Chords of meantone
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Below are listed the dyadic chords of 11-limit meantone temperament. By "meantone" is meant one of the two extensions of septimal meantone, which itself is the main extension of 5-limit meantone; this is the temperament tempering out 81/80, 99/98, and 126/125. Typing the chords requires consideration of the fact that meantone conflates 9/8 and 10/9 and also 9/7 and 14/11. If a transversal can be found which shows the chord to be essentially just, that transversal is listed along with a typing as otonal, utonal, or ambitonal. If the chord is essentially tempered, it is analyzed in terms of the transversal which employs 9/8 and 16/9.
(For the inversions, there has been no attempt to note any equivalencies. Keep in mind that 10/9 can be thought of as 9/8, 16/9 as 9/5, 9/7 as 14/11, and vice versa.)
Chords requiring tempering only by 81/80 are labeled didymic, by 99/98 mothwellsmic, by 126/125 starling, by 176/175 valinorsmic, by 225/224 marvel, and by 441/440 werckismic. Chords which require any two of 81/80, 99/98 or 441/440 are labeled euterpe, by and two of 81/80, 126/125, or 225/224 erato, and by any two of 99/98, 176/175, or 225/224 minerva. A chord requiring any three independent commas from those discussed above is labeled meantone.
The transversal is in generator order. This is useful because it tells how common the chords are: For instance, a chord that appears on the sixth generation will appear exactly once in meantone[7], six times in meantone[12], and 13 times in meantone[19].
The "as generated" column takes the intervals that were generated and places them in size order. The 1st and 2nd inversion (and so on) columns show the inversions of those generated tones. Note that this gives different results than you might be used to: For instance, the minor chord (1/1 – 6/5 – 3/2, or 10:12:15) is the second inversion of the generated 0 – 3 – 4 chord.
Though we're used to thinking of 10:12:15 as the definitive "minor chord", with all inversions coming from that, there is nothing definitive about calling these lists below "chord" or "inversion". That's just the way the generators came out.
Meantone has MOS of size 5, 7, 12, 19, 31, 43 and 74. While one might suppose meantone has been thoroughly explored, this really isn't true in the 7-limit, and it can hardly be said to have been explored at all in the 11-limit. The 19 note MOS would seem to be a good place to start such explorations.
The bolded inversions are named using ups and downs, to avoid aug, dim, double-aug and double-dim intervals. One up is −12 fifths, a descending Pythagorean comma. Thus ^1 = d2 and ^C = Dbb. One up represents ~64/63, ~45/44, and ~40/39. If c is the difference between 700 ¢ and the size of the generator in cents, then one up is equal to 12c.
| Genspan | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Cents (31edo) | 0 | 697 | 194 | 890 | 387 | 1084 | 581 | 77 | 774 | 271 | 968 | 465 | 1161 | 658 | 155 | 852 | 348 | 1045 | 542 |
| Ratio | 1/1 | 3/2 | 9/8 10/9 |
5/3 | 5/4 | 15/8 | 45/32 7/5 |
21/20 | 63/40 14/9 |
7/6 | 7/4 | 21/16 13/10 |
35/18 | 13/9 | 11/10 13/12 |
13/8 | 11/9 | 11/6 | 11/8 |
| Interval | P1 | P5 | M2 | M6 | M3 | M7 | A4 vd5 |
A1 vm2 |
A5 vm6 |
A2 vm3 |
A6 vm7 |
A3 v4 |
A7 v8 |
AA4 v5 |
AA1 vM2 |
AA5 vM6 |
AA2 vM3 |
AA6 vM7 |
AA3 vA4 |
| Note (in C) |
C | G | D | A | E | B | F# | C# | G# vAb |
D# vEb |
A# vBb |
E# vF |
B# vC |
Fx vG |
Cx vD |
Gx vA |
Dx vE |
Ax vB |
Ex vF# |
TODO: complete the tables
Triads
| # | Chord | Transversal | Type | As generated | 1st inversion | 2nd inversion | Name |
|---|---|---|---|---|---|---|---|
| 1 | 0 – 1 – 2 | 1 – 3/2 – 9/8 | ambitonal | 1/1 – 9/8 – 3/2 | 1/1 – 4/3 – 16/9 | 1/1 – 4/3 – 3/2 | C2 or C4 |
| 2 | 0 – 1 – 3 | 1 – 3/2 – 5/3 | otonal | 1/1 – 3/2 – 5/3 | 1/1 – 10/9 – 4/3 | 1/1 – 6/5 – 9/5 | Cm7no5 |
| 3 | 0 – 2 – 3 | 1 – 10/9 – 5/3 | utonal | 1/1 – 10/9 – 5/3 | 1/1 – 3/2 – 9/5 | 1/1 – 6/5 – 4/3 | C7no3 |
