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
Tunings
Tuning spectrum
| 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 |