The Kite Guitar Chord Shapes (downmajor tuning)

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Overview

There are many chords on the Kite Guitar to explore, but the obvious place to start is with those of intervallic odd-limit 9 or less. These chords are mostly subsets of the 4:5:6:7:9 pentad or the 9/(9:7:6:5:4) pentad. Thus most of these chords can be classified as either harmonic or subharmonic. Chords such as vM7, ^m7, vm7 and v6 are classified as stacked chords, because they are formed by stacking complimentary 3rds. Many chords fall outside these 3 categories.

Homonyms are to chords what modes are to scales. C6 and Am7 are homonyms (same notes, different root). In theory, every tetrad has 3 other homonyms, but in practice many are too implausible (e.g. Am7 = G6/9sus4no5). Most tetrads and pentads have at least one plausible homonym.

These tables list all chords of odd-limit 9, plus a few with downmajor 7ths that are odd-limit 15. The example chords are arbitrarily rooted on C. The chord shapes are written in tablature, using fret numbers. The root is placed arbitrarily on the 4th fret, even though C is not on the 4th fret. In these tables, the interval between open strings is always a downmajor 3rd. This makes the Kite guitar isomorphic, thus a tab like 4 6 3 5 can start on the 6th, 5th or 4th string, and of course any fret of that string. A skipped string is indicated by a period. Alternate fingerings are possible, especially for 2-finger and 3-finger chords.

Chords are named using ups and down notation, see also the notation guide for edos 5-72. Briefly, an up or down in the chord name immediately after the root affects the 3rd, 6th, 7th and/or the 11th, but not the 5th, 9th or 13th. Thus Gv9 is G vB D vF A. Alterations are enclosed in parentheses, as in Cvm7(b5). Additions are set off with a comma (the punctuation mark, not the interval!). In general, the comma is spoken as "add", e.g. Cv,9 = "C down add-9" = C vE G D. Chord progressions are written as Cv7 - vEb^m6 - Fv7 or Iv7 - vbIII^m6 - IVv7.

In general, an odd-limit 15 chord has only one 15-limit interval, and most of the others are much lower odd-limit. For example, the downmajor seven chord has intervals of odd-limit 3, 3, 5, 5, 5 and 15. The many low-limit intervals serve as "glue" to hold together the chord, despite the one 15-limit interval. This is the rationale for focusing on odd-limit 15 chords here and not those of odd-limit 11 or 13, for those chords have multiple intervals of high odd-limit. But see below, at the very end of this section.

These tables are fairly exhaustive. Don't get overwhelmed! The most essential chords are in the first two tables (triads and seventh chords). Here's a printer-friendly chart to get you started, with and without fingerings:

Chord chart 2.png
Chord chart.png


Triads

The alternate names for the voicings are explained in the next section. Other voicings are possible; these are just the most convenient ones. The upmajor chord is a particularly dissonant triad. See "Innate-comma chords" below for augmented triads. Added ninths are shown in parentheses. Adding a major 9th (ratio 9/4, example note D) to the up or down triad increases the intervallic odd-limit only slightly if at all. The up chord is arguably improved by adding a 9th.

chord type ----> sus4 up or

upmajor

(up add 9)

down or

downmajor

(down add 9)

upminor downminor sus2 updim downdim
example, with homonym C4 = F2 C^ (C^,9) Cv (Cv,9) C^m Cvm C2 = G4 C^dim or C^o Cvdim or Cvo
example notes C F G C ^E G C vE G C ^Eb G C vEb G C D G C ^Eb Gb C vEb Gb
ratio of the 3rd P4 = 4/3 ^M3 = 9/7 vM3 = 5/4 ^m3 = 6/5 vm3 = 7/6 M2 = 9/8 ^m3 = 6/5 vm3 = 7/6
ratio of the 5th P5 = 3/2 P5 = 3/2 P5 = 3/2 P5 = 3/2 P5 = 3/2 P5 = 3/2 d5 = 7/5 d5 = 7/5
close voicing R 3 5 8 (9)
frets 4 6 3 5 4 5 3 5 (2) 4 4 3 5 (2) 4 3 3 5 4 2 3 5 4 1 3 5 4 3 1 5 4 2 1 5
suggested fingerings 2 4 1 3 2 3 1 4 2 3 1 4