| 4 | 0 – 1 – 4 | 1 – 3/2 – 5/4 | otonal | 1/1 – 5/4 – 3/2 | 1/1 – 6/5 – 8/5 | 1/1 – 4/3 – 5/3 | C |
| 5 | 0 – 2 – 4 | 1 – 9/8 – 5/4 | otonal | 1/1 – 9/8 – 5/4 | 1/1 – 10/9 – 16/9 | 1/1 – 8/5 – 9/5 | Cadd9no5 |
| 6 | 0 – 3 – 4 | 1 – 5/3 – 5/4 | utonal | 1/1 – 5/4 – 5/3 | 1/1 – 4/3 – 8/5 | 1/1 – 6/5 – 3/2 | Cm |
| 7 | 0 – 2 – 6 | 1 – 9/8 – 7/5 | marvel | 1/1 – 9/8 – 7/5 | 1/1 – 5/4 – 16/9 | 1/1 – 10/7 – 8/5 | C7no5 |
| 8 | 0 – 3 – 6 | 1 – 5/3 – 7/5 | starling | 1/1 – 7/5 – 5/3 | 1/1 – 6/5 – 10/7 | 1/1 – 6/5 – 5/3 | Cdim |
| 9 | 0 – 4 – 6 | 1 – 5/4 – 7/5 | marvel | 1/1 – 5/4 – 7/5 | 1/1 – 9/8 – 8/5 | 1/1 – 10/7 – 16/9 | C(vb5) |
| 10 | 0 – 2 – 8 | 1 – 10/9 – 14/9 | otonal | 1/1 – 10/9 – 14/9 | 1/1 – 7/5 – 9/5 | 1/1 – 9/7 – 10/7 | C2(#5) or C^(b5) |
| 11 | 0 – 4 – 8 | 1 – 5/4 – 14/9 | marvel | 1/1 – 5/4 – 14/9 | 1/1 – 5/4 – 8/5 | 1/1 – 9/7 – 8/5 | Caug |
| 12 | 0 – 6 – 8 | 1 – 7/5 – 14/9 | utonal | 1/1 – 7/5 – 14/9 | 1/1 – 10/9 – 10/7 | 1/1 – 9/7 – 9/5 | C2(b5) or C^,7no5 |
| 13 | 0 – 1 – 9 | 1 – 3/2 – 7/6 | otonal | 1/1 – 7/6 – 3/2 | 1/1 – 9/7 – 12/7 | 1/1 – 4/3 – 14/9 | Cvm |
| 14 | 0 – 3 – 9 | 1 – 5/3 – 7/6 | otonal | 1/1 – 7/6 – 5/3 | 1/1 – 10/7 – 12/7 | 1/1 – 6/5 – 7/5 | Cdim7no3 or Cdim(v5) |
| 15 | 0 – 6 – 9 | 1 – 7/5 – 7/6 | utonal | 1/1 – 7/6 – 7/5 | 1/1 – 6/5 – 12/7 | 1/1 – 10/7 – 5/3 | Cvdim(v5) or Cdim7no5 |
| 16 | 0 – 8 – 9 | 1 – 14/9 – 7/6 | utonal | 1/1 – 7/6 – 14/9 | 1/1 – 4/3 – 12/7 | 1/1 – 9/7 – 3/2 | C^ |
| 17 | 0 – 1 – 10 | 1 – 3/2 – 7/4 | otonal | 1/1 – 3/2 – 7/4 | 1/1 – 7/6 – 4/3 | 1/1 – 8/7 – 12/7 | Cv7no3 |
| 18 | 0 – 2 – 10 | 1 – 9/8 – 7/4 | otonal | 1/1 – 9/8 – 7/4 | 1/1 – 14/9 – 16/9 | 1/1 – 8/7 – 9/7 | Cv9no35 |
| 19 | 0 – 4 – 10 | 1 – 5/4 – 7/4 | otonal | 1/1 – 5/4 – 7/4 | 1/1 – 7/5 – 8/5 | 1/1 – 8/7 – 10/7 | C,v7no5 |
| 20 | 0 – 6 – 10 | 1 – 7/5 – 7/4 | utonal | 1/1 – 7/5 – 7/4 | 1/1 – 5/4 – 10/7 | 1/1 – 8/7 – 8/5 | C(b5) |
| 21 | 0 – 8 – 10 | 1 – 14/9 – 7/4 | utonal | 1/1 – 14/9 – 7/4 | 1/1 – 9/8 – 9/7 | 1/1 – 8/7 – 16/9 | C^,9no5 |
| 22 | 0 – 9 – 10 | 1 – 7/6 – 7/4 | utonal | 1/1 – 7/6 – 7/4 | 1/1 – 3/2 – 12/7 | 1/1 – 8/7 – 4/3 | Cvm7no5 |
| 23 | 0 – 4 – 14 | 1 – 5/4 – 11/10 | valinorsmic | 1/1 – 11/10 – 5/4 | 1/1 – 8/7 – 20/11 | 1/1 – 8/5 – 7/4 | |
| 24 | 0 – 6 – 14 | 1 – 7/5 – 11/10 | otonal | 1/1 – 11/10 – 7/5 | 1/1 – 14/11 – 20/11 | 1/1 – 10/7 – 11/7 | |
| 25 | 0 – 8 – 14 | 1 – 11/7 – 11/10 | utonal | 1/1 – 11/10 – 11/7 | 1/1 – 10/7 – 20/11 | 1/1 – 14/11 – 7/5 | |
| 26 | 0 – 10 – 14 | 1 – 7/4 – 11/10 | valinorsmic | 1/1 – 11/10 – 7/4 | 1/1 – 8/5 – 20/11 | 1/1 – 8/7 – 5/4 | |
| 27 | 0 – 2 – 16 | 1 – 10/9 – 11/9 | otonal | 1/1 – 10/9 – 11/9 | 1/1 – 11/10 – 9/5 | 1/1 – 18/11 – 20/11 | |
| 28 | 0 – 6 – 16 | 1 – 7/5 – 11/9 | werckismic | 1/1 – 11/9 – 7/5 | 1/1 – 8/7 – 18/11 | 1/1 – 10/7 – 7/4 | |
| 29 | 0 – 8 – 16 | 1 – 14/9 – 11/9 | otonal | 1/1 – 11/9 – 14/9 | 1/1 – 14/11 – 18/11 | 1/1 – 9/7 – 11/7 | |
| 30 | 0 – 10 – 16 | 1 – 7/4 – 11/9 | werckismic | 1/1 – 11/9 – 7/4 | 1/1 – 10/7 – 18/11 | 1/1 – 8/7 – 7/5 | |
| 31 | 0 – 14 – 16 | 1 – 11/10 – 11/9 | utonal | 1/1 – 11/10 – 11/9 | 1/1 – 10/9 – 20/11 | 1/1 – 18/11 – 9/5 | |
| 32 | 0 – 1 – 17 | 1 – 3/2 – 11/6 | otonal | 1/1 – 3/2 – 11/6 | 1/1 – 11/9 – 4/3 | 1/1 – 12/11 – 18/11 | |
| 33 | 0 – 3 – 17 | 1 – 5/3 – 11/6 | otonal | 1/1 – 5/3 – 11/6 | 1/1 – 11/10 – 6/5 | 1/1 – 12/11 – 20/11 | |
| 34 | 0 – 8 – 17 | 1 – 11/7 – 11/6 | utonal | 1/1 – 11/7 – 11/6 | 1/1 – 7/6 – 14/11 | 1/1 – 12/11 – 12/7 | |
| 35 | 0 – 9 – 17 | 1 – 7/6 – 11/6 | otonal | 1/1 – 7/6 – 11/6 | 1/1 – 11/7 – 12/7 | 1/1 – 12/11 – 14/11 | |
| 36 | 0 – 14 – 17 | 1 – 11/10 – 11/6 | utonal | 1/1 – 11/10 – 11/6 | 1/1 – 5/3 – 20/11 | 1/1 – 12/11 – 6/5 | |
| 37 | 0 – 16 – 17 | 1 – 11/9 – 11/6 | utonal | 1/1 – 11/9 – 11/6 | 1/1 – 3/2 – 18/11 | 1/1 – 12/11 – 4/3 | |
| 38 | 0 – 1 – 18 | 1 – 3/2 – 11/8 | otonal | 1/1 – 11/8 – 3/2 | 1/1 – 12/11 – 16/11 | 1/1 – 4/3 – 11/6 | |
| 39 | 0 – 2 – 18 | 1 – 9/8 – 11/8 | otonal | 1/1 – 9/8 – 11/8 | 1/1 – 11/9 – 16/9 | 1/1 – 16/11 – 18/11 | |
| 40 | 0 – 4 – 18 | 1 – 5/4 – 11/8 | otonal | 1/1 – 5/4 – 11/8 | 1/1 – 11/10 – 8/5 | 1/1 – 16/11 – 20/11 | |
| 41 | 0 – 8 – 18 | 1 – 11/7 – 11/8 | utonal | 1/1 – 11/8 – 11/7 | 1/1 – 8/7 – 16/11 | 1/1 – 14/11 – 7/4 | |
| 42 | 0 – 9 – 18 | 1 – 7/6 – 11/8 | mothwellsmic | 1/1 – 7/6 – 11/8 | 1/1 – 7/6 – 12/7 | 1/1 – 16/11 – 12/7 | |
| 43 | 0 – 10 – 18 | 1 – 7/4 – 11/8 | otonal | 1/1 – 11/8 – 7/4 | 1/1 – 14/11 – 16/11 | 1/1 – 8/7 – 11/7 | |
| 44 | 0 – 14 – 18 | 1 – 11/10 – 11/8 | utonal | 1/1 – 11/10 – 11/8 | 1/1 – 5/4 – 20/11 | 1/1 – 16/11 – 8/5 | |
| 45 | 0 – 16 – 18 | 1 – 11/9 – 11/8 | utonal | 1/1 – 11/9 – 11/8 | 1/1 – 9/8 – 18/11 | 1/1 – 16/11 – 16/9 | |
| 46 | 0 – 17 – 18 | 1 – 11/6 – 11/8 | utonal | 1/1 – 11/8 – 11/6 | 1/1 – 4/3 – 16/11 | 1/1 – 12/11 – 3/2 |
Tetrads
| # | Chord | Transversal | Type | As generated | 1st inversion | 2nd inversion | 3rd inversion | Name |
|---|---|---|---|---|---|---|---|---|
| 1 | 0 – 1 – 2 – 3 | 1 – 3/2 – 9/8 – 5/3 | didymic | 1/1 – 9/8 – 3/2 – 5/3 | 1/1 – 4/3 – 3/2 – 16/9 | 1/1 – 9/8 – 4/3 – 3/2 | 1/1 – 6/5 – 4/3 – 9/5 | C7sus4 or C4,9 |
| 2 | 0 – 1 – 2 – 4 | 1 – 3/2 – 9/8 – 5/4 | otonal | 1/1 – 9/8 – 5/4 – 3/2 | 1/1 – 10/9 – 4/3 – 16/9 | 1/1 – 6/5 – 8/5 – 9/5 | 1/1 – 4/3 – 3/2 – 5/3 | Cadd9 |
| 3 | 0 – 1 – 3 – 4 | 1 – 3/2 – 5/3 – 5/4 | ambitonal | 1/1 – 5/4 – 3/2 – 5/3 | 1/1 – 6/5 – 4/3 – 8/5 | 1/1 – 9/8 – 4/3 – 5/3 | 1/1 – 6/5 – 3/2 – 9/5 | C6 or Cm7 |
| 4 | 0 – 2 – 3 – 4 | 1 – 10/9 – 5/3 – 5/4 | utonal | 1/1 – 10/9 – 5/4 – 5/3 | 1/1 – 9/8 – 3/2 – 9/5 | 1/1 – 4/3 – 8/5 – 16/9 | 1/1 – 6/5 – 4/3 – 3/2 | C9no3 |
| 5 | 0 – 2 – 3 – 6 | 1 – 9/8 – 5/3 – 7/5 | erato | 1/1 – 9/8 – 7/5 – 5/3 | 1/1 – 5/4 – 3/2 – 16/9 | 1/1 – 6/5 – 10/7 – 8/5 | 1/1 – 6/5 – 4/3 – 5/3 | C7 |
| 6 | 0 – 2 – 4 – 6 | 1 – 9/8 – 5/4 – 7/5 | erato | 1/1 – 9/8 – 5/4 – 7/5 | 1/1 – 10/9 – 5/4 – 16/9 | 1/1 – 9/8 – 8/5 – 9/5 | 1/1 – 10/7 – 8/5 – 9/5 | C9no5 |
| 7 | 0 – 3 – 4 – 6 | 1 – 5/3 – 5/4 – 7/5 | erato | 1/1 – 5/4 – 7/5 – 5/3 | 1/1 – 9/8 – 4/3 – 8/5 | 1/1 – 6/5 – 10/7 – 16/9 | 1/1 – 6/5 – 3/2 – 5/3 | Cm7(b5) or Cm6 |
| 8 | 0 – 2 – 4 – 8 | 1 – 9/8 – 5/4 – 14/9 | erato | 1/1 – 9/8 – 5/4 – 14/9 | 1/1 – 10/9 – 7/5 – 16/9 | 1/1 – 5/4 – 8/5 – 9/5 | 1/1 – 9/7 – 10/7 – 8/5 | Caug,9 |
| 9 | 0 – 2 – 6 – 8 | 1 – 9/8 – 7/5 – 14/9 | erato | 1/1 – 9/8 – 7/5 – 14/9 | 1/1 – 5/4 – 7/5 – 16/9 | 1/1 – 10/9 – 10/7 – 8/5 | 1/1 – 9/7 – 10/7 – 9/5 | C7(vb5) |
| 10 | 0 – 4 – 6 – 8 | 1 – 5/4 – 7/5 – 14/9 | erato | 1/1 – 5/4 – 7/5 – 14/9 | 1/1 – 9/8 – 5/4 – 8/5 | 1/1 – 10/9 – 10/7 – 16/9 | 1/1 – 9/7 – 8/5 – 9/5 | C9(b5)no3 |
| 11 | 0 – 1 – 3 – 9 | 1 – 3/2 – 5/3 – 7/6 | otonal | 1/1 – 7/6 – 3/2 – 5/3 | 1/1 – 9/7 – 10/7 – 12/7 | 1/1 – 10/9 – 4/3 – 14/9 | 1/1 – 6/5 – 7/5 – 9/5 | Cm7(vb5) |
| 12 | 0 – 3 – 6 – 9 | 1 – 5/3 – 7/5 – 7/6 | starling | 1/1 – 7/6 – 7/5 – 5/3 | 1/1 – 6/5 – 10/7 – 12/7 | 1/1 – 6/5 – 10/7 – 5/3 | 1/1 – 6/5 – 7/5 – 5/3 | Cdim7 |
| 13 | 0 – 6 – 8 – 9 | 1 – 7/5 – 14/9 – 7/6 | utonal | 1/1 – 7/6 – 7/5 – 14/9 | 1/1 – 6/5 – 4/3 – 12/7 | 1/1 – 10/9 – 10/7 – 5/3 | 1/1 – 9/7 – 3/2 – 9/5 | C^,7 |
| 14 | 0 – 1 – 2 – 10 | 1 – 3/2 – 9/8 – 7/4 | otonal | 1/1 – 9/8 – 3/2 – 7/4 | 1/1 – 4/3 – 14/9 – 16/9 | 1/1 – 7/6 – 4/3 – 3/2 | 1/1 – 8/7 – 9/7 – 12/7 | Cv7no3 or Cvm,11 |
| 15 | 0 – 1 – 4 – 10 | 1 – 3/2 – 5/4 – 7/4 | otonal | 1/1 – 5/4 – 3/2 – 7/4 | 1/1 – 6/5 – 7/5 – 8/5 | 1/1 – 7/6 – 4/3 – 5/3 | 1/1 – 8/7 – 10/7 – 12/7 | C,v7 |
| 16 | 0 – 2 – 4 – 10 | 1 – 9/8 – 5/4 – 7/4 | otonal | 1/1 – 9/8 – 5/4 – 7/4 | 1/1 – 10/9 – 14/9 – 16/9 | 1/1 – 7/5 – 8/5 – 9/5 | 1/1 – 8/7 – 9/7 – 10/7 | C9(v7)no5 |
| 17 | 0 – 2 – 6 – 10 | 1 – 9/8 – 7/5 – 7/4 | marvel | 1/1 – 9/8 – 7/5 – 7/4 | 1/1 – 5/4 – 14/9 – 16/9 | 1/1 – 5/4 – 10/7 – 8/5 | 1/1 – 8/7 – 9/7 – 8/5 | C7(#5) or Caug7 |
| 18 | 0 – 4 – 6 – 10 | 1 – 5/4 – 7/5 – 7/4 | marvel | 1/1 – 5/4 – 7/5 – 7/4 | 1/1 – 9/8 – 7/5 – 8/5 | 1/1 – 5/4 – 10/7 – 16/9 | 1/1 – 8/7 – 10/7 – 8/5 | C7(b5) |
