Chord names
(This page is part of a series on Kite's color notation)
7-limit JI offers a bewildering variety of chords with an incredible range of consonance and dissonance. Color notation gives us clear, concise names for them.
A triad is named after the color of its 3rd. The 5th is assumed to be wa. There are four main triads. They're shown here in close position with examples of both written names and spoken names. (The roots are mostly wa in these examples; the next chapter discusses root colors.)
Table 6.1 – Triads
| chord name | chord type | chord structure | examples | |||
|---|---|---|---|---|---|---|
| zo chord | minor chord | 1, z3, 5 | 1/1 – 7/6 – 3/2 | Fz | “F zo” | wF, zA♭, wC |
| gu chord | minor chord | 1, g3, 5 | 1/1 – 6/5 – 3/2 | Cg | “C gu” | wC, gE♭, wG |
| yo chord | major chord | 1, y3, 5 | 1/1 – 5/4 – 3/2 | Gy | “G yo” | wG, yB, wD |
| ru chord | major chord | 1, r3, 5 | 1/1 – 9/7 – 3/2 | B♭r | “B-flat ru” | wB♭, rD, wF |
Yo A is a note, whereas A yo is a chord. Chords can be referred to by structure as, say, y chords or zo chords. The chord type (major, minor, etc.) is analogous to interval quality, in that it's redundant (if it's yo, it must be major), it's not unique (there are other major triads available), and its main purpose is to indicate keyspan (both yo and ru triads will in close position have two intervals of 4 and 3 semitones each).
Table 6.2 – More triads, mostly dissonant
| chord name | chord type | chord structure | examples | ||
|---|---|---|---|---|---|
| wa chord | minor chord | 1, w3, 5 | 1/1 – 32/27 – 3/2 | Gw | wG, wB♭, wD |
| large wa chord | major chord | 1, Lw3, 5 | 1/1 – 81/64 – 3/2 | B♭Lw | wB♭, wD, wF |
| wa yo-5 chord | minor chord | 1, w3, y5 | 1/1 – 32/27 – 40/27 | Dw(y5) | wD, wF, yA |
| yo yo-5 chord | major chord | 1, y3, y5 | 1/1 – 5/4 – 40/27 | Gy(y5) | wG, yB, yD |
| four chord | four chord | 1, 4, 5 | 1/1 – 4/3 – 3/2 | C4 | wC, wF, wG |
| zo-four chord | four chord | 1, z4, 5 | 1/1 – 21/16 – 3/2 | C(z4) | wC, zF, wG |
Augmented and diminished triads are named after the color of the third and the fifth.
Table 6.3 – Augmented and diminished triads
| chord name | chord type | chord structure | examples | ||
|---|---|---|---|---|---|
| yo yoyo-5 chord | augmented | 1, y3, yy5 | 1/1 – 5/4 – 25/16 | A♭y(yy5) | gA♭, wC, yE |
| yo ruyo-5 chord | augmented | 1, y3, ry5 | 1/1 – 5/4 – 45/28 | B♭y(ry5) | wB♭, yD, ryF# |
| ru ruyo-5 chord | augmented | 1, r3, ry5 | 1/1 – 9/7 – 45/28 | B♭r(ry5) | wB♭, rD, ryF# |
| gu gugu-5 chord | diminished | 1, g3, gg5 | 1/1 – 6/5 – 36/25 | Eg(gg5) | yE, wG, gB♭ |
| gu zogu-5 chord | diminished | 1, g3, zg5 | 1/1 – 6/5 – 7/5 | Cg(zg5) | wC, gE♭, zgG♭ |
| zo zogu-5 chord | diminished | 1, b3, zg5 | 1/1 – 7/6 – 7/5 | Cz(zg5) | wC, zE♭, zgG♭ |
| yo ruyo-4 no 5 chord | maj dimin | 1, y3, ry4 | 1/1 – 5/4 – 10/7 | Cy,ry4no5 | wC, yE, ryF# |
| ru ruyo-4 no5 chord | maj dimin | 1, r3, ry4 | 1/1 – 9/7 – 10/7 | Cr,ry4no5 | wC, rE, ryF# |
Alterations are always enclosed in parentheses, and additions never are. Cg,zg5 would be a "C-gu add zogu-five" chord which has both w5 and zg5.
Augmented chords always have a high odd limit. They, along with full diminished tetrads, have no obvious yaza tuning. Min-maj chords, which contain an augmented triad, also fall into this category.
