Keemun extensions
Keemun has various competing extensions to the 11- and 13-limit. The following temperaments are discussed in this article:
- Tridecimal keemun (15 & 19) – tempering out 49/48, 56/55, 91/90, 100/99;
- Kimah (15f & 19) – tempering out 49/48, 56/55, 65/64, 100/99;
- Kumbaya (15 & 19f) – tempering out 40/39, 49/48, 56/55, 66/65;
- Qeema (15e & 19) – tempering out 45/44, 49/48, 78/77, 126/125;
- Darjeeling (15 & 19e) – tempering out 49/48, 55/54, 66/65, 77/75.
See Kleismic family #Keemun, #Kimah, #Kumbaya, #Qeema, and #Darjeeling for technical data.
Interval chain
| # | Approximate ratios | ||||
|---|---|---|---|---|---|
| Cents* | 7-limit | 13-limit extensions | |||
| Keemun (15 & 19) |
Kimah (4 & 19) |
Kumbaya (4 & 15) | |||
| 0 | 0.0 | 1/1 | |||
| 1 | 316.8 | 6/5 | 13/11, 16/13 | ||
| 2 | 633.7 | 10/7 | 13/9, 16/11 | 16/11 | 16/11 |
| 3 | 950.5 | 7/4, 12/7 | 26/15 | 22/13 | |
| 4 | 67.3 | 21/20, 25/24, 36/35 | 33/32, | 33/32, | 14/13, 33/32 |
| 5 | 384.1 | 5/4 | 14/11 | 14/11, 16/13 | 14/11 |
| 6 | 701.0 | 3/2 | 20/13 | ||
| 7 | 1017.8 | 9/5 | 20/11 | 20/11 | 20/11, 24/13 |
| 8 | 134.6 | 15/14 | 12/11, 13/12 | 12/11, 14/13 | 12/11 |
| 9 | 451.5 | 9/7, 21/16 | 13/10 | ||
| 10 | 768.3 | 25/16 | 20/13 | ||
| 11 | 1085.1 | 15/8 | 13/7 | 24/13 | |
| 12 | 202.0 | 9/8 | 15/13 | ||
| 13 | 518.8 | 15/11 | 15/11 | 15/11, 18/13 | |
| 14 | 835.6 | 13/8, 18/11 | 18/11, 21/13 | 18/11 | |
| 15 | 1152.4 | 27/14 | 25/13 | ||
| 16 | 269.3 | 13/11 | 15/13 | ||
| 17 | 586.1 | 45/32 | 18/13 | ||
| 18 | 902.9 | 27/16 | |||
| 19 | 19.8 | 81/80 | |||
* In 7-limit CWE tuning, octave reduced