Keemun: Difference between revisions

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The entire name section is just distracting. Move to temperament naming page
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{{Infobox regtemp
| Title = Keemun
| Subgroups = 2.3.5.7
| Comma basis = [[49/48]], [[126/125]]
| Edo join 1 = 15 | Edo join 2 = 19
| Mapping = 1; 6 5 3
| Generators = 6/5 | Generators tuning = 316.8 | Optimization method = CWE
| MOS scales = [[4L 3s]], [[4L 7s]], [[4L 11s]], [[15L 4s]]
| Odd limit 1 = 7 | Mistuning 1 = 17.8 | Complexity 1 = 7
}}
'''Keemun''' is an [[extension]] of the [[hanson]] temperament, and [[tempering out|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 [[49edo|49d]] and [[64edo|64bde]] coming closer to balancing the errors equally.
'''Keemun''' is an [[extension]] of the [[hanson]] temperament, and [[tempering out|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 [[49edo|49d]] and [[64edo|64bde]] coming closer to balancing the errors equally.


This temperament was originally discovered by [[Dave Keenan]] and named by [[Herman Miller]] in 2006 after the {{w|Keemun|Chinese black tea}}<ref>Dave Keenan's original write-up: [https://dkeenan.com/Music/ChainOfMinor3rds.htm ''11 note chain-of-minor-thirds scale'']</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_13712#13775 Yahoo! Tuning Group | ''Rich Holmes temperaments'']</ref>
This temperament was originally discovered by [[Dave Keenan]] and named by [[Herman Miller]] in 2006 after the {{w|Keemun|Chinese black tea}}<ref>Dave Keenan's original write-up: [https://dkeenan.com/Music/ChainOfMinor3rds.htm ''11 note chain-of-minor-thirds scale'']</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_13712#13775 Yahoo! Tuning Group | ''Rich Holmes temperaments'']</ref>.


See [[Kleismic family #Keemun]] for technical data.
See [[Kleismic family #Keemun]] for technical data.

Revision as of 10:08, 27 March 2026

Keemun
Subgroups 2.3.5.7
Comma basis 49/48, 126/125
Reduced mapping ⟨1; 6 5 3]
ET join 15 & 19
Generators (CWE) ~6/5 = 316.8 ¢
MOS scales 4L 3s, 4L 7s, 4L 11s, 15L 4s
Ploidacot alpha-hexacot
Minimax error 7-odd-limit: 17.8 ¢
Target scale size 7-odd-limit: 7 notes

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.

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
1 317.576 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

Music

Chris Vaisvil

References