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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
In [[regular temperament theory]], an '''associated temperament''' to a [[harmonic limit|''p''-limit]] [[comma]] is a ''p''-limit [[regular temperament]] [[tempering out]] that comma which shares the same [[optimal patent val]] as the [[codimension]]-1 temperament tempering out that comma. By definition, the optimal patent val defines the unique [[ET|rank-1]] associated temperament. For [[rank-2 temperament]]s, it is possible for more than one temperament to be associated, and some of these are listed below. The column headings are the comma being associated, the optimal patent val (OPV), the rank-2 temperament, and a [[comma basis]] for the rank-2 temperament.
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-02-07 10:49:00 UTC</tt>.<br>
: The original revision id was <tt>299301048</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">


=7 limit=
== 7-limit ==
|| Comma || OPV || Temperament || Basis ||
{| class="wikitable"
|| 64/63 || [[49edo]] || [[superpyth]] || 64/63, 245/243 ||
|-
|| 875/864 || [[41edo]] || [[magic]] || 225/224, 245/243 ||
! Comma
|| 3125/3087 || [[94edo]] || [[garibaldi]] || 225/224, 3125/3087 ||
! OPV
|| 2430/2401 || [[137edo]] || [[orwell]] || 225/224, 1728/1715 ||
! Temperament
|| 245/243 || [[283edo]] || [[Escapade family#Escaped|escaped]] || 245/243, 65625/65536 ||
! Basis
|| 126/125 || [[185edo]] || [[valentine]] || 126/125, 1029/1024 ||
|-
|| 1728/1715 || [[111edo]] || [[buzzard]] || 1728/1715, 5120/5103 ||
| [[28/27]]
|| 1728/1715 || [[111edo]] || [[semisept]] || 1728/1715, 3136/3125 ||
| [[15edo]]
|| 1029/1024 || [[190edo]] || [[unidec]] || 1029/1024, 4375/4374 ||
| [[Blacksmith]]
|| 225/224 || [[197edo]] || [[catakleismic]] || 225/224, 4375/4374 ||
| 28/27, [[49/48]]
|| 3136/3125 || [[446edo]] || [[Hemimean clan#Sengagen|sengagen]] || 3136/3125, 420175/419904 ||
|-
|| 5120/5103 || [[391edo]] || [[Hemifamity temperaments#Alphaquarter|alphaquarter]] || 5120/5103, 29360128/29296875 ||
| 1029/1000
|| 5120/5103 || [[391edo]] || [[Hemifamity temperaments#Septiquarter|septiquarter]] || 5120/5103, 420175/419904 ||
| [[55edo]]
| [[Liese]]
| [[81/80]], 686/675
|-
| [[36/35]]
| [[12edo]]
| [[Diminished]]
| 36/35, [[50/49]]
|-
| [[36/35]]
| [[12edo]]
| [[August]]
| 36/35, [[128/125]]
|-
| [[36/35]]
| [[12edo]]
| [[Dominant (temperament)|Dominant]]
| 36/35, [[64/63]]
|-
| [[525/512]]
| [[45edo]]
| [[Flattone]]
| 81/80, 525/512
|-
| [[49/48]]
| [[19edo]]
| [[Keemun]]
| 49/48, [[126/125]]
|-
| [[49/48]]
| [[19edo]]
| [[Godzilla]]
| 49/48, [[81/80]]
|-
| [[50/49]]
| [[48edo]]
| [[Doublewide]]
| 50/49, 875/864
|-
| [[64/63]]
| [[49edo]]
| [[Superpyth]]
| 64/63, [[245/243]]
|-
| 875/864
| [[41edo]]
| [[Magic]]
| [[225/224]], 245/243
|-
| 875/864
| [[41edo]]
| [[Superkleismic]]
| 875/864, [[1029/1024]]
|-
| 3125/3087
| [[94edo]]
| [[Garibaldi]]
| 225/224, 3125/3087
|-
| 2430/2401
| [[137edo]]
| [[Orwell]]
| [[225/224]], 1728/1715
|-
| 245/243
| [[283edo]]
| [[Escaped]]
| 245/243, 65625/65536
|-
| 126/125
| [[185edo]]
| [[Valentine]]
| 126/125, 1029/1024
|-
| 1728/1715
| [[111edo]]
| [[Buzzard]]
| 1728/1715, 5120/5103
|-
| 1728/1715
| [[111edo]]
| [[Semisept]]
| 1728/1715, 3136/3125
|-
| 1029/1024
| [[190edo]]
| [[Unidec]]
| 1029/1024, 4375/4374
|-
| 225/224
| [[197edo]]
| [[Catakleismic]]
| 225/224, 4375/4374
|-
| 16875/16807
| [[224edo]]
| [[Octoid]]
| 4375/4374, 16875/16807
|-
| 4802000/4782969
| [[1131edo]]
| [[Amicable]]
| 2401/2400, 1600000/1594323
|-
| 3136/3125
| [[446edo]]
| [[Sengagen]]
| 3136/3125, 420175/419904
|-
| 5120/5103
| [[391edo]]
| [[Alphaquarter]]
| 5120/5103, 29360128/29296875
|-
| 5120/5103
| [[391edo]]
| [[Septiquarter]]
| 5120/5103, 420175/419904
|-
| 6144/6125
| [[381edo]]
| [[Nessafof]]
| 6144/6125, 250047/250000
|-
| 65625/65536
| [[171edo]]
| [[Tertiaseptal]]
| 2401/2400, 65625/65536
|-
| 703125/702464
| [[2185edo]]
| [[Enneadecal]]
| 4375/4374, 703125/702464
|-
| 4375/4374
| [[8419edo]]
| [[Semidimi]]
| 4375/4374, 3955078125/3954653486
|-
| 250047/250000
| [[12555edo]]
|
| 250047/250000, 281484423828125/281474976710656
|}


</pre></div>
== 11-limit ==
<h4>Original HTML content:</h4>
{| class="wikitable"
