Color notation

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Color notation is a musical notation system for just intonation that was primarily developed by Kite Giedraitis.

Color notation has many features that other microtonal notations lack:

  • No new symbols: all new accidentals are familiar characters; hence they are immediately speed-readable.
  • Furthermore, they are all on the QWERTY keyboard, making the notation easily typeable.
  • Every new accidental has a spoken name (colorspeak), making the notation speakable.
  • Most importantly, one can name not only notes but also intervals. As a result, color notation can name scales, chords, chord progressions and even prime subgroups and temperaments.

Colorspeak is designed to be an international language, a sort of microtonal Esperanto quickly learned and spoken no matter what one's native language is. Almost every term in colorspeak is one syllable ending with a vowel. The five basic vowels are pronounced ah-eh-ee-oh-oo as in Spanish or Italian.

Color names for primes 3, 5 and 7

Every prime above 3 has two colors, an over color (prime in the numerator) and an under color (prime in the denominator). Over colors end with -o, and under colors end with -u. The color for 3-limit ends in -a for all, which includes over (3/2, 9/8), under (4/3, 16/9) and neither (1/1, 2/1).

3-all = wa = white (strong but colorless) = often perfect
5-over = yo = yellow (warm and sunny) = often major
5-under = gu ("goo") = green (not as bright as yellow) = often minor
7-over = zo = blue/azure (dark and bluesy) = often subminor
7-under = ru = red (alarming, inflamed) = often supermajor

The colors make 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 or Spanish/Portuguese azul), not b (blue), because b already means flat. Mnemonic: Z looks like 7 with an extra line on the bottom.

Interval names

A color and a degree indicate 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 always 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 rows, each one a chain of 5ths. Each row has its own color, and each color has its own row.


The following table lists all the intervals in this lattice. See the gallery of just intervals for many more examples.

ratio cents color & degree
1/1 wa unison w1
21/20 84¢ zogu 2nd zg2
16/15 112¢ gu 2nd g2
15/14 119¢ ruyo unison ry1
10/9 182¢ yo 2nd y2
9/8 204¢ wa 2nd w2
8/7 231¢ ru 2nd r2
7/6 267¢ zo 3rd z3
6/5 316¢ gu 3rd g3
5/4 386¢ yo 3rd y3
9/7 435¢ ru 3rd r3
21/16 471¢ zo 4th z4
4/3 498¢ wa 4th w4
7/5 583¢ zogu 5th zg5
10/7 617¢ ruyo 4th ry4
3/2 702¢ wa 5th w5
32/21 729¢ ru 5th r5
14/9 765¢ zo 6th z6
8/5 814¢ gu 6th g6
5/3 884¢ yo 6th y6
12/7 933¢ ru 6th r6
7/4 969¢ zo 7th z7
16/9 996¢ wa 7th w7
9/5 1018¢ gu 7th g7
28/15 1081¢ zogu octave zg8
15/8 1088¢ yo 7th y7
40/21 1116¢ ruyo 7th ry7
2/1 1200¢ wa octave 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 #Color Names for Higher Primes below for why). Intervals on the lattice's far right or far left are called not augmented and diminished but large and small, written as L and s, and abbreviated as la and sa. La and sa can always be distinguished from solfege's La and saregam's Sa by context. Central, the default, means neither large nor small. This lattice shows the boundaries between the large, small and central zones:


The general term for large/small/central is magnitude. Only intervals have a magnitude, notes never do, and L and s never appear on the staff. A ratio's magnitude is the sum of all the monzo exponents except the first one, divided by 7, and rounded off. 0 = central, 1 = large, 2 = double large, etc. 81/64 = [-6 4>, and 4/7 rounds to 1, so 81/64 = Lw3. 135/128 = [-7 3 1> = Ly1. Unfortunately, magnitudes do not add up predictably like colors and degrees: w2 + w2 = Lw3.

