Chords of huygens: Difference between revisions

Revision as of 21:57, 22 June 2025

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.

11-limit meantone's genchain
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

Chords of huygens: Difference between revisions

Revision as of 21:57, 22 June 2025

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-#REDIRECT [[Chords of huygens]]
+Below are listed the [[Dyadic_chord|dyadic chords]] of 11-limit [[Meantone_family#Septimal meantone-Unidecimal meantone aka Huygens|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 ({{nowrap|{{dash|1/1, 6/5, 3/2}}}}, or 10:12:15) is the second inversion of the generated {{nowrap|{{dash|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 {{nowrap|^1 {{=}} d2}} and {{nowrap|^C {{=}} Dbb}}. One up represents ~64/63, ~45/44, and ~40/39. If ''c'' is the difference between 700{{cent}} and the size of the generator in cents, then one up is equal to 12''c''.
+{| class="wikitable"
+|+ style="font-size: 105%;" | 11-limit meantone's genchain
+|-
+! 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<br />10/9
+| 5/3
+| 5/4
+| 15/8
+| 45/32<br />7/5
+| 21/20
+| 63/40<br />14/9
+| 7/6
+| 7/4
+| 21/16<br />13/10
+| 35/18
+| 13/9
+| 11/10<br />13/12
+| 13/8
+| 11/9
+| 11/6
+| 11/8
+|-
+! Interval
+| '''P1'''
+| P5
+| M2
+| M6
+| M3
+| M7
+| A4<br />vd5
+| A1<br />vm2
+| A5<br />vm6
+| A2<br />vm3
+| A6<br />vm7
+| A3<br />v4
+| A7<br />v8
+| AA4<br />v5
+| AA1<br />vM2
+| AA5<br />vM6
+| AA2<br />vM3
+| AA6<br />vM7
+| AA3<br />vA4
+|-
+! Note<br />(in C)
+| '''C'''
+| G
+| D
+| A
+| E
+| B
+| F#
+| C#
+| G#<br />vAb
+| D#<br />vEb
+| A#<br />vBb
+| E#<br />vF
+| B#<br />vC
+| Fx<br />vG
+| Cx<br />vD
+| Gx<br />vA
+| Dx<br />vE
+| Ax<br />vB
+| Ex<br />vF#
+|}
+'''''TODO: complete the tables'''''
+== Triads ==
+{| class="wikitable"
+|-
+! #
+! Chord
+! Transversal
+! Type
+! As generated
+! 1st inversion
+! 2nd inversion
+! Name
+|-
+| 1
+| {{dash|0, 1, 2}}
+| {{dash|1, 3/2, 9/8}}
+| ambitonal
+| {{dash|'''1/1, 9/8, 3/2'''}}
+| {{dash|1/1, 4/3, 16/9}}
+| {{dash|'''1/1, 4/3, 3/2'''}}
+| C2 <u>or</u> C4
+|-
+| 2
+| {{dash|0, 1, 3}}
+| {{dash|1, 3/2, 5/3}}
+| otonal
+| {{dash|1/1, 3/2, 5/3}}
+| {{dash|1/1, 10/9, 4/3}}
+| {{dash|'''1/1, 6/5, 9/5'''}}
+| Cm7no5
+|-
+| 3
+| {{dash|0, 2, 3}}
+| {{dash|1, 10/9, 5/3}}
+| utonal
+| {{dash|1/1, 10/9, 5/3}}
+| {{dash|'''1/1, 3/2, 9/5'''}}
+| {{dash|1/1, 6/5, 4/3}}
+| C7no3
+|-
+| 4
+| {{dash|0, 1, 4}}
+| {{dash|1, 3/2, 5/4}}
+| otonal
+| {{dash|'''1/1, 5/4, 3/2'''}}
+| {{dash|1/1, 6/5, 8/5}}
+| {{dash|1/1, 4/3, 5/3}}
+| C
+|-
+| 5
+| {{dash|0, 2, 4}}
+| {{dash|1, 9/8, 5/4}}
+| otonal
+| {{dash|'''1/1, 9/8, 5/4'''}}
+| {{dash|1/1, 10/9, 16/9}}
+| {{dash|1/1, 8/5, 9/5}}
+| Cadd9no5
+|-
+| 6
+| {{dash|0, 3, 4}}
+| {{dash|1, 5/3, 5/4}}
+| utonal
+| {{dash|1/1, 5/4, 5/3}}
+| {{dash|1/1, 4/3, 8/5}}
+| {{dash|'''1/1, 6/5, 3/2'''}}
+| Cm
+|-
+| 7
+| {{dash|0, 2, 6}}
+| {{dash|1, 9/8, 7/5}}
+| marvel
+| {{dash|1/1, 9/8, 7/5}}
+| {{dash|'''1/1, 5/4, 16/9'''}}
+| {{dash|1/1, 10/7, 8/5}}
+| C7no5
+|-
+| 8
+| {{dash|0, 3, 6}}
+| {{dash|1, 5/3, 7/5}}
+| starling
+| {{dash|1/1, 7/5, 5/3}}
+| {{dash|'''1/1, 6/5, 10/7'''}}
+| {{dash|1/1, 6/5, 5/3}}
+| Cdim
+|-
+| 9
+| {{dash|0, 4, 6}}
+| {{dash|1, 5/4, 7/5}}
+| marvel
+| {{dash|'''1/1, 5/4, 7/5'''}}
+| {{dash|1/1, 9/8, 8/5}}
+| {{dash|1/1, 10/7, 16/9}}
+| C(vb5)
+|-
+| 10
+| {{dash|0, 2, 8}}
+| {{dash|1, 10/9, 14/9}}
+| otonal
+| {{dash|'''1/1, 10/9, 14/9'''}}
+| {{dash|1/1, 7/5, 9/5}}
+| {{dash|'''1/1, 9/7, 10/7'''}}
+| C2(#5) <u>or</u> C^(b5)
+|-
+| 11
+| {{dash|0, 4, 8}}
+| {{dash|1, 5/4, 14/9}}
+| marvel
+| {{dash|'''1/1, 5/4, 14/9'''}}
+| {{dash|1/1, 5/4, 8/5}}
+| {{dash|1/1, 9/7, 8/5}}
+| Caug
+|-
+| 12
+| {{dash|0, 6, 8}}
+| {{dash|1, 7/5, 14/9}}
+| utonal
+| {{dash|1/1, 7/5, 14/9}}
+| {{dash|'''1/1, 10/9, 10/7'''}}
+| {{dash|'''1/1, 9/7, 9/5'''}}
+| C2(b5) <u>or</u> C^,7no5
+|-
+| 13
+| {{dash|0, 1, 9}}
+| {{dash|1, 3/2, 7/6}}
+| otonal
+| {{dash|'''1/1, 7/6, 3/2'''}}
+| {{dash|1/1, 9/7, 12/7}}
+| {{dash|1/1, 4/3, 14/9}}
+| Cvm
+|-
+| 14
+| {{dash|0, 3, 9}}
+| {{dash|1, 5/3, 7/6}}
+| otonal
+| {{dash|1/1, 7/6, 5/3}}
+| {{dash|'''1/1, 10/7, 12/7'''}}
+| {{dash|'''1/1, 6/5, 7/5'''}}
+| Cdim7no3 <u>or</u> Cdim(v5)
+|-
+| 15
+| {{dash|0, 6, 9}}
+| {{dash|1, 7/5, 7/6}}
+| utonal
+| {{dash|'''1/1, 7/6, 7/5'''}}
+| {{dash|'''1/1, 6/5, 12/7'''}}
+| {{dash|1/1, 10/7, 5/3}}
+| Cvdim(v5) <u>or</u> Cdim7no5
+|-
+| 16
+| {{dash|0, 8, 9}}
+| {{dash|1, 14/9, 7/6}}
+| utonal
+| {{dash|1/1, 7/6, 14/9}}
+| {{dash|1/1, 4/3, 12/7}}
+| {{dash|'''1/1, 9/7, 3/2'''}}
+| C^
+|-
+| 17
+| {{dash|0, 1, 10}}
+| {{dash|1, 3/2, 7/4}}
+| otonal
+| {{dash|'''1/1, 3/2, 7/4'''}}
+| {{dash|1/1, 7/6, 4/3}}
+| {{dash|1/1, 8/7, 12/7}}
+| Cv7no3
+|-
+| 18
+| {{dash|0, 2, 10}}
+| {{dash|1, 9/8, 7/4}}