| 19 | 0 – 2 – 8 – 10 | 1 – 9/8 – 14/9 – 7/4 | didymic | 1/1 – 9/8 – 14/9 – 7/4 | 1/1 – 7/5 – 14/9 – 16/9 | 1/1 – 9/8 – 9/7 – 10/7 | 1/1 – 8/7 – 9/7 – 16/9 | |
| 20 | 0 – 4 – 8 – 10 | 1 – 5/4 – 14/9 – 7/4 | marvel | 1/1 – 5/4 – 14/9 – 7/4 | 1/1 – 5/4 – 7/5 – 8/5 | 1/1 – 9/8 – 9/7 – 8/5 | 1/1 – 8/7 – 10/7 – 16/9 | |
| 21 | 0 – 6 – 8 – 10 | 1 – 7/5 – 14/9 – 7/4 | utonal | 1/1 – 7/5 – 14/9 – 7/4 | 1/1 – 10/9 – 5/4 – 10/7 | 1/1 – 9/8 – 9/7 – 9/5 | 1/1 – 8/7 – 8/5 – 16/9 | C,9(b5) |
| 22 | 0 – 1 – 9 – 10 | 1 – 3/2 – 7/6 – 7/4 | ambitonal | 1/1 – 7/6 – 3/2 – 7/4 | 1/1 – 9/7 – 3/2 – 12/7 | 1/1 – 7/6 – 4/3 – 14/9 | 1/1 – 8/7 – 4/3 – 12/7 | Cvm7 or C^6 |
| 23 | 0 – 6 – 9 – 10 | 1 – 7/5 – 7/6 – 7/4 | utonal | 1/1 – 7/6 – 7/5 – 7/4 | 1/1 – 6/5 – 3/2 – 12/7 | 1/1 – 5/4 – 10/7 – 5/3 | 1/1 – 8/7 – 4/3 – 8/5 | Cvm7(vb5) or Cm^6 or C6(b5) |
| 24 | 0 – 8 – 9 – 10 | 1 – 14/9 – 7/6 – 7/4 | utonal | 1/1 – 7/6 – 14/9 – 7/4 | 1/1 – 4/3 – 3/2 – 12/7 | 1/1 – 9/8 – 9/7 – 3/2 | 1/1 – 8/7 – 4/3 – 16/9 | Cvm7(#5) or C4^6 or C^,9 |
| 25 | 0 – 4 – 6 – 14 | 1 – 5/4 – 7/5 – 11/10 | minerva | 1/1 – 11/10 – 5/4 – 7/5 | 1/1 – 9/8 – 14/11 – 20/11 | 1/1 – 9/8 – 8/5 – 7/4 | 1/1 – 10/7 – 11/7 – 16/9 | |
| 26 | 0 – 4 – 8 – 14 | 1 – 5/4 – 14/9 – 11/10 | minerva | 1/1 – 11/10 – 5/4 – 14/9 | 1/1 – 9/8 – 10/7 – 20/11 | 1/1 – 5/4 – 8/5 – 7/4 | 1/1 – 9/7 – 7/5 – 8/5 | |
| 27 | 0 – 6 – 8 – 14 | 1 – 7/5 – 14/9 – 11/10 | euterpe | 1/1 – 11/10 – 7/5 – 14/9 | 1/1 – 14/11 – 10/7 – 20/11 | 1/1 – 10/9 – 10/7 – 11/7 | 1/1 – 9/7 – 7/5 – 9/5 | C^,7(vb5) |
| 28 | 0 – 4 – 10 – 14 | 1 – 5/4 – 7/4 – 11/10 | valinorsmic | 1/1 – 11/10 – 5/4 – 7/4 | 1/1 – 25/22 – 8/5 – 20/11 | 1/1 – 7/5 – 8/5 – 7/4 | 1/1 – 8/7 – 5/4 – 10/7 | C,^9(b5) |
| 29 | 0 – 6 – 10 – 14 | 1 – 7/5 – 7/4 – 11/10 | minerva | 1/1 – 11/10 – 7/5 – 7/4 | 1/1 – 14/11 – 8/5 – 20/11 | 1/1 – 5/4 – 10/7 – 11/7 | 1/1 – 8/7 – 5/4 – 8/5 | |
| 30 | 0 – 8 – 10 – 14 | 1 – 14/9 – 7/4 – 11/10 | minerva | 1/1 – 11/10 – 14/9 – 7/4 | 1/1 – 7/5 – 8/5 – 20/11 | 1/1 – 9/8 – 9/7 – 7/5 | 1/1 – 8/7 – 5/4 – 16/9 | |
| 31 | 0 – 2 – 6 – 16 | 1 – 9/8 – 7/5 – 11/9 | meantone | 1/1 – 9/8 – 11/9 – 7/5 | 1/1 – 11/10 – 5/4 – 16/9 | 1/1 – 8/7 – 18/11 – 20/11 | 1/1 – 10/7 – 8/5 – 7/4 | |
| 32 | 0 – 2 – 8 – 16 | 1 – 10/9 – 14/9 – 11/9 | otonal | 1/1 – 10/9 – 11/9 – 14/9 | 1/1 – 11/10 – 7/5 – 9/5 | 1/1 – 14/11 – 18/11 – 20/11 | 1/1 – 9/7 – 10/7 – 11/7 | |
| 33 | 0 – 6 – 8 – 16 | 1 – 7/5 – 14/9 – 11/9 | euterpe | 1/1 – 11/9 – 7/5 – 14/9 | 1/1 – 8/7 – 14/11 – 18/11 | 1/1 – 9/8 – 10/7 – 7/4 | 1/1 – 9/7 – 11/7 – 9/5 | |
| 34 | 0 – 2 – 10 – 16 | 1 – 9/8 – 7/4 – 11/9 | euterpe | 1/1 – 9/8 – 11/9 – 7/4 | 1/1 – 11/10 – 14/9 – 16/9 | 1/1 – 10/7 – 18/11 – 20/11 | 1/1 – 8/7 – 9/7 – 7/5 | |
| 35 | 0 – 6 – 10 – 16 | 1 – 7/5 – 7/4 – 11/9 | werckismic | 1/1 – 11/9 – 7/5 – 7/4 | 1/1 – 8/7 – 10/7 – 18/11 | 1/1 – 5/4 – 10/7 – 7/4 | 1/1 – 8/7 – 7/5 – 8/5 | |
| 36 | 0 – 8 – 10 – 16 | 1 – 14/9 – 7/4 – 11/9 | euterpe | 1/1 – 11/9 – 14/9 – 7/4 | 1/1 – 14/11 – 10/7 – 18/11 | 1/1 – 9/8 – 9/7 – 11/7 | 1/1 – 8/7 – 7/5 – 16/9 | |
| 37 | 0 – 6 – 14 – 16 | 1 – 7/5 – 11/10 – 11/9 | euterpe | 1/1 – 11/10 – 11/9 – 7/5 | 1/1 – 10/9 – 14/11 – 20/11 | 1/1 – 8/7 – 18/11 – 9/5 | 1/1 – 10/7 – 11/7 – 7/4 | |
| 38 | 0 – 8 – 14 – 16 | 1 – 11/7 – 11/10 – 11/9 | utonal | 1/1 – 11/10 – 11/9 – 11/7 | 1/1 – 10/9 – 10/7 – 20/11 | 1/1 – 9/7 – 18/11 – 9/5 | 1/1 – 14/11 – 7/5 – 14/9 | |
| 39 | 0 – 10 – 14 – 16 | 1 – 7/4 – 11/10 – 11/9 | meantone | 1/1 – 11/10 – 11/9 – 7/4 | 1/1 – 10/9 – 8/5 – 20/11 | 1/1 – 10/7 – 18/11 – 9/5 | 1/1 – 8/7 – 5/4 – 7/5 | |
| 40 | 0 – 1 – 3 – 17 | 1 – 3/2 – 5/3 – 11/6 | otonal | 1/1 – 3/2 – 5/3 – 11/6 | 1/1 – 10/9 – 11/9 – 4/3 | 1/1 – 11/10 – 6/5 – 9/5 | 1/1 – 12/11 – 18/11 – 20/11 | |
| 41 | 0 – 1 – 9 – 17 | 1 – 3/2 – 7/6 – 11/6 | otonal | 1/1 – 7/6 – 3/2 – 11/6 | 1/1 – 9/7 – 11/7 – 12/7 | 1/1 – 11/9 – 4/3 – 14/9 | 1/1 – 12/11 – 14/11 – 18/11 | |
| 42 | 0 – 3 – 9 – 17 | 1 – 5/3 – 7/6 – 11/6 | otonal | 1/1 – 7/6 – 5/3 – 11/6 | 1/1 – 10/7 – 11/7 – 12/7 | 1/1 – 11/10 – 6/5 – 7/5 | 1/1 – 12/11 – 14/11 – 20/11 | |
