Kite Guitar chord shapes (downmajor tuning)
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. The ^m7 and vm7 chords (and their homonyms v6 and ^6) are classified as stacked chords, because they are formed by stacking complimentary 3rds. Many chords fall outside these 3 categories.
These tables list all chords of odd-limit 9, plus a few with downmajor 7ths that are odd-limit 15. The chord shapes are written in tablature, using fret numbers. The root is placed arbitrarily 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, a "global" up or down immediately after the root affects the 3rd, 6th, 7th and/or the 11th, but not the 5th, 9th or 13th. Alterations are enclosed in parentheses, and 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:
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
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. Another voicing is the low-6 aka 3rd inversion (6 R 3 5). But this is the same as the close voicing of the corresponding 7th chord, 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), but with only 6 strings, it often isn't possible. 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, but can be added if the 5th is omitted. The chord becomes ambiguous. C^6,^9no5 is the same as ^Dv9no3. Cv6,v9no5 is vD^9no3. 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 | C^6 = ^Avm7 | Cv6 = vA^m7 | C^m6 = ^Avm7(b5)
(C^m6,11 = F^9) |
Cvm6 = vA^m7(b5) |
| 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 | ??? |
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 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-edos V7 -- I cadence: relaxed but not too relaxed. Note that adding the 5th would increase the odd-limit to 27.
The downmajor7sus4 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 CvM7(4) 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.
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 | Cv,7no5 = Bb2(b5) | CvM7(4) = F2,b5 | Cv7(b5) = Gbv,7(^b5) | Cv(b5) | Cv,b5 | CvM9,v#11 |
| 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) | 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 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) | |||||
The Ruyoyo comma implies augmented chords because 5/4, 5/4 and 9/7 add up to 2/1. There are three types of aug chord: upaug, downaug and down-halfaug. (Logically, the last one should be called down-doubledownsharp5 or down-double-up5, but those names are too long.) Each one is odd-limit 9, and each one is an inversion of the others.
The up-halfaug chord has ^M3 and ^^5. Its innate comma is the Zozoyo comma, which equates the octave with 9/7 plus 6/5 plus 9/7. In 1st inversion, it's the upminor-halfaug chord C^m(^^5). In 2nd inversion, it's the up-sesquiaug chord. All three chords are odd-limit 9.
Another possible aug chord is 7:9:11 = up-downsharp5 = C^(v#5) = C ^E vG#. Unfortunately it's very difficult to finger.
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.
| chord --> | upaug | downaug | downhalfaug | uphalfaug | upminor-halfaug | up-sesquiaug | updim7 | downdim7 |
|---|---|---|---|---|---|---|---|---|
| example | C^aug | Cvaug | Cv(vv#5) | C^(^^5) | C^m(^^5) | C^(^^#5) | C^o7 | Cvo7 |
| C ^E G# | C vE G# | C vE vvG# | C ^E ^^G | C ^Eb ^^G | C ^E ^^G# | C ^Eb Gb ^Bbb | C vEb Gb vBbb | |
| 3rd | ^M3 = 9/7 | vM3 = 5/4 | vM3 = 5/4 | ^M3 = 9/7 | ^m3 = 6/5 | ^M3 = 9/7 | ^m3 = 6/5 | vm3 = 7/6 |
| 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 |
d5 = 7/5 | d5 = 7/5 |
| 7th | ------ | ------ | ------ | ------ | ------ | ------ | ^d7 = M6 = 27/16 | vd7 = ~6 = 13/8 |
| close voicing R 3 5 7 (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) | 4 3 1 0 | 4 2 1 -1 |
| 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) | 4 3 2 1 | 4 3 2 1 |
| high-3 voicing R 5 7 (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 | 4 . 1 0 4 | 4 . 1 -1 3 |
| 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 | 3 . 2 1 4 | 3 . 2 1 4 |
| low-5 voicing 5 R 3 7 | ||||||||
| see vaug | see v(vv#5) | see ^aug | see ^(^^#5) | see ^(^^5) | see ^m(^^5) | (difficult) | (difficult) | |
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.