+| otonal
+| {{dash|'''1/1, 9/8, 7/4'''}}
+| {{dash|1/1, 14/9, 16/9}}
+| {{dash|1/1, 8/7, 9/7}}
+| Cv9no35
+|-
+| 19
+| {{dash|0, 4, 10}}
+| {{dash|1, 5/4, 7/4}}
+| otonal
+| {{dash|'''1/1, 5/4, 7/4'''}}
+| {{dash|1/1, 7/5, 8/5}}
+| {{dash|1/1, 8/7, 10/7}}
+| C,v7no5
+|-
+| 20
+| {{dash|0, 6, 10}}
+| {{dash|1, 7/5, 7/4}}
+| utonal
+| {{dash|1/1, 7/5, 7/4}}
+| {{dash|'''1/1, 5/4, 10/7'''}}
+| {{dash|1/1, 8/7, 8/5}}
+| C(b5)
+|-
+| 21
+| {{dash|0, 8, 10}}
+| {{dash|1, 14/9, 7/4}}
+| utonal
+| {{dash|1/1, 14/9, 7/4}}
+| {{dash|'''1/1, 9/8, 9/7'''}}
+| {{dash|1/1, 8/7, 16/9}}
+| C^,9no5
+|-
+| 22
+| {{dash|0, 9, 10}}
+| {{dash|1, 7/6, 7/4}}
+| utonal
+| {{dash|'''1/1, 7/6, 7/4'''}}
+| {{dash|1/1, 3/2, 12/7}}
+| {{dash|1/1, 8/7, 4/3}}
+| Cvm7no5
+|-
+| 23
+| {{dash|0, 4, 14}}
+| {{dash|1, 5/4, 11/10}}
+| valinorsmic
+| {{dash|1/1, 11/10, 5/4}}
+| {{dash|1/1, 8/7, 20/11}}
+| {{dash|1/1, 8/5, 7/4}}
+|
+|-
+| 24
+| {{dash|0, 6, 14}}
+| {{dash|1, 7/5, 11/10}}
+| otonal
+| {{dash|1/1, 11/10, 7/5}}
+| {{dash|1/1, 14/11, 20/11}}
+| {{dash|1/1, 10/7, 11/7}}
+|
+|-
+| 25
+| {{dash|0, 8, 14}}
+| {{dash|1, 11/7, 11/10}}
+| utonal
+| {{dash|1/1, 11/10, 11/7}}
+| {{dash|1/1, 10/7, 20/11}}
+| {{dash|1/1, 14/11, 7/5}}
+|
+|-
+| 26
+| {{dash|0, 10, 14}}
+| {{dash|1, 7/4, 11/10}}
+| valinorsmic
+| {{dash|1/1, 11/10, 7/4}}
+| {{dash|1/1, 8/5, 20/11}}
+| {{dash|1/1, 8/7, 5/4}}
+|
+|-
+| 27
+| {{dash|0, 2, 16}}
+| {{dash|1, 10/9, 11/9}}
+| otonal
+| {{dash|1/1, 10/9, 11/9}}
+| {{dash|1/1, 11/10, 9/5}}
+| {{dash|1/1, 18/11, 20/11}}
+|
+|-
+| 28
+| {{dash|0, 6, 16}}
+| {{dash|1, 7/5, 11/9}}
+| werckismic
+| {{dash|1/1, 11/9, 7/5}}
+| {{dash|1/1, 8/7, 18/11}}
+| {{dash|1/1, 10/7, 7/4}}
+|
+|-
+| 29
+| {{dash|0, 8, 16}}
+| {{dash|1, 14/9, 11/9}}
+| otonal
+| {{dash|1/1, 11/9, 14/9}}
+| {{dash|1/1, 14/11, 18/11}}
+| {{dash|1/1, 9/7, 11/7}}
+|
+|-
+| 30
+| {{dash|0, 10, 16}}
+| {{dash|1, 7/4, 11/9}}
+| werckismic
+| {{dash|1/1, 11/9, 7/4}}
+| {{dash|1/1, 10/7, 18/11}}
+| {{dash|1/1, 8/7, 7/5}}
+|
+|-
+| 31
+| {{dash|0, 14, 16}}
+| {{dash|1, 11/10, 11/9}}
+| utonal
+| {{dash|1/1, 11/10, 11/9}}
+| {{dash|1/1, 10/9, 20/11}}
+| {{dash|1/1, 18/11, 9/5}}
+|
+|-
+| 32
+| {{dash|0, 1, 17}}
+| {{dash|1, 3/2, 11/6}}
+| otonal
+| {{dash|1/1, 3/2, 11/6}}
+| {{dash|1/1, 11/9, 4/3}}
+| {{dash|1/1, 12/11, 18/11}}
+|
+|-
+| 33
+| {{dash|0, 3, 17}}
+| {{dash|1, 5/3, 11/6}}
+| otonal
+| {{dash|1/1, 5/3, 11/6}}
+| {{dash|1/1, 11/10, 6/5}}
+| {{dash|1/1, 12/11, 20/11}}
+|
+|-
+| 34
+| {{dash|0, 8, 17}}
+| {{dash|1, 11/7, 11/6}}
+| utonal
+| {{dash|1/1, 11/7, 11/6}}
+| {{dash|1/1, 7/6, 14/11}}
+| {{dash|1/1, 12/11, 12/7}}
+|
+|-
+| 35
+| {{dash|0, 9, 17}}
+| {{dash|1, 7/6, 11/6}}
+| otonal
+| {{dash|1/1, 7/6, 11/6}}
+| {{dash|1/1, 11/7, 12/7}}
+| {{dash|1/1, 12/11, 14/11}}
+|
+|-
+| 36
+| {{dash|0, 14, 17}}
+| {{dash|1, 11/10, 11/6}}
+| utonal
+| {{dash|1/1, 11/10, 11/6}}
+| {{dash|1/1, 5/3, 20/11}}
+| {{dash|1/1, 12/11, 6/5}}
+|
+|-
+| 37
+| {{dash|0, 16, 17}}
+| {{dash|1, 11/9, 11/6}}
+| utonal
+| {{dash|1/1, 11/9, 11/6}}
+| {{dash|1/1, 3/2, 18/11}}
+| {{dash|1/1, 12/11, 4/3}}
+|
+|-
+| 38
+| {{dash|0, 1, 18}}
+| {{dash|1, 3/2, 11/8}}
+| otonal
+| {{dash|1/1, 11/8, 3/2}}
+| {{dash|1/1, 12/11, 16/11}}
+| {{dash|1/1, 4/3, 11/6}}
+|
+|-
+| 39
+| {{dash|0, 2, 18}}
+| {{dash|1, 9/8, 11/8}}
+| otonal
+| {{dash|1/1, 9/8, 11/8}}
+| {{dash|1/1, 11/9, 16/9}}
+| {{dash|1/1, 16/11, 18/11}}
+|
+|-
+| 40
+| {{dash|0, 4, 18}}
+| {{dash|1, 5/4, 11/8}}
+| otonal
+| {{dash|1/1, 5/4, 11/8}}
+| {{dash|1/1, 11/10, 8/5}}
+| {{dash|1/1, 16/11, 20/11}}
+|
+|-
+| 41
+| {{dash|0, 8, 18}}
+| {{dash|1, 11/7, 11/8}}
+| utonal
+| {{dash|1/1, 11/8, 11/7}}
+| {{dash|1/1, 8/7, 16/11}}
+| {{dash|1/1, 14/11, 7/4}}
+|
+|-
+| 42
+| {{dash|0, 9, 18}}
+| {{dash|1, 7/6, 11/8}}
+| mothwellsmic
+| {{dash|1/1, 7/6, 11/8}}
+| {{dash|1/1, 7/6, 12/7}}
+| {{dash|1/1, 16/11, 12/7}}
+|
+|-
+| 43
+| {{dash|0, 10, 18}}
+| {{dash|1, 7/4, 11/8}}
+| otonal
+| {{dash|1/1, 11/8, 7/4}}
+| {{dash|1/1, 14/11, 16/11}}
+| {{dash|1/1, 8/7, 11/7}}
+|
+|-
+| 44
+| {{dash|0, 14, 18}}
+| {{dash|1, 11/10, 11/8}}
+| utonal
+| {{dash|1/1, 11/10, 11/8}}
+| {{dash|1/1, 5/4, 20/11}}
+| {{dash|1/1, 16/11, 8/5}}
+|
+|-
+| 45
+| {{dash|0, 16, 18}}
+| {{dash|1, 11/9, 11/8}}
+| utonal
+| {{dash|1/1, 11/9, 11/8}}
+| {{dash|1/1, 9/8, 18/11}}
+| {{dash|1/1, 16/11, 16/9}}
+|
+|-
+| 46
+| {{dash|0, 17, 18}}
+| {{dash|1, 11/6, 11/8}}
+| utonal
+| {{dash|1/1, 11/8, 11/6}}
+| {{dash|1/1, 4/3, 16/11}}
+| {{dash|1/1, 12/11, 3/2}}
+|
+|}
+== Tetrads ==
+{| class="wikitable"
+|-
+! #
+! Chord
+! Transversal
+! Type
+! As generated
+! 1st inversion
+! 2nd inversion
+! 3rd inversion
+! Name
+|-
+| 1
+| {{dash|0, 1, 2, 3}}
+| {{dash|1, 3/2, 9/8, 5/3}}
+| didymic
+| {{dash|1/1, 9/8, 3/2, 5/3}}
+| {{dash|'''1/1, 4/3, 3/2, 16/9'''}}
+| {{dash|'''1/1, 9/8, 4/3, 3/2'''}}