<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;Associated rank two temperaments&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;br /&gt;
|-
&lt;br /&gt;
! Comma
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x7 limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;7 limit&lt;/h1&gt;
! OPV
! Temperament
! Basis
|-
| 33/32
| [[16edo]]
| [[Armodue]]
| 33/32, 36/35, 45/44
|-
| 77/75
| [[39edo]]
| [[Triforce]]
| 49/48, 56/55, 77/75
|-
| 352/343
| [[22edo]]
| [[Hedgehog]]
| 50/49, 55/54, 99/98
|-
| 45/44
| [[45edo]]
| [[Flattone]]
| 45/44, 81/80, 385/384
|-
| 55/54
| [[51edo]]
| [[Porky]]
| 55/54, 100/99, 225/224
|-
| 56/55
| [[36edo]]
| [[Catnip]]
| 56/55, 81/80, 128/125
|-
| 245/242
| [[91edo]]
| [[Septimin]]
| 225/224, 245/242, 385/384
|-
| 99/98
| [[127edo]]
| [[Würschmidt]]
| 99/98, 176/175, 243/242
|-
| 100/99
| [[104edo]]
| [[Magic]]
| 100/99, 225/224, 245/243
|-
| 121/120
| [[99edo]]
| [[Hitchcock]]
| 121/120, 176/175, 2200/2187
|-
| 121/120
| [[99edo]]
| [[Hemiwur]]
| 121/120, 176/175, 1375/1372
|-
| 176/175
| [[111edo]]
| [[Semisept]]
| 176/175, 540/539, 1331/1323
|-
| 896/891
| [[208edo]]
| [[Metakleismic]]
| 896/891, 2200/2187, 14700/14641
|-
| 65536/65219
| [[282edo]]
| [[Septisuperfourth]]
| 540/539, 4000/3993, 5632/5625
|-
| 14641/14580
| [[410edo]]
| [[Floral]]
| 2401/2400, 9801/9800, 14641/14580
|-
| 243/242
| [[202edo]]
| [[Harry]]
| 243/242, 441/440, 4000/3993
|-
| 243/242
| [[202edo]]
| [[Tertiaseptal]]
| 243/242, 441/440, 65625/65536
|-
| 3388/3375
| [[316edo]]
| [[Semiparakleismic]]
| 3025/3024, 3136/3125, 4375/4374
|-
| 385/384
| [[284edo]]
| [[Quadritikleismic]]
| 385/384, 1375/1372, 6250/6237
|-
| 441/440
| [[320edo]]
| [[Octowerck]]
| 441/440, 8019/8000, 41503/41472
|-
| 540/539
| [[578edo]]
| [[Pogo]]
| 540/539, 4000/3993, 32805/32768
|-
| 4000/3993
| [[665edo]]
| [[Brahmagupta]]
| 4000/3993, 4375/4374, 131072/130977
|-
| 5632/5625
| [[1092edo]]
| [[Sextile]]
| 5632/5625, 9801/9800, 151263/151250
|-
| 3025/3024
| [[2554edo]]
| [[Semisupermajor]]
| 3025/3024, 4375/4374, 35156250/35153041
|}


== 13-limit ==
{| class="wikitable"
|-
! Comma
! OPV
! Temperament
! Basis
|-
| 26/25
| [[12edo]]
| [[Augustus]]
| 26/25, 36/35, 45/44, 56/55
|-
| 27/26
| [[35edo]]
| [[Secund]]
| 27/26, 45/44, 99/98, 385/384
|-
| 27/26
| [[35edo]]
| [[Greenwood]]
| 27/26, 45/44, 99/98, 640/637
|-
| 40/39
| [[15edo]]
| [[Blacksmith]]
| 28/27, 40/39, 49/48, 55/54
|-
| 65/64
| [[29edo]]
| [[Negril]]
| 49/48, 65/64, 91/90, 875/858
|-
| 65/64
| [[29edo]]
| [[Coendou]]
| 55/54, 65/64, 100/99, 105/104
|-
| 66/65
| [[31edo]]
| [[Winston]]
| 66/65, 99/98, 105/104, 121/120
|-
| 66/65
| [[31edo]]
| [[Mohajira]]
| 66/65, 81/80, 105/104, 121/120
|-
| 66/65
| [[31edo]]
| [[Squares]]
| 66/65, 81/80, 99/98, 121/120
|-
| 78/77
| [[43edo]]
| [[Amavil]]
| 78/77, 99/98, 144/143, 176/175
|-
| 78/77
| [[43edo]]
| [[Jerome]]
| 78/77, 81/80, 99/98, 144/143
|-
| 91/90
| [[102edo]]
| [[Echidnic]]
| 91/90, 169/168, 385/384, 441/440
|-
| 105/104
| [[91edo]]
| [[Septimin]]
| 105/104, 144/143, 196/195, 245/242
|-
| 275/273
| [[94edo]]
| [[Garibaldi]]
| 225/224, 275/273, 325/324, 385/384
|-
| 144/143
| [[84edo]]
| [[Merman]]
| 144/143, 225/224, 364/363, 441/440
|-
| 144/143
| [[84edo]]
| [[Secant]]
| 144/143, 351/350, 364/363, 441/440
|-
| 169/168
| [[152edo]]
| [[Octopus]]
| 169/168, 325/324, 364/363, 540/539
|-
| 196/195
| [[232edo]]
| [[Mystery]]
| 196/195, 352/351, 364/363, 676/675
|-
| 640/637
| [[205edo]]
| [[Quanic]]
| 352/351, 540/539, 729/728, 1331/1323
|-
| 1188/1183
| [[255edo]]
| [[Subsemifourth]]
| 540/539, 847/845, 1375/1372, 1575/1573
|-
| 1573/1568
| [[323edo]]
| [[Stockhausenic]]
| 676/675, 1001/1000, 1375/1372, 4096/4095
|-
| 325/324
| [[333edo]]
| [[Novemkleismic]]
| 325/324, 625/624, 1375/1372, 4000/3993
|-
| 351/350
| [[546edo]]
| [[Fermionic]]
| 351/350, 540/539, 40656/40625, 142884/142805
|-
| 352/351
| [[198edo]]
| [[Semihemi]]
| 352/351, 676/675, 847/845, 1716/1715
|-
| 352/351
| [[198edo]]
| [[Hemimist]]
| 352/351, 676/675, 847/845, 3025/3024
|-
| 847/845
| [[388edo]]
| [[Neusec]]
| 847/845, 1001/1000, 3025/3024, 4375/4374
|-
| 676/675
| [[940edo]]
| [[Decoid]]
| 676/675, 1001/1000, 1716/1715, 4225/4224
|-
| 2200/2197
| [[836edo]]
| [[Quasithird]]
| 2200/2197, 3025/3024, 4375/4374, 468512/468195
