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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]].
{{Infobox regtemp
| Title = Keemun
| Subgroups = 2.3.5.7, 2.3.5.7.11
| Comma basis = [[49/48]], [[126/125]] (7-limit) <br>[[49/48]], [[56/55]], [[100/99]] (11-limit)
| Edo join 1 = 15 | Edo join 2 = 19
| Mapping = 1; 6 5 3 -2
| Generators = 6/5 | Generators tuning = 317.6 | Optimization method = CWE
| MOS scales = [[4L 3s]], [[4L 7s]], [[4L 11s]], [[15L 4s]]
| Pergen = (P8, P12/6)
| Odd limit 1 = 7 | Mistuning 1 = 17.8 | Complexity 1 = 7
| Odd limit 2 = 11 | Mistuning 2 = 27.3 | Complexity 2 = 15
}}
'''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>.  


See [[Kleismic family #Keemun]] for technical data.
See [[Kleismic family #Keemun]] for technical data.
This temperament was originally discovered by [[Dave Keenan]]<ref>Dave Keenan's original write-up: https://dkeenan.com/Music/ChainOfMinor3rds.htm</ref>.


== Interval chain ==
== Interval chain ==
{| class="wikitable center-1 right-2"
{| class="wikitable center-1 right-2"
|-
|-
! rowspan="2"| #
! rowspan="2" | #
! rowspan="2"| Cents*
! rowspan="2" | Cents*
! rowspan="2"| 11-limit ratios
! rowspan="2" | 11-limit ratios
! colspan="3"| 13-limit ratios
! colspan="3" | 13-limit ratios
|-
|-
! Keemum <br>(4&amp;19)
! Keemun <br>(4 & 19)
! Kema <br>(15&amp;19)
! Kema <br>(15 & 19)
! Kumbaya <br>(4&amp;15)
! Kumbaya <br>(4 & 15)
|-
|-
| 0
| 0
Line 25: Line 37:
|-
|-
| 1
| 1
| 317.576
| 317.555
| 6/5
| 6/5
|  
|  
Line 32: Line 44:
|-
|-
| 2
| 2
| 635.151
| 635.109
| 10/7, '''16/11'''
| 10/7, '''16/11'''
|  
|  
Line 39: Line 51:
|-
|-
| 3
| 3
| 952.727
| 952.664
| '''7/4''', 12/7
| '''7/4''', 12/7
| 22/13
| 22/13
Line 46: Line 58:
|-
|-
| 4
| 4
| 70.302
| 70.219
| 21/20, 25/24, 33/32, 36/35
| 21/20, 25/24, 33/32, 36/35
|  
|  
Line 53: Line 65:
|-
|-
| 5
| 5
| 387.878
| 387.773
| '''5/4''', 14/11
| '''5/4''', 14/11
| '''16/13'''
| '''16/13'''
Line 60: Line 72:
|-
|-
| 6
| 6
| 705.453
| 705.328
| '''3/2'''
| '''3/2'''
|  
|  
Line 67: Line 79:
|-
|-
| 7
| 7
| 1023.029
| 1022.882
| 9/5, 20/11
| 9/5, 20/11
|  
|  
Line 74: Line 86:
|-
|-
| 8
| 8
| 140.605
| 140.437
| 12/11, 15/14
| 12/11, 15/14
| 14/13
| 14/13
Line 81: Line 93:
|-
|-
| 9
| 9
| 458.180
| 457.992
| 9/7, 21/16
| 9/7, 21/16
|  
|  
Line 88: Line 100:
|-
|-
| 10
| 10
| 775.756
| 775.546
| 25/16
| 25/16
| 20/13
| 20/13
Line 95: Line 107:
|-
|-
| 11
| 11
| 1093.331
| 1093.101
| 15/8
| 15/8
| 24/13
| 24/13
Line 102: Line 114:
|-
|-
| 12
| 12
| 210.907
| 210.656
| 9/8
| 9/8
|  
|  
Line 109: Line 121:
|-
|-
| 13
| 13
| 528.482
| 528.210
| 15/11
| 15/11
|  
|  
Line 116: Line 128:
|-
|-
| 14
| 14
| 846.058
| 845.765
| 18/11
| 18/11
| 21/13
| 21/13
Line 123: Line 135:
|-
|-
| 15
| 15
| 1163.634
| 1163.320
| 27/14
| 27/14
| 25/13
| 25/13
Line 130: Line 142:
|-
|-
| 16
| 16
| 281.209
| 280.874
|  
|  
| 15/13
| 15/13
Line 137: Line 149:
|-
|-
| 17
| 17
| 598.785
| 598.429
| 45/32
| 45/32
| 18/13
| 18/13
Line 144: Line 156:
|-
|-
| 18
| 18
| 916.360
| 915.984
| 27/16
| 27/16
|  
|  
Line 151: Line 163:
|-
|-
| 19
| 19
| 33.936
| 33.538
| 81/80
| 81/80
|  
|  
Line 157: Line 169:
|  
|  
|}
|}
<nowiki>*</nowiki> In 11-limit CWE tuning, octave reduced