Colors can be doubled or tripled, which are abbreviated bi- ("bee") and tri- ("tree"): 49/25= bizogu 9th = zzgg9 and 128/125 = trigu 2nd = g32. Bi- is only used if it shortens the name: 25/16 = yoyo 5th not biyo 5th. Likewise with magnitudes: double-large is lala and triple-large is trila. For quadruple, etc., see #Exponents.

Colors using only one prime above 3 are called primary colors. Thus gu and yoyo are primary and ruyo is non-primary.

Degrees can be negative: 50/49 = biruyo 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 notated as 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 dim unison.

Compound, abbreviated co- or c, is a conventional music theory term that means widened by an octave. 15/4 is a compound yo 7th = coyo 7th = cy7. 5/1 is a double-compound yo 3rd = cocoyo 3rd = ccy3. 9/1 is a tricowa 2nd = c3w2. More examples in the Gallery of just intervals. Mnemonic: co- as in co-pilot means auxiliary, thus a 9th is a co-2nd. See #Prime Subgroup Names below for another mnemonic.

Note names

Notes are named zEb, yyG#, etc. spoken as "zo E flat" and "yoyo G sharp". Notes are never large or small, only intervals are. Uncolored notes default to wa. The relative-notation lattice above can be mentally superimposed on this absolute-notation lattice to name every note and interval. For example, D + y3 = yF#, and from yE to ryF# = r2.


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 prime subgroup = 5-limit. Za = 7-all = 2.3.7 = no-fives 7-limit. Yaza = = 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 = Bohlen-Pierce. 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, and in certain theoretical discussions. However, an additional mnemonic for "co-" (compound, widened by an octave) is "clear-over", in the sense that the ratio's numerator is multiplied by 2.

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:

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 when with other words, it doesn't need i-, as in 11/7 = loru 5th. La when by itself becomes ila, to avoid confusion with the solfege note La, and also with la for large. 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 seven = C1o7 = 1/1 - 11/9 - 3/2 - 11/6 on C. Lolo is 1oo, trilu is 1u3, 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 Lulu aka Neutral 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, 14/13 = 3uz2 = thuzo 2nd.

Prime subgroups: yala =, zalatha nowa =, and yazalatha = = 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. This is the rationale for using large/small/central rather than major/minor. 11/9 is ambiguously major or minor, but unambiguously central. Intervals names and chord names become unambiguous for la and tha intervals. Another rationale is that 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, 17u and 17a. Iso is an alternate form of so, to distinguish it from the solfege syllable So. 17/12 = 17o5 = iso So. Isa is an alternate form of sa, to distinguish it from sa for small, and from the Indian saregam syllable Sa.

No = 19-over, nu = 19-under, and na = 19-all, abbreviated as 19o, 19u and 19a. Ino is an alternate form of no, because "no 3rd" could mean either 19/16 or thirdless. Inu is an alternate form of nu, to distinguish "the nu chord" from "the new chord".

The prefix i- is only used when confusion is possible. Thus 19/15 = nogu 4th not inogu 4th, and (implied by 12edo) is yasana not yasaina.

Twetho = 23-over, twethu = 23-under, and twetha = 23-all, abbreviated as 23o, 23u and 23a. = yaza23a = yazatwetha. 23/16 = 23o5 = twetho 5th, and 23/22 = 23o1u2 = twetholu 2nd. 529/512 = 23oo2 = bitwetho 2nd (not twethotho, because that means 23-over 13-over).

Similarly, tweno/-nu/-na = 29o/29u/29a, thiwo/-wu/-wa = 31o/31u/31a, etc. The abbreviations are twe-, thi-, fo-, fi- and si-. Note that wa by itself means 3-limit, but -wa as a suffix means "-one-all".

prime 5/4 7/4 11/8 13/8 17/16 19/16 23/16 29/16 31/16 37/32 41/32 43/32 47/32 53/32 59/32 61/32 67/64
y3 z7 1o4 3o6 17o2 19o3 23o5 29o7 31o7 37o3 41o3 43o4 47o5 53o6 59o7 61o7 67o2
word ya za (i)la tha (i)sa (i)na twetha twena thiwa thisa fowa fotha fosa fitha fina siwa sisa