|}


&lt;table class="wiki_table"&gt;
[[Category:Regular temperament theory]]
    &lt;tr&gt;
[[Category:Rank 2]]
        &lt;td&gt;Comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;OPV&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Temperament&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Basis&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;64/63&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/49edo"&gt;49edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/superpyth"&gt;superpyth&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;64/63, 245/243&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;875/864&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/41edo"&gt;41edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/magic"&gt;magic&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;225/224, 245/243&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3125/3087&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/94edo"&gt;94edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/garibaldi"&gt;garibaldi&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;225/224, 3125/3087&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2430/2401&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/137edo"&gt;137edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/orwell"&gt;orwell&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;225/224, 1728/1715&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;245/243&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/283edo"&gt;283edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Escapade%20family#Escaped"&gt;escaped&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;245/243, 65625/65536&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;126/125&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/185edo"&gt;185edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/valentine"&gt;valentine&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;126/125, 1029/1024&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1728/1715&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/111edo"&gt;111edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/buzzard"&gt;buzzard&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1728/1715, 5120/5103&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1728/1715&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/111edo"&gt;111edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/semisept"&gt;semisept&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1728/1715, 3136/3125&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1029/1024&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/190edo"&gt;190edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/unidec"&gt;unidec&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1029/1024, 4375/4374&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;225/224&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/197edo"&gt;197edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/catakleismic"&gt;catakleismic&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;225/224, 4375/4374&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3136/3125&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/446edo"&gt;446edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Hemimean%20clan#Sengagen"&gt;sengagen&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3136/3125, 420175/419904&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5120/5103&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/391edo"&gt;391edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Hemifamity%20temperaments#Alphaquarter"&gt;alphaquarter&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5120/5103, 29360128/29296875&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5120/5103&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/391edo"&gt;391edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Hemifamity%20temperaments#Septiquarter"&gt;septiquarter&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5120/5103, 420175/419904&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;/body&gt;&lt;/html&gt;</pre></div>
Retrieved from "https://en.xen.wiki/w/Associated_temperament"