+| {{dash|1/1, 6/5, 4/3, 9/5}}
+| C7sus4 <u>or</u> C4,9
+|-
+| 2
+| {{dash|0, 1, 2, 4}}
+| {{dash|1, 3/2, 9/8, 5/4}}
+| otonal
+| {{dash|'''1/1, 9/8, 5/4, 3/2'''}}
+| {{dash|1/1, 10/9, 4/3, 16/9}}
+| {{dash|1/1, 6/5, 8/5, 9/5}}
+| {{dash|1/1, 4/3, 3/2, 5/3}}
+| Cadd9
+|-
+| 3
+| {{dash|0, 1, 3, 4}}
+| {{dash|1, 3/2, 5/3, 5/4}}
+| ambitonal
+| {{dash|'''1/1, 5/4, 3/2, 5/3'''}}
+| {{dash|1/1, 6/5, 4/3, 8/5}}
+| {{dash|1/1, 9/8, 4/3, 5/3}}
+| {{dash|'''1/1, 6/5, 3/2, 9/5'''}}
+| C6 <u>or</u> Cm7
+|-
+| 4
+| {{dash|0, 2, 3, 4}}
+| {{dash|1, 10/9, 5/3, 5/4}}
+| utonal
+| {{dash|1/1, 10/9, 5/4, 5/3}}
+| {{dash|'''1/1, 9/8, 3/2, 9/5'''}}
+| {{dash|1/1, 4/3, 8/5, 16/9}}
+| {{dash|1/1, 6/5, 4/3, 3/2}}
+| C9no3
+|-
+| 5
+| {{dash|0, 2, 3, 6}}
+| {{dash|1, 9/8, 5/3, 7/5}}
+| erato
+| {{dash|1/1, 9/8, 7/5, 5/3}}
+| {{dash|'''1/1, 5/4, 3/2, 16/9'''}}
+| {{dash|1/1, 6/5, 10/7, 8/5}}
+| {{dash|1/1, 6/5, 4/3, 5/3}}
+| C7
+|-
+| 6
+| {{dash|0, 2, 4, 6}}
+| {{dash|1, 9/8, 5/4, 7/5}}
+| erato
+| {{dash|1/1, 9/8, 5/4, 7/5}}
+| {{dash|'''1/1, 10/9, 5/4, 16/9'''}}
+| {{dash|1/1, 9/8, 8/5, 9/5}}
+| {{dash|1/1, 10/7, 8/5, 9/5}}
+| C9no5
+|-
+| 7
+| {{dash|0, 3, 4, 6}}
+| {{dash|1, 5/3, 5/4, 7/5}}
+| erato
+| {{dash|1/1, 5/4, 7/5, 5/3}}
+| {{dash|1/1, 9/8, 4/3, 8/5}}
+| {{dash|'''1/1, 6/5, 10/7, 16/9'''}}
+| {{dash|'''1/1, 6/5, 3/2, 5/3'''}}
+| Cm7(b5) <u>or</u> Cm6
+|-
+| 8
+| {{dash|0, 2, 4, 8}}
+| {{dash|1, 9/8, 5/4, 14/9}}
+| erato
+| {{dash|'''1/1, 9/8, 5/4, 14/9'''}}
+| {{dash|1/1, 10/9, 7/5, 16/9}}
+| {{dash|1/1, 5/4, 8/5, 9/5}}
+| {{dash|1/1, 9/7, 10/7, 8/5}}
+| Caug,9
+|-
+| 9
+| {{dash|0, 2, 6, 8}}
+| {{dash|1, 9/8, 7/5, 14/9}}
+| erato
+| {{dash|1/1, 9/8, 7/5, 14/9}}
+| {{dash|'''1/1, 5/4, 7/5, 16/9'''}}
+| {{dash|1/1, 10/9, 10/7, 8/5}}
+| {{dash|1/1, 9/7, 10/7, 9/5}}
+| C7(vb5)
+|-
+| 10
+| {{dash|0, 4, 6, 8}}
+| {{dash|1, 5/4, 7/5, 14/9}}
+| erato
+| {{dash|1/1, 5/4, 7/5, 14/9}}
+| {{dash|1/1, 9/8, 5/4, 8/5}}
+| {{dash|'''1/1, 10/9, 10/7, 16/9'''}}
+| {{dash|1/1, 9/7, 8/5, 9/5}}
+| C9(b5)no3
+|-
+| 11
+| {{dash|0, 1, 3, 9}}
+| {{dash|1, 3/2, 5/3, 7/6}}
+| otonal
+| {{dash|1/1, 7/6, 3/2, 5/3}}
+| {{dash|1/1, 9/7, 10/7, 12/7}}
+| {{dash|1/1, 10/9, 4/3, 14/9}}
+| {{dash|'''1/1, 6/5, 7/5, 9/5'''}}
+| Cm7(vb5)
+|-
+| 12
+| {{dash|0, 3, 6, 9}}
+| {{dash|1, 5/3, 7/5, 7/6}}
+| starling
+| {{dash|1/1, 7/6, 7/5, 5/3}}
+| {{dash|'''1/1, 6/5, 10/7, 12/7'''}}
+| {{dash|1/1, 6/5, 10/7, 5/3}}
+| {{dash|1/1, 6/5, 7/5, 5/3}}
+| Cdim7
+|-
+| 13
+| {{dash|0, 6, 8, 9}}
+| {{dash|1, 7/5, 14/9, 7/6}}
+| utonal
+| {{dash|1/1, 7/6, 7/5, 14/9}}
+| {{dash|1/1, 6/5, 4/3, 12/7}}
+| {{dash|1/1, 10/9, 10/7, 5/3}}
+| {{dash|'''1/1, 9/7, 3/2, 9/5'''}}
+| C^,7
+|-
+| 14
+| {{dash|0, 1, 2, 10}}
+| {{dash|1, 3/2, 9/8, 7/4}}
+| otonal
+| {{dash|'''1/1, 9/8, 3/2, 7/4'''}}
+| {{dash|1/1, 4/3, 14/9, 16/9}}
+| {{dash|'''1/1, 7/6, 4/3, 3/2'''}}
+| {{dash|1/1, 8/7, 9/7, 12/7}}
+| Cv7no3 <u>or</u> Cvm,11
+|-
+| 15
+| {{dash|0, 1, 4, 10}}
+| {{dash|1, 3/2, 5/4, 7/4}}
+| otonal
+| {{dash|'''1/1, 5/4, 3/2, 7/4'''}}
+| {{dash|1/1, 6/5, 7/5, 8/5}}
+| {{dash|1/1, 7/6, 4/3, 5/3}}
+| {{dash|1/1, 8/7, 10/7, 12/7}}
+| C,v7
+|-
+| 16
+| {{dash|0, 2, 4, 10}}
+| {{dash|1, 9/8, 5/4, 7/4}}
+| otonal
+| {{dash|'''1/1, 9/8, 5/4, 7/4'''}}
+| {{dash|1/1, 10/9, 14/9, 16/9}}
+| {{dash|1/1, 7/5, 8/5, 9/5}}
+| {{dash|1/1, 8/7, 9/7, 10/7}}
+| C9(v7)no5
+|-
+| 17
+| {{dash|0, 2, 6, 10}}
+| {{dash|1, 9/8, 7/5, 7/4}}
+| marvel
+| {{dash|1/1, 9/8, 7/5, 7/4}}
+| {{dash|'''1/1, 5/4, 14/9, 16/9'''}}
+| {{dash|1/1, 5/4, 10/7, 8/5}}
+| {{dash|1/1, 8/7, 9/7, 8/5}}
+| C7(#5) <u>or</u> Caug7
+|-
+| 18
+| {{dash|0, 4, 6, 10}}
+| {{dash|1, 5/4, 7/5, 7/4}}
+| marvel
+| {{dash|1/1, 5/4, 7/5, 7/4}}
+| {{dash|1/1, 9/8, 7/5, 8/5}}
+| {{dash|'''1/1, 5/4, 10/7, 16/9'''}}
+| {{dash|1/1, 8/7, 10/7, 8/5}}
+| C7(b5)
+|-
+| 19
+| {{dash|0, 2, 8, 10}}
+| {{dash|1, 9/8, 14/9, 7/4}}
+| didymic
+| {{dash|1/1, 9/8, 14/9, 7/4}}
+| {{dash|1/1, 7/5, 14/9, 16/9}}
+| {{dash|1/1, 9/8, 9/7, 10/7}}
+| {{dash|1/1, 8/7, 9/7, 16/9}}
+|
+|-
+| 20
+| {{dash|0, 4, 8, 10}}
+| {{dash|1, 5/4, 14/9, 7/4}}
+| marvel
+| {{dash|1/1, 5/4, 14/9, 7/4}}
+| {{dash|1/1, 5/4, 7/5, 8/5}}
+| {{dash|1/1, 9/8, 9/7, 8/5}}
+| {{dash|1/1, 8/7, 10/7, 16/9}}
+|
+|-
+| 21
+| {{dash|0, 6, 8, 10}}
+| {{dash|1, 7/5, 14/9, 7/4}}
+| utonal
+| {{dash|1/1, 7/5, 14/9, 7/4}}
+| {{dash|'''1/1, 10/9, 5/4, 10/7'''}}
+| {{dash|1/1, 9/8, 9/7, 9/5}}
+| {{dash|1/1, 8/7, 8/5, 16/9}}
+| C,9(b5)
+|-
+| 22
+| {{dash|0, 1, 9, 10}}
+| {{dash|1, 3/2, 7/6, 7/4}}
+| ambitonal
+| {{dash|'''1/1, 7/6, 3/2, 7/4'''}}
+| {{dash|'''1/1, 9/7, 3/2, 12/7'''}}
+| {{dash|1/1, 7/6, 4/3, 14/9}}
+| {{dash|1/1, 8/7, 4/3, 12/7}}
+| Cvm7 <u>or</u> C^6
+|-
+| 23
+| {{dash|0, 6, 9, 10}}
+| {{dash|1, 7/5, 7/6, 7/4}}
+| utonal
+| {{dash|'''1/1, 7/6, 7/5, 7/4'''}}
+| {{dash|'''1/1, 6/5, 3/2, 12/7'''}}