Tetrads: We assume a wa 5th. If the 6th/7th is the same color as the 3rd, the chord is named analogous to CM6 or Cm7, with a color replacing "M" or "m". Otherwise the 6th/7th is an added note. Here are my favorite tetrads:
Table 6.4 – Some low odd limit tetrads
| yo-6 chord | maj6 | 1, y3, 5, y6 | Cy6 | wC, yE, wG, yA | |
| gu-7 chord | min7 | 1, g3, 5, g7 | Cg7 | wC, gE♭, wG, gB♭ | (inversion of yo-6) |
| zo-7 chord | min7 | 1, z3, 5, b7 | Cz7 | wC, bE♭, wG, zB♭ | |
| ru-6 chord | maj6 | 1, r3, 5, r6 | Cr6 | wC, rE, wG, rA | (inversion of zo-6) |
| zo yo-6 chord | min6 | 1, z3, 5, y6 | Cz,y6 | wC, zE♭, wG, yA | |
| gu-7 zogu-5 | half-dim | 1, g3, zg5, g7 | Cg7(zg5) | wC, gE♭, zgG♭, gB♭ | (inversion of zo yo-6) |
| zo-7 zogu-5 | half-dim | 1, z3, zg5, z7 | Cz7(zg5) | wC, zE♭, zgG♭, zB♭ | |
| gu ru-6 (or sub-7) nchord | min6 | 1, g3, 5, r6 | Cg,r6 or Cs7 | wC, gE♭, wG, rA | (inversion of zo-7 zogu-5) |
| yo zo-7 (or aitch-7) chord | dom7 | 1, y3, 5, z7 | Cy,z7 or Ch7 | wC, yE, wG, zB♭ | |
| ru gu-7 chord | dom7 | 1, r3, w5, g7 | Cr,g7 | wC, rE, wG, gB♭ | |
| yo-7 chord | maj7 | 1, y3, 5, y7 | Cy7 | wC, yE, wG, yB |
The y,z7 and g,r6 chords have alternate names, because they follow the harmonic or subharmonic series. Note that the s7 chord doesn't have a 7th.
Because Amin7 and Cmaj6 have the same notes, the min7 chord and the maj6 chord are said to be homonyns of each other (a conventional music theory term). This concept is extended to just intonation for two chords containing the same ratios, and hence having the same lattice shape. The next diagram indicates homonym pairs with an equal sign:
Note that the over colors yo and zo go together, as do the under colors, gu and ru. Imagine the harmonic lattice rotated so that you're looking at the rows end-on; you can see which colors go with which.
Figure 6.1 – Cross section of the harmonic lattice
Neighboring colors, colors connected by a line, go together. Mixing non-neighboring colors makes more dissonant intervals with large numbers like 25, 35 and 49 in them, as in the first two chords in the next table:
Table 6.5 – Examples of tetrads with a high odd limit
| yo gu-7 chord | dom7 | 1, y3, 5, g7 | Cy,g7 | wC, yE, wG, gB♭ | odd limit = 25 |
| gu zo-7 chord | min7 | 1, g3, 5, z7 | Cg,z7 | wC, gE♭, wG, zB♭ | odd limit = 35 |
| yo wa-6 chord | maj6 | 1, y3, 5, w6 | Fy,w6 | wF, yA, wC, wD | odd limit = 27 |
| yo wa-7 chord | dom7 | 1, y3, 5, w7 | Cy,w7 | wC, yE, wG, wB♭ | odd limit = 45 |
Even though the last two chords use only neighboring colors, they have high odd limits. Neighboring colors don't guarantee consonant chords.
Full diminished tetrads are mostly non-neighboring, and always have a high odd limit.
