Kite's color notation: Difference between revisions
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'''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. | ||
Prime subgroups: yala = 2.3.5.11, zalatha nowa = 2.7.11.13, and yazalatha = 2.3.5.7.11.13 = the full 13-limit. '''Noya''' is a descriptive adjective, not used in actual subgroup names, that indicates the absence of 5 and the presence of higher primes, e.g. zala, latha and zalatha are all noya. Likewise, there's '''noza''', '''noyaza''', etc. | Prime subgroups: yala = 2.3.5.11, zalatha nowa = 2.7.11.13, and yazalatha = 2.3.5.7.11.13 = the full 13-limit. '''Noya''' is a descriptive adjective, not used in actual prime subgroup names, that indicates the absence of 5 and the presence of higher primes, e.g. zala, latha and zalatha are all noya. Likewise, there's '''noza''', '''noyaza''', etc. | ||
On the score and in note names, the 1o accidental either raises by 33/32 or lowers by 729/704. The meaning will usually be clear from context, however it's safer to write at the top of the page either "1o4 = P4" or "1o4 = A4". Likewise, 3o6 should be noted as either m6 or M6. While the note 11/8 above C can be written two ways, either as 1oF or as 1oF#, the interval 11/8 can only be written one way, as 1o4. Likewise, 13/8 above C is either 3oA or 3oAb, but 13/8 is only 3o6. <u>This is the rationale for using large/small/central rather than major/minor</u>. 11/9 is ambiguously major or minor, but unambiguously central. Intervals names and chord names become unambiguous for la and tha intervals. Another rationale: commonly used intervals and chords are all central, and get concise names: gu 3rd not gu minor 3rd, A gu not A gu minor, etc. (see chord names below). | On the score and in note names, the 1o accidental either raises by 33/32 or lowers by 729/704. The meaning will usually be clear from context, however it's safer to write at the top of the page either "1o4 = P4" or "1o4 = A4". Likewise, 3o6 should be noted as either m6 or M6. While the note 11/8 above C can be written two ways, either as 1oF or as 1oF#, the interval 11/8 can only be written one way, as 1o4. Likewise, 13/8 above C is either 3oA or 3oAb, but 13/8 is only 3o6. <u>This is the rationale for using large/small/central rather than major/minor</u>. 11/9 is ambiguously major or minor, but unambiguously central. Intervals names and chord names become unambiguous for la and tha intervals. Another rationale: commonly used intervals and chords are all central, and get concise names: gu 3rd not gu minor 3rd, A gu not A gu minor, etc. (see chord names below). | ||
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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...|. (An | 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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Temperaments are named after the color of the comma(s) they temper out. Many words are abbreviated. Large becomes la and small becomes sa. Double, triple, etc, become bi-, tri-, quad- and quin-. Sextuple is tribi-, and septuple is sep-. Eleven-fold is le- = "e'''<u>l</u>'''even '''<u>e</u>'''xponent". | Temperaments are named after the color of the comma(s) they temper out. Many words are abbreviated. Large becomes la and small becomes sa. Double, triple, etc, become bi-, tri-, quad- and quin-. Sextuple is tribi-, and septuple is sep-. Eleven-fold is le- = "e'''<u>l</u>'''even '''<u>e</u>'''xponent". | ||
[[Meantone]] is the Gu temperament. [[Srutal]] is Sagugu. [[Porcupine]] is Triyo. Some multi-comma temperaments have multiple commas in their name, and some don't. [[Meantone family#Septimal meantone|Septimal Meantone]] is Gu, but [[Meantone family#Dominant|Dominant Meantone]] is Gu & Rugu. Untempered primes are included with a plus sign | [[Meantone]] is the Gu temperament. [[Srutal]] is Sagugu. [[Porcupine]] is Triyo. Some multi-comma temperaments have multiple commas in their name, and some don't. [[Meantone family#Septimal meantone|Septimal Meantone]] is Gu, but [[Meantone family#Dominant|Dominant Meantone]] is Gu & Rugu. Untempered primes are included with a plus sign. The 2.3.5.7 prime subgroup with 81/80 tempered out is Gu + za. | ||
Every wa comma implies an edo, and a temperament with such a comma uses that edo in its name. Thus Catler is 12-edo plus za. An exception is made for 5-edo and 7-edo: Blackwood is Sawa + ya and Whitewood is Lawa + ya. | |||
The color name of a rank-2 temperament can be used to name MOS and MODMOS scales, as in Triyo[8]. Individual modes can be named as 2nd Triyo[8], 3rd Triyo[7] b7, etc. This notation is discussed here: [[Naming Rank-2 Scales using Mode Numbers]]. | The color name of a rank-2 temperament can be used to name MOS and MODMOS scales, as in Triyo[8]. Individual modes can be named as 2nd Triyo[8], 3rd Triyo[7] b7, etc. This notation is discussed here: [[Naming Rank-2 Scales using Mode Numbers]]. | ||
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== Ups and Downs, Lifts and Drops, Plain and Mid == | == Ups and Downs, Lifts and Drops, Plain and Mid == | ||
