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'''Keemun''' 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.
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{| 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
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|-
|-
| 1
| 1
| 317.576
| 317.555
| 6/5
| 6/5
|  
|  
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|-
|-
| 2
| 2
| 635.151
| 635.109
| 10/7, '''16/11'''
| 10/7, '''16/11'''
|  
|  
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|-
|-
| 3
| 3
| 952.727
| 952.664
| '''7/4''', 12/7
| '''7/4''', 12/7
| 22/13
| 22/13
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|-
|-
| 4
| 4
| 70.302
| 70.219
| 21/20, 25/24, 33/32, 36/35
| 21/20, 25/24, 33/32, 36/35
|  
|  
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|-
|-
| 5
| 5
| 387.878
| 387.773
| '''5/4''', 14/11
| '''5/4''', 14/11
| '''16/13'''
| '''16/13'''
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|-
|-
| 6
| 6
| 705.453
| 705.328
| '''3/2'''
| '''3/2'''
|  
|  
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|-
|-
| 7
| 7
| 1023.029
| 1022.882
| 9/5, 20/11
| 9/5, 20/11
|  
|  
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|-
|-
| 8
| 8
| 140.605
| 140.437
| 12/11, 15/14
| 12/11, 15/14
| 14/13
| 14/13
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|-
|-
| 9
| 9
| 458.180
| 457.992
| 9/7, 21/16
| 9/7, 21/16
|  
|  
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|-
|-
| 10
| 10
| 775.756
| 775.546
| 25/16
| 25/16
| 20/13
| 20/13
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|-
|-
| 11
| 11
| 1093.331
| 1093.101
| 15/8
| 15/8
| 24/13
| 24/13
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|-
|-
| 12
| 12
| 210.907
| 210.656
| 9/8
| 9/8
|  
|  
Line 107: Line 121:
|-
|-
| 13
| 13
| 528.482
| 528.210
| 15/11
| 15/11
|  
|  
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|-
|-
| 14
| 14
| 846.058
| 845.765
| 18/11
| 18/11
| 21/13
| 21/13
Line 121: Line 135:
|-
|-
| 15
| 15
| 1163.634
| 1163.320
| 27/14
| 27/14
| 25/13
| 25/13
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|-
|-
| 16
| 16
| 281.209
| 280.874
|  
|  
| 15/13
| 15/13
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|-
|-
| 17
| 17
| 598.785
| 598.429
| 45/32
| 45/32
| 18/13
| 18/13
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|-
|-
| 18
| 18
| 916.360
| 915.984
| 27/16
| 27/16
|  
|  
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|-
|-
| 19
| 19
| 33.936
| 33.538
| 81/80
| 81/80
|  
|  
|  
|  
|  
|  
|}
<nowiki>*</nowiki> In 11-limit CWE 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}}
|}
|}


<nowiki>*</nowiki> in 11-limit POTE tuning, octave reduced
{| 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}}
|}
 
=== 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:Temperament]]
[[Category:Keemun| ]] <!-- main article -->
[[Category:Keemun]]
[[Category:Rank-2 temperaments]]
[[Category:Kleismic family]]
[[Category:Kleismic family]]
[[Category:Starling]]
[[Category:Semaphoresmic clan]]
[[Category:Starling temperaments]]
[[Category:Listen]]
[[Category:Listen]]
Retrieved from "https://en.xen.wiki/w/Keemun"