Mnemonic (sung to the tune of "Supercalifragilisticexpialidocious"):

Yaza latha sana twetha twena thiwa thisa / Fowa fotha fosa fitha fina siwa sisa

Unfortunately seventy can't become se- because that already means 17-exponent (see #Exponents below). Setho means 1317-over, so it can't mean 73-over. So starting at 71, one might use the longer form: 71o is seventy-wo, 73o is seventy-tho, etc. 103o is hundred-tho and 113o is one-ten-tho. Or one might use these terms:

prime 71/64 73/64 79/64 83/64 89/64 97/64 101/64 103/64 107/64 109/64 113/64 127/64
71o2 73o2 79o3 83o4 89o4 97o5 101o6 103o6 107o6 109o6 113o7 127o8
word fitwewa fitwetha fitwena fithitha fithina fifosa fifiwa fifitha fifisa fifina fisitha sisisa

Note that 23/16 = 628¢ is a 5th, not a 4th. Furthermore, 31/16 = 1145¢ is a 7th not an 8ve, and 37/32 = 251¢ is a 3rd not a 2nd. For any prime P, the degree of the ratio P/1 is chosen to minimize negative intervals. It is determined by its 8ve-reduced cents, and how it relates to 12edo:

unison 2nd 3rd 4th 5th 6th 7th 8ve
0-50¢ 50-250¢ 250-450¢ 450-600¢ 600-750¢ 750-950¢ 950-1150¢ 1150-1200¢

This makes the "pseudo-edomapping" <7 11 16 20 24 26 29 30 32 34 37...]. An alternative method would use the actual 7edo edomapping, but that requires using every other 14edostep as boundaries, harder to remember and much less convenient than the 24edo boundaries used here. Since negative intervals will arise no matter what, convenience is prioritized. For the first 26 primes, the 24edo-based degrees correspond to 7klmrs-edo.


Exponent syllables aka multiplier syllables provide a way to shorten names that have repeated syllables. For example, 250/243 = 21 * 3-5 * 53 is a yoyoyo unison which shortens to triyo 1sn. Exponents can apply to magnitudes (Wa-22 = sasasawa 4th --> trisawa 4th) or octaves (13/1 = cococotho 6th --> tricotho 6th).

We've seen bi- for double and tri- for triple. Quadruple and quintuple are abbreviated quad- and quin-, as in quadyo or quingu. Colorspeak syllables usually end in one of the five basic vowels. Quad and quin are both exceptions, so quad may optionally be spoken as "kwah", and quin as "kwee".

Except for quad, all exponent syllables are prime numbers. Septuple is sep-. Above 7, all exponent syllables are the root color word plus -e. Eleven-fold is le- = "eleven exponent", pronounced as in "legitimate". Thirteen-fold is the- as in "thesaurus". Note that sep- means seven-fold and se- means seventeen-fold.

Exponents can be combined: sextuple = tribi-, 8-fold = quadbi-, 9-fold = tritri-, 10-fold = quinbi-, 12-fold = quadtri-, 14-fold = sepbi-, 15-fold = quintri-, 16-fold = quadquad-, etc. The component syllables are simply the number's prime factors in descending order, except that quad replaces bibi and comes before tri.

Exponents affect all subsequent syllables until the -a- delimiter occurs: trizogu = z3g3, but trizo-agu = z3g. The "a" in la- and sa- also acts as a delimiter: trilayo = L3y, not L3y3, which would be trila-triyo.

Long color names use hyphens to make the name easier to parse. There are strict rules for hyphenation, to ensure uniformity.

  • Put a hyphen before every -a- delimiter
  • Put a hyphen after the magnitude (after the final la- or sa-)
  • Put a hyphen after coco-, trico-, etc.
  • Put a hyphen before and after "seventy", "eighty", etc.

The hyphen is generally omitted if it would create a subunit of 1 syllable. Thus despite the 2nd rule, layo, lalagu and sagugu are all unhyphenated. And despite the 3rd rule, coyo, cozogu and cocowa are unhyphenated. However, the last rule always holds, e.g. 284/243 = 22 * 3-5 * 71 is a sa-seventy-wo 3rd.

