Kite's color notation

This is a "crash course". For a full explanation, see Kite's book, "Alternative Tunings: Theory, Notation and Practice", available at www.TallKite.com.

Interval Names

Every prime above 3 has two color names, one for over (prime in the numerator) and one for under (prime in the denominator). Over colors end with -o, and under colors with -u. Here's the colors for primes 3, 5 and 7:

Wa = white (strong but colorless) = 3-limit

Yo = yellow (warm and sunny) = 5-over = major

Gu ("goo") = green (not as bright as yellow) = 5-under = minor

Zo = blue/azure (dark and bluesy) = 7-over = subminor

Ru = red (alarming, inflamed) = 7-under = supermajor

The colors come in a red-yellow-green-blue rainbow, with warm/cool colors indicating sharp/flat intervals. The rainbow of 3rds = 9/7 - 5/4 - 6/5 - 7/6. Azure is used instead of blue because b looks like a flat sign. Mnemonic: Z looks like 7 with an extra line on the bottom.

A color and a degree indicates a ratio, and vice versa. 2/1 = wa 8ve = w8. 7/5 = zogu 5th = zg5 (not guzo, higher primes always come first). Interval arithmetic always holds: 7/5 is a 5th because zg5 = z3 + g3, and two 3rds make a 5th. Opposite colors cancel: y3 + g3 = w5.

21/10 = zogu 9th = zg9. 25/16 = yoyo 5th = yy5. 128/125 = triple gu 2nd = g³2. 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 neg 2nd.

More remote intervals are large (fifthward) and small (fourthward), abbreviated L and s. Central means neither large nor small. The magnitude is found by adding up all the monzo exponents but the first, dividing by 7, and rounding 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.

See Gallery of Just Intervals for more examples of interval names.

Prime Subgroup Names

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 subgroup = 5-limit. Za = 7-all = 2.3.7. Yaza = 2.3.5.7 = 7-limit. Yaza nowa = 2.5.7.

Prime 2 is clear, abbreviated ca, and yaza noca = 3.5.7. 2-limit intervals like w8 are called wa not clear, for simplicity.

Note Names and Chord Names

Notes are named wC, zE♭, yyG#, etc. Notes are never large or small, only intervals are. Notes with no explicit color are assumed to be wa.

Interval arithmetic: wD + y3 = yF#. From yE to wG = g3.

Triads are named after their 3rd: Cy, Gz, etc. The four main yaza triads:

If the root isn't wa, the root color is added to the interval color: yAg = yA + (w1 g3 w5) = yA + wC + yE.

Tetrads are named Cy6, Dg7, etc. The 11 main yaza tetrads, with homonyms equated:

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 it has no 7th. There are h9 chords, s11 chords, etc.

Alterations are in parentheses, additions never are. Omissions are indicated by "no". Examples: Ch7(zg5)zg9 = w1 y3 zg5 z7 zg9.

The color of the 6th, 7th, and/or the 11th matches the color of the 3rd: Cy11 = C yE G yB D yF#.

Chord Progressions and Keys

The tonic is always wa. The root of each chord has a color, which defaults to wa. C - Am - F - G would be Cy - yAg - Fy - Gy.

In relative notation, the I, IV and V chords are assumed to have wa roots unless otherwise specified, so this becomes Iy -- yVIg -- IVy -- Vy.

Staff notation: Here's Ih7 -- IVh7 -- Ih7 -- Vh7 in B flat:

Keys are named as C gu, D zo yo, etc. Analogous to the relative and parallel major or minor, there is relative gu, parallel ru, etc.

Higher Primes

Colors for primes > 7 are named after the number itself:

Lova = 11-over, lu = 11-under, la = 11-all = 2.3.11. (Lova not lo, because "lo C" sounds like "low C".) Lova and lu are abbreviated to 1o and 1u on the score and in interval names and chord names, e.g. lova A = 1oA, lova 4th = 1o4 = 11/8 and C lova-7 = C1o7 = 1/1 - 11/9 - 3/2 - 11/6. The associated color is lavender (mnemonic: "e-leven-der"), which is a pseudocolor referring to both lova and lu, since they are only 7.1¢ apart (e.g. lo 3rd = 11/9 and lu 3rd = 27/22). More precisely, lova notes are lovender, and lu notes are luvender.

While the note 11/8 from C can be written two ways, either as 1oF or as 1oF#, the interval 11/8 can only be written one way, as 1o4.

Tho = 13-over, thu = 13-under, 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.

Yala = 2.3.5.11, yazalatha = 2.3.5.7.11.13 = 13-limit, and yalatha nowa = 2.5.11.13.

So = 17-over, su = 17-under, sa = 17-all, abbreviated as 17o and 17u. Sova is an alternate form of so, to distinguish it from the solfege syllable Sol.

Nova = 19-over, nunda = 19-under, na = 19-all, abbreviated as 19o and 19u. Nova because "no 3rd" could mean either 19/16 or thirdless. Nunda because "the nu key" sounds like "the new key".

Twenty-tho = 23-over, twenty-thu = 23-under, twenty-tha =23-all, abbreviated as 23o and 23u.

Twenty-no/-nu/-na = 29, thirty-wo/-wu/-wa = 31, thirty-so/-su/-sa = 37, etc.

The alternate forms with -ova or -unda are only needed when the color word appears alone. Thus 11/7 = loru 5th, not lovaru 5th.

Temperament Names

Temperaments are named after the color of the comma(s) they temper out. Meantone = the green temperament = gT. 5-limit Porcupine = triple yo = y³T. 7-limit porcupine = triple yo and ru = y³&rT. The magnitude is part of the name: Schismic is LyT. The degree is as well, if the comma is not the smallest of the 7 ratios of that magnitude and color: Mavila is Ly1T and Father is g2T. The temperament name indicates the prime subgroup and the rank of the temperament.