2 2 1 4

2 1 1 3 3 1 2 4 3 1 2 4 3 2 1 4 3 2 1 4
open or high-3 voicing R 5 8 3
frets 4 . 3 5 7 4 . 3 5 6 4 . 3 5 5 4 . 3 5 4 4 . 3 5 3 4 . 3 5 2 4 . 1 5 4 4 . 1 5 3
suggested fingerings 2 . 1 3 4 2 . 1 3 4 2 . 1 3 4

2 . 1 4 4

2 . 1 4 3 3 . 1 4 2 3 . 2 4 1 2 . 1 4 3 3 . 1 4 2
high-R voicing 3 5 8 (9) (1st inversion)
frets 5 2 4 4 2 4 (1) 3 2 4 (1) 2 2 4 1 2 4 0 2 4 2 0 4 1 0 4
suggested fingerings 4 1 3 2 1 3 2 1 3 1 1 3 1 2 4 1 2 4 2 1 4 2 1 4
low-5 voicing 5 R 3 5 (2nd inversion)
frets 2 4 6 3 2 4 5 3 2 4 4 3 2 4 3 3 2 4 2 3 2 4 1 3 (difficult) (difficult)
suggested fingerings 1 3 4 2 1 3 4 2 1 3 4 2 1 4 2 3

1 3 2 2

1 3 1 2 2 4 1 3

Seventh chords

It's generally impossible to voice 7th chords in 1st, 2nd or 3rd inversion close voicings, because the 7th occurs on the same string as the 8ve. Instead voicings are named as close (root position, R 3 5 7), high-3 (3rd raised an 8ve) and low-5 (5th lowered an 8ve). A high-3 low-5 voicing (5 R 7 3) uses all 6 strings, thus is only sometimes possible. A high-3-7 voicing (R 5 3 7) requires 7 strings. Half-dim chords can alternatively be named as dim add-7 chords, e.g. the uphalfdim chord is C^dim^7 or C^o^7, spoken as updim-upseven.

See "Innate-comma chords" below for dim7 chords. The upmajor7 chord C^M7 = C ^E G ^B is a possibility, but it's quite dissonant, with ^M7 = 27/14.

9ths are shown in parentheses. Adding a major 9th (ratio 9/4, example note D) to any of the first 4 tetrads increases the intervallic odd-limit only slightly if at all. The up-7 chord is arguably improved by adding a 9th. The no3, no5 and no7 (i.e. add9) versions of the ^9 and v9 chords are all 9-odd-limit chords.

11th chords include vM11 (4 4 3 3 2 0), v11 (4 4 3 1 2 0), and ^m11 (4 3 3 2 2 1). All these chords contain a wolf 11th. Rather than 8/3, the vM11 and v11 chords have 21/8, and the ^m11 chord has 27/10. The mid-11th, ratio 11/4, is also available. However 4:5:6:7:9:11 is very difficult to play.

chord type ----> downmajor7

(downmajor9)

up7

(up9)

down7

(down9)

upminor7

(upminor9)

downminor7 uphalfdim downhalfdim
example, with

homonym

CvM7

(CvM9)

C^7

(C^9)

Cv7

(Cv9)

C^m7 = ^Ebv6

(C^m9)

