Chords of meantone
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.
Triads
Number | Chord | Transversal | Type | As generated | 1st inversion | 2nd inversion |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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
Number | Chord | Transversal | Type | As generated | 1st inversion | 2nd inversion | 3rd inversion |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |