Kite's color notation: Difference between revisions
No edit summary |
updated temperament names |
||
| 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. | 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. Higher multipliers: 6 = tribi-, 7 = '''sep-''', 8 = quabi-, 9 = tritri- and 10 = quinbi-. | ||
[[File:Lattice41a.png|833x833px]] | [[File:Lattice41a.png|833x833px]] | ||
Degrees can be negative: 50/49 = double ruyo negative 2nd = rryy-2. It's a negative 2nd because it goes up in pitch but down the scale: zg5 + rryy-2 = ry4. Negative is different than descending, from ry4 to zg5 is a descending negative 2nd. There are also diminished unisons, which raise the pitch but diminish the quality. For example, if 11/8 is a P4, two of them are a m7 of 121/64 = 1102¢. Going from a yo M7 = 1088¢ up to this m7 raises the pitch, and 121/120 is a | Degrees can be negative: 50/49 = double ruyo negative 2nd = rryy-2. It's a negative 2nd because it goes up in pitch but down the scale: zg5 + rryy-2 = ry4. Negative is different than descending, from ry4 to zg5 is a descending negative 2nd. There are also diminished unisons, which raise the pitch but diminish the quality. For example, if 11/8 is a P4, two of them are a m7 of 121/64 = 1102¢. Going from a yo M7 = 1088¢ up to this m7 raises the pitch, and 121/120 is a dim unison. | ||
The double-large wa negative 2nd (LLw-2, the pyth comma) is simply called the wa comma. 3-limit commas such as L<sup>3</sup>w-2 = (-30, 19) can be abbreviated as w-19, the wa-19 comma. | |||
'''Wide''', abbreviated '''W''', means widened by an octave. 15/4 = Wy7 = wide yo 7th. 5/1 = WWy3 = double-wide yo 3rd. | '''Wide''', abbreviated '''W''', means widened by an octave. 15/4 = Wy7 = wide yo 7th. 5/1 = WWy3 = double-wide yo 3rd. More examples [[Gallery of just intervals#Intervals larger than an octave|here]]. | ||
== Note Names == | == Note Names == | ||
| Line 181: | Line 181: | ||
Colors for primes greater than 7 are named after the number itself, using the prefix '''i-''' for disambiguation as needed: | Colors for primes greater than 7 are named after the number itself, using the prefix '''i-''' for disambiguation as needed: | ||
'''Lo''' = 11-over, '''lu''' = 11-under, and '''la''' = 11-all = 2.3.11 Because "lo C" sounds like "low C", lo when by itself becomes '''ilo''' ("ee-LOW"). But with other words it doesn't use i-, as in 11/7 = loru 5th. Lo and lu are abbreviated to '''1o''' and '''1u''' on the score and in interval names and chord names, e.g. ilo A = 1oA, ilo 4th = 1o4 = 11/8, and C ilo seven = C1o7 = 1/1 - 11/9 - 3/2 - 11/6 on C. Lolo is 1oo, triple-lu is 1u<sup>3</sup>, etc. The associated color is lavender (mnemonic: "e-leven-der"), which refers to both ilo and lu, since they are only 7.1¢ apart. Lavender is a '''pseudocolor''' that implies the [http://x31eq.com/cgi-bin/rt.cgi?ets=24_17&limit=2_3_11 Neuter] temperament. IIo notes could be called lovender, and lu notes could be called luvender. Both are "shades" of lavender. | '''Lo''' = 11-over, '''lu''' = 11-under, and '''la''' = 11-all = 2.3.11 Because "lo C" sounds like "low C", lo when by itself becomes '''ilo''' ("ee-LOW"). But with other words it doesn't use i-, as in 11/7 = loru 5th. La when by itself may become '''ila''', to avoid confusion with the solfege note La, and also with large (see "Temperament names" below). Lo and lu are abbreviated to '''1o''' and '''1u''' on the score and in interval names and chord names, e.g. ilo A = 1oA, ilo 4th = 1o4 = 11/8, and C ilo seven = C1o7 = 1/1 - 11/9 - 3/2 - 11/6 on C. Lolo is 1oo, triple-lu is 1u<sup>3</sup>, etc. The associated color is lavender (mnemonic: "e-leven-der"), which refers to both ilo and lu, since they are only 7.1¢ apart. Lavender is a '''pseudocolor''' that implies the [http://x31eq.com/cgi-bin/rt.cgi?ets=24_17&limit=2_3_11 Neuter] temperament. IIo notes could be called lovender, and lu notes could be called luvender. Both are "shades" of lavender. | ||
'''Tho''' = 13-over, '''thu''' = 13-under, and '''tha''' = 13-all. Tho and thu are abbreviated as '''3o''' and '''3u''' on the score and in interval names, e.g. 13/8 = 3o6 = tho 6th, 14/13 = 3uz2 = thuzo 2nd. | '''Tho''' = 13-over, '''thu''' = 13-under, and '''tha''' = 13-all. Tho and thu are abbreviated as '''3o''' and '''3u''' on the score and in interval names, e.g. 13/8 = 3o6 = tho 6th, 14/13 = 3uz2 = thuzo 2nd. | ||
| Line 259: | Line 259: | ||
== Temperament Names == | == Temperament Names == | ||
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]], | 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 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¢. | ||
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. | |||
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. | 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. | 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]]. | |||
== Ups and Downs, Lifts and Drops, Plain and Mid == | == Ups and Downs, Lifts and Drops, Plain and Mid == | ||
| Line 278: | Line 282: | ||
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]]. | 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== | ==Translations== | ||
:''For translations of color notation terms into other languages, see [[Color notation/Translations]].'' | :''For translations of color notation terms into other languages, see [[Color notation/Translations]].'' [[Category:color_notation]] [[Category:ji]] [[Category:notation]] | ||