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(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 white. 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 white in these examples; the next chapter discusses root colors.)
Table 6.1 – Triads
chord name
chord type
chord structure
examples
blue chord
minor chord
1, b3, 5
1/1 – 7/6 – 3/2
Fb
“F blue”
wF, bA, wC
green chord
minor chord
1, g3, 5
1/1 – 6/5 – 3/2
Cg
“C green”
wC, gE, wG
yellow chord
major chord
1, y3, 5
1/1 – 5/4 – 3/2
Gy
“G yellow”
wG, yB, wD
red chord
major chord
1, r3, 5
1/1 – 9/7 – 3/2
B♭r
“B-flat red”
wB, rD, wF

lattice62.png

Yellow A is a note, whereas A yellow is a chord. Chords can be referred to by structure as, say, y chords or b chords. The chord type (major, minor, etc.) is analogous to interval quality, in that it's redundant (if it's yellow, it must be major), it's not unique (there are other major triads available), and its main purpose is to indicate keyspan (both yellow and red triads will in close position have two intervals of 4 and 3 semitones each).
Like ratios, a chord's dissonance mostly comes from its "bigness" and "utonalness". The bigness is the odd limit; the previous four triads all have an odd limit of 9 or less. Yellow and blue are otonal, green and red are utonal.
Table 6.2 – More triads, mostly dissonant
chord name
chord type
chord structure
examples
white chord
minor chord
1, w3, 5
1/1 – 32/27 – 3/2
Gw
wG, wB, wD
large white chord
major chord
1, Lw3, 5
1/1 – 81/64 – 3/2
BLw
wB, wD, wF
white yellow-5 chord
minor chord
1, w3, y5
1/1 – 32/27 – 40/27
Dw(y5)
wD, wF, yA
yellow yellow-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
blue four chord
four chord
1, b4, 5
1/1 – 21/16 – 3/2
C(b4)
wC, bF, wG
All but one of these chords have a fairly large odd limit, as seen by the size of the numbers in the 4th column. The first two are white chords, the bane of 3-limit JI. The next two are yellow-5 chords, the bane of 5-limit JI. The b4 chord shows up as a suspension in a V7 – I cadence, if the 7th in V7 is blue: G – yB – D – bF to G – C – bF to G – C – yE.
Augmented and diminished triads are named after the color of the third and the fifth. However if the fifth has a deep color, the third's color is implied. The terms bluish and reddish always refer to the bluish 5th and the reddish 4th, unless otherwise specified.
Table 6.3 – Augmented and diminished triads
chord name
chord type
chord structure
examples
yellow deep-yellow-5 chord
augmented
1, y3, yy5
1/1 – 5/4 – 25/16
Ay(yy5)
gA, wC, yE
yellow reddish-5 chord
augmented
1, y3, ry5
1/1 – 5/4 – 45/28
By(ry5)
wB, yD, ryF#
red reddish-5 chord
augmented
1, r3, ry5
1/1 – 9/7 – 45/28
Br(ry5)
wB, rD, ryF#
green deep-green-5 chord
diminished
1, g3, gg5
1/1 – 6/5 – 36/25
Eg(gg5)
yE, wG, gB
green bluish-5 chord
diminished
1, g3, bg5
1/1 – 6/5 – 7/5
Cg(bg5)
wC, gE, bgG
blue bluish-5 chord
diminished
1, b3, bg5
1/1 – 7/6 – 7/5
Cb(bg5)
wC, bE, bgG
yellow reddish-4 no 5 chord
maj dimin
1, y3, ry4
1/1 – 5/4 – 10/7
Cy,ry4no5
wC, yE, ryF#
red reddish-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,bg5 would be a "C-green add bluish-five" chord which has both w5 and bg5.

