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'''Cotoneum temperament''' is temperament for the 7, 11, 13, 17, and 19 [[Harmonic limit|prime limits]]. It is a member of [[hemimage temperaments]], [[quince clan]], and [[garischismic clan]]. [[217edo|217EDO]] is an excellent tuning for cotoneum, with a fifth generator of 127\217, and MOS of 12, 17, 29, 41, 53, 94, 135, or 176 notes are available.
'''Cotoneum temperament''' is temperament for the 7, 11, 13, 17, and 19 [[Harmonic limit|prime limits]]. It is a member of [[hemimage temperaments]], [[quince clan]], and [[garischismic clan]]. [[217edo|217EDO]] is an excellent tuning for cotoneum, with a fifth generator of 127\217, and MOS of 12, 17, 29, 41, 53, 94, 135, or 176 notes are available.


See [[Hemimage temperaments #Cotoneum]] for more technical data.
== Temperament data ==
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Cotoneum Temperament (41&amp;176)</div>
<div class="mw-collapsible-content">
Subgroup: 2.3.5.7.11.13.17.19
 
[[Comma list]]: 343/342, 364/363, 441/440, 595/594, 1216/1215, 1729/1728
 
[[Mapping]]: [{{val| 1 2 -18 -3 13 29 41 -14 }}, {{val| 0 -1 49 14 -23 -61 -89 44 }}]
 
[[POTE generator]]:
* 7-limit: ~4/3 = 497.68302
* 11-limit: ~4/3 = 497.69730
* 13-limit: ~4/3 = 497.69399
* 17-limit: ~4/3 = 497.69334
* 19-limit: ~4/3 = 497.69225
 
[[TOP tuning|TOP generator]]s:
* 7-limit: ~2 = 1200.03878, ~4/3 = 497.69910
* 11-limit: ~2 = 1199.86324, ~4/3 = 497.64058
* 13-limit: ~2 = 1199.89014, ~4/3 = 497.64843
* 17-limit: ~2 = 1199.89426, ~4/3 = 497.64949
* 19-limit: ~2 = 1199.87700, ~4/3 = 497.64124
 
[[Diamond monotone]] ranges:
* 7-odd-limit: ~4/3 = [497.14286, 498.46154] (29\70 to 27\65)
* 9-odd-limit: ~4/3 = [497.14286, 498.11321] (29\70 to 22\53)
* 11-odd-limit: ~4/3 = [497.56098, 497.87234] (17\41 to 39\94)
* 13 and 15-odd-limit: ~4/3 = [497.56098, 497.77778] (17\41 to 56\135)
* 17, 19, and 21-odd-limit: ~4/3 = [497.56098, 497.72727] (17\41 to 73\176)
 
[[Diamond tradeoff]] ranges:
* 7, 9, 11, and 13-odd-limit: ~4/3 = [497.64251, 498.04500]
* 15 and 17-odd-limit: ~4/3 = [497.63067, 498.04500]
* 19 and 21-odd-limit: ~4/3 = [497.62290, 498.04500]
 
Diamond monotone and tradeoff ranges:
* 7 and 9-odd-limit: [497.64251, 498.04500]
* 11-odd-limit: [497.64251, 497.87234]
* 13-odd-limit: [497.64251, 497.77778]
* 15-odd-limit: [497.63067, 497.77778]
* 17-odd-limit: [497.63067, 497.72727]
* 19 and 21-odd-limit: [497.62290, 497.72727]
 
[[Val]]s:
* 7-limit: {{Val list| 41, 176, 217, 258, 475 }}
* 11, 13, 17, and 19-limit: {{Val list| 41, 176, 217 }}
 
[[Badness]]:
* 7-limit: 0.105632
* 11-limit: 0.050966
* 13-limit: 0.036951
* 17-limit: 0.029495
* 19-limit: 0.021811
</div></div>


