Keemun
The keemun temperament is an extension of the hanson temperament, which tempers out 49/48, 56/55, and 100/99 in the 11-limit. EDOs that support keemun include 15edo, 19edo, and 34edo.
See Kleismic family #Keemun for technical data.
This temperament was originally discovered by Dave Keenan[1].
Interval chain
| # | Cents* | 11-limit ratios | 13-limit ratios | ||
|---|---|---|---|---|---|
| Keemum (4&19) |
Kema (15&19) |
Kumbaya (4&15) | |||
| 0 | 0.000 | 1/1 | |||
| 1 | 317.576 | 6/5 | 13/11, 16/13 | ||
| 2 | 635.151 | 10/7, 16/11 | 13/9 | ||
| 3 | 952.727 | 7/4, 12/7 | 22/13 | 26/15 | |
| 4 | 70.302 | 21/20, 25/24, 33/32, 36/35 | 14/13 | ||
| 5 | 387.878 | 5/4, 14/11 | 16/13 | ||
| 6 | 705.453 | 3/2 | 20/13 | ||
| 7 | 1023.029 | 9/5, 20/11 | 24/13 | ||
| 8 | 140.605 | 12/11, 15/14 | 14/13 | 13/12 | |
| 9 | 458.180 | 9/7, 21/16 | 13/10 | ||
| 10 | 775.756 | 25/16 | 20/13 | ||
| 11 | 1093.331 | 15/8 | 24/13 | 13/7 | |
| 12 | 210.907 | 9/8 | 15/13 | ||
| 13 | 528.482 | 15/11 | 18/13 | ||
| 14 | 846.058 | 18/11 | 21/13 | 13/8 | |
| 15 | 1163.634 | 27/14 | 25/13 | ||
| 16 | 281.209 | 15/13 | 13/11 | ||
| 17 | 598.785 | 45/32 | 18/13 | ||
| 18 | 916.360 | 27/16 | |||
| 19 | 33.936 | 81/80 | |||
* in 11-limit POTE tuning, octave reduced
Name
As he did for the comma now known as the "keenanisma", Dave Keenan resisted the temperament being named after him, and for the same reason: Dave prefers descriptive names to eponymous ones, because they are more useful. Unfortunately, by the time Dave's preference reached Paul Erlich, Paul had already begun to use the name "Keenan" in a series of diagrams, and so renaming it to something descriptive such as "Minorthirds" at this point would require an inordinate amount of reordering busywork. Due to this, the effort to rename the temperament continued, but with the additional constraint that the name could not alter its alphabetical ordering with respect to its nearest neighboring temperaments in Paul's diagrams. The name chosen in the end, "Keemun", was suggested by Herman Miller as a reference to the famous tea[2]. While this name satisfies Paul's alphabetical ordering preservation constraint, it does not satisfy Dave's descriptiveness constraint, and thereby misses the point of Dave's original request for it not to be named after him.
Music
The Fallen of Kleismic15play by Chris Vaisvil
References
- ↑ Dave Keenan's original write-up: https://dkeenan.com/Music/ChainOfMinor3rds.htm
- ↑ https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_13712#13775