183edo: Difference between revisions

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m Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"
 
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Infobox ET}}
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
The '''183 equal divisions of the octave''' ('''183edo'''), or the '''183(-tone) equal temperament''' ('''183tet''', '''183et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 183 [[equal]] parts of about 6.56 [[cent]]s each, a size close to [[243/242]], the rastma.  
: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-06-23 16:58:34 UTC</tt>.<br>
: The original revision id was <tt>238459661</tt>.<br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<h4>Original Wikitext content:</h4>
<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">//183edo// divides the octave into 183 equal parts of 6.557 [[cent]]s each. It is notable as a higher limit system, especially when 7 is left out of the picture. It tempers out the [[schisma]], 32805/32768, in the [[5-limit]]. In the [[7-limi]]t, it tempers out 6144/6125, 19683/19600 and the no-twos comma defining the [[Mirkwai clan]], 16875/16807. In the [[11-limit]] it tempers out 540/539 and 3025/3024; in the [[13-limit]], 351/350 and 676/675; in the [[17-limit]] 442/441, 561/560 and 715/714; and in the [[19-limit]] 456/455. It is the [[optimal patent val]] for 13-, 17- and 19-limit [[Mirkwai clan|mirkat temperament]], the 72&amp;183 temperament, and an excellent tuning for the [[rank-three temperament]]s [[The Archipelago|madagascar and borneo]].


As a no-sevens temperament, it tempers out 32805/32768, 5632/5625, 8019/8000, 676/675, 4425/4424, 6656/6655, 936/935, 1089/1088, and 1377/1375.</pre></div>
== Theory ==
<h4>Original HTML content:</h4>
183edo is notable as a higher-limit system, [[consistency|distinctly consistent]] in the [[17-odd-limit]], or the no-19 no-31 [[33-odd-limit]]. It has especially low errors in ''all'' [[prime limit]]s from 11 to 29, although its bad rendering of [[19/1|19]] makes it fail to be consistent in the [[19-odd-limit]]. It is however a strong no-19's [[29-limit]] system with the addition of an essentially perfectly accurate prime [[43/1|43]].
<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;183edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;em&gt;183edo&lt;/em&gt; divides the octave into 183 equal parts of 6.557 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s each. It is notable as a higher limit system, especially when 7 is left out of the picture. It tempers out the &lt;a class="wiki_link" href="/schisma"&gt;schisma&lt;/a&gt;, 32805/32768, in the &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt;. In the &lt;a class="wiki_link" href="/7-limi"&gt;7-limi&lt;/a&gt;t, it tempers out 6144/6125, 19683/19600 and the no-twos comma defining the &lt;a class="wiki_link" href="/Mirkwai%20clan"&gt;Mirkwai clan&lt;/a&gt;, 16875/16807. In the &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt; it tempers out 540/539 and 3025/3024; in the &lt;a class="wiki_link" href="/13-limit"&gt;13-limit&lt;/a&gt;, 351/350 and 676/675; in the &lt;a class="wiki_link" href="/17-limit"&gt;17-limit&lt;/a&gt; 442/441, 561/560 and 715/714; and in the &lt;a class="wiki_link" href="/19-limit"&gt;19-limit&lt;/a&gt; 456/455. It is the &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt; for 13-, 17- and 19-limit &lt;a class="wiki_link" href="/Mirkwai%20clan"&gt;mirkat temperament&lt;/a&gt;, the 72&amp;amp;183 temperament, and an excellent tuning for the &lt;a class="wiki_link" href="/rank-three%20temperament"&gt;rank-three temperament&lt;/a&gt;s &lt;a class="wiki_link" href="/The%20Archipelago"&gt;madagascar and borneo&lt;/a&gt;.&lt;br /&gt;
 
&lt;br /&gt;
As an equal temperament, 183et [[tempering out|tempers out]] the [[schisma]] in the [[5-limit]]. In the [[7-limit]], it tempers out porwell, [[6144/6125]], cataharry, [[19683/19600]] and mirkwai, [[16875/16807]]. In the [[11-limit]], it tempers out [[540/539]], 1375/1372, [[3025/3024]], [[5632/5625]], and [[8019/8000]]; in the [[13-limit]], [[351/350]], [[676/675]], [[729/728]], [[1001/1000]], [[1573/1568]], [[2080/2079]], [[4096/4095]], [[4225/4224]], and [[6656/6655]]; in the [[17-limit]] [[442/441]], [[561/560]], [[715/714]], [[936/935]], [[1089/1088]], and [[1156/1155]]; and in the [[19-limit]] [[456/455]]. It is the [[optimal patent val]] for 13- and 17-limit [[mirkat]], the {{nowrap|72 &amp; 111}} temperament, and an excellent tuning for the [[rank-3 temperament]]s [[madagascar]] and [[borneo]]. It allows [[essentially tempered chord]] including [[ratwolfsmic chords]], [[swetismic chords]], [[squbemic chords]], [[sinbadmic chords]], and [[lambeth chords]] in the 13-odd-limit, in addition to [[island chords]] in the 15-odd-limit.  
As a no-sevens temperament, it tempers out 32805/32768, 5632/5625, 8019/8000, 676/675, 4425/4424, 6656/6655, 936/935, 1089/1088, and 1377/1375.&lt;/body&gt;&lt;/html&gt;</pre></div>
 
It is even stronger if 7 is left out of the picture. As a no-7 temperament, it tempers out 5632/5625, 8019/8000, 676/675, 4225/4224, 6656/6655, 936/935, 1089/1088, and 1377/1375.
 
