Kite's color notation: Difference between revisions
No edit summary |
No edit summary |
||
| Line 10: | Line 10: | ||
7-under = '''Ru''' = red (alarming, inflamed) = often supermajor | 7-under = '''Ru''' = red (alarming, inflamed) = often supermajor | ||
The colors come in a red-yellow-green-blue rainbow, with warm/cool colors indicating sharp/flat intervals. The rainbow of 3rds runs 9/7 - 5/4 - 6/5 - 7/6. Colors are abbreviated as w, y, z | The colors come in a red-yellow-green-blue rainbow, with warm/cool colors indicating sharp/flat intervals. The rainbow of 3rds runs 9/7 - 5/4 - 6/5 - 7/6. Colors are abbreviated as '''w''', '''y''', '''g''', '''z''' and '''r'''. Use z (azure) not b (blue), because b already means flat. Mnemonic: Z looks like 7 with an extra line on the bottom. | ||
== Interval Names == | == Interval Names == | ||
| Line 163: | Line 163: | ||
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 d1. | 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 d1. | ||
Any ratio under 50¢ can be called a '''comma''', allowing us to omit the magnitude and degree in the spoken name. Thus sgg2 is not the small gugu 2nd, but simply the gugu comma. The double-large wa negative 2nd (LLw-2, the pyth comma) is simply the wa comma. 81/80 = g1 is the gu comma. LLg-2 (the sum of g1 and LLw-2) is also gu and also a comma, but LLg-2 is not <u>the</u> gu comma, because its [[Odd limit|double odd limit]] is higher. Thus its name can't be shortened. 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. | |||
== Note Names == | == Note Names == | ||
| Line 173: | Line 175: | ||
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, | 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. | ||
== Color Names for Higher Primes == | == Color Names for Higher Primes == | ||
| Line 184: | Line 186: | ||
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 general term, 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''' and '''noyaza'''. | 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 general term, 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''' and '''noyaza'''. | ||
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 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. | 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). | ||
'''So''' = 17-over, '''su''' = 17-under, and '''sa''' = 17-all, abbreviated as '''17o''' and '''17u'''. '''Iso''' is an alternate form of so, to distinguish it from the solfege syllable | '''So''' = 17-over, '''su''' = 17-under, and '''sa''' = 17-all, abbreviated as '''17o''' and '''17u'''. '''Iso''' is an alternate form of so, to distinguish it from the solfege syllable So. 17/12 = 17o5 = iso So. | ||
'''Ino''' = 19-over, '''nu''' = 19-under, and '''na''' = 19-all, abbreviated as '''19o''' and '''19u'''. Ino because "no 3rd" could mean either 19/16 or thirdless. '''Inu''' is an alternate form of nu, to distinguish "the nu key" from "the new key". 12edo implies yasana = 2.3.5.17.19. | '''Ino''' = 19-over, '''nu''' = 19-under, and '''na''' = 19-all, abbreviated as '''19o''' and '''19u'''. Ino because "no 3rd" could mean either 19/16 or thirdless. '''Inu''' is an alternate form of nu, to distinguish "the nu key" from "the new key". 12edo implies yasana = 2.3.5.17.19. | ||
'''Twenty-tho''' = 23-over, '''twenty-thu''' = 23-under, '''twenty-tha''' =23-all, abbreviated as '''23o''', '''23u''' and '''23a'''. 2.3.5.7.23 = yaza23a = | '''Twenty-tho''' = 23-over, '''twenty-thu''' = 23-under, '''twenty-tha''' =23-all, abbreviated as '''23o''', '''23u''' and '''23a'''. 2.3.5.7.23 = yaza23a = yaza-twenty-tha. 23/16 = 23o5 = twenty-tho 5th, and 23/22 = 23o1u2 = twenty-tholu 2nd. | ||
Similarly, '''twenty-no/-nu/-na''' = 29o/29u/29a, '''thirty-wo/-wu/-wa''' = 31o/31u/31a, '''thirty-so/-su/-sa''' = 37o/37u/37a, etc. | Similarly, '''twenty-no/-nu/-na''' = 29o/29u/29a, '''thirty-wo/-wu/-wa''' = 31o/31u/31a, '''thirty-so/-su/-sa''' = 37o/37u/37a, etc. | ||
| Line 203: | Line 205: | ||
Converting a color name: Let S be the stepspan of the interval, S = degree - sign (degree). Let M be the magnitude of the color name, with L = 1, LL = 2, etc. Small is negative and central is zero. Let the monzo be |a b c d e...>. The colors directly give you all the monzo entries except a and b. Let X = the dot product of |0 0 c d e...> with the 7edo edomapping. Then b = (2S - 2X + 3) mod 7 + 7M - 3, and a = (S - X - 11b) / 7. Convert the monzo to a ratio. | Converting a color name: Let S be the stepspan of the interval, S = degree - sign (degree). Let M be the magnitude of the color name, with L = 1, LL = 2, etc. Small is negative and central is zero. Let the monzo be |a b c d e...>. The colors directly give you all the monzo entries except a and b. Let X = the dot product of |0 0 c d e...> with the 7edo edomapping. Then b = (2S - 2X + 3) mod 7 + 7M - 3, and a = (S - X - 11b) / 7. Convert the monzo to a ratio. | ||