== Interval chain ==
== Interval chain ==
Line 574: Line 628:
{| class="wikitable center-all"
{| class="wikitable center-all"
|-
|-
! ET <br>generator
! [[eigenmonzo|eigenmonzo<br>(unchanged interval]])
! [[eigenmonzo|eigenmonzo<br>(unchanged interval]])
! fifth<br>(¢)
! fifth<br>(¢)
! comments
! comments
|-
|-
|
| 4/3
| 4/3
| 701.9550
| 701.9550
|  
|  
|-
|-
|
| 9/7
| 9/7
| 702.1928
| 702.1928
|  
|  
|-
|-
|
| 7/6
| 7/6
| 702.2086
| 702.2086
|  
|  
|-
|-
| 79\135
|
| 702.2222
|
|-
|
| 8/7
| 8/7
| 702.2267
| 702.2267
|  
|  
|-
|-
|
| 14/11
| 14/11
| 702.2295
| 702.2295
|  
|  
|-
|-
|
| 11/8
| 11/8
| 702.2312
| 702.2312
|  
|  
|-
|-
|
| 22/21
| 22/21
| 702.2371
| 702.2371
|  
|  
|-
|-
|
| 20/19
| 20/19
| 702.2399
| 702.2399
|  
|  
|-
|-
|
| 12/11
| 12/11
| 702.2438
| 702.2438
|  
|  
|-
|-
|
| 21/16
| 21/16
| 702.2476
| 702.2476
|  
|  
|-
|-
|
| 11/9
| 11/9
| 702.2575
| 702.2575
|  
|  
|-
|-
| 103\176
|
| 702.2727
|
|-
|
| 14/13
| 14/13
| 702.2894
| 702.2894
|  
|  
|-
|-
|
| 11/10
| 11/10
| 702.2917
| 702.2917
| 11 and 13-odd-limit minimax
| 11 and 13-odd-limit minimax
|-
|-
|
| 17/14
| 17/14
| 702.2925
| 702.2925
|  
|  
|-
|-
|
| 26/21
| 26/21
| 702.2939
| 702.2939
|  
|  
|-
|-
|
| 22/19
| 22/19
| 702.2956
| 702.2956
|  
|  
|-
|-
|
| 21/17
| 21/17
| 702.2958
| 702.2958
|  
|  
|-
|-
|
| 15/11
| 15/11
| 702.2965
| 702.2965
| 15, 17, 19, and 21-odd-limit minimax  
| 15, 17, 19, and 21-odd-limit minimax  
|-
|-
|
| 17/13
| 17/13
| 702.3010
| 702.3010
|  
|  
|-
|-
|
| 17/16
| 17/16
| 702.3029
| 702.3029
|  
|  
|-
|-
|
| 16/13
| 16/13
| 702.3037
| 702.3037
|  
|  
|-
|-
| 127\217
|
| 702.3041
|
|-
|
| 10/9
| 10/9
| 702.3058
| 702.3058
| 9-odd-limit minimax
| 9-odd-limit minimax
|-
|-
|
| 24/17
| 24/17
| 702.3068
| 702.3068
|  
|  
|-
|-
|
| 20/17
| 20/17
| 702.3090
| 702.3090
|  
|  
|-
|-
|
| 13/12
| 13/12
| 702.3095
| 702.3095
|  
|  
|-
|-
|
| 18/17
| 18/17
| 702.3109
| 702.3109
|  
|  
|-
|-
|
| 13/10
| 13/10
| 702.3110
| 702.3110
|  
|  
|-
|-
|
| 19/15
| 19/15
| 702.3111
| 702.3111
|  
|  
|-
|-
|
| 17/15
| 17/15
| 702.3116
| 702.3116
|  
|  
|-
|-
|
| 19/17
| 19/17
| 702.3116
| 702.3116
|  
|  
|-
|-
|
| 6/5
| 6/5
| 702.3128
| 702.3128
| 5 and 7-odd-limit minimax
| 5 and 7-odd-limit minimax
|-
|-
|
| 19/18
| 19/18
| 702.3130
| 702.3130
|  
|  
|-
|-
|
| 15/13
| 15/13
| 702.3143
| 702.3143
|  
|  
|-
|-
|
| 26/19
| 26/19
| 702.3144
| 702.3144
|  
|  
|-
|-
|
| 18/13
| 18/13
| 702.3156
| 702.3156
|  
|  
|-
|-
|
| 5/4
| 5/4
| 702.3201
| 702.3201
|  
|  
|-
|-
|
| 24/19
| 24/19
| 702.3209
| 702.3209
|  
|  
|-
|-
| 151\258
|
| 702.2727
|
|-
|
| 16/15
| 16/15
| 702.3277
| 702.3277
|  
|  
|-
|-
|
| 22/17
| 22/17
| 702.3278
| 702.3278
|  
|  
|-
|-
|
| 19/16
| 19/16
| 702.3292
| 702.3292
|  
|  
|-
|-
| 175\299
|
| 702.3411
|
|-
|
| 21/20
| 21/20
| 702.3463
| 702.3463
|  
|  
|-
|-
|
| 13/11
| 13/11
| 702.3476
| 702.3476
|  
|  
|-
|-
|
| 7/5
| 7/5
| 702.3575
| 702.3575
|  
|  
|-
|-
|
| 21/19
| 21/19
| 702.3635
| 702.3635
|  
|  
|-
|-
|
| 15/14
| 15/14
| 702.3693
| 702.3693
|  
|  
|-
|-
|
| 19/14
| 19/14
| 702.3771
| 702.3771
|
|-
| 24\41
|
| 702.4390
|  
|  
|}
|}
Line 848: Line 825:
* [[Cotoneum41]] - proper [[12L 29s]]
* [[Cotoneum41]] - proper [[12L 29s]]
* [[Cotoneum53]] - improper [[41L 12s]]
* [[Cotoneum53]] - improper [[41L 12s]]
* [[Cotoneum94]] - improper [[41L 53s]]
* [[Cotoneum135]] - [[41L 94s]] scale. The boundary of propriety is [[176edo|176EDO]].
* [[Cotoneum176]] - [[41L 135s]] scale. The boundary of propriety is [[217edo|217EDO]].


[[Category:Hemimage temperaments]]
[[Category:Hemimage temperaments]]
Retrieved from "https://en.xen.wiki/w/Cotoneum"