Converting a ratio to/from a color name

Often a ratio can be converted by breaking it down into simpler ratios with familiar color names, then adding. For example, 45/32 is 5/4 times 9/8, which is y3 plus w2. The colors and degrees are summed, making y4. The magnitude is not summed, and must be found either visually from the lattices above, or from the monzo directly. 45/32 = [-5 2 1>, and (2+1)/7 rounds to 0, so it's central, and 45/32 = y4.

For more complex ratios, a more direct method is needed:

Converting a ratio: Find the monzo by prime factorization. To find the color, combine all the appropriate colors for each prime > 3, higher primes first. To find the degree, first find the stepspan, which is the dot product of the monzo with the "pseudo-edomapping" discussed above <7 11 16 20 24 26 29 30...]. Then add 1, or subtract 1 if the stepspan is negative. To find the magnitude, add up all the monzo exponents except the first one, divide by 7, and round off. Combine the magnitude, color and degree to make the color name. If the interval is > 1200¢, octave-reduce as desired (e.g. a 9th may or may not become a compound 2nd). Add one co- prefix for every octave removed. Combine repeated syllables so that three yo's becomes triyo, etc. For the exact combination "grammar", see Color notation/Temperament Names.

Example: ratio = 63/40

  • monzo = [-3 2 -1 1>
  • color = zogu
  • stepspan = <7 11 16 20] dot [-3 2 -1 1> = -21 + 22 - 16 + 20 = 5 steps
  • degree = 5 + 1 = a 6th
  • magnitude = round [(2 + (-1) + 1) / 7] = round (2/7) = 0 = central
  • interval = zogu 6th or zg6 (63/20 would be zg13 = czg6)

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 C be the number of "co-" prefixes. Let the monzo be [a b c d e...>. The colors directly give you all the monzo entries except a and b. Let S' = the dot product of [0 0 c d e...> with the pseudo-edomapping. Let M' = round ((2 (S - S') + c + d + e + ...) / 7). Then a = -3 (S - S') - 11 (M - M') + C and b = 2 (S - S') + 7 (M - M'). (Derivation here) Convert the monzo to a ratio.

Example: interval = sgg2 = sagugu 2nd

  • S = 2 - 1 = 1 step, M = small = -1, C = 0. Monzo = [a b -2>
  • S' = <7 11 16] dot [0 0 -2> = -32. S - S' = 1 - (-32) = 33.
  • M' = round ((2·33 + (-2)) / 7) = round (64 / 7) = 9. M - M' = -1 - 9 = -10.
  • a = -3 (S - S') - 11 (M - M') + C = -3·33 - 11·(-10) + 0 = -99 + 110 = 11.
  • b = 2 (S - S') + 7 (M - M') = 2·33 + 7·(-10) = 66 - 70 = -4
  • Monzo = [11 -4 -2>, ratio = 2048/2025.

Staff notation

Notes on the staff default to wa. Non-wa notes have a color accidental like g, ry, etc. Like conventional sharp/flat accidentals, they apply to every such note in the measure and in the same octave. Unlike conventional accidentals which apply to a note (e.g. A), color accidentals only apply to one specific "version" of that note (e.g. A flat or A natural). For example, the yo accidental in the first chord applies to all the D-naturals in that measure, but not to the D-flats.

Notation example 1.png

L and s never appear on the staff. Tripled colors are written as y3 not y3 or yyy. In MuseScore, color accidentals are made by adding fingerings to the notes, then editing the fingering text. A fingering can be copied from one note and pasted to another note. The font used here is Arial Black.

This 10-page score uses the free open-source font Petaluma Script. The letters are 9pt, except that a "z" between two staff lines is 8pt. File:Evening Rondo colors.pdf

Color signatures

Staff notation can optionally include a color signature written above the staff. This makes color notation more similar to Johnston notation.