| 43 | 0 – 8 – 9 – 17 | 1 – 14/9 – 7/6 – 11/6 | mothwellsmic | 1/1 – 7/6 – 14/9 – 11/6 | 1/1 – 4/3 – 11/7 – 12/7 | 1/1 – 7/6 – 9/7 – 3/2 | 1/1 – 12/11 – 14/11 – 12/7 | |
| 44 | 0 – 8 – 14 – 17 | 1 – 11/7 – 11/10 – 11/6 | utonal | 1/1 – 11/10 – 11/7 – 11/6 | 1/1 – 10/7 – 5/3 – 20/11 | 1/1 – 7/6 – 14/11 – 7/5 | 1/1 – 12/11 – 6/5 – 12/7 | |
| 45 | 0 – 8 – 16 – 17 | 1 – 11/7 – 11/9 – 11/6 | utonal | 1/1 – 11/9 – 11/7 – 11/6 | 1/1 – 9/7 – 3/2 – 18/11 | 1/1 – 7/6 – 14/11 – 14/9 | 1/1 – 12/11 – 4/3 – 12/7 | |
| 46 | 0 – 14 – 16 – 17 | 1 – 11/10 – 11/9 – 11/6 | utonal | 1/1 – 11/10 – 11/9 – 11/6 | 1/1 – 10/9 – 5/3 – 20/11 | 1/1 – 3/2 – 18/11 – 9/5 | 1/1 – 12/11 – 6/5 – 4/3 | |
| 47 | 0 – 1 – 2 – 18 | 1 – 3/2 – 9/8 – 11/8 | otonal | 1/1 – 9/8 – 11/8 – 3/2 | 1/1 – 11/9 – 4/3 – 16/9 | 1/1 – 12/11 – 16/11 – 18/11 | 1/1 – 4/3 – 3/2 – 11/6 | |
| 48 | 0 – 1 – 4 – 18 | 1 – 3/2 – 5/4 – 11/8 | otonal | 1/1 – 5/4 – 11/8 – 3/2 | 1/1 – 11/10 – 6/5 – 8/5 | 1/1 – 12/11 – 16/11 – 20/11 | 1/1 – 4/3 – 5/3 – 11/6 | |
| 49 | 0 – 2 – 4 – 18 | 1 – 9/8 – 5/4 – 11/8 | otonal | 1/1 – 9/8 – 5/4 – 11/8 | 1/1 – 10/9 – 11/9 – 16/9 | 1/1 – 11/10 – 8/5 – 9/5 | 1/1 – 16/11 – 18/11 – 20/11 | |
| 50 | 0 – 2 – 8 – 18 | 1 – 9/8 – 14/9 – 11/8 | euterpe | 1/1 – 9/8 – 11/8 – 14/9 | 1/1 – 11/9 – 7/5 – 16/9 | 1/1 – 8/7 – 16/11 – 18/11 | 1/1 – 9/7 – 10/7 – 7/4 | |
| 51 | 0 – 4 – 8 – 18 | 1 – 5/4 – 14/9 – 11/8 | minerva | 1/1 – 5/4 – 11/8 – 14/9 | 1/1 – 11/10 – 5/4 – 8/5 | 1/1 – 8/7 – 16/11 – 20/11 | 1/1 – 9/7 – 8/5 – 7/4 | |
| 52 | 0 – 1 – 9 – 18 | 1 – 3/2 – 7/6 – 11/8 | mothwellsmic | 1/1 – 7/6 – 11/8 – 3/2 | 1/1 – 7/6 – 9/7 – 12/7 | 1/1 – 12/11 – 16/11 – 12/7 | 1/1 – 4/3 – 14/9 – 11/6 | |
| 53 | 0 – 8 – 9 – 18 | 1 – 14/9 – 7/6 – 11/8 | mothwellsmic | 1/1 – 7/6 – 11/8 – 14/9 | 1/1 – 7/6 – 4/3 – 12/7 | 1/1 – 8/7 – 16/11 – 12/7 | 1/1 – 9/7 – 3/2 – 7/4 | |
| 54 | 0 – 1 – 10 – 18 | 1 – 3/2 – 7/4 – 11/8 | otonal | 1/1 – 11/8 – 3/2 – 7/4 | 1/1 – 12/11 – 14/11 – 16/11 | 1/1 – 7/6 – 4/3 – 11/6 | 1/1 – 8/7 – 11/7 – 12/7 | |
| 55 | 0 – 2 – 10 – 18 | 1 – 9/8 – 7/4 – 11/8 | otonal | 1/1 – 9/8 – 11/8 – 7/4 | 1/1 – 11/9 – 14/9 – 16/9 | 1/1 – 14/11 – 16/11 – 18/11 | 1/1 – 8/7 – 9/7 – 11/7 | |
| 56 | 0 – 4 – 10 – 18 | 1 – 5/4 – 7/4 – 11/8 | otonal | 1/1 – 5/4 – 11/8 – 7/4 | 1/1 – 11/10 – 7/5 – 8/5 | 1/1 – 14/11 – 16/11 – 20/11 | 1/1 – 8/7 – 10/7 – 11/7 | |
| 57 | 0 – 8 – 10 – 18 | 1 – 14/9 – 7/4 – 11/8 | mothwellsmic | 1/1 – 11/8 – 14/9 – 7/4 | 1/1 – 8/7 – 14/11 – 16/11 | 1/1 – 9/8 – 9/7 – 7/4 | 1/1 – 8/7 – 11/7 – 16/9 | |
| 58 | 0 – 9 – 10 – 18 | 1 – 7/6 – 7/4 – 11/8 | mothwellsmic | 1/1 – 7/6 – 11/8 – 7/4 | 1/1 – 7/6 – 3/2 – 12/7 | 1/1 – 14/11 – 16/11 – 12/7 | 1/1 – 8/7 – 4/3 – 11/7 | |
| 59 | 0 – 4 – 14 – 18 | 1 – 5/4 – 11/10 – 11/8 | valinorsmic | 1/1 – 11/10 – 5/4 – 11/8 | 1/1 – 8/7 – 5/4 – 20/11 | 1/1 – 11/10 – 8/5 – 7/4 | 1/1 – 16/11 – 8/5 – 20/11 | |
| 60 | 0 – 8 – 14 – 18 | 1 – 11/7 – 11/10 – 11/8 | utonal | 1/1 – 11/10 – 11/8 – 11/7 | 1/1 – 5/4 – 10/7 – 20/11 | 1/1 – 8/7 – 16/11 – 8/5 | 1/1 – 14/11 – 7/5 – 7/4 | |
| 61 | 0 – 10 – 14 – 18 | 1 – 7/4 – 11/10 – 11/8 | minerva | 1/1 – 11/10 – 11/8 – 7/4 | 1/1 – 5/4 – 8/5 – 20/11 | 1/1 – 14/11 – 16/11 – 8/5 | 1/1 – 8/7 – 5/4 – 11/7 | |
| 62 | 0 – 2 – 16 – 18 | 1 – 9/8 – 11/9 – 11/8 | didymic | 1/1 – 9/8 – 11/9 – 11/8 | 1/1 – 11/10 – 11/9 – 16/9 | 1/1 – 9/8 – 18/11 – 20/11 | 1/1 – 16/11 – 18/11 – 16/9 | |
| 63 | 0 – 8 – 16 – 18 | 1 – 11/7 – 11/9 – 11/8 | utonal | 1/1 – 11/9 – 11/8 – 11/7 | 1/1 – 9/8 – 9/7 – 18/11 | 1/1 – 8/7 – 16/11 – 16/9 | 1/1 – 14/11 – 14/9 – 7/4 | |
| 64 | 0 – 10 – 16 – 18 | 1 – 7/4 – 11/9 – 11/8 | euterpe | 1/1 – 11/9 – 11/8 – 7/4 | 1/1 – 9/8 – 10/7 – 18/11 | 1/1 – 14/11 – 16/11 – 16/9 | 1/1 – 8/7 – 7/5 – 11/7 | |
| 65 | 0 – 14 – 16 – 18 | 1 – 11/10 – 11/9 – 11/8 | utonal | 1/1 – 11/10 – 11/9 – 11/8 | 1/1 – 10/9 – 5/4 – 20/11 | 1/1 – 9/8 – 18/11 – 9/5 | 1/1 – 16/11 – 8/5 – 16/9 | |