+| {{dash|'''1/1, 5/4, 10/7, 5/3'''}}
+| {{dash|1/1, 8/7, 4/3, 8/5}}
+| Cvm7(vb5) <u>or</u> Cm^6 <u>or</u> C6(b5)
+|-
+| 24
+| {{dash|0, 8, 9, 10}}
+| {{dash|1, 14/9, 7/6, 7/4}}
+| utonal
+| {{dash|'''1/1, 7/6, 14/9, 7/4'''}}
+| {{dash|'''1/1, 4/3, 3/2, 12/7'''}}
+| {{dash|'''1/1, 9/8, 9/7, 3/2'''}}
+| {{dash|1/1, 8/7, 4/3, 16/9}}
+| Cvm7(#5) <u>or</u> C4^6 <u>or</u> C^,9
+|-
+| 25
+| {{dash|0, 4, 6, 14}}
+| {{dash|1, 5/4, 7/5, 11/10}}
+| minerva
+| {{dash|1/1, 11/10, 5/4, 7/5}}
+| {{dash|1/1, 9/8, 14/11, 20/11}}
+| {{dash|1/1, 9/8, 8/5, 7/4}}
+| {{dash|1/1, 10/7, 11/7, 16/9}}
+|
+|-
+| 26
+| {{dash|0, 4, 8, 14}}
+| {{dash|1, 5/4, 14/9, 11/10}}
+| minerva
+| {{dash|1/1, 11/10, 5/4, 14/9}}
+| {{dash|1/1, 9/8, 10/7, 20/11}}
+| {{dash|1/1, 5/4, 8/5, 7/4}}
+| {{dash|1/1, 9/7, 7/5, 8/5}}
+|
+|-
+| 27
+| {{dash|0, 6, 8, 14}}
+| {{dash|1, 7/5, 14/9, 11/10}}
+| euterpe
+| {{dash|1/1, 11/10, 7/5, 14/9}}
+| {{dash|1/1, 14/11, 10/7, 20/11}}
+| {{dash|1/1, 10/9, 10/7, 11/7}}
+| {{dash|'''1/1, 9/7, 7/5, 9/5'''}}
+| C^,7(vb5)
+|-
+| 28
+| {{dash|0, 4, 10, 14}}
+| {{dash|1, 5/4, 7/4, 11/10}}
+| valinorsmic
+| {{dash|1/1, 11/10, 5/4, 7/4}}
+| {{dash|1/1, 25/22, 8/5, 20/11}}
+| {{dash|1/1, 7/5, 8/5, 7/4}}
+| {{dash|'''1/1, 8/7, 5/4, 10/7'''}}
+| C,^9(b5)
+|-
+| 29
+| {{dash|0, 6, 10, 14}}
+| {{dash|1, 7/5, 7/4, 11/10}}
+| minerva
+| {{dash|1/1, 11/10, 7/5, 7/4}}
+| {{dash|1/1, 14/11, 8/5, 20/11}}
+| {{dash|1/1, 5/4, 10/7, 11/7}}
+| {{dash|1/1, 8/7, 5/4, 8/5}}
+|
+|-
+| 30
+| {{dash|0, 8, 10, 14}}
+| {{dash|1, 14/9, 7/4, 11/10}}
+| minerva
+| {{dash|1/1, 11/10, 14/9, 7/4}}
+| {{dash|1/1, 7/5, 8/5, 20/11}}
+| {{dash|1/1, 9/8, 9/7, 7/5}}
+| {{dash|1/1, 8/7, 5/4, 16/9}}
+|
+|-
+| 31
+| {{dash|0, 2, 6, 16}}
+| {{dash|1, 9/8, 7/5, 11/9}}
+| meantone
+| {{dash|1/1, 9/8, 11/9, 7/5}}
+| {{dash|1/1, 11/10, 5/4, 16/9}}
+| {{dash|1/1, 8/7, 18/11, 20/11}}
+| {{dash|1/1, 10/7, 8/5, 7/4}}
+|
+|-
+| 32
+| {{dash|0, 2, 8, 16}}
+| {{dash|1, 10/9, 14/9, 11/9}}
+| otonal
+| {{dash|1/1, 10/9, 11/9, 14/9}}
+| {{dash|1/1, 11/10, 7/5, 9/5}}
+| {{dash|1/1, 14/11, 18/11, 20/11}}
+| {{dash|1/1, 9/7, 10/7, 11/7}}
+|
+|-
+| 33
+| {{dash|0, 6, 8, 16}}
+| {{dash|1, 7/5, 14/9, 11/9}}
+| euterpe
+| {{dash|1/1, 11/9, 7/5, 14/9}}
+| {{dash|1/1, 8/7, 14/11, 18/11}}
+| {{dash|1/1, 9/8, 10/7, 7/4}}
+| {{dash|1/1, 9/7, 11/7, 9/5}}
+|
+|-
+| 34
+| {{dash|0, 2, 10, 16}}
+| {{dash|1, 9/8, 7/4, 11/9}}
+| euterpe
+| {{dash|1/1, 9/8, 11/9, 7/4}}
+| {{dash|1/1, 11/10, 14/9, 16/9}}
+| {{dash|1/1, 10/7, 18/11, 20/11}}
+| {{dash|1/1, 8/7, 9/7, 7/5}}
+|
+|-
+| 35
+| {{dash|0, 6, 10, 16}}
+| {{dash|1, 7/5, 7/4, 11/9}}
+| werckismic
+| {{dash|1/1, 11/9, 7/5, 7/4}}
+| {{dash|1/1, 8/7, 10/7, 18/11}}
+| {{dash|1/1, 5/4, 10/7, 7/4}}
+| {{dash|1/1, 8/7, 7/5, 8/5}}
+|
+|-
+| 36
+| {{dash|0, 8, 10, 16}}
+| {{dash|1, 14/9, 7/4, 11/9}}
+| euterpe
+| {{dash|1/1, 11/9, 14/9, 7/4}}
+| {{dash|1/1, 14/11, 10/7, 18/11}}
+| {{dash|1/1, 9/8, 9/7, 11/7}}
+| {{dash|1/1, 8/7, 7/5, 16/9}}
+|
+|-
+| 37
+| {{dash|0, 6, 14, 16}}
+| {{dash|1, 7/5, 11/10, 11/9}}
+| euterpe
+| {{dash|1/1, 11/10, 11/9, 7/5}}
+| {{dash|1/1, 10/9, 14/11, 20/11}}
+| {{dash|1/1, 8/7, 18/11, 9/5}}
+| {{dash|1/1, 10/7, 11/7, 7/4}}
+|
+|-
+| 38
+| {{dash|0, 8, 14, 16}}
+| {{dash|1, 11/7, 11/10, 11/9}}
+| utonal
+| {{dash|1/1, 11/10, 11/9, 11/7}}
+| {{dash|1/1, 10/9, 10/7, 20/11}}
+| {{dash|1/1, 9/7, 18/11, 9/5}}
+| {{dash|1/1, 14/11, 7/5, 14/9}}
+|
+|-
+| 39
+| {{dash|0, 10, 14, 16}}
+| {{dash|1, 7/4, 11/10, 11/9}}
+| meantone
+| {{dash|1/1, 11/10, 11/9, 7/4}}
+| {{dash|1/1, 10/9, 8/5, 20/11}}
+| {{dash|1/1, 10/7, 18/11, 9/5}}
+| {{dash|1/1, 8/7, 5/4, 7/5}}
+|
+|-
+| 40
+| {{dash|0, 1, 3, 17}}
+| {{dash|1, 3/2, 5/3, 11/6}}
+| otonal
+| {{dash|1/1, 3/2, 5/3, 11/6}}
+| {{dash|1/1, 10/9, 11/9, 4/3}}
+| {{dash|1/1, 11/10, 6/5, 9/5}}
+| {{dash|1/1, 12/11, 18/11, 20/11}}
+|
+|-
+| 41
+| {{dash|0, 1, 9, 17}}
+| {{dash|1, 3/2, 7/6, 11/6}}
+| otonal
+| {{dash|1/1, 7/6, 3/2, 11/6}}
+| {{dash|1/1, 9/7, 11/7, 12/7}}
+| {{dash|1/1, 11/9, 4/3, 14/9}}
+| {{dash|1/1, 12/11, 14/11, 18/11}}
+|
+|-
+| 42
+| {{dash|0, 3, 9, 17}}
+| {{dash|1, 5/3, 7/6, 11/6}}
+| otonal
+| {{dash|1/1, 7/6, 5/3, 11/6}}
+| {{dash|1/1, 10/7, 11/7, 12/7}}
+| {{dash|1/1, 11/10, 6/5, 7/5}}
+| {{dash|1/1, 12/11, 14/11, 20/11}}
+|
+|-
+| 43
+| {{dash|0, 8, 9, 17}}
+| {{dash|1, 14/9, 7/6, 11/6}}
+| mothwellsmic
+| {{dash|1/1, 7/6, 14/9, 11/6}}
+| {{dash|1/1, 4/3, 11/7, 12/7}}
+| {{dash|1/1, 7/6, 9/7, 3/2}}
+| {{dash|1/1, 12/11, 14/11, 12/7}}
+|
+|-
+| 44
+| {{dash|0, 8, 14, 17}}
+| {{dash|1, 11/7, 11/10, 11/6}}
+| utonal
+| {{dash|1/1, 11/10, 11/7, 11/6}}
+| {{dash|1/1, 10/7, 5/3, 20/11}}
+| {{dash|1/1, 7/6, 14/11, 7/5}}
+| {{dash|1/1, 12/11, 6/5, 12/7}}
+|
+|-
+| 45
+| {{dash|0, 8, 16, 17}}
+| {{dash|1, 11/7, 11/9, 11/6}}
+| utonal
+| {{dash|1/1, 11/9, 11/7, 11/6}}
+| {{dash|1/1, 9/7, 3/2, 18/11}}
