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| Odd limit 2 = 13-limit 21 | Mistuning 2 = 12.8 | Complexity 2 = 34
| Odd limit 2 = 13-limit 21 | Mistuning 2 = 12.8 | Complexity 2 = 34
}}
}}
The '''monkey''' [[regular temperament|temperament]] is one of the [[7-limit]] [[extension]]s of [[tetracot]], the [[5-limit]] temperament [[tempering out]] the [[tetracot comma]] (15625/15552), and is naturally a full [[13-limit]] temperament.  
The '''monkey''' [[regular temperament|temperament]] is one of the [[7-limit]] [[extension]]s of [[tetracot]], the [[5-limit]] temperament [[tempering out]] the [[tetracot comma]] (20000/19683), and is naturally a full [[13-limit]] temperament.  


In addition to the tetracot comma, monkey tempers out [[875/864]], making it a [[keemic temperaments|keemic temperament]]. It also tempers out [[5120/5103]], making it a [[hemifamity temperaments|hemifamity temperament]], so the [[septimal comma]] is equated with the [[syntonic comma]]. At 7 generator steps, this [[diesis (interval region)|diesis-sized]] interval also represents [[40/39]], [[45/44]], [[55/54]], [[65/64]], [[66/65]], and [[121/120]] in the [[2.3.5.7.13 subgroup|2.3.5.7.13-subgroup]] version of tetracot, and divides the [[chromatic semitone]] in four. The same interval is now used to bridge septimal intervals with Pythagorean intervals alike.  
In addition to the tetracot comma, monkey tempers out [[875/864]], making it a [[keemic temperaments|keemic temperament]]. It also tempers out [[5120/5103]], making it a [[hemifamity temperaments|hemifamity temperament]], so the [[septimal comma]] is equated with the [[syntonic comma]]. At 7 generator steps, this [[diesis (interval region)|diesis-sized]] interval also represents [[40/39]], [[45/44]], [[55/54]], [[65/64]], [[66/65]], and [[121/120]] in the [[2.3.5.11.13 subgroup|2.3.5.11.13-subgroup]] version of tetracot, and divides the [[chromatic semitone]] in four. The same interval is now used to bridge septimal intervals with Pythagorean intervals alike.  


Additionally, the generator can be taken to represent [[21/19]], which gives us an extension for prime 19 at -12 generator steps.  
Additionally, the generator can be taken to represent [[21/19]], which gives us an extension for prime 19 at -12 generator steps.  
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In the following tables, odd harmonics 1–13 and their inverses are in '''bold'''.  
In the following tables, odd harmonics 1–13 and their inverses are in '''bold'''.  


{| class="wikitable right-1 right-2"
{| class="wikitable center-1 right-2"
|-
|-
! #
! #
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| 1
| 1
| 175.6
| 175.6
| 11/10, 10/9
| 10/9, 11/10
|-
|-
| 2
| 2
Line 144: Line 144:


== Tunings ==
== 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: ~10/9 = 175.6758{{c}}
| CWE: ~10/9 = 175.6622{{c}}
| POTE: ~10/9 = 175.6588{{c}}
|}
{| 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: ~10/9 = 175.5978{{c}}
| CWE: ~10/9 = 175.5750{{c}}
| POTE: ~10/9 = 175.5703{{c}}
|}
{| class="wikitable mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | 13-limit norm-based tunings
|-
! rowspan="2" |
! colspan="3" | Euclidean
|-
! Constrained
! Constrained & skewed
! Destretched
|-
! Tenney
| CTE: ~10/9 = 175.6185{{c}}
| CWE: ~10/9 = 175.6217{{c}}
| POTE: ~10/9 = 175.6224{{c}}
|}
=== Tuning spectrum ===
=== Tuning spectrum ===
{| class="wikitable center-all left-3"
{| class="wikitable center-all left-4"
|-
|-
! [[Eigenmonzo|Eigenmonzo<br>(unchanged-interval)]]
! Edo<br>generator
! [[Eigenmonzo|Eigenmonzo<br>(unchanged-interval)]]*
! Generator (¢)
! Generator (¢)
! Comments
! Comments
|-
|-
|
| 11/10
| 11/10
| 165.004
| 165.004
|  
|  
|-
|-
| 1\7
|
| 171.429
|
|-
|
| 11/9
| 11/9
| 173.704
| 173.704
|  
|  
|-
|-
| 14/13
|  
| 13/7
| 174.746
| 174.746
|  
|  
|-
|-
| 12/11
|  
| 11/6
| 174.894
| 174.894
|  
|  
|-
|-
| 7\48
|
| 175.000
| Lower bound of 7-, 9-, 11-, and 13-odd-limit diamond monotone
|-
|
| 11/8
| 11/8
| 175.132
| 175.132
|  
|  
|-
|-
| 14/11
|  
| 11/7
| 175.300
| 175.300
| 11-odd-limit minimax
| 11-odd-limit minimax
|-
|-
| 8/7
|  
| 7/4
| 175.412
| 175.412
|  
|  
|-
|-
|
| 7/6
| 7/6
| 175.428
| 175.428
|  
|  
|-
|-
|
| 9/7
| 9/7
| 175.438
| 175.438
|  
|  
|-
|-
| 4/3
|  
| 3/2
| 175.489
| 175.489
|  
|  
|-
|-
| 6\41
|
| 175.610
| 15-odd-limit diamond monotone (singleton)
|-
|
| 15/14
| 15/14
| 175.694
| 175.694
|  
|  
|-
|-
|
| 7/5
| 7/5
| 175.729
| 175.729
| 7, 9, 13 and 15-odd-limit minimax
| 7-, 9-, 13- and 15-odd-limit minimax
|-
|-
|
| 13/11
| 13/11
| 175.899
| 175.899
|  
|  
|-
|-
| 16/15
|  
| 15/8
| 176.021
| 176.021
|  
|  
|-
|-
|
| 5/4
| 5/4
| 176.257
| 176.257
| 5-odd-limit minimax
| 5-odd-limit minimax
|-
|-
| 18/13
|  
| 13/9
| 176.338
| 176.338
|  
|  
|-
|-
| 5\34
|
| 176.471
| Upper bound of 7-, 9-, 11-, and 13-odd-limit diamond monotone
|-
|
| 15/13
| 15/13
| 176.516
| 176.516
|  
|  
|-
|-
| 6/5
|  
| 5/3
| 176.872
| 176.872
|  
|  
|-
|-
|
| 13/10
| 13/10
| 176.890
| 176.890
|  
|  
|-
|-
|
| 13/12
| 13/12
| 176.905
| 176.905
|  
|  
|-
|-
| 4\27
|
| 177.778
| 27de val
|-
|
| 15/11
| 15/11
| 178.984
| 178.984
|  
|  
|-
|-
| 16/13
|  
| 13/8
| 179.736
| 179.736
|  
|  
|-
|-
| 10/9
| 3\20
|
| 180.000
| 20cdde val
|-
|
| 9/5
| 182.404
| 182.404
|  
|  
|}
|}
<nowiki/>* Besides the octave


[[Category:Monkey| ]] <!-- main article -->
[[Category:Monkey| ]] <!-- main article -->
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[[Category:Tetracot family]]
[[Category:Tetracot family]]
[[Category:Keemic temperaments]]
[[Category:Keemic temperaments]]
[[Category:Hemifamity temperaments]]
[[Category:Aberschismic temperaments]]
Retrieved from "https://en.xen.wiki/w/Monkey"