Xenharmonic Wiki

Monkey: Difference between revisions

← Older editNewer edit →
VisualWikitext
mNo edit summary
Birth
Tag: Removed redirect
Line 1: Line 1:
#redirect [[Tetracot family #Monkey]]
{{Infobox regtemp
| Title = Monkey
| Subgroups = 2.3.5.7, 2.3.5.7.11, 2.3.5.7.11.13
| Comma basis = [[875/864]], [[5120/5103]] (7-limit);<br>[[100/99]], [[243/242]], [[385/384]] (11-limit)<br>[[100/99]], [[144/143]], [[243/242]], [[385/384]]<br>(13-limit)
| Edo join 1 = 41 | Edo join 2 = 48
| Mapping = 1; 4 9 -15 10 -2
| Generators = 10/9
| Generators tuning = 175.6
| Optimization method = CWE
| MOS scales = [[6L 1s]], [[7L 6s]], [[7L 13s]], [[7L 20s]]
| Odd limit 1 = 9 | Mistuning 1 = 6.68 | Complexity 1 = 27
| 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.


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.
Additionally, the generator can be taken to represent [[21/19]], which gives us an extension for prime 19 at -12 generator steps.
See [[Tetracot family #Monkey]] for technical data.
== Interval chain ==
In the following tables, odd harmonics 1–13 and their inverses are in '''bold'''.
{| class="wikitable right-1 right-2"
|-
! #
! Cents*
! Approximate ratios
|-
| 0
| 0.00
| '''1/1'''
|-
| 1
| 175.62
| 11/10, 10/9
|-
| 2
| 351.24
| 11/9, '''16/13'''
|-
| 3
| 526.87
| 15/11
|-
| 4
| 702.49
| '''3/2'''
|-
| 5
| 878.11
| 5/3
|-
| 6
| 1053.73
| 11/6, 24/13
|-
| 7
| 29.36
| 55/54, 45/44, 40/39
|-
| 8
| 204.98
| 9/8
|-
| 9
| 380.60
| '''5/4'''
|-
| 10
| 556.22
| '''11/8''', 18/13
|-
| 11
| 731.85
| 20/13
|-
| 12
| 907.47
| 22/13
|-
| 13
| 1083.09
| 13/7, 15/8
|-
| 14
| 58.71
| 33/32, 27/26, 25/24
|-
| 15
| 234.34
| '''8/7''', 15/13
|-
| 16
| 409.96
|
|-
| 17
| 585.58
| 45/32
|-
| 18
| 761.20
|
|-
| 19
| 936.83
| 12/7
|-
| 20
| 1112.45
|
|-
| 21
| 88.07
|
|-
| 22
| 263.69
|
|-
| 23
| 439.31
| 9/7
|-
| 24
| 614.94
| 10/7
|-
| 25
| 790.56
| 11/7
|-
| 26
| 966.18
|
|-
| 27
| 1141.80
| 27/14
|-
| 28
| 117.43
| 15/14
|}
<nowiki/>* in 13-limit POTE tuning
== Tunings ==
=== Tuning spectrum ===
{| class="wikitable center-all left-3"
|-
! [[Eigenmonzo|Eigenmonzo<br>(unchanged-interval)]]
! Generator (¢)
! Comments
|-
| 11/10
| 165.004
|
|-
| 11/9
| 173.704
|
|-
| 14/13
| 174.746
|
|-
| 12/11
| 174.894
|
|-
| 11/8
| 175.132
|
|-
| 14/11
| 175.300
| 11-odd-limit minimax
|-
| 8/7
| 175.412
|
|-
| 7/6
| 175.428
|
|-
| 9/7
| 175.438
|
|-
| 4/3
| 175.489
|
|-
| 15/14
| 175.694
|
|-
| 7/5
| 175.729
| 7, 9, 13 and 15-odd-limit minimax
|-
| 13/11
| 175.899
|
|-
| 16/15
| 176.021
|
|-
| 5/4
| 176.257
| 5-odd-limit minimax
|-
| 18/13
| 176.338
|
|-
| 15/13
| 176.516
|
|-
| 6/5
| 176.872
|
|-
| 13/10
| 176.890
|
|-
| 13/12
| 176.905
|
|-
| 15/11
| 178.984
|
|-
| 16/13
| 179.736
|
|-
| 10/9
| 182.404
|
|}
[[Category:Monkey| ]] <!-- main article -->
[[Category:Rank-2 temperaments]]
[[Category:Rank-2 temperaments]]
[[Category:Tetracot family]]
[[Category:Tetracot family]]
[[Category:Keemic temperaments]]
[[Category:Keemic temperaments]]
[[Category:Hemifamity temperaments]]
[[Category:Hemifamity temperaments]]
Retrieved from "https://en.xen.wiki/w/Monkey"