Cvm7 = vEb^6 C^m7(b5) = ^Ebvm6 Cvm7(b5) = vEb^m6
example notes C vE G vB C ^E G ^Bb C vE G vBb C ^Eb G ^Bb C vEb G vBb C ^Eb Gb ^Bb C vEb Gb vBb
ratio of the 3rd vM3 = 5/4 ^M3 = 9/7 vM3 = 5/4 ^m3 = 6/5 vm3 = 7/6 ^m3 = 6/5 vm3 = 7/6
ratio of the 5th P5 = 3/2 P5 = 3/2 P5 = 3/2 P5 = 3/2 P5 = 3/2 d5 = 7/5 d5 = 7/5
ratio of the 7th vM7 =15/8 ^m7 = 9/5 vm7 = 7/4 ^m7 = 9/5 vm7 = 7/4 ^m7 = 9/5 vm7 = 7/4
close voicing R 3 5 7 (9)
frets 4 4 3 3 (2) 4 5 3 2 (2) 4 4 3 1 (2) 4 3 3 2 (2) 4 2 3 1 4 3 1 2 4 2 1 1
suggested fingerings 3 4 2 2 (1)

3 3 2 2 (1)

1 1 1 1 (1)

3 4 2 1 (1) 3 4 2 1

4 4 3 1 (2)

4 2 3 1 (1)

4 3 2 1 (1)

3 2 2 1 (1)

4 2 3 1 4 3 1 2 4 2 1 1
high-3 voicing R 5 7 3
frets 4 . 3 3 5 4 . 3 2 6 4 . 3 1 5 4 . 3 2 4 4 . 3 1 3 4 . 1 2 4 4 . 1 1 3
suggested fingerings 2 . 1 1 3 3 . 2 1 4 3 . 2 1 4 3 . 2 1 4

2 . 1 1 4

4 . 2 1 3 3 . 1 2 4 4 . 1 1 3
low-5 voicing 5 R 3 7 (9)
frets 2 4 4 . 3 (2) 2 4 5 . 2 (2) 2 4 4 . 1 (2) 2 4 3 . 2 (2) 2 4 2 . 1 (difficult) (difficult)
suggested fingerings 1 3 4 . 2 (1) 1 3 4 . 2 (2)

1 3 4 . 1 (1)

2 3 4 . 1

2 3 4 . 2 (1)

1 4 3 . 2 (2)

1 3 2 . 1 (1)

2 4 2 . 1

Flat-nine chords are possible. The plain minor 9th is 21/10, which is the sum of 7/5 and 3/2, thus a m9 works with either a perfect or diminished 5th. Examples:

  • the upminor-7 flat-9 chord = C^m7,b9 = C ^Eb G ^Bb Db = 4 3 3 2 0
  • the upminor-7 flat-5 flat-9 chord = C^m7(b5)b9 = C ^Eb Gb ^Bb Db = 4 3 1 2 0
  • the downminor-7 flat-9 chord = Cvm7,b9 = C vEb G vBb Db = 4 2 3 1 0
  • the downminor-7 flat-5 flat-9 chord = Cvm7(b5)b9 = C vEb Gb vBb Db = 4 2 1 1 0

The upminor 9th (15/7) is also possible, but hard to play, Example: the downmajor-7 upflat-9 chord = CvM7,^b9 = C vE G vB ^Db. Note that ^Db is enharmonically equivalent to C#, the augmented 8ve. Thus this chord's homonym is vE^m6/C.

Sixth chords

Every 6th chord has a 7th chord homonym, and vice versa. But a 7th chord with some sort of major 7th doesn't "flip" to a 6th chord as easily, because the 6th would be some sort of minor, which is rare.

Sixth chords are hard to voice. A close voicing in root position is generally impossible, because the 6th occurs on the same string as the 5th. One solution is to play a riff that alternates between the 5th and the 6th (3/6 in the tab indicates alternating between the 3rd and 6th fret). Another is to omit the 5th, but then the chord can be mistaken for a triad in 1st inversion. It helps to double the root at the octave, i.e. play R 3 6 8 not R 3 6. Another voicing is the low-6 (6 R 3 5) i.e. the 3rd inversion. But this is the same as the close voicing of its 7th chord homonym, and again the chord can be mistaken. A non-ambiguous voicing is low-5 (5 R 3 6), but it can be a difficult stretch. Also the 9th from the 5th to the 6th is usually not a plain 9th, and can be dissonant. The best voicing is high-3-5 (R 6 3 5 or R 6 8 3 5), but with only 6 strings, it's only possible for root-4 chords. Other possibilities are high-3-6 (R 5 3 6), high-5 (R 3 6 5 or R 3 6 8 5) and high-6 (R 3 5 8 6).