Notation example 2.png

Po and qu

Po and qu ("coo") (short forms p and q) are two optional accidentals that indicate raising/lowering by a pythagorean comma. (Mnemonics: p stands for pythagorean, and q is the mirror image of p.) Why would one want to do that? Because by first subtracting that comma and then adding it on again, one can rename a note as another note. This is similar to Sagittal notation (see Sagittal-JI-Translated-To-Colors.png).

For example, F# minus a pythagorean comma is Gb. And Gb plus a pythagorean comma is po Gb. Thus an alternate name for F# is po Gb. Adding po raises the degree by one. The new note name is always a 12edo equivalent of the old note name. Adding qu lowers the degree: Gb = qu F#. If one is resolving from Gb to G, one can rename Gb as qF#.

Subtracting po lowers the degree. Thus ruyopo Db = ruyo C#.

Po and qu can be used with intervals as well. A ruyo 1sn becomes a ruyopo 2nd. Neither the color nor the magnitude changes.

One reason to change the degree is for ease of naming chords. See the Hendrix chord in the next section. Another reason is to avoid an awkward unison trill. Notation example 5a.png

Chord names

Triads are named after their 3rd, e.g. a yo chord has a yo 3rd. A yo chord rooted on C is a Cy chord = "C yo" = C yE G. Qualities such as major and minor aren't used, because a chord with an 11/9 3rd is hard to classify. Thirdless dyads are written C5 = w1 w5 or C(zg5) = w1 zg5. The four main yaza triads:


Tetrads are named e.g. "C yo-six" = Cy6 = C yE G yA. The 11 main yaza tetrads, with chord homonyms (same shape, different root) equated:


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 added 11th defaults to wa, as in z7,11:


Alterations are always in parentheses, 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. The sus note defaults to wa. A 6:8:9 chord could be written C(4), but the parentheses rule is relaxed to allow the conventional C4. Likewise 8:9:12 is C2. But if the sus note isn't wa, parentheses must be used. Thus w1 z4 w5 = C(z4) = "C zo-four". More examples:

  • 6:7:8:9 = Cz,4 = "C zo add-four"
  • w1 w4 w5 y7 w9 = Cy9(4) = "C yo-nine sus-four"
  • w1 z4 w5 z7 = Cz7(z4) or C(z4),z7 = "C zo-seven zo-four" or "C zo-four zo-seven"

Omissions are indicated by "no". The Hendrix chord is Ch7z10no5. (To write it as a sharp-9 chord, use po/qu: 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 called the h7 chord ("har-seven"), because it's part of the harmonic series. Ch9 = Cy,z7,w9 and Ch11 = Cy,z7,w9,1o11. The s7 ("sub-seven") chord is part of the subharmonic series. It's the first 7 subharmonics, with the 7th subharmonic becoming the root. Cs9 = Cr,g7,w9 and Cs11 = C1o11(1or5,1og9). Note that s9 is not s7 plus a 9th, but a completely different chord. Usually the 9th ascends from the root, but in a sub9 chord it descends from the top note, and becomes the new root. Thus the s7 chord is contained in the upper four notes of the s9 chord, not the lower four.

Cs6 = Cg,r6 = 12/(12:10:8:7). Other than the s6 chord, all harmonic/subharmonic numbers must be odd, Ch6 and Ch8 are invalid. For any odd number N >= 7, ChN is 1:3:5:7...N and CsN is N/(N...7:3:5:1). Additions, alterations and omissions refer to degrees, not harmonics or subharmonics: Ch7,11 adds w11, not 1o11. Ch9no5 omits w5, not y3. However, all numbers > 13 refer to (sub)harmonics, e.g. Ch9,15 adds y7 and Ch19no15 omits it.

Chords can be classified as bicolored (e.g. g7 or r6), tricolored (e.g. z7(zg5) or z,y6), quadricolored (e.g. s6(zg5) or h7,zg9), etc.