Color notation merely renames ratios more conveniently, and strictly speaking, it only applies to just intonation. However, ratios are often used to loosely describe [[EDO|edo]] notes, and colors can be used as well. A more precise | Color notation merely renames ratios more conveniently, and strictly speaking, it only applies to just intonation. However, ratios are often used to loosely describe [[EDO|edo]] notes, and colors can be used as well. A more precise notation uses [[Ups and Downs Notation|'''ups''' '''and''' '''downs''']] (^ and v) as "virtual colors", accidentals that always map to exactly one edostep. Ups and downs are used on the score just like color accidentals are. Notes are named e.g. up C sharp = ^C#. Some edos like 9, 12, 16, 19, 23 and 26 don't require ups and downs. | ||
Unlike actual colors, virtual colors generally add up to something simpler, e.g. three of 22edo's ups adds up to an A1. Unlike actual colors, virtual colors combine with major, minor, etc. Intervals are named upmajor 3rd = ^M3, up 4th = ^4, downaug 5th = vA5, etc. | Unlike actual colors, virtual colors generally add up to something simpler, e.g. three of 22edo's ups adds up to an A1. Unlike actual colors, virtual colors combine with major, minor, etc. Intervals are named upmajor 3rd = ^M3, up 4th = ^4, downaug 5th = vA5, etc. | ||
'''Plain''' means neither up nor down, analogous to natural meaning neither sharp nor flat. '''Mid''', abbreviated ~, means exactly midway between major and minor. The mid 4th is midway between perfect and augmented, i.e. | '''Plain''' means neither up nor down, analogous to natural meaning neither sharp nor flat. '''Mid''', abbreviated ~, means exactly midway between major and minor. The mid 4th is midway between perfect and augmented, i.e. halfway-augmented, and the mid 5th is halfway-diminished. There is no mid unison or octave. Mid simplifies 72edo notation: m2, ^m2, v~2, ~2, ^~2, vM2, M2. In 72edo, upmid (^~) means one edostep above mid, but in 53edo it means one <u>half</u> edostep above mid. Mid is only used in relative notation, it never applies to notes and never appears on the staff. In 24-edo or 31-edo, the 3rd of C~ is vE or ^Eb, but in 41-edo, it's vvE or ^^Eb. | ||
Chords are named similarly to color notation, with the various qualities downmajor, upminor, mid, etc. replacing colors. Major is the default quality, thus C = C major and Cv = C downmajor. The 6th, 7th and 11th inherit their quality from the 3rd, thus C upminor 9th = C ^Eb G ^Bb D. Chord roots can have ups and downs, as in Cv - Gv - vA^m - Fv or Iv - Vv - vVI^m - IVv. In roman numeral notation, chord roots can be downflat, mid, etc., as in Iv7 - vbIII^m6 - IVv7 or I~7 - ~III - V7. Lower-case roman numerals are never used for minor chords, because vii could mean either seven-minor or down-two-minor. Instead vii is written either VIIm or vIIm. See the [http://tallkite.com/misc_files/notation%20guide%20for%20edos%205-72.pdf notation guide for edos 5-72] | Chords are named similarly to color notation, with the various qualities downmajor, upminor, mid, etc. replacing colors. Major is the default quality, thus C = C major and Cv = C downmajor. The 6th, 7th and 11th inherit their quality from the 3rd, thus C upminor 9th = C ^Eb G ^Bb D. Chord roots can have ups and downs, as in Cv - Gv - vA^m - Fv or Iv - Vv - vVI^m - IVv. In roman numeral notation, chord roots can be downflat, mid, etc., as in Iv7 - vbIII^m6 - IVv7 or I~7 - ~III - V7. Lower-case roman numerals are never used for minor chords, because vii could mean either seven-minor or down-two-minor. Instead vii is written either VIIm or vIIm. See the [http://tallkite.com/misc_files/notation%20guide%20for%20edos%205-72.pdf notation guide for edos 5-72] | ||
[[Tour of Regular Temperaments|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]]. | [[Tour of Regular Temperaments|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 add lift-seven = C^,/7 = C ^E G /Bb, C uplift-seven = C^/7 = C ^/E G ^/Bb, etc. See [[Pergen|pergens]]. | ||
== 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. | ||
The multiplier bi- is only used for compound colors like ruyo: 50/49 is biruyo, but 25/24 is yoyo. | The multiplier bi- is only used for compound colors like ruyo: 50/49 is biruyo, but 25/24 is yoyo not biyo. | ||
{| class="wikitable" style="text-align:center" | {| class="wikitable" style="text-align:center" | ||
|+ | |+ | ||
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|- | |- | ||
| colspan="2" |nowa | | colspan="2" |nowa | ||
|remove 3 (wa) from the subgroup, i.e. no-threes | |remove 3 (wa) from the prime subgroup, i.e. no-threes | ||
|2.5.7 = yaza nowa, 2.5.7 with 50/49 = Biruyo nowa | |2.5.7 = yaza nowa, 2.5.7 with 50/49 = Biruyo nowa | ||
|- | |- | ||
| colspan="2" |noca | | colspan="2" |noca | ||
|remove 2 (clear) from the subgroup, i.e. non-8ve | |remove 2 (clear) from the prime subgroup, i.e. non-8ve | ||
|3.5.7 = yaza noca, 3.5.7 with 245/243 = Zozoyo noca | |3.5.7 = yaza noca, 3.5.7 with 245/243 = Zozoyo noca | ||
|- | |- | ||
| colspan="2" |nowaca | | colspan="2" |nowaca | ||
|remove both 2 and 3 from the subgroup | |remove both 2 and 3 from the prime subgroup | ||
|5.7.11 = yazala nowaca | |5.7.11 = yazala nowaca | ||
|- | |- | ||
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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]] | ||