Example: interval = sgg2, S = 2 - 1 = 1 step, M = small = -1, monzo = |a b -2>, X = <7 11 16| dot |0 0 -2> = -32, b = (2·1 - 2·(-32) + 3) mod 7 + 7·(-1) - 3 = | Example: interval = sgg2, S = 2 - 1 = 1 step, M = small = -1, monzo = |a b -2>, X = <7 11 16| dot |0 0 -2> = -32, b = (2·1 - 2·(-32) + 3) mod 7 + 7·(-1) - 3 = 69 mod 7 - 7 - 3 = -4, a = (1 - (-32) - 11·(-4)) / 7 = 77/7 = 11, monzo = |11 -4 -2>, ratio = 2048/2025. | ||
== Staff notation == | == Staff notation == | ||
| Line 214: | Line 216: | ||
[[File:Notation example 2.png|786x786px]] | [[File:Notation example 2.png|786x786px]] | ||
Color notation can optionally be made more similar to Sagittal notation by including two more accidentals, p and q (long forms '''po''' and '''qu''' = "ku"), to indicate raising/lowering by a pythagorean comma. (See [http://tallkite.com/misc_files/Sagittal-JI-Translated-To-Colors.png Sagittal-JI-Translated-To-Colors.png].) For example, yF# = ypGb, and zEb = zqD#. This allows trills to always be written as a 2nd, less cluttered.[[File:Notation example 5a.png|992x992px]] | Color notation can optionally be made more similar to Sagittal notation by including two more accidentals, '''p''' and '''q''' (long forms '''po''' and '''qu''' = "ku"), to indicate raising/lowering by a pythagorean comma. (See [http://tallkite.com/misc_files/Sagittal-JI-Translated-To-Colors.png Sagittal-JI-Translated-To-Colors.png].) For example, yF# = ypGb, and zEb = zqD#. This allows trills to always be written as a 2nd, less cluttered.[[File:Notation example 5a.png|992x992px]] | ||
L and s never appear on the staff. Tripled colors are written as y3 not yyy. In MuseScore, color accidentals are made by adding fingerings to the notes, then editing the fingering text. The font used here is Arial Black. | L and s never appear on the staff. Tripled colors are written as y3 not yyy. In MuseScore, color accidentals are made by adding fingerings to the notes, then editing the fingering text. The font used here is Arial Black. | ||
| Line 232: | Line 234: | ||
<u>Alterations are always in parentheses</u>, additions never are, e.g. z7(zg5) and z,y6. An alteration's degree must match a note in the chord, e.g. Cz7(y6) is invalid. But an exception is made for sus chords, where degree 2 or 4 alter the 3rd: C(z4) = w1 z4 w5. The sus note defaults to wa: Cy9(4) = w1 w4 w5 y7 w9. | <u>Alterations are always in parentheses</u>, additions never are, e.g. z7(zg5) and z,y6. An alteration's degree must match a note in the chord, e.g. Cz7(y6) is invalid. But an exception is made for sus chords, where degree 2 or 4 alter the 3rd: C(z4) = w1 z4 w5. The sus note defaults to wa: Cy9(4) = w1 w4 w5 y7 w9. | ||
Omissions are indicated by "no", the Hendrix chord might be Ch7z10no5. <u> | Omissions are indicated by "no", the Hendrix chord might be Ch7z10no5. Unless using po or qu, <u>enharmonic substitutions aren't allowed</u>. 7/3 is a 10th, never a 9th unless it's a qu 9th (e.g. Ch7zq9no5). A no3 tetrad can also be written as a 5 chord with an added 6th or 7th: Cy6no3 = C5y6, and Cz7(zg5)no3 = C(zg5)z7. | ||
The y,z7 chord is also called the h7 chord ("aitch-seven"), because it's part of the harmonic series. The s7 ("sub-seven") chord is part of the subharmonic series. It's the first 7 subharmonics, with the 3rd subharmonic becoming the root. Note that s7 has no 7th. Ch9 = y,z7,w9 and Ch11 = y,z7,w9,1o11. Cs9 = g,r6,w11 and Cs11 = g,r6,w11,1u9. All harmonic numbers must be odd, Ch8 is invalid. <u>Additions refer to harmonics or subharmonics</u>, not degrees: Cs7,11 adds 1u9, not w11. To add w11, use colors: Cs7,w11. <u>Alterations and omissions refer to degrees</u>, not (sub)harmonics | The y,z7 chord is also called the h7 chord ("aitch-seven"), because it's part of the harmonic series. The s7 ("sub-seven") chord is part of the subharmonic series. It's the first 7 subharmonics, with the 3rd subharmonic becoming the root. Note that s7 has no 7th. Ch9 = y,z7,w9 and Ch11 = y,z7,w9,1o11. Cs9 = g,r6,w11 and Cs11 = g,r6,w11,1u9. All harmonic numbers must be odd, Ch8 is invalid. For any odd number N > 7, ChN would be 1:3:5:7...N and CsN would be 3/(1:3:5:7...N). <u>Additions refer to harmonics or subharmonics</u>, not degrees: Cs7,11 adds 1u9, not w11. To add w11, use colors: Cs7,w11. <u>Alterations and omissions refer to degrees</u>, not (sub)harmonics: Cs7(zg5) alters the w5, not the 5th subharmonic g3. Ch9no5 omits w5, not y3. However, Ch19no15 refers to the 15th harmonic, since degrees above 13 aren't conventionally used. | ||
