Superkleismic

Superkleismic is a regular temperament defined in the 7-, 11-, and 13-limit. It is a member of shibboleth family as well as of the gamelismic clan. The minor-third generator of superkleismic is ~6.3 cents sharp of 6/5, even wider than the kleismic minor third (~317 cents), and from this it derives its name. The two mappings unite at 15edo. While not as simple or accurate as kleismic in the 5-limit, it comes into its own as a 7- and 11-limit temperament, approximating both simply and accurately in good tunings. Discarding the harmonics 3 and 5 and concentrating purely on that subgroup gets you orgone. 41edo is a good tuning for superkleismic, with a minor-third generator of 11\41, and mosses of 11, 15, or 26 notes are available.

See Shibboleth family #Superkleismic for more technical data.

Interval chain

In the following table, odd harmonics 1–21 are bolded.

#	Cents*	Approximate Ratios
0	0.00	1/1
1	321.99	6/5
2	643.99	13/9, 16/11
3	965.98	7/4
4	87.98	21/20, 22/21
5	409.97	14/11
6	731.96	20/13, 32/21
7	1053.96	11/6, 24/13
8	175.95	10/9, 11/10
9	497.94	4/3
10	819.94	8/5
11	1141.93	35/18, 48/25, 52/27, 64/33
12	263.93	7/6
13	585.92	7/5
14	907.91	22/13
15	29.91	40/39, 49/48, 56/55, 64/63
16	351.90	11/9, 16/13
17	673.90	22/15
18	995.89	16/9
19	117.88	14/13, 16/15
20	439.88	32/25, 35/27
21	761.87	14/9
22	1083.87	28/15

* in 13-limit POTE tuning

Tuning spectrum

Gencom: [2 6/5; 100/99 105/104 144/143 245/242]

Gencom mapping: [⟨1 4 5 2 4 8], ⟨0 -9 -10 3 -2 -16]]

Eigenmonzo (Unchanged-interval)	Generator (¢)	Comments
6/5	315.641
18/13	317.420
15/13	318.309
11/10	320.626
12/11	321.338
15/11	321.356
5/4	321.369	5-odd-limit minimax
16/15	321.670
11/9	321.713
7/5	321.732	7 and 11-odd-limit minimax
15/14	321.844
4/3	322.005	9 and 15-odd-limit minimax
9/7	322.139
13/11	322.199	13-odd-limit minimax
7/6	322.239
16/13	322.467
14/13	322.542
10/9	322.800
8/7	322.942
13/12	323.061
14/11	323.502
13/10	324.298
11/8	324.341