The up-6 chord is particularly dissonant, unless voiced as its homonym, the vm7 chord.

Adding a major 9th (ratio 9/4) to any of these chords will make a wolf 4th with the 6th. A 9th that is a P4 above the 6th (^M9 or vM9) will clash with the 5th. It can be safely added if the 5th is omitted, but then the chord becomes ambiguous. Cv6,v9no5 is the same as vD^9no3 (or vD^m9no3). C^6,^9no5 is ^Dv9no3. C^m6,^9no5 and Cvm6,v9no5 both have an awkward interval from the 3rd up to the 9th: a M7 = 40/21.

Adding an 11th (ratio 8/3) to either the ^m6 or the vm6 chord won't increase the intervallic odd-limit above 9. But a Cvm6,11 chord is the same as an Fv9 chord, and every easy fingering puts the F in the bass, so it's hardly a distinct chord. Adding an 11th to a Cv6 chord makes Cv6,11, which is an FvM9 chord. Again, every easy fingering has F in the bass, and Cv6,11 isn't a distinct chord.

chord type ----> up-6 or

upmajor-6

down-6 or

downmajor-6

upminor-6

(upminor-6 add-11)

downminor-6
example, with homonym(s) C^6 = ^Avm7 Cv6 = vA^m7 C^m6 = ^Avm7(b5)

(C^m6,11 = F^9)

Cvm6 = vA^m7(b5)

= Fv9noR

example notes C ^E G ^A C vE G vA C ^Eb G ^A C vEb G vA
ratio of the 3rd ^M3 = 9/7 vM3 = 5/4 ^m3 = 6/5 vm3 = 7/6
ratio of the 5th P5 = 3/2 P5 = 3/2 P5 = 3/2 P5 = 3/2
ratio of the 6th ^M6 = 12/7 vM6 = 5/3 ^M6 = 12/7 vM6 = 5/3
close voicing for riffing R 3 5/6 (8)
frets 4 5 3/7 4 4 3/6 4 3 3/7 (5) 4 2 3/6
suggested fingerings 2 3 1/4 2 3 1/4 2 1 1/4 (3) 3 1 2/4
close no-5th voicing R 3 6 8
homonyms C^6no5 = ^Avm Cv6no5 = vA^m C^m6no5 = ^Avdim Cvm6no5 = vA^dim
frets 4 5 7 5 4 4 6 5 4 3 7 5 4 2 6 5
suggested fingerings 1 2 4 3 1 1 3 2 2 1 4 3 2 1 4 3
low-6 voicing 6 R 3 5 (11)
frets 6 4 5 3 5 4 4 3 6 4 3 3 . (7) 5 4 2 3
suggested fingerings 4 2 3 1 4 2 3 1 4 2 1 1

3 2 1 1 . (4)

4 3 1 2
low-5 voicing 5 R 3 6
frets 2 4 5 7 2 4 4 6 2 4 3 7 2 4 2 6
suggested fingerings 1 2 3 4 1 2 3 4 1 3 2 4 1 3 1 4
high-3-5 voicing R 6 (8) 3 5
frets 4 . 7 . 6 4 4 . 6 (5) 5 4 4 . 7 (5) 4 4 4 . 6 (5) 3 4
suggested fingerings 1 . 4 . 3 2

1 . 4 . 3 1

1 . 4 . 3 2

1 . 4 (2) 3 1

1 . 4 (2) 1 1 T . 4 (3) 1 2

(T = thumb)

If you play a 7th chord in close root position on the upper 4 strings, you can drop the 3rd of the chord down an octave to get a high-3-5 voicing of the corresponding 6th chord.