Chord progressions, keys, scales and modulations

The tonic is always wa. The root of each chord has a color, which defaults to wa. C - Am - F - G7 might become Cy - yAg - Fy - Gy,w7, spoken as "C yo, yo A gu, F yo, G yo wa-seven". If the root isn't wa, the root color is added to each interval's color. Thus yAg = yA + (w1 g3 w5) = yA + wC + yE.

In relative notation, the previous example becomes Iy - yVIg - IVy - Vy,w7, spoken as "one yo, yo-six gu, four yo, five yo wa-seven". Never use lower-case roman numerals for minor chords: ii becomes IIg or IIz. A IIIy chord has a w3 root, which is 32/27 not 81/64. The latter would be a LwIIIy chord (use L and s, not # and b; #IIIy is invalid).

In adaptive JI, chords are just, but roots move by tempered intervals. Comma pumps are indicated with brackets roughly halfway through he pump: Cy - yAg - [y=w]Dg - Gy - Cy. The pattern is [old=new]: the previous chord implies yDg and the following chord implies wDg. See Comma pump examples.

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, scales can be classified as bicolored (A gu), tricolored (Bb yo zo), etc.

Analogous to the relative and parallel major or minor, one can modulate to relative gu, parallel ru, etc. Modulating from a yo key to the relative gu means using gu chords on yo roots. Modulating from yo to the parallel gu means using gu chords on wa roots. Going from yo zo to the relative gu means using chords with gu and/or ru in them on yo roots. Going to the relative ru means using the same chords on zo roots. Going from yo zo to the parallel gu ru means using the same chords on wa roots. One can also modulate fourthward or fifthward, abbreviated 4thwd or 5thwd. Modulating in either direction is modulating waward. Modulating from a yo key to the relative gu, then from there to the parallel yo is modulating yoward. A root movement by a yo interval (e.g. Iy - yVIg) is a yoward move. Likewise, there's guward, and yaward includes both. Likewise, there's zoward, ruward, zaward, iloward, etc.

Temperament names and comma names

Temperaments are named after the comma(s) they temper out. Commas are named using an alternate format that omits the degree. Meantone is the Gu temperament. Srutal is Sagugu. Porcupine is Triyo or y3T, where "T" stands for temperament. Certain commas over 90¢ use the -bi suffix, e.g. Mavila is Layobi or Ly#2T, because Layo is Schismic. Certain wa commas use yet another alternate format, e.g. Mercator's comma is Wa-53 or w-53.

Multi-comma temperaments have multiple commas in their name. Septimal Meantone is Gu & Ruyoyo and Dominant Meantone is Gu & Rugu. Untempered primes are included with a plus sign. The prime subgroup with 81/80 tempered out is Gu + za.

MOS and MODMOS scales can be named as e.g. Triyo[8]. Individual modes can be named as 2nd Triyo[8], 3rd Triyo[7] b7, etc. See Naming Rank-2 Scales using Mode Numbers.

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 intervals in edos, and colors can be used as well. A more precise notation uses 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 (5, 7, 9, 12, 16, 19, 23, etc.) 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.

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. 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 notation guide for edos 5-72

Rank-2 temperaments can be notated with ups and downs as well. Plain and mid are also used in this context. Certain 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 pergens.

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 = Exponent = repeated syllable: triyo = yoyoyo = 125-over.

prime -o ("oh") for over -u ("oo") for under -a ("ah") for all -e ("eh") for exponent
2 (clear) bi ("bee") squared
3 wa (white) tri ("tree") cubed
5 yo (yellow) y gu (green) g ya quin ^5
7 zo (azul) z ru (red) r za sep ^7
11 ilo 1o lu 1u ila 1a le ^11
13 tho 3o thu 3u tha 3a the ^13
17 so 17o su 17u isa 17a se ^17
19 ino 19o inu 19u na 19a ne ^19
23 twetho 23o twethu 23u twetha 23a twethe ^23

Higher primes: 29o = tweno, 31o = thiwo, 37o = thiso, 41o = fowo, 43o = fotho, 47o = foso, 53o = fitho, 59o = fino, 61o = siwo, 67o = siso.

