Keemun: Difference between revisions

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'''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.
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<nowiki>*</nowiki> In 11-limit POTE tuning, octave reduced
<nowiki>*</nowiki> In 11-limit POTE tuning, octave reduced
== Name ==
As he did for the comma now known as the [[Keenanisma #Etymology|''keenanisma'']], Dave Keenan resisted the temperament being named after him, and preferred descriptive names to eponymous ones because they would be 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. Although this name did not satisfy Dave's request for descriptiveness, it fulfilled the ultimate goal of distinguishing itself from the name ''kleismic'', thereby ending the unfortunate practice of calling this temperament, a 7-limit extension of hanson with a much lower accuracy, by ''kleismic'' also.


== Music ==
== Music ==

Revision as of 09:52, 27 March 2026

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

  1. ↑ Dave Keenan's original write-up: 11 note chain-of-minor-thirds scale
  2. ↑ Yahoo! Tuning Group | Rich Holmes temperaments
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