  • x x A x E ^G ^C (clearly A^m7)
  • x x A ^C E ^G x (ambiguous but slightly more A^m7)
  • ^C x A x E ^G x (clearly ^C6)

Innate-comma chords

We've covered every chord that maps to a JI chord of intervallic odd-limit 9. However there are many Kite guitar chords that don't, although their individual intervals do. These chords are called innate-comma chords aka essentially tempered chords. Such chords often have a mysterious sound. Almost every easily reachable interval on the fretboard is odd-limit 9. The only exceptions are ~4, ~5, vM7, ^M7, vm9 and ^m9. Thus the majority of random Kite guitar chord shapes are intervallic odd-limit 9.

For example, the downadd7no5 chord has 5/4 and 16/9. The interval from 5/4 up to 16/9 is 64/45. But because 41edo tempers out the Ruyoyo comma of only 8¢, 64/45 is equivalent to 10/7. The high-3 voicing inverts this into an even smoother 7/5. This dom7 chord is often appropriate for translating 12-edo's V7 -- I cadence: relaxed but not too relaxed. Adding the 5th creates a plain minor 3rd interval with the 7th. If the m3 is interpreted as 32/27, this increases the odd limit to 27. But if interpreted as 13/11, the odd limit is only 13.

The sus4downmajor7 chord (odd-limit 15) also has an innate Ruyoyo comma. The chord is quite striking in close voicing. The interval from 4/3 up to 15/8 is 45/32, equivalent to 7/5. The homonym of C4,vM7 = C F G vB is the sus2addb5 chord F2,b5 = F G Cb C. In 41-edo, Cb is enharmonically equivalent to vB. In chord names, "(b5)" means alter the 5th by flattening it, but ",b5" means add a flat 5th alongside the perfect 5th.

The down7flat5 chord (odd-limit 9) is also innate-ruyoyo. The interval from 5/4 up to 7/5 is 28/25, equivalent to 9/8. The homonym of Cv7(b5) is the Gb downadd7upflat5 chord Gbv,7(^b5) = Gb vBb ^Dbb Fb. Enharmonic equivalences: ^Dbb = C, Fb = vE, and upflat 5th = aug 4th = 10/7.

All three of these chords contain the chord shape 4 1 1. This 3-note "nugget" implies the Ruyoyo comma: 9/8 plus 5/4 equals 7/5. By itself, it's the v,7no5 chord in low-7 voicing. The v7(b5) chord in close voicing (4 4 1 1) also contains the octave inverse of this nugget, 4 4 1. By itself, this inverse nugget makes Cv(b5) = C vE Gb (odd-limit 9). Beware, "C-down flat-5" = Cv(b5) sounds much like "C downflat-5" = C(vb5) = C E vGb = C E ^^F. Fortunately, the latter chord is very unlikely. But to be very clear, one could say "C-downmajor flat-5".

The downaddflat5 chord Cv,b5 (odd-limit 15) has both a perfect and a diminished 5th. This chord is best voiced low-5. In other voicings, the two 5ths are on the same string, and one must play a riff that alternates between the two (indicated as 1/3 in the tab, 1st and 3rd fret).

When the added b5 is voiced an 8ve higher, it becomes a v#11, and suggests the downmajor7downsharp11 and downmajor9downsharp11 chords (both odd-limit 15). No need to omit the 3rd, it makes a pleasant M9 = 9/4 with the 11th.