Augmented chords always have a high odd limit. They, along with full diminished tetrads, have no obvious 7-limit JI intonation. Min-maj chords, which contain an augmented triad, also fall into this category.
Tetrads: We assume a white 5th and name the chord after the 3rd and the 6th/7th. We assume the 6th/7th lies in the “sweet spot” from 5/3 to 9/5 (I call this type of interval a subseventh, a name inspired by pentatonicism; see chapter 19.) We assume it is not white, which allows us to dispense with the terms 6th and 7th. Here are my favorite tetrads:
Table 6.4 – Some low odd limit tetrads
yellow-6 chord
maj6
1, y3, 5, y6
Cy6
wC, yE, wG, yA

green-7 chord
min7
1, g3, 5, g7
Cg7
wC, gE, wG, gB
(inversion of yellow yellow)
blue-7 chord
min7
1, b3, 5, b7
Cb7
wC, bE, wG, bB

red-6 chord
maj6
1, r3, 5, r6
Cr6
wC, rE, wG, rA
(inversion of blue blue)
blue yellow-6 chord
min6
1, b3, 5, y6
Cb,y6
wC, bE, wG, yA

green-7 bluish-5
half-dim
1, g3, bg5, g7
Cg7(bg5)
wC, gE, bgG, gB
(inversion of blue yellow)
blue-7 bluish-5
half-dim
1, b3, bg5, b7
Cb7(bg5)
wC, bE, bgG, bB

green red-6 chord
min6
1, g3, 5, r6
Cg,r6
wC, gE, wG, rA
(inversion of blue blue bluish)
yellow blue-7 chord
dom7
1, y3, 5, b7
Cy,b7 or Ch7

wC, yE, wG, bB

red green-7 chord
dom7
1, r3, w5, g7
Cr,g7
wC, rE, wG, gB

yellow-7 chord
maj7
1, y3, 5, y7
Cy7
wC, yE, wG, yB


lattice63.png

To my ears, the y7 chord, whose odd limit is 15, is considerably more consonant than the g,r6 chord, odd limit 7. The g,r6 chord has smaller numbers, but the green and red make it far more utonal and hence more dissonant.
Note that the otonal colors yellow and blue go together, as do the utonal colors, green and red. 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
lattice61.png
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
yellow green-7 chord
dom7
1, y3, 5, g7
Cy,g7
wC, yE, wG, gB
odd limit = 25
green blue-7 chord
min7
1, g3, 5, b7
Cg,b7
wC, gE, wG, yB
odd limit = 35
yellow white-6 chord
maj6
1, y3, 5, w6
Fy,w6
wF, yA, wC, wD
odd limit = 27
yellow white-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
green red-6 bluish-5 chord
dim7
1, g3, bg5, r6
Cg,r6(bg5)
wC, gE, bgG, rA
odd limit = 49
blue yellow-6 bluish-5 chord
dim7
1, b3, bg5, y6
Cb,y6(bg5)
wC, bE, bgG, yA
odd limit = 25
white yellow-6 green-5 chord
dim7
1, w3, g5, y6
Cw,y6(g5)
wC, wE, gG, yA
odd limit = 75
green yellow-6 deep-green-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 white dyad, aka a power chord)
bluish-5 chord
dim five chord
1, bg5
C(bg5)no3
wC, bgG
(or bluish dyad)

Table 6.8 – Chords without a 3rd, but with a 6th or 7th
5 blue-7 chord
dom7, no 3rd
1, 5, b7
C5b7
wC, wG, bB

5 red-6 chord
maj6, no 3rd
1, 5, r6
C5r6
wC, wG, rA

5 yellow-6 chord
maj6, no 3rd
1, 5, y6
C5y6
wC, wG, yA

5 green-7 chord
dom7, no 3rd
1, 5, g7
C5g7
wC, wG, gB

bluish-5 blue-7 chord
half-dim, no 3rd
1, bg5, b7
C(bg5)b7
wC, bgG, bB
(inversion of yellow reddish)

Table 6.9 – Some fifth-less chords
blue-7 no-5 chord
min7, no 5
1, b3, b7
Cb7no5
wC, bE, bB

green red-6 no-5 chord
min6, no 5
1, g3, r6
Cg,r6no5
wC, gE, rA
(inversion of blue bluish)
blue yellow-6 no-5 chord
min6, no 5
1, b3, y6
Cb,y6no5
wC, bE, yA
(inversion of green bluish)

In pentads and hexads, the 9th & 11th are assumed to be white. A 9th implies a 7th, and an 11th implies a 9th. A white 9th goes well with many chords with a major 3rd, and a white 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)
lattice64.png

Chords can be classified by the number of colors they contain (including white) 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





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