| 66 | 0 – 1 – 17 – 18 | 1 – 3/2 – 11/6 – 11/8 | ambitonal | 1/1 – 11/8 – 3/2 – 11/6 | 1/1 – 12/11 – 4/3 – 16/11 | 1/1 – 11/9 – 4/3 – 11/6 | 1/1 – 12/11 – 3/2 – 18/11 | |
| 67 | 0 – 8 – 17 – 18 | 1 – 11/7 – 11/6 – 11/8 | utonal | 1/1 – 11/8 – 11/7 – 11/6 | 1/1 – 8/7 – 4/3 – 16/11 | 1/1 – 7/6 – 14/11 – 7/4 | 1/1 – 12/11 – 3/2 – 12/7 | |
| 68 | 0 – 9 – 17 – 18 | 1 – 7/6 – 11/6 – 11/8 | mothwellsmic | 1/1 – 7/6 – 11/8 – 11/6 | 1/1 – 7/6 – 11/7 – 12/7 | 1/1 – 4/3 – 16/11 – 12/7 | 1/1 – 12/11 – 14/11 – 3/2 | |
| 69 | 0 – 14 – 17 – 18 | 1 – 11/10 – 11/6 – 11/8 | utonal | 1/1 – 11/10 – 11/8 – 11/6 | 1/1 – 5/4 – 5/3 – 20/11 | 1/1 – 4/3 – 16/11 – 8/5 | 1/1 – 12/11 – 6/5 – 3/2 | |
| 70 | 0 – 16 – 17 – 18 | 1 – 11/9 – 11/6 – 11/8 | utonal | 1/1 – 11/9 – 11/8 – 11/6 | 1/1 – 9/8 – 3/2 – 18/11 | 1/1 – 4/3 – 16/11 – 16/9 | 1/1 – 12/11 – 4/3 – 3/2 |
Pentads
| Chord | Transversal | Type | As generated | First inversion | Second inversion | Third inversion | Fourth inversion |
|---|---|---|---|---|---|---|---|
| 0 – 1 – 2 – 3 – 4 | 1 – 3/2 – 9/8 – 5/3 – 5/4 | didymic | 1/1 – 9/8 – 5/4 – 3/2 – 5/3 | 1/1 – 10/9 – 4/3 – 3/2 – 16/9 | 1/1 – 6/5 – 4/3 – 8/5 – 9/5 | 1/1 – 10/9 – 4/3 – 3/2 – 5/3 | 1/1 – 6/5 – 4/3 – 3/2 – 9/5 |
| 0 – 2 – 3 – 4 – 6 | 1 – 9/8 – 5/3 – 5/4 – 7/5 | erato | 1/1 – 9/8 – 5/4 – 7/5 – 5/3 | 1/1 – 10/9 – 5/4 – 3/2 – 16/9 | 1/1 – 10/9 – 4/3 – 8/5 – 9/5 | 1/1 – 6/5 – 10/7 – 8/5 – 9/5 | 1/1 – 6/5 – 4/3 – 3/2 – 5/3 |
| 0 – 2 – 4 – 6 – 8 | 1 – 9/8 – 5/4 – 7/5 – 14/9 | erato | 1/1 – 9/8 – 5/4 – 7/5 – 14/9 | 1/1 – 10/9 – 5/4 – 7/5 – 16/9 | 1/1 – 10/9 – 5/4 – 8/5 – 9/5 | 1/1 – 10/9 – 10/7 – 8/5 – 9/5 | 1/1 – 9/7 – 10/7 – 8/5 – 9/5 |
| 0 – 1 – 2 – 4 – 10 | 1 – 3/2 – 9/8 – 5/4 – 7/4 | otonal | 1/1 – 9/8 – 5/4 – 3/2 – 7/4 | 1/1 – 10/9 – 4/3 – 14/9 – 16/9 | 1/1 – 6/5 – 7/5 – 8/5 – 9/5 | 1/1 – 7/6 – 4/3 – 3/2 – 5/3 | 1/1 – 8/7 – 9/7 – 10/7 – 12/7 |
| 0 – 2 – 4 – 6 – 10 | 1 – 9/8 – 5/4 – 7/5 – 7/4 | erato | 1/1 – 9/8 – 5/4 – 7/5 – 7/4 | 1/1 – 10/9 – 5/4 – 14/9 – 16/9 | 1/1 – 10/9 – 7/5 – 8/5 – 9/5 | 1/1 – 5/4 – 10/7 – 8/5 – 9/5 | 1/1 – 8/7 – 9/7 – 10/7 – 8/5 |
| 0 – 2 – 4 – 8 – 10 | 1 – 9/8 – 5/4 – 14/9 – 7/4 | erato | 1/1 – 9/8 – 5/4 – 14/9 – 7/4 | 1/1 – 10/9 – 7/5 – 14/9 – 16/9 | 1/1 – 5/4 – 7/5 – 8/5 – 9/5 | 1/1 – 9/8 – 9/7 – 10/7 – 8/5 | 1/1 – 8/7 – 9/7 – 10/7 – 16/9 |
| 0 – 2 – 6 – 8 – 10 | 1 – 9/8 – 7/5 – 14/9 – 7/4 | erato | 1/1 – 9/8 – 7/5 – 14/9 – 7/4 | 1/1 – 5/4 – 7/5 – 14/9 – 16/9 | 1/1 – 10/9 – 5/4 – 10/7 – 8/5 | 1/1 – 9/8 – 9/7 – 10/7 – 9/5 | 1/1 – 8/7 – 9/7 – 8/5 – 16/9 |
| 0 – 4 – 6 – 8 – 10 | 1 – 5/4 – 7/5 – 14/9 – 7/4 | erato | 1/1 – 5/4 – 7/5 – 14/9 – 7/4 | 1/1 – 9/8 – 5/4 – 7/5 – 8/5 | 1/1 – 10/9 – 5/4 – 10/7 – 9/5 | 1/1 – 9/8 – 9/7 – 8/5 – 9/5 | 1/1 – 8/7 – 10/7 – 8/5 – 16/9 |
| 0 – 6 – 8 – 9 – 10 | 1 – 7/5 – 14/9 – 7/6 – 7/4 | utonal | 1/1 – 7/6 – 7/5 – 14/9 – 7/4 | 1/1 – 6/5 – 4/3 – 3/2 – 12/7 | 1/1 – 10/9 – 5/4 – 10/7 – 5/3 | 1/1 – 9/8 – 9/7 – 3/2 – 9/5 | 1/1 – 8/7 – 4/3 – 8/5 – 16/9 |
| 0 – 4 – 6 – 8 – 14 | 1 – 5/4 – 7/5 – 14/9 – 11/10 | meantone | 1/1 – 11/10 – 5/4 – 7/5 – 14/9 | 1/1 – 9/8 – 14/11 – 10/7 – 20/11 | 1/1 – 10/9 – 5/4 – 8/5 – 7/4 | 1/1 – 10/9 – 10/7 – 11/7 – 9/5 | 1/1 – 9/7 – 7/5 – 8/5 – 9/5 |
| 0 – 4 – 6 – 10 – 14 | 1 – 5/4 – 7/5 – 7/4 – 11/10 | minerva | 1/1 – 11/10 – 5/4 – 7/5 – 7/4 | 1/1 – 9/8 – 14/11 – 8/5 – 20/11 | 1/1 – 10/9 – 7/5 – 8/5 – 7/4 | 1/1 – 5/4 – 10/7 – 11/7 – 9/5 | 1/1 – 8/7 – 5/4 – 10/7 – 8/5 |
| 0 – 4 – 8 – 10 – 14 | 1 – 5/4 – 14/9 – 7/4 – 11/10 | minerva | 1/1 – 11/10 – 5/4 – 14/9 – 7/4 | 1/1 – 9/8 – 7/5 – 8/5 – 20/11 | 1/1 – 5/4 – 7/5 – 8/5 – 7/4 | 1/1 – 9/8 – 9/7 – 7/5 – 8/5 | 1/1 – 8/7 – 5/4 – 10/7 – 16/9 |
| 0 – 6 – 8 – 10 – 14 | 1 – 7/5 – 14/9 – 7/4 – 11/10 | meantone | 1/1 – 11/10 – 7/5 – 14/9 – 7/4 | 1/1 – 14/11 – 7/5 – 8/5 – 20/11 | 1/1 – 10/9 – 5/4 – 10/7 – 11/7 | 1/1 – 9/8 – 9/7 – 7/5 – 9/5 | 1/1 – 8/7 – 5/4 – 8/5 – 16/9 |