+| {{dash|1/1, 7/6, 14/11, 14/9}}
+| {{dash|1/1, 12/11, 4/3, 12/7}}
+|
+|-
+| 46
+| {{dash|0, 14, 16, 17}}
+| {{dash|1, 11/10, 11/9, 11/6}}
+| utonal
+| {{dash|1/1, 11/10, 11/9, 11/6}}
+| {{dash|1/1, 10/9, 5/3, 20/11}}
+| {{dash|1/1, 3/2, 18/11, 9/5}}
+| {{dash|1/1, 12/11, 6/5, 4/3}}
+|
+|-
+| 47
+| {{dash|0, 1, 2, 18}}
+| {{dash|1, 3/2, 9/8, 11/8}}
+| otonal
+| {{dash|1/1, 9/8, 11/8, 3/2}}
+| {{dash|1/1, 11/9, 4/3, 16/9}}
+| {{dash|1/1, 12/11, 16/11, 18/11}}
+| {{dash|1/1, 4/3, 3/2, 11/6}}
+|
+|-
+| 48
+| {{dash|0, 1, 4, 18}}
+| {{dash|1, 3/2, 5/4, 11/8}}
+| otonal
+| {{dash|1/1, 5/4, 11/8, 3/2}}
+| {{dash|1/1, 11/10, 6/5, 8/5}}
+| {{dash|1/1, 12/11, 16/11, 20/11}}
+| {{dash|1/1, 4/3, 5/3, 11/6}}
+|
+|-
+| 49
+| {{dash|0, 2, 4, 18}}
+| {{dash|1, 9/8, 5/4, 11/8}}
+| otonal
+| {{dash|1/1, 9/8, 5/4, 11/8}}
+| {{dash|1/1, 10/9, 11/9, 16/9}}
+| {{dash|1/1, 11/10, 8/5, 9/5}}
+| {{dash|1/1, 16/11, 18/11, 20/11}}
+|
+|-
+| 50
+| {{dash|0, 2, 8, 18}}
+| {{dash|1, 9/8, 14/9, 11/8}}
+| euterpe
+| {{dash|1/1, 9/8, 11/8, 14/9}}
+| {{dash|1/1, 11/9, 7/5, 16/9}}
+| {{dash|1/1, 8/7, 16/11, 18/11}}
+| {{dash|1/1, 9/7, 10/7, 7/4}}
+|
+|-
+| 51
+| {{dash|0, 4, 8, 18}}
+| {{dash|1, 5/4, 14/9, 11/8}}
+| minerva
+| {{dash|1/1, 5/4, 11/8, 14/9}}
+| {{dash|1/1, 11/10, 5/4, 8/5}}
+| {{dash|1/1, 8/7, 16/11, 20/11}}
+| {{dash|1/1, 9/7, 8/5, 7/4}}
+|
+|-
+| 52
+| {{dash|0, 1, 9, 18}}
+| {{dash|1, 3/2, 7/6, 11/8}}
+| mothwellsmic
+| {{dash|1/1, 7/6, 11/8, 3/2}}
+| {{dash|1/1, 7/6, 9/7, 12/7}}
+| {{dash|1/1, 12/11, 16/11, 12/7}}
+| {{dash|1/1, 4/3, 14/9, 11/6}}
+|
+|-
+| 53
+| {{dash|0, 8, 9, 18}}
+| {{dash|1, 14/9, 7/6, 11/8}}
+| mothwellsmic
+| {{dash|1/1, 7/6, 11/8, 14/9}}
+| {{dash|1/1, 7/6, 4/3, 12/7}}
+| {{dash|1/1, 8/7, 16/11, 12/7}}
+| {{dash|1/1, 9/7, 3/2, 7/4}}
+|
+|-
+| 54
+| {{dash|0, 1, 10, 18}}
+| {{dash|1, 3/2, 7/4, 11/8}}
+| otonal
+| {{dash|1/1, 11/8, 3/2, 7/4}}
+| {{dash|1/1, 12/11, 14/11, 16/11}}
+| {{dash|1/1, 7/6, 4/3, 11/6}}
+| {{dash|1/1, 8/7, 11/7, 12/7}}
+|
+|-
+| 55
+| {{dash|0, 2, 10, 18}}
+| {{dash|1, 9/8, 7/4, 11/8}}
+| otonal
+| {{dash|1/1, 9/8, 11/8, 7/4}}
+| {{dash|1/1, 11/9, 14/9, 16/9}}
+| {{dash|1/1, 14/11, 16/11, 18/11}}
+| {{dash|1/1, 8/7, 9/7, 11/7}}
+|
+|-
+| 56
+| {{dash|0, 4, 10, 18}}
+| {{dash|1, 5/4, 7/4, 11/8}}
+| otonal
+| {{dash|1/1, 5/4, 11/8, 7/4}}
+| {{dash|1/1, 11/10, 7/5, 8/5}}
+| {{dash|1/1, 14/11, 16/11, 20/11}}
+| {{dash|1/1, 8/7, 10/7, 11/7}}
+|
+|-
+| 57
+| {{dash|0, 8, 10, 18}}
+| {{dash|1, 14/9, 7/4, 11/8}}
+| mothwellsmic
+| {{dash|1/1, 11/8, 14/9, 7/4}}
+| {{dash|1/1, 8/7, 14/11, 16/11}}
+| {{dash|1/1, 9/8, 9/7, 7/4}}
+| {{dash|1/1, 8/7, 11/7, 16/9}}
+|
+|-
+| 58
+| {{dash|0, 9, 10, 18}}
+| {{dash|1, 7/6, 7/4, 11/8}}
+| mothwellsmic
+| {{dash|1/1, 7/6, 11/8, 7/4}}
+| {{dash|1/1, 7/6, 3/2, 12/7}}
+| {{dash|1/1, 14/11, 16/11, 12/7}}
+| {{dash|1/1, 8/7, 4/3, 11/7}}
+|
+|-
+| 59
+| {{dash|0, 4, 14, 18}}
+| {{dash|1, 5/4, 11/10, 11/8}}
+| valinorsmic
+| {{dash|1/1, 11/10, 5/4, 11/8}}
+| {{dash|1/1, 8/7, 5/4, 20/11}}
+| {{dash|1/1, 11/10, 8/5, 7/4}}
+| {{dash|1/1, 16/11, 8/5, 20/11}}
+|
+|-
+| 60
+| {{dash|0, 8, 14, 18}}
+| {{dash|1, 11/7, 11/10, 11/8}}
+| utonal
+| {{dash|1/1, 11/10, 11/8, 11/7}}
+| {{dash|1/1, 5/4, 10/7, 20/11}}
+| {{dash|1/1, 8/7, 16/11, 8/5}}
+| {{dash|1/1, 14/11, 7/5, 7/4}}
+|
+|-
+| 61
+| {{dash|0, 10, 14, 18}}
+| {{dash|1, 7/4, 11/10, 11/8}}
+| minerva
+| {{dash|1/1, 11/10, 11/8, 7/4}}
+| {{dash|1/1, 5/4, 8/5, 20/11}}
+| {{dash|1/1, 14/11, 16/11, 8/5}}
+| {{dash|1/1, 8/7, 5/4, 11/7}}
+|
+|-
+| 62
+| {{dash|0, 2, 16, 18}}
+| {{dash|1, 9/8, 11/9, 11/8}}
+| didymic
+| {{dash|1/1, 9/8, 11/9, 11/8}}
+| {{dash|1/1, 11/10, 11/9, 16/9}}
+| {{dash|1/1, 9/8, 18/11, 20/11}}
+| {{dash|1/1, 16/11, 18/11, 16/9}}
+|
+|-
+| 63
+| {{dash|0, 8, 16, 18}}
+| {{dash|1, 11/7, 11/9, 11/8}}
+| utonal
+| {{dash|1/1, 11/9, 11/8, 11/7}}
+| {{dash|1/1, 9/8, 9/7, 18/11}}
+| {{dash|1/1, 8/7, 16/11, 16/9}}
+| {{dash|1/1, 14/11, 14/9, 7/4}}
+|
+|-
+| 64
+| {{dash|0, 10, 16, 18}}
+| {{dash|1, 7/4, 11/9, 11/8}}
+| euterpe
+| {{dash|1/1, 11/9, 11/8, 7/4}}
+| {{dash|1/1, 9/8, 10/7, 18/11}}
+| {{dash|1/1, 14/11, 16/11, 16/9}}
+| {{dash|1/1, 8/7, 7/5, 11/7}}
+|
+|-
+| 65
+| {{dash|0, 14, 16, 18}}
+| {{dash|1, 11/10, 11/9, 11/8}}
+| utonal
+| {{dash|1/1, 11/10, 11/9, 11/8}}
+| {{dash|1/1, 10/9, 5/4, 20/11}}
+| {{dash|1/1, 9/8, 18/11, 9/5}}
+| {{dash|1/1, 16/11, 8/5, 16/9}}
+|
+|-
+| 66
+| {{dash|0, 1, 17, 18}}
+| {{dash|1, 3/2, 11/6, 11/8}}
+| ambitonal
+| {{dash|1/1, 11/8, 3/2, 11/6}}
+| {{dash|1/1, 12/11, 4/3, 16/11}}
+| {{dash|1/1, 11/9, 4/3, 11/6}}
+| {{dash|1/1, 12/11, 3/2, 18/11}}
+|
+|-
+| 67
+| {{dash|0, 8, 17, 18}}
+| {{dash|1, 11/7, 11/6, 11/8}}
+| utonal
+| {{dash|1/1, 11/8, 11/7, 11/6}}
+| {{dash|1/1, 8/7, 4/3, 16/11}}
+| {{dash|1/1, 7/6, 14/11, 7/4}}
+| {{dash|1/1, 12/11, 3/2, 12/7}}
+|
+|-
+| 68