chord type ----> downadd7no5 downmaj7sus4 down7flat5 down-flat5 downaddflat5 downmaj9down#11
example w homonym Cv,7no5 = Bb2(b5) C4,vM7 = F2,b5 Cv7(b5) = Gbv,7(^b5) Cv(b5) Cv,b5 CvM9,v#11
example notes C vE Bb C F G vB C vE Gb vBb C vE Gb C vE Gb G C vE G vB D vF#
ratio of the 3rd vM3 = 5/4 P4 = 4/3 vM3 = 5/4 vM3 = 5/4 vM3 = 5/4 vM3 = 5/4
ratio of the 5th ------ P5 = 3/2 d5 = 7/5 d5 = 7/5 P5 = 3/2 P5 = 3/2
ratio of the 7th m7 = 16/9 vM7 = 15/8 vm7 = 7/4 ------ ------ vM7 =15/8
other ------ ------ ------ ------ d5 = 7/5 v#11 = b12 = 14/5
close voicing R 3 5 7 (8)
frets 4 4 8 (5) (5) (4) 4 6 3 3 4 4 1 1 4 4 1 (5) 4 4 1/3 4 4 3 3 2 2
suggested fingerings 1 1 4 (2) (2) (1) 2 4 1 1 3 4 1 1 3 4 1
2 3 1 (4)
3 4 1/2 3 4 2 2 1 1
high-3 voicing R 5 7 (8) 3
frets 4 . 8 (5) 5 4 . 3 3 7 4 . 1 1 5 4 . 1 (5) 5 4 . 1/3 (5) 5 4 . 3 3 5 2 (no 9th)
suggested fingerings 1 . 4 . 2
1 . 4 (1) 1
2 . 1 1 4 3 . 1 1 4 2 . 1 (3) 4 3 . 1/2 . 4
2 . 1/3 (3) 4
2 . 3 3 4 1
low-5 voicing 5 R 3 7
frets (N/A) (difficult) 0 4 4 . 1 (difficult) 2 4 4 1 2 4 4 . 3 2 2 (7 strings)
suggested fingerings 1 3 4 . 2 2 3 4 1 1 3 4 . 2 1 1
low-7 voicing 7 R 3 (7)
frets 7 4 4 (8) (N/A) (N/A) (N/A) (N/A) (N/A)
suggested fingerings 3 1 1 (4)

Augmented Chords

The Ruyoyo comma implies an augmented chord because it lets 5/4, 5/4 and 9/7 add up to 2/1. In 12-edo, the aug chord is symmetrical, and it is its own homonym. But in 41edo, it's asymmetrical. Its homonyms are also augmented chords, but of a different type. Thus there are three augmented chords: upaug, downaug and down-halfaug. Logically, the last chord should be called down-doubledownsharp5 or down-double-up5, but those names are rather long. Instead it's named after its half-augmented 5th. This 5th is spelled as vv#5 rather than ^^5 so that the interval from the 3rd to the 5th is spelled as vM3 not ^3m3.

There is another group of aug chords: up-halfaug, upminor-halfaug and up-sesquiaug. Their innate comma is the Zozoyo comma, which equates the octave with 9/7 plus 9/7 plus 6/5. Thus one 3rd is quite smaller than the other two. The upminor-halfaug chord's lowest 3rd is this small 3rd, and it's debatable if it can be called an augmented chord. "Sesqui-" means one-and-a-half, and the up-sesquiaug chord has ^^#5, a sesqui-augmented 5th. This is equivalent to a downmajor 6th, and again, it's debatable if this is really an augmented chord.

All six chords are odd-limit 9. Another possible aug chord is odd-limit 11. Unlike the others, it has no innate comma. 7:9:11 = up-downsharp5 = C^(v#5) = C ^E vG#. Unfortunately it's very difficult to finger. Using an open string, it's x56x0x.

chord type --> upaug downaug downhalfaug uphalfaug upminor-halfaug up-sesquiaug
example with homonyms C^aug = ^Ev(vv#5)

= ^Abvaug

Cvaug = vE^aug

= ^Abv(vv#5)

Cv(vv#5) = vEvaug

= vAb^aug

C^(^^5) = ^E^m(^^5)

= vAb^(^^#5)

C^m(^^5) = ^Eb^(^^#5)

= vAb^(^^5)