| 0 – 2 – 6 – 8 – 16 | 1 – 9/8 – 7/5 – 14/9 – 11/9 | meantone | 1/1 – 9/8 – 11/9 – 7/5 – 14/9 | 1/1 – 11/10 – 5/4 – 7/5 – 16/9 | 1/1 – 8/7 – 14/11 – 18/11 – 20/11 | 1/1 – 10/9 – 10/7 – 8/5 – 7/4 | 1/1 – 9/7 – 10/7 – 11/7 – 9/5 |
| 0 – 2 – 6 – 10 – 16 | 1 – 9/8 – 7/5 – 7/4 – 11/9 | meantone | 1/1 – 9/8 – 11/9 – 7/5 – 7/4 | 1/1 – 11/10 – 5/4 – 14/9 – 16/9 | 1/1 – 8/7 – 10/7 – 18/11 – 20/11 | 1/1 – 5/4 – 10/7 – 8/5 – 7/4 | 1/1 – 8/7 – 9/7 – 7/5 – 8/5 |
| 0 – 2 – 8 – 10 – 16 | 1 – 9/8 – 14/9 – 7/4 – 11/9 | euterpe | 1/1 – 9/8 – 11/9 – 14/9 – 7/4 | 1/1 – 11/10 – 7/5 – 14/9 – 16/9 | 1/1 – 14/11 – 10/7 – 18/11 – 20/11 | 1/1 – 9/8 – 9/7 – 10/7 – 11/7 | 1/1 – 8/7 – 9/7 – 7/5 – 16/9 |
| 0 – 6 – 8 – 10 – 16 | 1 – 7/5 – 14/9 – 7/4 – 11/9 | euterpe | 1/1 – 11/9 – 7/5 – 14/9 – 7/4 | 1/1 – 8/7 – 14/11 – 10/7 – 18/11 | 1/1 – 10/9 – 5/4 – 10/7 – 7/4 | 1/1 – 9/8 – 9/7 – 11/7 – 9/5 | 1/1 – 8/7 – 7/5 – 8/5 – 16/9 |
| 0 – 6 – 8 – 14 – 16 | 1 – 7/5 – 14/9 – 11/10 – 11/9 | euterpe | 1/1 – 11/10 – 11/9 – 7/5 – 14/9 | 1/1 – 10/9 – 14/11 – 10/7 – 20/11 | 1/1 – 8/7 – 14/11 – 18/11 – 9/5 | 1/1 – 10/9 – 10/7 – 11/7 – 7/4 | 1/1 – 9/7 – 7/5 – 11/7 – 9/5 |
| 0 – 6 – 10 – 14 – 16 | 1 – 7/5 – 7/4 – 11/10 – 11/9 | meantone | 1/1 – 11/10 – 11/9 – 7/5 – 7/4 | 1/1 – 10/9 – 14/11 – 8/5 – 20/11 | 1/1 – 8/7 – 10/7 – 18/11 – 9/5 | 1/1 – 5/4 – 10/7 – 11/7 – 7/4 | 1/1 – 8/7 – 5/4 – 7/5 – 8/5 |
| 0 – 8 – 10 – 14 – 16 | 1 – 14/9 – 7/4 – 11/10 – 11/9 | meantone | 1/1 – 11/10 – 11/9 – 14/9 – 7/4 | 1/1 – 10/9 – 7/5 – 8/5 – 20/11 | 1/1 – 14/11 – 10/7 – 18/11 – 9/5 | 1/1 – 9/8 – 9/7 – 7/5 – 11/7 | 1/1 – 8/7 – 5/4 – 7/5 – 16/9 |
| 0 – 1 – 3 – 9 – 17 | 1 – 3/2 – 5/3 – 7/6 – 11/6 | otonal | 1/1 – 7/6 – 3/2 – 5/3 – 11/6 | 1/1 – 9/7 – 10/7 – 11/7 – 12/7 | 1/1 – 10/9 – 11/9 – 4/3 – 14/9 | 1/1 – 11/10 – 6/5 – 7/5 – 9/5 | 1/1 – 12/11 – 14/11 – 18/11 – 20/11 |
| 0 – 8 – 14 – 16 – 17 | 1 – 11/7 – 11/10 – 11/9 – 11/6 | utonal | 1/1 – 11/10 – 11/9 – 11/7 – 11/6 | 1/1 – 10/9 – 10/7 – 5/3 – 20/11 | 1/1 – 9/7 – 3/2 – 18/11 – 9/5 | 1/1 – 7/6 – 14/11 – 7/5 – 14/9 | 1/1 – 12/11 – 6/5 – 4/3 – 12/7 |
| 0 – 1 – 2 – 4 – 18 | 1 – 3/2 – 9/8 – 5/4 – 11/8 | otonal | 1/1 – 9/8 – 5/4 – 11/8 – 3/2 | 1/1 – 10/9 – 11/9 – 4/3 – 16/9 | 1/1 – 11/10 – 6/5 – 8/5 – 9/5 | 1/1 – 12/11 – 16/11 – 18/11 – 20/11 | 1/1 – 4/3 – 3/2 – 5/3 – 11/6 |
| 0 – 2 – 4 – 8 – 18 | 1 – 9/8 – 5/4 – 14/9 – 11/8 | meantone | 1/1 – 9/8 – 5/4 – 11/8 – 14/9 | 1/1 – 10/9 – 11/9 – 7/5 – 16/9 | 1/1 – 11/10 – 5/4 – 8/5 – 9/5 | 1/1 – 8/7 – 16/11 – 18/11 – 20/11 | 1/1 – 9/7 – 10/7 – 8/5 – 7/4 |
| 0 – 1 – 2 – 10 – 18 | 1 – 3/2 – 9/8 – 7/4 – 11/8 | otonal | 1/1 – 9/8 – 11/8 – 3/2 – 7/4 | 1/1 – 11/9 – 4/3 – 14/9 – 16/9 | 1/1 – 12/11 – 14/11 – 16/11 – 18/11 | 1/1 – 7/6 – 4/3 – 3/2 – 11/6 | 1/1 – 8/7 – 9/7 – 11/7 – 12/7 |
| 0 – 1 – 4 – 10 – 18 | 1 – 3/2 – 5/4 – 7/4 – 11/8 | otonal | 1/1 – 5/4 – 11/8 – 3/2 – 7/4 | 1/1 – 11/10 – 6/5 – 7/5 – 8/5 | 1/1 – 12/11 – 14/11 – 16/11 – 20/11 | 1/1 – 7/6 – 4/3 – 5/3 – 11/6 | 1/1 – 8/7 – 10/7 – 11/7 – 12/7 |
| 0 – 2 – 4 – 10 – 18 | 1 – 9/8 – 5/4 – 7/4 – 11/8 | otonal | 1/1 – 9/8 – 5/4 – 11/8 – 7/4 | 1/1 – 10/9 – 11/9 – 14/9 – 16/9 | 1/1 – 11/10 – 7/5 – 8/5 – 9/5 | 1/1 – 14/11 – 16/11 – 18/11 – 20/11 | 1/1 – 8/7 – 9/7 – 10/7 – 11/7 |
| 0 – 2 – 8 – 10 – 18 | 1 – 9/8 – 14/9 – 7/4 – 11/8 | euterpe | 1/1 – 9/8 – 11/8 – 14/9 – 7/4 | 1/1 – 11/9 – 7/5 – 14/9 – 16/9 | 1/1 – 8/7 – 14/11 – 16/11 – 18/11 | 1/1 – 9/8 – 9/7 – 10/7 – 7/4 | 1/1 – 8/7 – 9/7 – 11/7 – 16/9 |
| 0 – 4 – 8 – 10 – 18 | 1 – 5/4 – 14/9 – 7/4 – 11/8 | minerva | 1/1 – 5/4 – 11/8 – 14/9 – 7/4 | 1/1 – 11/10 – 5/4 – 7/5 – 8/5 | 1/1 – 8/7 – 14/11 – 16/11 – 20/11 | 1/1 – 9/8 – 9/7 – 8/5 – 7/4 | 1/1 – 8/7 – 10/7 – 11/7 – 16/9 |
| 0 – 1 – 9 – 10 – 18 | 1 – 3/2 – 7/6 – 7/4 – 11/8 | mothwellsmic | 1/1 – 7/6 – 11/8 – 3/2 – 7/4 | 1/1 – 7/6 – 9/7 – 3/2 – 12/7 | 1/1 – 12/11 – 14/11 – 16/11 – 12/7 | 1/1 – 7/6 – 4/3 – 14/9 – 11/6 | 1/1 – 8/7 – 4/3 – 11/7 – 12/7 |
| 0 – 8 – 9 – 10 – 18 | 1 – 14/9 – 7/6 – 7/4 – 11/8 | mothwellsmic | 1/1 – 7/6 – 11/8 – 14/9 – 7/4 | 1/1 – 7/6 – 4/3 – 3/2 – 12/7 | 1/1 – 8/7 – 14/11 – 16/11 – 12/7 | 1/1 – 9/8 – 9/7 – 3/2 – 7/4 | 1/1 – 8/7 – 4/3 – 11/7 – 16/9 |
