 13-fold becomes '''the-''' (unvoiced "th"),17 = '''se-''' (not to be confused with sep- for 7), 19 = '''ne-''', 23 = '''twenty-the-''', etc. See the [[Comma]] page for examples.
+Many words are abbreviated. Large becomes '''la''' and small becomes '''sa'''. Double, triple, etc, become bi-, tri-, quad- and quin-. Higher multipliers: 6 = tribi-, 7 = '''sep-''', 8 =  quabi-, 9 = tritri- and 10 = quinbi-. Higher primes use their color word, but with the suffix '''-e''' for exponent. Thus 11-fold becomes '''le-''' ("leh"), 13-fold becomes '''the-''' (unvoiced "th"),17 = '''se-''' (not to be confused with sep-), 19 = '''ne-''', 23 = '''twenty-the-''', etc. See the [[Comma]] lists for examples.
 If the comma is wa, an edo is implied. The temperament is named after the edo, not the wa comma. 2.3.5.7 and the pyth comma and 225/224 is 12edo&ryyT. If the comma(s) don't include every prime in the subgroup, some primes are untempered. These primes are added with '''plus''': [[Blackwood]] is 5edo+yT = 5-edo plus ya. The 2.3.5.7.11 subgroup with 81/80 tempered out is g+z1aT = gu plus zala.
 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.
 Temperament names are further explained here: [[Color notation/Temperament Names]].
@@ Line 282: / Line 280: @@
 Rank-2 temperaments can be notated with ups and downs as well. Plain and mid are also used in this context. Some temperaments require an additional pair of virtual colors, '''lifts''' and '''drops''' (/ and \). Notes are named lift C = /C, downdrop F sharp = v\F#, etc. Intervals are named drop 4th = \4, uplift major 3rd = ^/M3, etc. Plain means neither up nor down nor lifted nor dropped. There may be upmid or liftmid intervals. Chords are named C-up lift-seven = C^,/7 = C ^E G /Bb, C uplift-seven = C^/7 = C ^/E G ^/Bb, etc. See [[Pergen|pergens]].
 ==Translations==
-:''For translations of color notation terms into other languages, see [[Color notation/Translations]].''           [[Category:color_notation]]           [[Category:ji]]           [[Category:notation]]
+:''For translations of color notation terms into other languages, see [[Color notation/Translations]].''            [[Category:color_notation]]            [[Category:ji]]            [[Category:notation]]