Rough draft of an upcoming article
Categories of scales
There are three broad categories of 12-edo scales: pentatonic, diatonic and chromatic. Pentatonic scales have scale steps of a major 2nd or a minor 3rd. In 12-edo, these steps are 2 edosteps and 3 edosteps respectively. Any melody using only these two steps will sound pentatonic.
| scale type --> | pentatonic | diatonic | chromatic | ||
|---|---|---|---|---|---|
| scale steps | M2 | m3 | m2 | M2 | A1 or m2 |
| edosteps | 2 | 3 | 1 | 2 | 1 |
In practice, there is much overlap between the categories. The melody of "Ash Grove" is mostly diatonic, but the occasional augmented 4th makes it slightly chromatic. The melody of "Greensleeves" is mostly diatonic, but the occasional major 7th makes it slightly chromatic. The melodies of "Let It Be" and "In My Life" are mostly pentatonic, but the occasional perfect 4th makes it slightly diatonic. Blues melodies can be thought of as a combination of pentatonic and chromatic. 41-edo has a much larger variety of scales. The pentatonic scales depend on the prime subgroups used. In color notation, these subgroups are named wa = 2.3, ya = 2.3.5, za = 2.3.7, and ila = 2.3.11. 41-edo doesn't distinguish between the ila subgroup and the tha subgroup 2.3.13, so tha is lumped in with ila.
| scale type --> | wa pentatonic | ya pentatonic | za pentatonic | ila pentatonic | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| scale steps | M2 | m3 | vM2 | M2 | m3 | ^m3 | M2 | ^M2 | vm3 | m3 | ~2 | M2 | m3 | ~3 |
| edosteps | 7 | 10 | 6 | 7 | 10 | 11 | 7 | 8 | 9 | 10 | 5 | 7 | 10 | 12 |
These categories can be combined. For example, harmonics 5-10 make a yaza pentatonic scale.
| scale type --> | yaza pentatonic | yala pentatonic | zala pentatonic | yazala pentatonic | ||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| scale steps | vM2 | M2 | ^M2 | vm3 | m3 | ^m3 | ~2 | vM2 | M2 | m3 | ^m3 | ~3 | ~2 | M2 | ^M2 | vm3 | m3 | ~3 | ~2 | vM2 | M2 | ^M2 | vm3 | m3 | ^m3 | ~3 |
| edosteps | 6 | 7 | 8 | 9 | 10 | 11 | 5 | 6 | 7 | 10 | 11 | 12 | 5 | 7 | 8 | 9 | 10 | 12 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
Next the diatonic scales:
| scale type --> | wa diatonic | ya diatonic | za diatonic | ila diatonic | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| scale steps | m2 | M2 | m2 | ^m2 | vM2 | M2 | vm2 | m2 | M2 | ^M2 | m2 | ~2 | M2 |
| edosteps | 3 | 7 | 3 | 4 | 6 | 7 | 2 | 3 | 7 | 8 | 3 | 5 | 7 |
Again, these categories can be combined. For example, harmonics 7-14 make a yazala diatonic scale.
| scale type --> | yaza diatonic | yala diatonic | zala diatonic | yazala diatonic | |||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| scale steps | vm2 | m2 | ^m2 | vM2 | M2 | ^M2 | m2 | ^m2 | ~2 | vM2 | M2 | vm2 | m2 | ~2 | M2 | ^M2 | vm2 | m2 | ^m2 | ~2 | vM2 | M2 | ^M2 |
| edosteps | 2 | 3 | 4 | 6 | 7 | 8 | 3 | 4 | 5 | 6 | 7 | 2 | 3 | 5 | 7 | 8 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| scale type --> | old chromatic | chromatic | microtonal | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| scale steps | A1 or m2 | vb2 or b2 | ^1 or vvb2 | |||||||||||
| edosteps | 4 or 5 | 2 or 3 | 1 | |||||||||||