| 0 – 4 – 8 – 14 – 18 | 1 – 5/4 – 14/9 – 11/10 – 11/8 | minerva | 1/1 – 11/10 – 5/4 – 11/8 – 14/9 | 1/1 – 9/8 – 5/4 – 10/7 – 20/11 | 1/1 – 11/10 – 5/4 – 8/5 – 7/4 | 1/1 – 8/7 – 16/11 – 8/5 – 20/11 | 1/1 – 9/7 – 7/5 – 8/5 – 7/4 |
| 0 – 4 – 10 – 14 – 18 | 1 – 5/4 – 7/4 – 11/10 – 11/8 | minerva | 1/1 – 11/10 – 5/4 – 11/8 – 7/4 | 1/1 – 9/8 – 5/4 – 8/5 – 20/11 | 1/1 – 11/10 – 7/5 – 8/5 – 7/4 | 1/1 – 14/11 – 16/11 – 8/5 – 20/11 | 1/1 – 8/7 – 5/4 – 10/7 – 11/7 |
| 0 – 8 – 10 – 14 – 18 | 1 – 14/9 – 7/4 – 11/10 – 11/8 | minerva | 1/1 – 11/10 – 11/8 – 14/9 – 7/4 | 1/1 – 5/4 – 7/5 – 8/5 – 20/11 | 1/1 – 8/7 – 14/11 – 16/11 – 8/5 | 1/1 – 9/8 – 9/7 – 7/5 – 7/4 | 1/1 – 8/7 – 5/4 – 11/7 – 16/9 |
| 0 – 2 – 8 – 16 – 18 | 1 – 9/8 – 14/9 – 11/9 – 11/8 | euterpe | 1/1 – 9/8 – 11/9 – 11/8 – 14/9 | 1/1 – 11/10 – 11/9 – 7/5 – 16/9 | 1/1 – 9/8 – 14/11 – 18/11 – 20/11 | 1/1 – 8/7 – 16/11 – 18/11 – 16/9 | 1/1 – 9/7 – 10/7 – 11/7 – 7/4 |
| 0 – 2 – 10 – 16 – 18 | 1 – 9/8 – 7/4 – 11/9 – 11/8 | euterpe | 1/1 – 9/8 – 11/9 – 11/8 – 7/4 | 1/1 – 11/10 – 11/9 – 14/9 – 16/9 | 1/1 – 9/8 – 10/7 – 18/11 – 20/11 | 1/1 – 14/11 – 16/11 – 18/11 – 16/9 | 1/1 – 8/7 – 9/7 – 7/5 – 11/7 |
| 0 – 8 – 10 – 16 – 18 | 1 – 14/9 – 7/4 – 11/9 – 11/8 | euterpe | 1/1 – 11/9 – 11/8 – 14/9 – 7/4 | 1/1 – 9/8 – 14/11 – 10/7 – 18/11 | 1/1 – 8/7 – 14/11 – 16/11 – 16/9 | 1/1 – 9/8 – 9/7 – 11/7 – 7/4 | 1/1 – 8/7 – 7/5 – 11/7 – 16/9 |
| 0 – 8 – 14 – 16 – 18 | 1 – 11/7 – 11/10 – 11/9 – 11/8 | utonal | 1/1 – 11/10 – 11/9 – 11/8 – 11/7 | 1/1 – 10/9 – 5/4 – 10/7 – 20/11 | 1/1 – 9/8 – 9/7 – 18/11 – 9/5 | 1/1 – 8/7 – 16/11 – 8/5 – 16/9 | 1/1 – 14/11 – 7/5 – 14/9 – 7/4 |
| 0 – 10 – 14 – 16 – 18 | 1 – 7/4 – 11/10 – 11/9 – 11/8 | meantone | 1/1 – 11/10 – 11/9 – 11/8 – 7/4 | 1/1 – 10/9 – 5/4 – 8/5 – 20/11 | 1/1 – 9/8 – 10/7 – 18/11 – 9/5 | 1/1 – 14/11 – 16/11 – 8/5 – 16/9 | 1/1 – 8/7 – 5/4 – 7/5 – 11/7 |
| 0 – 1 – 9 – 17 – 18 | 1 – 3/2 – 7/6 – 11/6 – 11/8 | mothwellsmic | 1/1 – 7/6 – 11/8 – 3/2 – 11/6 | 1/1 – 7/6 – 9/7 – 11/7 – 12/7 | 1/1 – 12/11 – 4/3 – 16/11 – 12/7 | 1/1 – 11/9 – 4/3 – 14/9 – 11/6 | 1/1 – 12/11 – 14/11 – 3/2 – 18/11 |
| 0 – 8 – 9 – 17 – 18 | 1 – 14/9 – 7/6 – 11/6 – 11/8 | mothwellsmic | 1/1 – 7/6 – 11/8 – 14/9 – 11/6 | 1/1 – 7/6 – 4/3 – 11/7 – 12/7 | 1/1 – 8/7 – 4/3 – 16/11 – 12/7 | 1/1 – 7/6 – 9/7 – 3/2 – 7/4 | 1/1 – 12/11 – 14/11 – 3/2 – 12/7 |
| 0 – 8 – 14 – 17 – 18 | 1 – 11/7 – 11/10 – 11/6 – 11/8 | utonal | 1/1 – 11/10 – 11/8 – 11/7 – 11/6 | 1/1 – 5/4 – 10/7 – 5/3 – 20/11 | 1/1 – 8/7 – 4/3 – 16/11 – 8/5 | 1/1 – 7/6 – 14/11 – 7/5 – 7/4 | 1/1 – 12/11 – 6/5 – 3/2 – 12/7 |
| 0 – 8 – 16 – 17 – 18 | 1 – 11/7 – 11/9 – 11/6 – 11/8 | utonal | 1/1 – 11/9 – 11/8 – 11/7 – 11/6 | 1/1 – 9/8 – 9/7 – 3/2 – 18/11 | 1/1 – 8/7 – 4/3 – 16/11 – 16/9 | 1/1 – 7/6 – 14/11 – 14/9 – 7/4 | 1/1 – 12/11 – 4/3 – 3/2 – 12/7 |
| 0 – 14 – 16 – 17 – 18 | 1 – 11/10 – 11/9 – 11/6 – 11/8 | utonal | 1/1 – 11/10 – 11/9 – 11/8 – 11/6 | 1/1 – 10/9 – 5/4 – 5/3 – 20/11 | 1/1 – 9/8 – 3/2 – 18/11 – 9/5 | 1/1 – 4/3 – 16/11 – 8/5 – 16/9 | 1/1 – 12/11 – 6/5 – 4/3 – 3/2 |
Hexads
| Number | Chord | Transversal | Type |
|---|---|---|---|
| 1 | 0 – 2 – 4 – 6 – 8 – 10 | 1 – 9/8 – 5/4 – 7/5 – 14/9 – 7/4 | erato |
| 2 | 0 – 4 – 6 – 8 – 10 – 14 | 1 – 5/4 – 7/5 – 14/9 – 7/4 – 11/10 | meantone |
| 3 | 0 – 2 – 6 – 8 – 10 – 16 | 1 – 9/8 – 7/5 – 14/9 – 7/4 – 11/9 | meantone |
| 4 | 0 – 6 – 8 – 10 – 14 – 16 | 1 – 7/5 – 14/9 – 7/4 – 11/10 – 11/9 | meantone |
| 5 | 0 – 1 – 2 – 4 – 10 – 18 | 1 – 3/2 – 9/8 – 5/4 – 7/4 – 11/8 | otonal |
| 6 | 0 – 2 – 4 – 8 – 10 – 18 | 1 – 9/8 – 5/4 – 14/9 – 7/4 – 11/8 | meantone |
| 7 | 0 – 4 – 8 – 10 – 14 – 18 | 1 – 5/4 – 14/9 – 7/4 – 11/10 – 11/8 | minerva |
| 8 | 0 – 2 – 8 – 10 – 16 – 18 | 1 – 9/8 – 14/9 – 7/4 – 11/9 – 11/8 | euterpe |
| 9 | 0 – 8 – 10 – 14 – 16 – 18 | 1 – 14/9 – 7/4 – 11/10 – 11/9 – 11/8- | meantone |
| 10 | 0 – 8 – 14 – 16 – 17 – 18 | 1 – 11/7 – 11/10 – 11/9 – 11/6 – 11/8 | utonal |