C^(^^#5) = ^E^(^^5)

= vA^m(^^5)

example notes C ^E G# C vE G# C vE vvG# C ^E ^^G C ^Eb ^^G C ^E ^^G#
3rd ^M3 = 9/7 vM3 = 5/4 vM3 = 5/4 ^M3 = 9/7 ^m3 = 6/5 ^M3 = 9/7
5th A5 = ^m6 = 8/5 A5 = ^m6 = 8/5 vvA5 = vm6 = 14/9 ^^5 = vm6 = 14/9 ^^5 = vm6 = 14/9 ^^A5 = vM6 = 5/3
close voicing R 3 5 (8)
frets 4 5 5 (5) 4 4 5 (5) 4 4 4 (5) 4 5 4 (5) 4 3 4 (5) 4 5 6 (5)
fingerings 1 2 2 (2) 1 1 2 (2) 1 1 1 (2) 1 3 2 (4) 2 1 3 (4) 1 2 4 (3)
high-3 voicing R 5 (8) 3
frets 4 . 5 (5) 6 4 . 5 (5) 5 4 . 4 (5) 5 4 . 4 (5) 6 4 . 4 (5) 4 4 . 6 (5) 6
fingerings 1 . 2 (2) 3 1 . 2 (2) 2 1 . 1 (2) 2 1 . 1 (2) 3 1 . 2 (4) 3 1 . 3 (2) 4
high-R voicing 3 5 8 (3) (1st inversion)
see v(vv#5) see ^aug see vaug see ^m(^^5) see ^(^^#5) see ^(^^5)
low-5 voicing 5 R 3 (5) (2nd inversion)
see vaug see v(vv#5) see ^aug see ^(^^#5) see ^(^^5) see ^m(^^5)

Diminished Chords

The updim7 and downdim7 chords are formed from stacked 6/5's and 7/6's, alternating to make 7/5's. The 7ths are rather dissonant. The updim7 chord has an innate Ruyoyo comma which equates its ^d7 = 42/25 to a M6 = 27/16. The downdim7 chord has an innate Thuzozogu comma which equates vd7 = 49/30 with ~6 = 13/8. Thus its odd-limit and prime-limit are both 13.

In 12-edo, the dim7 chord is symmetrical, and is its own homonym. But in 41-edo, it has homonyms. The most plausible one has the 3rd becoming the new root to make a 6th chord. This is a chord with a minor 3rd, a dim 5th and a major 6th. Such a chord in 12edo is identical to a dim7 chord, but in 41edo it isn't. Extrapolating from the terms maj6 and min6 gives us its name, a dim6 chord.

All these chords span 5 or 6 frets, and are quite a stretch. To avoid negative fret numbers, the chords start on the 6th fret.

chord type --> updim7 downdim6 downdim7 updim6
example with homonym C^dim7 = ^Ebvdim6 Cvdim6 = vA^dim7 Cvdim7 = vEb^dim6 C^dim6 = ^Avdim7
example notes C ^Eb Gb ^Bbb C vEb Gb vA C vEb Gb vBbb C ^Eb Gb ^A
3rd ^m3 = 6/5 vm3 = 7/6 vm3 = 7/6 ^m3 = 6/5
5th d5 = 7/5 d5 = 7/5 d5 = 7/5 d5 = 7/5
6th or 7th ^d7 = M6 = 27/16 vM6 = 5/3 vd7 = ~6 = 13/8 ^M6 = 12/7
close voicing R 3 5 7 = 6 R 3 5
frets 6 5 3 2 6 5 3 2 6 4 3 1 6 4 3 1
fingerings 4 3 2 1 4 3 2 1 4 3 2 1 4 3 2 1
high-3 voicing R 5 7 3
frets 6 . 3 2 6 (N/A) 6 . 3 1 5 (N/A)
fingerings 3 . 2 1 4 3 . 2 1 4
high-3-5 voicing R 6 (8) 3 5
frets (difficult) 4 . 6 (5) 3 2 (difficult) 3 . 6 (4) 3 1
fingerings T . 4 (3) 2 1 T . 4 (3) 2 1