Pronunciation: exponent syllables like bi or tri are always unaccented. To emphasize the prime limit, the first occurrence of the highest prime is always accented: Biruyo, Bizozogu. In longer names, the 1st occurrence of sa/la and/or of lower primes may also be accented: Sasa-gugu, Zozotrigu.

word meaning example
quad quadruple, exponent of 4 Diminished temperament = 648/625 = Quadgu = g4T
Wa- w- alternate interval format, only used for 3-limit commas Mercator's comma = Wa-53 = w-53
-bi #2 as a suffix, 2nd smallest comma in the row segment Meantone = 81/80 = Gu = gT, Father = 16/15 = Gubi = g#2T
la L large, augmented by 2187/2048 from the central ratio 32/27 = wa 3rd = w3, 81/64 = lawa 3rd = Lw3
sa s small, diminished by 2187/2048 from the central ratio 27/16 = wa 6th = w6, 128/81 = sawa 6th = sw6
nowa remove 3 (wa) from the prime subgroup, i.e. no-threes 2.5.7 = yaza nowa, 2.5.7 with 50/49 = Biruyo nowa
noca remove 2 (clear) from the prime subgroup, i.e. non-8ve 3.5.7 = yaza noca, 3.5.7 with 245/243 = Zozoyo noca
nowaca remove both 2 and 3 from the prime subgroup 5.7.11 = yazala nowaca
plus + add an untempered prime to the temperament Blackwood = 2.3.5 with 256/243 tempered out = Sawa + ya
and & joins commas that are tempered out 7-limit Porcupine = with 250/243 & 64/63 = Triyo & Ru
i- disambiguation prefix no 3rd = omit the 3rd, ino 3rd = 19/16
-a- delimits an exponent such as bi-, tri-, etc. Trizogu = z3g3 = 1029/1000, Trizo-agu = z3g = 343/320
co- c compound (conventional term for widened by an 8ve) 7/4 = zo 7th = z7, 7/2 = compound zo 7th = cozo 7th = cz7
-ward -wd refers to the direction of chord root movement Iy - IVy = 4thwd, Iy - Vy = 5thwd, Iy - yIIIy = yoward, Ig - gIIIg = guward
har h refers to a harmonic series (otonal) chord 4:5:6:7 = C har seven = Ch7
sub s refers to a subharmonic series (utonal) chord 7/(7:6:5:4) = C sub seven = Cs7
po p adds a pythagorean comma, to change the degree 15/14 = ruyo unison = ry1 = ruyopo 2nd = ryp2
qu q subtracts a pythagorean comma 49/48 = zozo 2nd = zz2 = zozoqu unison = zzq1


  • "wa" means both "3-all" and "-one-all" (e.g. thiwa means 31-all). The meaning is always clear from context.
  • "la" means both "11-all" and "large", and also the solfege note La. Thus 1a may become "ila".
  • "lo" means both "11-over" and "low", as in "low C". Thus 1o may become "ilo".
  • "sa" means both "17-all" and "small", and also the Saregam note Sa. Thus 17a may become "isa".
  • "so" means both "17-over" and the solfege note So. Thus 17o may become "iso".
  • "no" means both "19-over" and "omit", as in no3. Thus 19o may become "ino".
  • "nu" means both "19-under" and "new", as in "the new key". Thus 19u may become "inu".

Temperaments use "virtual colors" represented with ^ v and / \:

word meaning
up ^ raised by some comma
down v lowered by some comma
lift / raised by some other comma
drop \ lowered by some other comma
plain neither up nor down nor lifted nor dropped
mid ~ for 2nds, 3rd, 6ths and 7ths, exactly halfway between major and minor

for 4ths, halfway-augmented, and for 5ths, halfway-diminished


For translations of color notation terms into other languages, see Color notation/Translations. Translating avoids using sounds not in one's native language. For example, in many European languages, "th-" for prime 13 becomes "tr-".

See also

  • xen-calc - A web app that converts to/from ratios, monzos and color notation, and also supports ups and downs notation.

Further reading