+| {{dash|0, 9, 17, 18}}
+| {{dash|1, 7/6, 11/6, 11/8}}
+| mothwellsmic
+| {{dash|1/1, 7/6, 11/8, 11/6}}
+| {{dash|1/1, 7/6, 11/7, 12/7}}
+| {{dash|1/1, 4/3, 16/11, 12/7}}
+| {{dash|1/1, 12/11, 14/11, 3/2}}
+|
+|-
+| 69
+| {{dash|0, 14, 17, 18}}
+| {{dash|1, 11/10, 11/6, 11/8}}
+| utonal
+| {{dash|1/1, 11/10, 11/8, 11/6}}
+| {{dash|1/1, 5/4, 5/3, 20/11}}
+| {{dash|1/1, 4/3, 16/11, 8/5}}
+| {{dash|1/1, 12/11, 6/5, 3/2}}
+|
+|-
+| 70
+| {{dash|0, 16, 17, 18}}
+| {{dash|1, 11/9, 11/6, 11/8}}
+| utonal
+| {{dash|1/1, 11/9, 11/8, 11/6}}
+| {{dash|1/1, 9/8, 3/2, 18/11}}
+| {{dash|1/1, 4/3, 16/11, 16/9}}
+| {{dash|1/1, 12/11, 4/3, 3/2}}
+|
+|}
+== Pentads ==
+{| class="wikitable"
+|-
+! Chord
+! Transversal
+! Type
+! As generated
+! First inversion
+! Second inversion
+! Third inversion
+! Fourth inversion
+|-
+| {{dash|0, 1, 2, 3, 4}}
+| {{dash|1, 3/2, 9/8, 5/3, 5/4}}
+| didymic
+| {{dash|1/1, 9/8, 5/4, 3/2, 5/3  }}
+| {{dash|1/1, 10/9, 4/3, 3/2, 16/9  }}
+| {{dash|1/1, 6/5, 4/3, 8/5, 9/5  }}
+| {{dash|1/1, 10/9, 4/3, 3/2, 5/3  }}
+| {{dash|1/1, 6/5, 4/3, 3/2, 9/5  }}
+|-
+| {{dash|0, 2, 3, 4, 6}}
+| {{dash|1, 9/8, 5/3, 5/4, 7/5}}
+| erato
+| {{dash|1/1, 9/8, 5/4, 7/5, 5/3  }}
+| {{dash|1/1, 10/9, 5/4, 3/2, 16/9  }}
+| {{dash|1/1, 10/9, 4/3, 8/5, 9/5  }}
+| {{dash|1/1, 6/5, 10/7, 8/5, 9/5  }}
+| {{dash|1/1, 6/5, 4/3, 3/2, 5/3  }}
+|-
+| {{dash|0, 2, 4, 6, 8}}
+| {{dash|1, 9/8, 5/4, 7/5, 14/9}}
+| erato
+| {{dash|1/1, 9/8, 5/4, 7/5, 14/9  }}
+| {{dash|1/1, 10/9, 5/4, 7/5, 16/9  }}
+| {{dash|1/1, 10/9, 5/4, 8/5, 9/5  }}
+| {{dash|1/1, 10/9, 10/7, 8/5, 9/5  }}
+| {{dash|1/1, 9/7, 10/7, 8/5, 9/5  }}
+|-
+| {{dash|0, 1, 2, 4, 10}}
+| {{dash|1, 3/2, 9/8, 5/4, 7/4}}
+| otonal
+| {{dash|1/1, 9/8, 5/4, 3/2, 7/4  }}
+| {{dash|1/1, 10/9, 4/3, 14/9, 16/9  }}
+| {{dash|1/1, 6/5, 7/5, 8/5, 9/5  }}
+| {{dash|1/1, 7/6, 4/3, 3/2, 5/3  }}
+| {{dash|1/1, 8/7, 9/7, 10/7, 12/7  }}
+|-
+| {{dash|0, 2, 4, 6, 10}}
+| {{dash|1, 9/8, 5/4, 7/5, 7/4}}
+| erato
+| {{dash|1/1, 9/8, 5/4, 7/5, 7/4  }}
+| {{dash|1/1, 10/9, 5/4, 14/9, 16/9  }}
+| {{dash|1/1, 10/9, 7/5, 8/5, 9/5  }}
+| {{dash|1/1, 5/4, 10/7, 8/5, 9/5  }}
+| {{dash|1/1, 8/7, 9/7, 10/7, 8/5  }}
+|-
+| {{dash|0, 2, 4, 8, 10}}
+| {{dash|1, 9/8, 5/4, 14/9, 7/4}}
+| erato
+| {{dash|1/1, 9/8, 5/4, 14/9, 7/4  }}
+| {{dash|1/1, 10/9, 7/5, 14/9, 16/9  }}
+| {{dash|1/1, 5/4, 7/5, 8/5, 9/5  }}
+| {{dash|1/1, 9/8, 9/7, 10/7, 8/5  }}
+| {{dash|1/1, 8/7, 9/7, 10/7, 16/9  }}
+|-
+| {{dash|0, 2, 6, 8, 10}}
+| {{dash|1, 9/8, 7/5, 14/9, 7/4}}
+| erato
+| {{dash|1/1, 9/8, 7/5, 14/9, 7/4  }}
+| {{dash|1/1, 5/4, 7/5, 14/9, 16/9  }}
+| {{dash|1/1, 10/9, 5/4, 10/7, 8/5  }}
+| {{dash|1/1, 9/8, 9/7, 10/7, 9/5  }}
+| {{dash|1/1, 8/7, 9/7, 8/5, 16/9  }}
+|-
+| {{dash|0, 4, 6, 8, 10}}
+| {{dash|1, 5/4, 7/5, 14/9, 7/4}}
+| erato
+| {{dash|1/1, 5/4, 7/5, 14/9, 7/4  }}
+| {{dash|1/1, 9/8, 5/4, 7/5, 8/5  }}
+| {{dash|1/1, 10/9, 5/4, 10/7, 9/5  }}
+| {{dash|1/1, 9/8, 9/7, 8/5, 9/5  }}
+| {{dash|1/1, 8/7, 10/7, 8/5, 16/9  }}
+|-
+| {{dash|0, 6, 8, 9, 10}}
+| {{dash|1, 7/5, 14/9, 7/6, 7/4}}
+| utonal
+| {{dash|1/1, 7/6, 7/5, 14/9, 7/4  }}
+| {{dash|1/1, 6/5, 4/3, 3/2, 12/7  }}
+| {{dash|1/1, 10/9, 5/4, 10/7, 5/3  }}
+| {{dash|1/1, 9/8, 9/7, 3/2, 9/5  }}
+| {{dash|1/1, 8/7, 4/3, 8/5, 16/9  }}
+|-
+| {{dash|0, 4, 6, 8, 14}}
+| {{dash|1, 5/4, 7/5, 14/9, 11/10}}
+| meantone
+| {{dash|1/1, 11/10, 5/4, 7/5, 14/9  }}
+| {{dash|1/1, 9/8, 14/11, 10/7, 20/11 }}
+| {{dash|1/1, 10/9, 5/4, 8/5, 7/4  }}
+| {{dash|1/1, 10/9, 10/7, 11/7, 9/5  }}
+| {{dash|1/1, 9/7, 7/5, 8/5, 9/5  }}
+|-
+| {{dash|0, 4, 6, 10, 14}}
+| {{dash|1, 5/4, 7/5, 7/4, 11/10}}
+| minerva
+| {{dash|1/1, 11/10, 5/4, 7/5, 7/4  }}
+| {{dash|1/1, 9/8, 14/11, 8/5, 20/11 }}
+| {{dash|1/1, 10/9, 7/5, 8/5, 7/4  }}
+| {{dash|1/1, 5/4, 10/7, 11/7, 9/5  }}
+| {{dash|1/1, 8/7, 5/4, 10/7, 8/5  }}
+|-
+| {{dash|0, 4, 8, 10, 14}}
+| {{dash|1, 5/4, 14/9, 7/4, 11/10}}
+| minerva
+| {{dash|1/1, 11/10, 5/4, 14/9, 7/4  }}
+| {{dash|1/1, 9/8, 7/5, 8/5, 20/11 }}
+| {{dash|1/1, 5/4, 7/5, 8/5, 7/4  }}
+| {{dash|1/1, 9/8, 9/7, 7/5, 8/5  }}
+| {{dash|1/1, 8/7, 5/4, 10/7, 16/9  }}
+|-
+| {{dash|0, 6, 8, 10, 14}}
+| {{dash|1, 7/5, 14/9, 7/4, 11/10}}
+| meantone
+| {{dash|1/1, 11/10, 7/5, 14/9, 7/4  }}
+| {{dash|1/1, 14/11, 7/5, 8/5, 20/11 }}
+| {{dash|1/1, 10/9, 5/4, 10/7, 11/7  }}
+| {{dash|1/1, 9/8, 9/7, 7/5, 9/5  }}
+| {{dash|1/1, 8/7, 5/4, 8/5, 16/9  }}
+|-
+| {{dash|0, 2, 6, 8, 16}}
+| {{dash|1, 9/8, 7/5, 14/9, 11/9}}
+| meantone
+| {{dash|1/1, 9/8, 11/9, 7/5, 14/9  }}
+| {{dash|1/1, 11/10, 5/4, 7/5, 16/9  }}
+| {{dash|1/1, 8/7, 14/11, 18/11, 20/11 }}
+| {{dash|1/1, 10/9, 10/7, 8/5, 7/4  }}
+| {{dash|1/1, 9/7, 10/7, 11/7, 9/5  }}
+|-
+| {{dash|0, 2, 6, 10, 16}}
+| {{dash|1, 9/8, 7/5, 7/4, 11/9}}
+| meantone
+| {{dash|1/1, 9/8, 11/9, 7/5, 7/4  }}
+| {{dash|1/1, 11/10, 5/4, 14/9, 16/9  }}
+| {{dash|1/1, 8/7, 10/7, 18/11, 20/11 }}
