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), written L and s, and sometimes abbreviated '''la''' and '''sa''' (especially in temperament names). '''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), written L and s, and sometimes abbreviated '''la''' and '''sa''' (especially in temperament names). '''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 | 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 (50/49) and Trigu (128/125). Bi- is only used if it shortens the name: yoyo not biyo. Quadruple and quintuple are abbreviated '''quad-''' and '''quin-''', as in quadyo or quingu. For sextuple, etc., see "Temperament Names" below. | ||
Colors using only one prime above 3 are called '''primary''' colors. Thus gu and yoyo are primary and ruyo is non-primary. | Colors using only one prime above 3 are called '''primary''' colors. Thus gu and yoyo are primary and ruyo is non-primary. | ||
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Just as wa means 3-all or 3-limit, '''ya''' means 5-all and includes wa, yo, gu, yoyo, gugu, etc. Ya = the 2.3.5 prime subgroup = 5-limit. '''Za''' = 7-all = 2.3.7. Yaza = 2.3.5.7 = the full 7-limit. '''Nowa''' means without wa, and yaza nowa = 2.5.7. | Just as wa means 3-all or 3-limit, '''ya''' means 5-all and includes wa, yo, gu, yoyo, gugu, etc. Ya = the 2.3.5 prime subgroup = 5-limit. '''Za''' = 7-all = 2.3.7. Yaza = 2.3.5.7 = the full 7-limit. '''Nowa''' means without wa, and yaza nowa = 2.5.7. | ||
Prime 2 (even more colorless than wa) is '''clear''', abbreviated '''ca''', and yaza '''noca''' = 3.5.7. 2-limit intervals like 2/1 are called wa not clear, for simplicity. '''Nowaca''' means without 2 or 3, thus 5.7.11 is yazala nowaca. Clear/ca is only ever used in the terms noca and nowaca. | Prime 2 (even more colorless than wa) is '''clear''', abbreviated '''ca''', and yaza '''noca''' = 3.5.7. 2-limit intervals like 2/1 are called wa not clear, for simplicity. '''Nowaca''' means without 2 or 3, thus 5.7.11 is yazala nowaca. Clear/ca is only ever used in the terms noca and nowaca. However, a good mnemonic for "co-" (compound, widened by an octave) is "clear-over". | ||
== Color Names for Higher Primes == | == Color Names for Higher Primes == | ||
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The prefix i- is only used when confusion is possible. Thus 19/15 = nogu 4th, not inogu 4th, and 29o = twenty-no, not twenty-ino. | The prefix i- is only used when confusion is possible. Thus 19/15 = nogu 4th, not inogu 4th, and 29o = twenty-no, not twenty-ino. | ||
For any prime P, the degree of the ratio P/1 is determined by its 8ve-reduced cents, and how it relates to 12edo: 0-50¢ = 1sn, 50-250¢ = 2nd, 250-450¢ = 3rd, 450-600¢ = 4th, 600-750¢ = 5th, 750-950¢ = 6th, 950-1150¢ = 7th, and 1150-1200¢ = 8ve. Thus 23/16 = 628¢ is a 5th, 31/16 = 1145¢ is a 7th, and 37/32 = 251¢ is a 3rd. This makes the "pseudo-edomapping" <7 11 16 20 24 26 29 30 32 34 34 37... | While a double-yo ratio such as 25/24 is yoyo, a double-twenty-tho ratio is not twenty-thotho, because that means a ratio that's both 23-over and 13-over. Twenty-tho doubled is bi-twenty-tho. | ||
For any prime P, the degree of the ratio P/1 is determined by its 8ve-reduced cents, and how it relates to 12edo: 0-50¢ = 1sn, 50-250¢ = 2nd, 250-450¢ = 3rd, 450-600¢ = 4th, 600-750¢ = 5th, 750-950¢ = 6th, 950-1150¢ = 7th, and 1150-1200¢ = 8ve. Thus 23/16 = 628¢ is a 5th, 31/16 = 1145¢ is a 7th, and 37/32 = 251¢ is a 3rd. This makes the "pseudo-edomapping" <7 11 16 20 24 26 29 30 32 34 34 37...]. (An alternative method is to use the 7edo [[edomapping]], but that requires using every other 14edostep as boundaries, harder to remember and much less convenient than the 24edo boundaries used here.) | |||
== Converting a Ratio to/from a Color Name == | == Converting a Ratio to/from a Color Name == | ||
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== Glossary / Crash Course == | == Glossary / Crash Course == | ||
Over = prime in the numerator, under = prime in the denominator. All = over, under or neither: wa = 3-limit, ya = 2.3.5, yaza = 2.3.5.7. | Over = prime in the numerator, under = prime in the denominator. All = over, under or neither: wa = 3-limit, ya = 2.3.5, yaza = 2.3.5.7. | ||
{| class="wikitable" style="text-align:center" | {| class="wikitable" style="text-align:center" | ||
|+ | |+ | ||
!prime | !prime | ||
! colspan="2" |-o for over | ! colspan="2" |-o ("oh") for over | ||
! colspan="2" |-u ("oo") for under | ! colspan="2" |-u ("oo") for under | ||
! colspan="2" |-a for all | ! colspan="2" |-a ("ah") for all | ||
!multiplier | !multiplier | ||
|- | |- | ||
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|- | |- | ||
| colspan="2" | -a- | | colspan="2" | -a- | ||
|delimits a multiplier | |delimits a multiplier such as bi-, tri-, etc. | ||
| | |Trizogu = z<sup>3</sup>g<sup>3</sup> = 1029/1000, Trizo-agu = z<sup>3</sup>g = 343/320 | ||
|- | |- | ||
|co- | |co- | ||
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==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]] | ||