Mid-5th Chords

At the beginning of this article, chords of prime-limit 11 or 13 were dismissed because "those chords have multiple intervals of high odd-limit." But when innate-comma chords are allowed, this no longer holds true. For example, the mid-5th can be interpreted as either 16/11 or 13/9. Each of the following chords contain this interval, but all the other intervals in the chord are at most odd-limit 5, 7 or 9, depending on the chord. The one exception is the vM7(~5) chord, odd-limit 15.

  • the downminor mid-5 chord = Cvm(~5) = C vEb vvG = 4 2 2
  • the downminor-7 mid-5 chord = Cvm7(~5) = C vEb vvG vBb = 4 2 2 1 or 4 . 2 1 3
  • the down up-six chord = Cv,^6 = C vE G ^A = 4 . 7 . 5 4, a homonym of ^Avm7(~5)
  • the upminor mid-5 chord = C^m(~5) = C ^Eb ^^Gb = 4 3 2
  • the upminor-7 mid-5 chord = C^m7(~5) = C ^Eb ^^Gb ^Bb = 4 3 2 2 or 4 . 2 2 4
  • the upminor down-6 chord = C^m,v6 = C ^Eb G vA, a homonym of vA^m7(~5)
  • the downmajor mid-5 chord = Cv(~5) = C vE vvG = 4 4 2
  • the downmajor-7 mid-5 chord = CvM7(~5) = C vE vvG vB = 4 4 2 3 or 4 . 2 3 5

Note that the mid-5th is spelled as a double-up dim 5th from the chord root (^^Gb) if the 3rd is upped, but as a double-down 5th (vvG) if the 3rd is downed. This avoids the interval from the 3rd to the 5th being spelled with a triple up or down.

Parallels with 12-edo Jazz Guitar

Jazz guitarists often play 4 or 5 note chords that are movable, i.e. don't use open strings. A root-6 chord (root on the 6th string) often has a R-5-7-3-x-x or R-5-7-3-5-x voicing. For example, A7 might be voiced 57565x, Am7b5 might be 5655xx, etc. A root-5 chord might be voiced x-R-5-7-3-x.

On a 12edo guitar, a root-5 chord is a different shape than a root-6 chord, whereas on a Kite guitar, the shape is the same. Thus the terms root-5 and root-6 are less useful on the Kite guitar. But a very useful concept when arranging for a 6-string Kite guitar is tonic-4 vs. tonic-5 vs. tonic-6. This indicates which string the tonic appears on. For example, Kite's translation of "I Will Survive" in D is tonic-5, and his translation in ^Bb is tonic-6. On a 6-string, certain bass lines require the tonic to appear on certain strings. In 12-edo, the same concept applies, but tonic-4 is rare.

12-edo Major Thirds Tuning

In the early 1960's, jazz guitarist Ralph Patt adopted an all-major-3rds tuning. He said it "makes the hard things easy and the easy things hard." Because of the reduced range, he used first a 7-string guitar, and later an 8-string guitar. He placed the dots on every other fret.

The chord shapes are very similar to the Kite guitar, see http://www.ralphpatt.com/Tune/Chords.html. After learning the Kite guitar, playing a 12-edo guitar tuned in 3rds is a very odd experience! From his website:

"Disadvantage of the major third tuning.

It's not easy to play simple folk chords. They are quite difficult to play with this tuning. If all you want to do with the guitar is sing folk tunes, don't try this.

Much of the classical guitar literature becomes difficult or impossible to play because of frequent use of open D and A strings. However, I found Bach and early lute music easier to play with this tuning. Jim DiSerio made my eight string classical guitar with a capo on the low Ab string, bringing it up to an A without affecting the tuning. That solved the problem of the "open" A string."

See also https://www.tonycorman.com/m3-guitar