+| {{dash|1/1, 5/4, 10/7, 8/5, 7/4  }}
+| {{dash|1/1, 8/7, 9/7, 7/5, 8/5  }}
+|-
+| {{dash|0, 2, 8, 10, 16}}
+| {{dash|1, 9/8, 14/9, 7/4, 11/9}}
+| euterpe
+| {{dash|1/1, 9/8, 11/9, 14/9, 7/4  }}
+| {{dash|1/1, 11/10, 7/5, 14/9, 16/9  }}
+| {{dash|1/1, 14/11, 10/7, 18/11, 20/11 }}
+| {{dash|1/1, 9/8, 9/7, 10/7, 11/7  }}
+| {{dash|1/1, 8/7, 9/7, 7/5, 16/9  }}
+|-
+| {{dash|0, 6, 8, 10, 16}}
+| {{dash|1, 7/5, 14/9, 7/4, 11/9}}
+| euterpe
+| {{dash|1/1, 11/9, 7/5, 14/9, 7/4  }}
+| {{dash|1/1, 8/7, 14/11, 10/7, 18/11 }}
+| {{dash|1/1, 10/9, 5/4, 10/7, 7/4  }}
+| {{dash|1/1, 9/8, 9/7, 11/7, 9/5  }}
+| {{dash|1/1, 8/7, 7/5, 8/5, 16/9  }}
+|-
+| {{dash|0, 6, 8, 14, 16}}
+| {{dash|1, 7/5, 14/9, 11/10, 11/9}}
+| euterpe
+| {{dash|1/1, 11/10, 11/9, 7/5, 14/9  }}
+| {{dash|1/1, 10/9, 14/11, 10/7, 20/11 }}
+| {{dash|1/1, 8/7, 14/11, 18/11, 9/5  }}
+| {{dash|1/1, 10/9, 10/7, 11/7, 7/4  }}
+| {{dash|1/1, 9/7, 7/5, 11/7, 9/5  }}
+|-
+| {{dash|0, 6, 10, 14, 16}}
+| {{dash|1, 7/5, 7/4, 11/10, 11/9}}
+| meantone
+| {{dash|1/1, 11/10, 11/9, 7/5, 7/4  }}
+| {{dash|1/1, 10/9, 14/11, 8/5, 20/11 }}
+| {{dash|1/1, 8/7, 10/7, 18/11, 9/5  }}
+| {{dash|1/1, 5/4, 10/7, 11/7, 7/4  }}
+| {{dash|1/1, 8/7, 5/4, 7/5, 8/5  }}
+|-
+| {{dash|0, 8, 10, 14, 16}}
+| {{dash|1, 14/9, 7/4, 11/10, 11/9}}
+| meantone
+| {{dash|1/1, 11/10, 11/9, 14/9, 7/4  }}
+| {{dash|1/1, 10/9, 7/5, 8/5, 20/11 }}
+| {{dash|1/1, 14/11, 10/7, 18/11, 9/5  }}
+| {{dash|1/1, 9/8, 9/7, 7/5, 11/7  }}
+| {{dash|1/1, 8/7, 5/4, 7/5, 16/9  }}
+|-
+| {{dash|0, 1, 3, 9, 17}}
+| {{dash|1, 3/2, 5/3, 7/6, 11/6}}
+| otonal
+| {{dash|1/1, 7/6, 3/2, 5/3, 11/6  }}
+| {{dash|1/1, 9/7, 10/7, 11/7, 12/7  }}
+| {{dash|1/1, 10/9, 11/9, 4/3, 14/9  }}
+| {{dash|1/1, 11/10, 6/5, 7/5, 9/5  }}
+| {{dash|1/1, 12/11, 14/11, 18/11, 20/11 }}
+|-
+| {{dash|0, 8, 14, 16, 17}}
+| {{dash|1, 11/7, 11/10, 11/9, 11/6}}
+| utonal
+| {{dash|1/1, 11/10, 11/9, 11/7, 11/6  }}
+| {{dash|1/1, 10/9, 10/7, 5/3, 20/11 }}
+| {{dash|1/1, 9/7, 3/2, 18/11, 9/5  }}
+| {{dash|1/1, 7/6, 14/11, 7/5, 14/9  }}
+| {{dash|1/1, 12/11, 6/5, 4/3, 12/7  }}
+|-
+| {{dash|0, 1, 2, 4, 18}}
+| {{dash|1, 3/2, 9/8, 5/4, 11/8}}
+| otonal
+| {{dash|1/1, 9/8, 5/4, 11/8, 3/2  }}
+| {{dash|1/1, 10/9, 11/9, 4/3, 16/9  }}
+| {{dash|1/1, 11/10, 6/5, 8/5, 9/5  }}
+| {{dash|1/1, 12/11, 16/11, 18/11, 20/11 }}
+| {{dash|1/1, 4/3, 3/2, 5/3, 11/6  }}
+|-
+| {{dash|0, 2, 4, 8, 18}}
+| {{dash|1, 9/8, 5/4, 14/9, 11/8}}
+| meantone
+| {{dash|1/1, 9/8, 5/4, 11/8, 14/9  }}
+| {{dash|1/1, 10/9, 11/9, 7/5, 16/9  }}
+| {{dash|1/1, 11/10, 5/4, 8/5, 9/5  }}
+| {{dash|1/1, 8/7, 16/11, 18/11, 20/11 }}
+| {{dash|1/1, 9/7, 10/7, 8/5, 7/4  }}
+|-
+| {{dash|0, 1, 2, 10, 18}}
+| {{dash|1, 3/2, 9/8, 7/4, 11/8}}
+| otonal
+| {{dash|1/1, 9/8, 11/8, 3/2, 7/4  }}
+| {{dash|1/1, 11/9, 4/3, 14/9, 16/9  }}
+| {{dash|1/1, 12/11, 14/11, 16/11, 18/11 }}
+| {{dash|1/1, 7/6, 4/3, 3/2, 11/6  }}
+| {{dash|1/1, 8/7, 9/7, 11/7, 12/7  }}
+|-
+| {{dash|0, 1, 4, 10, 18}}
+| {{dash|1, 3/2, 5/4, 7/4, 11/8}}
+| otonal
+| {{dash|1/1, 5/4, 11/8, 3/2, 7/4  }}
+| {{dash|1/1, 11/10, 6/5, 7/5, 8/5  }}
+| {{dash|1/1, 12/11, 14/11, 16/11, 20/11 }}
+| {{dash|1/1, 7/6, 4/3, 5/3, 11/6  }}
+| {{dash|1/1, 8/7, 10/7, 11/7, 12/7  }}
+|-
+| {{dash|0, 2, 4, 10, 18}}
+| {{dash|1, 9/8, 5/4, 7/4, 11/8}}
+| otonal
+| {{dash|1/1, 9/8, 5/4, 11/8, 7/4  }}
+| {{dash|1/1, 10/9, 11/9, 14/9, 16/9  }}
+| {{dash|1/1, 11/10, 7/5, 8/5, 9/5  }}
+| {{dash|1/1, 14/11, 16/11, 18/11, 20/11 }}
+| {{dash|1/1, 8/7, 9/7, 10/7, 11/7  }}
+|-
+| {{dash|0, 2, 8, 10, 18}}
+| {{dash|1, 9/8, 14/9, 7/4, 11/8}}
+| euterpe
+| {{dash|1/1, 9/8, 11/8, 14/9, 7/4  }}
+| {{dash|1/1, 11/9, 7/5, 14/9, 16/9  }}
+| {{dash|1/1, 8/7, 14/11, 16/11, 18/11 }}
+| {{dash|1/1, 9/8, 9/7, 10/7, 7/4  }}
+| {{dash|1/1, 8/7, 9/7, 11/7, 16/9  }}
+|-
+| {{dash|0, 4, 8, 10, 18}}
+| {{dash|1, 5/4, 14/9, 7/4, 11/8}}
+| minerva
+| {{dash|1/1, 5/4, 11/8, 14/9, 7/4  }}
+| {{dash|1/1, 11/10, 5/4, 7/5, 8/5  }}
+| {{dash|1/1, 8/7, 14/11, 16/11, 20/11 }}
+| {{dash|1/1, 9/8, 9/7, 8/5, 7/4  }}
+| {{dash|1/1, 8/7, 10/7, 11/7, 16/9  }}
+|-
+| {{dash|0, 1, 9, 10, 18}}
+| {{dash|1, 3/2, 7/6, 7/4, 11/8}}
+| mothwellsmic
+| {{dash|1/1, 7/6, 11/8, 3/2, 7/4  }}
+| {{dash|1/1, 7/6, 9/7, 3/2, 12/7  }}
+| {{dash|1/1, 12/11, 14/11, 16/11, 12/7  }}
+| {{dash|1/1, 7/6, 4/3, 14/9, 11/6  }}
+| {{dash|1/1, 8/7, 4/3, 11/7, 12/7  }}
+|-
+| {{dash|0, 8, 9, 10, 18}}
+| {{dash|1, 14/9, 7/6, 7/4, 11/8}}
+| mothwellsmic
+| {{dash|1/1, 7/6, 11/8, 14/9, 7/4  }}
+| {{dash|1/1, 7/6, 4/3, 3/2, 12/7  }}
+| {{dash|1/1, 8/7, 14/11, 16/11, 12/7  }}
+| {{dash|1/1, 9/8, 9/7, 3/2, 7/4  }}
+| {{dash|1/1, 8/7, 4/3, 11/7, 16/9  }}
+|-
+| {{dash|0, 4, 8, 14, 18}}
+| {{dash|1, 5/4, 14/9, 11/10, 11/8}}
+| minerva
+| {{dash|1/1, 11/10, 5/4, 11/8, 14/9  }}
+| {{dash|1/1, 9/8, 5/4, 10/7, 20/11 }}
+| {{dash|1/1, 11/10, 5/4, 8/5, 7/4  }}
