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Monkey: Difference between revisions

VisualWikitext
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**Imported revision 246786179 - Original comment: **
 
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Infobox regtemp
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| Title = Monkey
: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-08-18 16:22:56 UTC</tt>.<br>
| Subgroups = 2.3.5.7, 2.3.5.7.11, 2.3.5.7.11.13
: The original revision id was <tt>246786179</tt>.<br>
| 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)
: The revision comment was: <tt></tt><br>
| Edo join 1 = 41 | Edo join 2 = 48
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| Mapping = 1; 4 9 -15 10 -2
<h4>Original Wikitext content:</h4>
| Generators = 10/9
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">See [[Tetracot family#Monkey]].</pre></div>
| Generators tuning = 175.6
<h4>Original HTML content:</h4>
| Optimization method = CWE
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Monkey&lt;/title&gt;&lt;/head&gt;&lt;body&gt;See &lt;a class="wiki_link" href="/Tetracot%20family#Monkey"&gt;Tetracot family&lt;/a&gt;.&lt;/body&gt;&lt;/html&gt;</pre></div>
| 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]] (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 [[2.3.5.11.13 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.
 
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 center-1 right-2"
|-
! #
! Cents*
! Approximate ratios
|-
| 0
| 0.0
| '''1/1'''
|-
| 1
| 175.6
| 10/9, 11/10
|-
| 2
| 351.2
| 11/9, '''16/13'''
|-
| 3
| 526.9
| 15/11
|-
| 4
| 702.5
| '''3/2'''
|-
| 5
| 878.1
| 5/3
|-
| 6
| 1053.7
| 11/6, 24/13
|-
| 7
| 29.4
| 40/39, 45/44, 55/54, 64/63
|-
| 8
| 205.0
| '''9/8'''
|-
| 9
| 380.6
| '''5/4'''
|-
| 10
| 556.2
| '''11/8''', 18/13
|-
| 11
| 731.8
| 20/13, 32/21
|-
| 12
| 907.5
| 22/13
|-
| 13
| 1083.1
| 13/7, 15/8
|-
| 14
| 58.7
| 25/24, 27/26, 33/32, 36/35
|-
| 15
| 234.3
| '''8/7''', 15/13
|-
| 16
| 409.9
| 33/26
|-
| 17
| 585.6
| 45/32, 88/63
|-
| 18
| 761.2
| 25/16, 54/35
|-
| 19
| 936.8
| 12/7
|-
| 20
| 1112.4
| 40/21
|-
| 21
| 88.1
| 22/21
|-
| 22
| 263.7
| 75/64, 81/70
|-
| 23
| 439.3
| 9/7
|-
| 24
| 614.9
| 10/7
|-
| 25
| 790.5
| 11/7
|-
| 26
| 966.2
| 225/128, 243/140, 256/147
|-
| 27
| 1141.8
| 27/14
|}
<nowiki/>* In 13-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: ~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 ===
{| class="wikitable center-all left-4"
|-
! Edo<br>generator
! [[Eigenmonzo|Eigenmonzo<br>(unchanged-interval)]]*
! Generator (¢)
! Comments
|-
|
| 11/10
| 165.004
|
|-
| 1\7
|
| 171.429
|
|-
|
| 11/9
| 173.704
|
|-
|
| 13/7
| 174.746
|
|-
|
| 11/6
| 174.894
|
|-
| 7\48
|
| 175.000
| Lower bound of 7-, 9-, 11-, and 13-odd-limit diamond monotone
|-
|
| 11/8
| 175.132
|
|-
|
| 11/7
| 175.300
| 11-odd-limit minimax
|-
|
| 7/4
| 175.412
|
|-
|
| 7/6
| 175.428
|
|-
|
| 9/7
| 175.438
|
|-
|
| 3/2
| 175.489
|
|-
| 6\41
|
| 175.610
| 15-odd-limit diamond monotone (singleton)
|-
|
| 15/14
| 175.694
|
|-
|
| 7/5
| 175.729
| 7-, 9-, 13- and 15-odd-limit minimax
|-
|
| 13/11
| 175.899
|
|-
|
| 15/8
| 176.021
|
|-
|
| 5/4
| 176.257
| 5-odd-limit minimax
|-
|
| 13/9
| 176.338
|
|-
| 5\34
|
| 176.471
| Upper bound of 7-, 9-, 11-, and 13-odd-limit diamond monotone
|-
|
| 15/13
| 176.516
|
|-
|
| 5/3
| 176.872
|
|-
|
| 13/10
| 176.890
|
|-
|
| 13/12
| 176.905
|
|-
| 4\27
|
| 177.778
| 27de val
|-
|
| 15/11
| 178.984
|
|-
|
| 13/8
| 179.736
|
|-
| 3\20
|
| 180.000
| 20cdde val
|-
|
| 9/5
| 182.404
|
|}
<nowiki/>* Besides the octave
 
[[Category:Monkey| ]] <!-- main article -->
[[Category:Rank-2 temperaments]]
[[Category:Tetracot family]]
[[Category:Keemic temperaments]]
[[Category:Aberschismic temperaments]]
Retrieved from "https://en.xen.wiki/w/Monkey"