=== Prime harmonics ===
{{Harmonics in equal|183|columns=11}}
{{Harmonics in equal|183|columns=11|start=12|collapsed=true|title=Approximation of prime harmonics in 183edo (continued)}}
 
=== Subsets and supersets ===
Since 183 factors into primes as {{nowrap| 3 × 61 }}, 183edo contains [[3edo]] and [[61edo]] as its subsets.
 
== Approximation to JI ==
=== Interval mappings ===
{{Q-odd-limit intervals}}
 
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
|-
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.3
| {{monzo| -290 183 }}
| {{mapping| 183 290 }}
| +0.0996
| 0.100
| 1.52
|-
| 2.3.5
| 32805/32768, {{val| 10 23 -20 }}
| {{mapping| 183 290 425 }}
| −0.0157
| 0.182
| 2.78
|-
| 2.3.5.7
| 6144/6125, 16875/16807, 19683/19600
| {{mapping| 183 290 425 514 }}
| −0.1601
| 0.296
| 4.51
|-
| 2.3.5.7.11
| 540/539, 1375/1372, 5632/5625, 8019/8000
| {{mapping| 183 290 425 514 633 }}
| −0.0993
| 0.291
| 4.44
|-
| 2.3.5.7.11.13
| 351/350, 540/539, 676/675, 1375/1372, 4096/4095
| {{mapping| 183 290 425 514 633 677 }}
| −0.0295
| 0.308
| 4.70
|-
| 2.3.5.7.11.13.17
| 351/350, 442/441, 540/539, 561/560, 1375/1372, 4096/4095
| {{mapping| 183 290 425 514 633 677 748 }}
| −0.0240
| 0.286
| 4.36
|}
* 183et has lower absolute errors in the 13-, 17-, 19-, and 23-limit than any previous equal temperaments, after [[130edo|130]], [[171edo|171]], [[161edo|161]], and [[159edo|159]], respectively. In the 13-, 19-, and 23-limit it is superseded by [[190edo|190g]]. In the 17-limit, where it is the strongest, by [[217edo|217]].
 
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|-
! Periods<br>per 8ve
! Generator*
! Cents*
! Associated<br>ratio*
! Temperaments
|-
| 1
| 10\183
| 65.57
| 27/26
| [[Luminal]]
|-
| 1
| 16\183
| 104.92
| 17/16
| [[Septendesemi]]
|-
| 1
| 17\183
| 111.48
| 16/15
| [[Stockhausenic]]
|-
| 1
| 38\183
| 249.18
| 15/13
| [[Hemischis]]
|-
| 1
| 58\183
| 380.33
| 56/45
| [[Quanharuk]]
|-
| 1
| 59\183
| 386.89
| 5/4
| [[Grendel]]
|-
| 1
| 76\183
| 498.36
| 4/3
| [[Helmholtz (temperament)|Helmholtz]]
|-
| 1
| 77\183
| 504.92
| 104976/78125
| [[Countermeantone]]
|-
| 3
| 21\183
| 137.70
| 13/12
| [[Avicenna]]
|-
| 3
| 24\183
| 157.38
| 35/32
| [[Nessafof]]
|-
| 3
| 28\183
| 183.61
| 10/9
| [[Mirkat]]
|-
| 3
| 38\183<br>(23\183)
| 249.18<br>(150.82)
| 15/13<br>(12/11)
| [[Hemiterm]]
|-
| 3
| 76\183<br>(15\183)
| 498.36<br>(98.36)
| 4/3<br>(200/189)
| [[Term]] / terminator
|-
| 61
| 38\183<br>(2\183)
| 249.18<br>(13.11)
| 13750/11907<br>(?)
| [[Promethium]]
|}
<nowiki/>* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct
 
== Music ==
; [[birdshite stalactite]]
* from ''meticulous clutter'' (2022)
** "cursed owl windchimes" – [https://open.spotify.com/track/0A9z6gw5HuNWS7eYjvtCa1 Spotify] | [https://birdshitestalactite.bandcamp.com/track/cursed-owl-windchimes Bandcamp] | [https://www.youtube.com/watch?v=vyTbwHhdoXE YouTube] – madagascar[19] in 183edo tuning
** "octopus bones" – [https://open.spotify.com/track/6TUm7uXjVaO6MGACWswoL7 Spotify] | [https://birdshitestalactite.bandcamp.com/track/octopus-bones Bandcamp] | [https://www.youtube.com/watch?v=ej80dEpC-DQ YouTube] – madagascar[19] in 183edo tuning and parakleismic[19] in 61edo tuning
* "lemon drizzle" from ''tropical nosebleed'' (2023) – [https://open.spotify.com/track/3dBXs1KjzTjSWJ7KF4BjlK Spotify] | [https://birdshitestalactite.bandcamp.com/track/lemon-drizzle Bandcamp] | [https://www.youtube.com/watch?v=VJ_bAvWB8W0 YouTube]
 
[[Category:Borneo]]
[[Category:Madagascar]]
[[Category:Mirkat]]
[[Category:Listen]]