+| {{dash|1/1, 8/7, 16/11, 8/5, 20/11 }}
+| {{dash|1/1, 9/7, 7/5, 8/5, 7/4  }}
+|-
+| {{dash|0, 4, 10, 14, 18}}
+| {{dash|1, 5/4, 7/4, 11/10, 11/8}}
+| minerva
+| {{dash|1/1, 11/10, 5/4, 11/8, 7/4  }}
+| {{dash|1/1, 9/8, 5/4, 8/5, 20/11 }}
+| {{dash|1/1, 11/10, 7/5, 8/5, 7/4  }}
+| {{dash|1/1, 14/11, 16/11, 8/5, 20/11 }}
+| {{dash|1/1, 8/7, 5/4, 10/7, 11/7  }}
+|-
+| {{dash|0, 8, 10, 14, 18}}
+| {{dash|1, 14/9, 7/4, 11/10, 11/8}}
+| minerva
+| {{dash|1/1, 11/10, 11/8, 14/9, 7/4  }}
+| {{dash|1/1, 5/4, 7/5, 8/5, 20/11 }}
+| {{dash|1/1, 8/7, 14/11, 16/11, 8/5  }}
+| {{dash|1/1, 9/8, 9/7, 7/5, 7/4  }}
+| {{dash|1/1, 8/7, 5/4, 11/7, 16/9  }}
+|-
+| {{dash|0, 2, 8, 16, 18}}
+| {{dash|1, 9/8, 14/9, 11/9, 11/8}}
+| euterpe
+| {{dash|1/1, 9/8, 11/9, 11/8, 14/9  }}
+| {{dash|1/1, 11/10, 11/9, 7/5, 16/9  }}
+| {{dash|1/1, 9/8, 14/11, 18/11, 20/11 }}
+| {{dash|1/1, 8/7, 16/11, 18/11, 16/9  }}
+| {{dash|1/1, 9/7, 10/7, 11/7, 7/4  }}
+|-
+| {{dash|0, 2, 10, 16, 18}}
+| {{dash|1, 9/8, 7/4, 11/9, 11/8}}
+| euterpe
+| {{dash|1/1, 9/8, 11/9, 11/8, 7/4  }}
+| {{dash|1/1, 11/10, 11/9, 14/9, 16/9  }}
+| {{dash|1/1, 9/8, 10/7, 18/11, 20/11 }}
+| {{dash|1/1, 14/11, 16/11, 18/11, 16/9  }}
+| {{dash|1/1, 8/7, 9/7, 7/5, 11/7  }}
+|-
+| {{dash|0, 8, 10, 16, 18}}
+| {{dash|1, 14/9, 7/4, 11/9, 11/8}}
+| euterpe
+| {{dash|1/1, 11/9, 11/8, 14/9, 7/4  }}
+| {{dash|1/1, 9/8, 14/11, 10/7, 18/11 }}
+| {{dash|1/1, 8/7, 14/11, 16/11, 16/9  }}
+| {{dash|1/1, 9/8, 9/7, 11/7, 7/4  }}
+| {{dash|1/1, 8/7, 7/5, 11/7, 16/9  }}
+|-
+| {{dash|0, 8, 14, 16, 18}}
+| {{dash|1, 11/7, 11/10, 11/9, 11/8}}
+| utonal
+| {{dash|1/1, 11/10, 11/9, 11/8, 11/7  }}
+| {{dash|1/1, 10/9, 5/4, 10/7, 20/11 }}
+| {{dash|1/1, 9/8, 9/7, 18/11, 9/5  }}
+| {{dash|1/1, 8/7, 16/11, 8/5, 16/9  }}
+| {{dash|1/1, 14/11, 7/5, 14/9, 7/4  }}
+|-
+| {{dash|0, 10, 14, 16, 18}}
+| {{dash|1, 7/4, 11/10, 11/9, 11/8}}
+| meantone
+| {{dash|1/1, 11/10, 11/9, 11/8, 7/4  }}
+| {{dash|1/1, 10/9, 5/4, 8/5, 20/11 }}
+| {{dash|1/1, 9/8, 10/7, 18/11, 9/5  }}
+| {{dash|1/1, 14/11, 16/11, 8/5, 16/9  }}
+| {{dash|1/1, 8/7, 5/4, 7/5, 11/7  }}
+|-
+| {{dash|0, 1, 9, 17, 18}}
+| {{dash|1, 3/2, 7/6, 11/6, 11/8}}
+| mothwellsmic
+| {{dash|1/1, 7/6, 11/8, 3/2, 11/6  }}
+| {{dash|1/1, 7/6, 9/7, 11/7, 12/7  }}
+| {{dash|1/1, 12/11, 4/3, 16/11, 12/7  }}
+| {{dash|1/1, 11/9, 4/3, 14/9, 11/6  }}
+| {{dash|1/1, 12/11, 14/11, 3/2, 18/11 }}
+|-
+| {{dash|0, 8, 9, 17, 18}}
+| {{dash|1, 14/9, 7/6, 11/6, 11/8}}
+| mothwellsmic
+| {{dash|1/1, 7/6, 11/8, 14/9, 11/6  }}
+| {{dash|1/1, 7/6, 4/3, 11/7, 12/7  }}
+| {{dash|1/1, 8/7, 4/3, 16/11, 12/7  }}
+| {{dash|1/1, 7/6, 9/7, 3/2, 7/4  }}
+| {{dash|1/1, 12/11, 14/11, 3/2, 12/7  }}
+|-
+| {{dash|0, 8, 14, 17, 18}}
+| {{dash|1, 11/7, 11/10, 11/6, 11/8}}
+| utonal
+| {{dash|1/1, 11/10, 11/8, 11/7, 11/6  }}
+| {{dash|1/1, 5/4, 10/7, 5/3, 20/11 }}
+| {{dash|1/1, 8/7, 4/3, 16/11, 8/5  }}
+| {{dash|1/1, 7/6, 14/11, 7/5, 7/4  }}
+| {{dash|1/1, 12/11, 6/5, 3/2, 12/7  }}
+|-
+| {{dash|0, 8, 16, 17, 18}}
+| {{dash|1, 11/7, 11/9, 11/6, 11/8}}
+| utonal
+| {{dash|1/1, 11/9, 11/8, 11/7, 11/6  }}
+| {{dash|1/1, 9/8, 9/7, 3/2, 18/11 }}
+| {{dash|1/1, 8/7, 4/3, 16/11, 16/9  }}
+| {{dash|1/1, 7/6, 14/11, 14/9, 7/4  }}
+| {{dash|1/1, 12/11, 4/3, 3/2, 12/7  }}
+|-
+| {{dash|0, 14, 16, 17, 18}}
+| {{dash|1, 11/10, 11/9, 11/6, 11/8}}
+| utonal
+| {{dash|1/1, 11/10, 11/9, 11/8, 11/6  }}
+| {{dash|1/1, 10/9, 5/4, 5/3, 20/11 }}
+| {{dash|1/1, 9/8, 3/2, 18/11, 9/5  }}
+| {{dash|1/1, 4/3, 16/11, 8/5, 16/9  }}
+| {{dash|1/1, 12/11, 6/5, 4/3, 3/2  }}
+|}
+== Hexads ==
+{| class="wikitable"
+|-
+! Number
+! Chord
+! Transversal
+! Type
+|-
+| 1
+| {{dash|0, 2, 4, 6, 8, 10}}
+| {{dash|1, 9/8, 5/4, 7/5, 14/9, 7/4}}
+| erato
+|-
+| 2
+| {{dash|0, 4, 6, 8, 10, 14}}
+| {{dash|1, 5/4, 7/5, 14/9, 7/4, 11/10}}
+| meantone
+|-
+| 3
+| {{dash|0, 2, 6, 8, 10, 16}}
+| {{dash|1, 9/8, 7/5, 14/9, 7/4, 11/9}}
+| meantone
+|-
+| 4
+| {{dash|0, 6, 8, 10, 14, 16}}
+| {{dash|1, 7/5, 14/9, 7/4, 11/10, 11/9}}
+| meantone
+|-
+| 5
+| {{dash|0, 1, 2, 4, 10, 18}}
+| {{dash|1, 3/2, 9/8, 5/4, 7/4, 11/8}}
+| otonal
+|-
+| 6
+| {{dash|0, 2, 4, 8, 10, 18}}
+| {{dash|1, 9/8, 5/4, 14/9, 7/4, 11/8}}
+| meantone
+|-
+| 7
+| {{dash|0, 4, 8, 10, 14, 18}}
+| {{dash|1, 5/4, 14/9, 7/4, 11/10, 11/8}}
+| minerva
+|-
+| 8
+| {{dash|0, 2, 8, 10, 16, 18}}
+| {{dash|1, 9/8, 14/9, 7/4, 11/9, 11/8}}
+| euterpe
+|-
+| 9
+| {{dash|0, 8, 10, 14, 16, 18}}
+| {{dash|1, 14/9, 7/4, 11/10, 11/9, 11/8-}}
+| meantone
+|-
+| 10
+| {{dash|0, 8, 14, 16, 17, 18}}
+| {{dash|1, 11/7, 11/10, 11/9, 11/6, 11/8}}
+| utonal
+|}
+[[Category:Lists of chords]]
+[[Category:Dyadic chords]]
+[[Category:11-limit]]
+[[Category:Meantone]]

Chords of huygens: Difference between revisions

Revision as of 21:57, 22 June 2025

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