Table 6.6 – Examples of full diminished tetrads
| gu ru-6 zogu-5 or sub-7 zogu-5 chord | dim7 | 1, g3, zg5, r6 | Cg,r6(zg5) or Cs7(zg5) | wC, gE♭, zgG♭, rA | odd limit = 49 |
| zo yo-6 zogu-5 chord | dim7 | 1, z3, zg5, y6 | Cz,y6(zg5) | wC, zE♭, zgG♭, yA | odd limit = 25 |
| wa yo-6 gu-5 chord | dim7 | 1, w3, g5, y6 | Cw,y6(g5) | wC, wE♭, gG♭, yA | odd limit = 75 |
| gu yo-6 gugu-5 chord | dim7 | 1, g3, gg5, y6 | Cg,y6(gg5) | wC, gE♭, ggG♭, yA | odd limit = 125 |
Many interesting chords are subsets of tetrads. The simplest ones contain only a fifth:
Table 6.7 – "Five" chords (dyads)
| 5 chord | five chord | 1, 5 | C5 | wC, wG | (or wa dyad, aka a power chord) |
| zogu-5 chord | dim five chord | 1, zg5 | C(zg5) | wC, zgG♭ | a type of 5 chord, hence thirdless |
Table 6.8 – Chords without a 3rd, but with a 6th or 7th
| 5 zo-7 chord | dom7, no 3rd | 1, 5, b7 | C5b7 | wC, wG, bB♭ | |
| 5 ru-6 chord | maj6, no 3rd | 1, 5, r6 | C5r6 | wC, wG, rA | |
| 5 yo-6 chord | maj6, no 3rd | 1, 5, y6 | C5y6 | wC, wG, yA | |
| 5 gu-7 chord | dom7, no 3rd | 1, 5, g7 | C5g7 | wC, wG, gB♭ | |
| zogu-5 zo-7 chord | half-dim, no 3rd | 1, zg5, z7 | C(zg5)z7 | wC, zgG♭, zB♭ | (inversion of yo ruyo-4 no-5 chord) |
Table 6.9 – Some fifth-less chords
| zo-7 no-5 chord | min7, no 5 | 1, z3, z7 | Cz7no5 | wC, zE♭, zB♭ | |
| gu ru-6 no-5 chord | min6, no 5 | 1, g3, r6 | Cg,r6no5 | wC, gE♭, rA | (inversion of zo zogu-5) |
| zo yo-6 no-5 chord | min6, no 5 | 1, z3, y6 | Cz,y6no5 | wC, zE♭, yA | (inversion of guzogu-5) |
In pentads and hexads, the 9th & 11th are assumed to be wa. A 9th implies a 7th, and an 11th implies a 9th. A wa 9th goes well with many chords with a major 3rd, and a wa 11th goes well with many minor-3rd chords.
Table 6.10 – Chords with 9ths and/or 11ths
| yellow add 9 chord | add 9 | 1, y3, 5, w9 | Cy,9 | wC, yE, wG, wD | |
| yellow blue-7, 9 chord | 9 chord | 1, y3, 5, b7, w9 | Cy,b7,9 | wC, yE, wG, bB♭, wD | |
| yellow-9 chord | maj7 + 9 | 1, y3, 5, y7, w9 | Cy9 | wC, yE, wG, yB, wD | |
| red-6 9 chord | maj6 + 9 | 1, r3, 5, r6, w9 | Cr6,9 | wC, rE, wG, rA, wD | |
| blue-7 11 chord
|
min7 add 11 | 1, b3, 5, b7, w11 | Cb7,11 | wC, bE♭, wG, bB♭, wF | |
| blue 11 no-3 chord
|
11 chord, no 3 | 1, 5, b7, w9, b11 | Cb11no3 | wC, wG, bB♭, wD, bF | (inversion ofblue blue add 11) |
| red green-7 9 chord | 9 chord | 1, r3, 5, g7, w9 | Cr,g7,9 | wC, rE, wG, gB♭, wD | |
| green red-6 11 chord
|
min6 add 11 | 1, g3, 5, r6, w11 | Cg,r6,11 | wC, gE♭, wG, rA, wF | (inversion of red green 9) |
Chords can be classified by the number of colors they contain (including wa) as a rough measure of their complexity. For example, the triads in table 6.1 are bicolored, but the aug & dim triads in table 6.3 are all tricolored.
To name larger chords, see chapter 3.8, JI chord names Part II. Excerpts from this chapter:
The most basic chord names are formed from stacked 3rds. 6th chords are also a stack of 3rds, if you think of the 6th as being below the root. These chords are named similar to CM7, Cm9, etc., but with a color replacing "M" or "m". The chord is formed by two chains of white 5ths. One chain has the root, the 5th, perhaps the 9th, and perhaps the 13th too, all white. The other chain has the 3rd, the 6th or 7th, and perhaps the 11th, all the same color.
