Kite's color notation: Difference between revisions
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A color and a degree indicates a ratio, and vice versa. Every ratio has a spoken name and a written name. For 3/2, they are wa 5th and w5. Colors and degrees <u>always</u> add up predictably: z3 + g3 = zg5 = zogu 5th. Zogu not guzo, higher primes always come first. Opposite colors cancel: y3 + g3 = w5. | A color and a degree indicates a ratio, and vice versa. Every ratio has a spoken name and a written name. For 3/2, they are wa 5th and w5. Colors and degrees <u>always</u> add up predictably: z3 + g3 = zg5 = zogu 5th. Zogu not guzo, higher primes always come first. Opposite colors cancel: y3 + g3 = w5. | ||
The JI lattice consists of many ''' | The JI lattice consists of many '''rows''', each one a chain of 5ths. Each row has its own color, and each color has its own row. | ||
[[File:Lattice32.png|694x694px]] | [[File:Lattice32.png|694x694px]] | ||
Colors can be doubled or tripled: 25/16 = yoyo 5th = yy5 and 128/125 = triple gu 2nd = g<sup>3</sup>2. 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. | Colors can be doubled or tripled: 25/16 = yoyo 5th = yy5 and 128/125 = triple gu 2nd = g<sup>3</sup>2. 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. | ||
The next table lists all the intervals in the lattice | The next table lists all the intervals in the lattice above. See the [[Gallery of Just Intervals]] for many more examples. | ||
{| class="wikitable" | {| class="wikitable" | ||
!'''ratio''' | !'''ratio''' | ||
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|w8 | |w8 | ||
|} | |} | ||
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 below for why). Instead of augmented and diminished, remote intervals are '''large''' (fifthward) and '''small''' (fourthward), abbreviated L and s. '''Central''' 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. 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 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. Magnitudes do not add up predictably like colors and degrees do: w2 + w2 = Lw3. | ||
[[File:Lattice41a.png|833x833px]] | [[File:Lattice41a.png|833x833px]] | ||
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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. | 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, e.g. 5.7 is yaza nowaca. | ||
== Color Names for Higher Primes == | == Color Names for Higher Primes == | ||
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-7 = C1o7 = 1/1 - 11/9 - 3/2 - 11/6. 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. Languages without a "th" sound might use '''tro''', '''tru''' and '''tra'''. See the appendix in [http://www.tallkite.com/AlternativeTunings.html Kite's book] for more on translating colors into other languages. | '''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. Languages without a "th" sound might use '''tro''', '''tru''' and '''tra'''. See the appendix in [http://www.tallkite.com/AlternativeTunings.html Kite's book] for more on translating colors into other languages. | ||
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. | 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 3oA♭, 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. Also, 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 3oA♭, 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. Also, 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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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. | ||
The | The prefix i- is only needed when confusion is possible. Thus 19/15 = nogu 4th, not inogu 4th, and 29o = twenty-no, not twenty-ino. | ||
== Converting a ratio to/from a color name == | == Converting a ratio to/from a color name == | ||
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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. There are h9 chords, s11 chords, etc. The number must be odd, Ch8 is invalid. Ch9,13 = w1 y3 w5 z7 w9 3o13 has an added 13th harmonic. | 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. There are h9 chords, s11 chords, etc. The number must be odd, Ch8 is invalid. Ch9,13 = w1 y3 w5 z7 w9 3o13 has an added 13th harmonic. | ||
A 9th chord contains a 3rd, 5th and 7th. An 11th chord contains all these plus a 9th. A 13th chord contains all these plus an 11th. The 5th, 9th and/or 13th default to wa. The 6th, 7th, and/or 11th default to the color of the 3rd. Thus Cy13 = w1 y3 w5 y7 w9 y11 w13, and Cy9 and Cy11 are subsets of this chord. However, an add-11 chord defaults to a wa 11: Cz7,11 = w1 z3 w5 z7 w11. Added 9ths default to wa: Cy,9 = w1 y3 w5 w9. | A 9th chord contains a 3rd, 5th and 7th. An 11th chord contains all these plus a 9th. A 13th chord contains all these plus an 11th. The 5th, 9th and/or 13th default to wa. The 6th, 7th, and/or 11th default to the color of the 3rd. Thus Cy13 = w1 y3 w5 y7 w9 y11 w13, and Cy9 and Cy11 are subsets of this chord. However, an add-11 chord defaults to a wa 11: Cz7,11 = w1 z3 w5 z7 w11. Added 9ths also default to wa: Cy,9 = w1 y3 w5 w9. | ||
<u>Alterations are always in parentheses</u>, additions never are, e.g. z7(zg5). An alteration's degree must match a note in the chord, e.g. z7(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). An alteration's degree must match a note in the chord, e.g. z7(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. | ||