Chords can be classified as '''bicolored''' (e.g. g7 or r6), '''tricolored''' (e.g. z7(zg5) or z,y6), '''quadricolored''', etc. | Chords can be classified as '''bicolored''' (e.g. g7 or r6), '''tricolored''' (e.g. z7(zg5) or z,y6), '''quadricolored''', etc. | ||
| Line 243: | Line 245: | ||
In relative notation, the I, IV and V chords default to a wa root. But II, III, VI and VII <u>must</u> have an explicit root-color. The previous example becomes Iy - yVIg - IVy - Vy,w7, spoken as "one yo, yo-six gu, four yo, five yo wa-seven". | In relative notation, the I, IV and V chords default to a wa root. But II, III, VI and VII <u>must</u> have an explicit root-color. The previous example becomes Iy - yVIg - IVy - Vy,w7, spoken as "one yo, yo-six gu, four yo, five yo wa-seven". | ||
In adaptive JI, chords are just, but roots move by tempered intervals. Comma pumps are indicated with brackets: Cy - yAg - [y=w]Dg - Gy - Cy. | In adaptive JI, chords are just, but roots move by tempered intervals. Comma pumps are indicated with brackets: Cy - yAg - [y=w]Dg - Gy - Cy. | ||
Keys and scales are loosely named after the colors used. Wa is assumed present. In 5-limit JI, the key/scale of A minor is A gu. The Bbh7 - Ebh7 - Bbh7 - Fh9 example in the staff notation section is in Bb yo zo. Like chords, keys can be classified as bicolored (A gu), tricolored (Bb yo zo), etc. | Keys and scales are loosely named after the colors used. Wa is assumed present. In 5-limit JI, the key/scale of A minor is A gu. The Bbh7 - Ebh7 - Bbh7 - Fh9 example in the staff notation section is in Bb yo zo. Like chords, keys can be classified as bicolored (A gu), tricolored (Bb yo zo), etc. | ||
| Line 254: | Line 256: | ||
The magnitude is part of the name: Schismic is LyT and shrutal 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]] is g2T. The degree is never needed if the comma is ≤ 90¢. | The magnitude is part of the name: Schismic is LyT and shrutal 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]] is g2T. The degree is never needed if the comma is ≤ 90¢. | ||
If the comma is wa, an edo is implied. The temperament is named after the edo, not the 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 are | If the comma is wa, an edo is implied. The temperament is named after the edo, not the 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 are added with '''plus''': Blackwood is 5edo+yT = 5-edo plus ya. 2.3.5.7.11 and 81/80 = 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. | 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. | ||
| Line 260: | Line 262: | ||
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 single-comma 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 single-comma temperaments better. The question of which name to use is not yet fully resolved. | ||
== Ups and Downs, Lifts and Drops == | == 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 notes, and colors can be used as well. A more precise application is to use 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#. Unlike actual colors, virtual colors generally add up to something simpler, e.g. | 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 notes, and colors can be used as well. A more precise application is to use [[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. Chords are named C upminor 7th = C^m7, etc. | |||
'''Plain''' means neither up nor down, analogous to natural meaning neither sharp nor flat. '''Mid''', abbreviated ~, means exactly midway between major and minor. Mid simplifies 72edo notation: m2, ^m2, v~2, ~2, ^~2, vM2, M2. Upmid (^~) means one edostep above mid in 72edo, but one half edostep above mid in 53edo. Mid is only used in relative notation, it never applies to notes or appears on the staff. | |||
Rank-2 temperaments can be notated with ups and downs as well. Some require an additional pair of virtual colors, lifts and drops (/ and \). See [[Pergen|pergens]]. | Rank-2 temperaments can be notated with ups and downs as well. Some temperaments require an additional pair of virtual colors, '''lifts''' and '''drops''' (/ and \). Plain and mid apply to rank-2. See [[Pergen|pergens]]. | ||
[[Category:color_notation]] | [[Category:color_notation]] | ||
[[Category:ji]] | [[Category:ji]] | ||
[[Category:notation]] | [[Category:notation]] | ||