<nowiki>*</nowiki> in 11-limit POTE tuning, octave reduced
== Tunings ==
{| class="wikitable mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | 7-limit norm-based tunings
|-
! rowspan="2" |
! colspan="3" | Euclidean
|-
! Constrained
! Constrained & skewed
! Destretched
|-
! Tenney
| CTE: ~6/5 = 317.3927{{c}}
| CWE: ~6/5 = 316.8293{{c}}
| POTE: ~6/5 = 316.4727{{c}}
|}


== Name ==
{| class="wikitable mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | 11-limit norm-based tunings
|-
! rowspan="2" |
! colspan="3" | Euclidean
|-
! Constrained
! Constrained & skewed
! Destretched
|-
! Tenney
| CTE: ~6/5 = 317.5063{{c}}
| CWE: ~6/5 = 317.5546{{c}}
| POTE: ~6/5 = 317.5756{{c}}
|}


[[Keenanisma#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 [[Wikipedia:Keemun|the famous tea]]<ref>https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_13712#13775</ref>. 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.
=== Tuning spectrum ===
This tuning spectrum assumes undecimal keemun.
{| class="wikitable center-all left-4"
|-
! Edo <br>generator
! [[Eigenmonzo|Eigenmonzo <br>(unchanged interval)]]*
! Generator (¢)
! Comments
|-
| [[4edo|1\4]]
|
| 300.000
| Lower bound of 5- and 7-odd-limit diamond monotone
|-
|
| 7/5
| 308.744
|
|-
|
| 7/6
| 311.043
|
|-
| [[23edo|6\23]]
|
| 313.043
| 23d val
|-
|
| 15/14
| 314.930
|
|-
|
| 9/7
| 315.009
|
|-
|
| 5/3
| 315.641
|
|-
| [[19edo|5\19]]
|
| 315.789
| Lower bound of 9- and 11-odd-limit diamond monotone
|-
|
| 9/5
| 316.799
| 1/7-kleisma
|-
| [[53edo|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
|-
| [[34edo|9\34]]
|
| 317.647
|
|-
|
| 11/9
| 318.042
| 11-odd-limit minimax
|-
|
| 15/11
| 318.227
|
|-
|
| 11/10
| 319.285
|
|-
| [[49edo|13\49]]
|
| 318.367
| 49d val
|-
|
| 11/6
| 318.830
|
|-
| [[15edo|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
|
|-
| [[11edo|3\11]]
|
| 327.273
| 11b val, upper bound of 5- and 7-odd-limit diamond monotone
|}
<nowiki/>* Besides the octave


== Music ==
== Music ==
[http://chrisvaisvil.com/the-fallen-of-kleismic15/ The Fallen of Kleismic15][http://micro.soonlabel.com/53edo/20130903_Kleismic%5b15%5d.mp3 play] by [[Chris Vaisvil]]
; [[Chris Vaisvil]]
* ''The Fallen of Kleismic{{lbrack}}15{{rbrack}}'' – [https://https://www.chrisvaisvil.com/the-fallen-of-kleismic15/ blog] | [https://web.archive.org/web/20240511033402/http://micro.soonlabel.com/53edo/20130903_Kleismic{{lbrack}}15{{rbrack}}.mp3 play] – in [[53edo]]
 
== References ==
<references/>


[[Category:Keemun]]
[[Category:Keemun| ]] <!-- main article -->
[[Category:Rank-2 temperaments]]
[[Category:Kleismic family]]
[[Category:Kleismic family]]
[[Category:Semaphoresmic clan]]
[[Category:Starling temperaments]]
[[Category:Starling temperaments]]
[[Category:Listen]]
[[Category:Listen]]
== References ==
<references/>
{{IoT}}
Retrieved from "https://en.xen.wiki/w/Keemun"