| Cy | C yellow | w1 y3 w5 | the triad is named after the color of the 3rd |
| Cy6 | C yellow six | w1 y3 w5 y6 | the 6th's color matches the 3rd |
| Cy7 | C yellow seven | w1 y3 w5 y7 | the 7th's color matches the 3rd |
| Cy9 | C yellow nine | w1 y3 w5 y7 w9 | the 9th is assumed to be white |
| Cy11 | C yellow eleven | w1 y3 w5 y7 w9 y11 | the 11th's color matches the 7th |
| Cy13 | C yellow thirteen | w1 y3 w5 y7 w9 y11 w13 | the 13th is assumed to be white |
Added notes are listed after the stacked-3rds chord, using commas as needed:
| Cy,9 | C yellow, add nine | w1 y3 w5 w9 | needs a comma to distinguish it from Cy9 |
| Cy6,9 | C yellow six, nine | w1 y3 w5 y6 w9 | |
| Cy6,11 | C yellow six, eleven | w1 y3 w5 y6 w11 | an added 11th is assumed to be white... |
| Cy7,11 | C yellow seven, eleven | w1 y3 w5 y7 w11 | ...even when there's a non-white 7th |
| Cy7y11 | C yellow seven, yellow eleven | w1 y3 w5 y7 y11 | could instead be written Cy11no9 |
Harmonic-series chords, if named explicitly, would have cumbersome names. So there is a special format for them. "h" followed by a number means harmonic.
| Ch7 | 4:5:6:7 | w1 y3 w5 b7 | Cy,b7 | "C harmonic seven" or "C aitch seven" |
| Ch8 | invalid, no even numbers allowed | |||
| Ch9 | 4:5:6:7:9 | w1 y3 w5 b7 w9 | Cy,b7,9 | |
| Ch11 | 4:5:6:7:9:11 | w1 y3 w5 b7 w9 j11 | Cy,b7,9j11 | |
| Ch11no3 | 4:6:7:9:11 | w1 w5 b7 w9 j11 | Cb9j11no3 | the 3rd degree, not the 3rd harmonic |
| Ch11no5 | 4:5:7:9:11 | w1 y3 b7 w9 j11 | Cy,b7,9j11no5 | the 5th degree, not the 5th harmonic |
| Ch13 | 4:5:6:7:9:11:13 | w1 y3 w5 b7 w9 j11 e13 | Cy,b7,9j11e13 | |
| Ch13no11 | 4:5:6:7:9:13 | w1 y3 w5 b7 w9 e13 | Cy,b7,9e13 | |
Subharmonic-series chords: "s" followed by a color means small, but "s" followed by a number means subharmonic. The chords are pronounced "C subharmonic seven" or "C sub seven" or "C ess seven". The root of the chord is the 3rd subharmonic, to ensure the presence of a 3rd and a 5th. There is no correlation between subharmonic numbers and scale degrees. Omissions refer to degrees, but all other numbers refer to subharmonics. However, omissions larger than 13 refer to subharmonics: no15 means no 15th subharmonic (no minor 6th). Beware, the s7 chord is actually a min6 chord! It's an upside-down h7 chord. The h7's root is the s7's 5th, and the s7's root is the h7's 5th.
| Cs7 | 6/(4:5:6:7) | w5 g3 w1 r6 | Cg,r6 | |
| Cs9 | 6/(4:5:6:7:9) | w5 g3 w1 r6 w4 | Cg,r6,11 | or Cg,4r6 |
| Cs9no3 | 6/(4:6:7:9) | w5 w1 r6 w4 | C4r6 | no 5th subharmonic, g3 |
| Cs9no6 | 6/(4:5:6:9) | w5 g3 w1 w4 | Cg,4 | no 7th subharmonic, r6 |
| Cs11 | 6/(4:5:6:7:9:11) | w5 g3 w1 r6 w4 a9 | Cg,r6a9,11 | |
| Cs11no11 | 6/(4:5:6:7:11) | w5 g3 w1 r6 a9 | Cg,r6a9 | no 9th subharmonic, w11 |
| Cs13 | 6/(4:5:6:7:9:11:13) | w5 g3 w1 r6 w4 a9 o7 | Cg,r6o7a9,11 | |
| Cs9,15 | 6/(4:5:6:7:9:15) | w5 g3 w1 r6 w4 g6 | Cg6r6,11 | or Cg6,4r6 |
| Cs17no15 | 6/(4:5:6:7:9:11:13:17) | w5 g3 w1 r6 w4 a2 o7 17q4 | no 15th subharmonic, g6 |