Keemun
Keemun is an extension of the hanson temperament, and tempers out 49/48, 56/55, and 100/99 in the 11-limit. This means it uses the same simple mappings for the 7th and 11th harmonics as orgone. Unfortunately, the optimal tunings for the 3rd and 5th harmonics is substantially flatter than that for the 7th & 11th ones, requiring you to compromise one set for the other. The edos that support keemun in their patent vals are 4edo, 15edo, 19edo, and 34edo, with 49d and 64bde coming closer to balancing the errors equally.
| Keemun |
49/48, 56/55, 100/99 (11-limit)
11-odd-limit: 27.3 ¢
11-odd-limit: 15 notes
This temperament was originally discovered by Dave Keenan and named by Herman Miller in 2006 after the Chinese black tea[1][2].
See Kleismic family #Keemun for technical data.
Interval chain
| # | Cents* | 11-limit ratios | 13-limit ratios | ||
|---|---|---|---|---|---|
| Keemun (4 & 19) |
Kema (15 & 19) |
Kumbaya (4 & 15) | |||
| 0 | 0.000 | 1/1 | |||
| 1 | 317.555 | 6/5 | 13/11, 16/13 | ||
| 2 | 635.109 | 10/7, 16/11 | 13/9 | ||
| 3 | 952.664 | 7/4, 12/7 | 22/13 | 26/15 | |
| 4 | 70.219 | 21/20, 25/24, 33/32, 36/35 | 14/13 | ||
| 5 | 387.773 | 5/4, 14/11 | 16/13 | ||
| 6 | 705.328 | 3/2 | 20/13 | ||
| 7 | 1022.882 | 9/5, 20/11 | 24/13 | ||
| 8 | 140.437 | 12/11, 15/14 | 14/13 | 13/12 | |
| 9 | 457.992 | 9/7, 21/16 | 13/10 | ||
| 10 | 775.546 | 25/16 | 20/13 | ||
| 11 | 1093.101 | 15/8 | 24/13 | 13/7 | |
| 12 | 210.656 | 9/8 | 15/13 | ||
| 13 | 528.210 | 15/11 | 18/13 | ||
| 14 | 845.765 | 18/11 | 21/13 | 13/8 | |
| 15 | 1163.320 | 27/14 | 25/13 | ||
| 16 | 280.874 | 15/13 | 13/11 | ||
| 17 | 598.429 | 45/32 | 18/13 | ||
| 18 | 915.984 | 27/16 | |||
| 19 | 33.538 | 81/80 | |||
* In 11-limit CWE tuning, octave reduced
Tunings
| Euclidean | |||
|---|---|---|---|
| Constrained | Constrained & skewed | Destretched | |
| Tenney | CTE: ~6/5 = 317.3927 ¢ | CWE: ~6/5 = 316.8293 ¢ | POTE: ~6/5 = 316.4727 ¢ |
| Euclidean | |||
|---|---|---|---|
| Constrained | Constrained & skewed | Destretched | |
| Tenney | CTE: ~6/5 = 317.5063 ¢ | CWE: ~6/5 = 317.5546 ¢ | POTE: ~6/5 = 317.5756 ¢ |
Tuning spectrum
This tuning spectrum assumes undecimal keemun.
| Edo generator |
Eigenmonzo (unchanged interval)* |
Generator (¢) | Comments |
|---|---|---|---|
| 1\4 | 300.000 | Lower bound of 5- and 7-odd-limit diamond monotone | |
| 7/5 | 308.744 | ||
| 7/6 | 311.043 | ||
| 6\23 | 313.043 | 23d val | |
| 15/14 | 314.930 | ||
| 9/7 | 315.009 | ||
| 5/3 | 315.641 | ||
| 5\19 | 315.789 | Lower bound of 9- and 11-odd-limit diamond monotone | |
| 9/5 | 316.799 | 1/7-kleisma | |
| 14\53 | 316.981 | 53de val | |
| 3/2 | 316.993 | 5-, 7- and 9-odd-limit minimax, 1/6-kleisma | |
| 15/8 | 317.115 | 2/11-kleisma | |
| 5/4 | 317.263 | 1/5-kleisma | |
| 9\34 | 317.647 | ||
| 11/9 | 318.042 | 11-odd-limit minimax | |
| 15/11 | 318.227 | ||
| 11/10 | 319.285 | ||
| 13\49 | 318.367 | 49d val | |
| 11/6 | 318.830 | ||
| 4\15 | 320.000 | Upper bound of 9- and 11-odd-limit diamond monotone | |
| 7/4 | 322.942 | ||
| 11/7 | 323.502 | ||
| 11/8 | 324.341 | ||
| 3\11 | 327.273 | 11b val, upper bound of 5- and 7-odd-limit diamond monotone |
* Besides the octave
Music
References
- ↑ Dave Keenan's original write-up: 11 note chain-of-minor-thirds scale
- ↑ Yahoo! Tuning Group | Rich Holmes temperaments