Associated temperament: Difference between revisions

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**Imported revision 300010624 - Original comment: **
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**Imported revision 300011212 - Original comment: **
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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>2012-02-09 01:41:43 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-02-09 01:47:22 UTC</tt>.<br>
: The original revision id was <tt>300010624</tt>.<br>
: The original revision id was <tt>300011212</tt>.<br>
: The revision comment was: <tt></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>
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>
<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">By an //associated temperament// to a p-limit comma is meant a p-limit temperament which shares the same [[optimal patent val]] as the [[Rank and codimension|codimension one]] temperament tempering out that comma. By definition, the optimal patent val defines the unique rank one associated temperament. For rank two temperaments, 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, the rank two temperament, and a comma basis for the rank two temperament.
<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">By an //associated temperament// to a p-limit comma is meant a p-limit temperament tempering out that comma which shares the same [[optimal patent val]] as the [[Rank and codimension|codimension one]] temperament tempering out that comma. By definition, the optimal patent val defines the unique rank one associated temperament. For rank two temperaments, 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, the rank two temperament, and a comma basis for the rank two temperament.


=7 limit=
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</pre></div>
</pre></div>
<h4>Original HTML content:</h4>
<h4>Original HTML 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;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;By an &lt;em&gt;associated temperament&lt;/em&gt; to a p-limit comma is meant a p-limit temperament which shares the same &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt; as the &lt;a class="wiki_link" href="/Rank%20and%20codimension"&gt;codimension one&lt;/a&gt; temperament tempering out that comma. By definition, the optimal patent val defines the unique rank one associated temperament. For rank two temperaments, 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, the rank two temperament, and a comma basis for the rank two temperament.&lt;br /&gt;
<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;By an &lt;em&gt;associated temperament&lt;/em&gt; to a p-limit comma is meant a p-limit temperament tempering out that comma which shares the same &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt; as the &lt;a class="wiki_link" href="/Rank%20and%20codimension"&gt;codimension one&lt;/a&gt; temperament tempering out that comma. By definition, the optimal patent val defines the unique rank one associated temperament. For rank two temperaments, 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, the rank two temperament, and a comma basis for the rank two temperament.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&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;
&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;

Revision as of 01:47, 9 February 2012

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author genewardsmith and made on 2012-02-09 01:47:22 UTC.
The original revision id was 300011212.
The revision comment was:

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Original Wikitext content:

By an //associated temperament// to a p-limit comma is meant a p-limit temperament tempering out that comma which shares the same [[optimal patent val]] as the [[Rank and codimension|codimension one]] temperament tempering out that comma. By definition, the optimal patent val defines the unique rank one associated temperament. For rank two temperaments, 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, the rank two temperament, and a comma basis for the rank two temperament.

=7 limit=
|| Comma || OPV || Temperament || Basis ||
|| 28/27 || [[15edo]] || [[blacksmith]] || 28/27, 49/48 ||
|| 1029/1000 || [[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]] || 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]] || [[Escapade family#Escaped|escaped]] || 245/243, 65625/65536 ||
|| 126/125 || [[185edo]] || [[valentine]] || 126/125, 1029/1024 ||
|| 1728/1715 || [[111edo]] || [[Hemifamity temperaments#Buzzard|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 ||
|| 3136/3125 || [[446edo]] || [[Hemimean clan#Sengagen|sengagen]] || 3136/3125, 420175/419904 ||
|| 5120/5103 || [[391edo]] || [[Hemifamity temperaments#Alphaquarter|alphaquarter]] || 5120/5103, 29360128/29296875 ||
|| 5120/5103 || [[391edo]] || [[Hemifamity temperaments#Septiquarter|septiquarter]] || 5120/5103, 420175/419904 ||
|| 6144/6125 || [[381edo]] || [[Porwell temperaments#Nessafof|nessafof]] || 6144/6125, 250047/250000 ||
|| 65625/65536 || [[171edo]] || [[Breedsmic temperaments#Tertiaseptal|tertiaseptal]] || 2401/2400, 65625/65536 ||
|| 703125/702464 || [[2185edo]] || [[Ragismic microtemperaments#Enneadecal|enneadecal]] || 4375/4374, 703125/702464 ||
|| 4375/4374 || [[8419edo]] || [[Ragismic microtemperaments#Semidimi|semidimi]] || 4375/4374, 3955078125/3954653486 ||
|| 250047/250000 || [[12555edo]] || || 250047/250000, 281484423828125/281474976710656 ||

=11 limit=
|| Comma || OPV || Temperament || Basis ||
|| 33/32 || [[16edo]] || [[Pelogic family#Armodue|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]] || [[Pythagorean family#Catler temperament|catcall]] || 56/55, 81/80, 128/125 ||
|| 245/242 || [[91edo]] || [[septimin]] || 225/224, 245/242, 385/384 ||
|| 99/98 || [[127edo]] || [[Würschmidt family#Würschmidt|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]] || [[Würschmidt family#Hemiwürschmidt|hemiwur]] || 121/120, 176/175, 1375/1372 ||
|| 176/175 || [[111edo]] || [[semisept]] || 176/175, 540/539, 1331/1323 ||
|| 896/891 || [[208edo]] || [[Kleismic family#Metakleismic|metakleismic]] ||  896/891, 2200/2187, 14700/14641 ||
|| 65536/65219 || [[282edo]] || [[Porwell temperaments#Septisuperfourth|septisuperfourth]] || 540/539, 4000/3993, 5632/5625 ||
|| 243/242 || [[202edo]] || [[harry]] || 243/242, 441/440, 4000/3993 ||
|| 243/242 || [[202edo]] || [[Breedsmic temperaments#Tertiaseptal|tertiaseptal]] || 243/242, 441/440, 65625/65536 ||
|| 3388/3375 || [[316edo]] || [[Ragismic microtemperaments#Semiparakleismic|semiparakleismic]] || 3025/3024, 3136/3125, 4375/4374 ||
|| 385/384 || [[284edo]] || [[quadritikleismic]] || 385/384, 1375/1372, 6250/6237 ||
|| 441/400 || [[320edo]] || [[octowerck]] || 441/440, 8019/8000, 41503/41472 ||
|| 540/539 || [[578edo]] || [[Schismatic family#Pogo|pogo]] || 540/539, 4000/3993, 32805/32768 ||
|| 4000/3993 || [[665edo]] || [[Ragismic microtemperaments#Brahmagupta|brahmagupta]] || 4000/3993, 4375/4374, 131072/130977 ||
|| 5632/5625 || [[1092edo]] || [[Landscape microtemperaments#Sextile|sextile]] || 5632/5625, 9801/9800, 151263/151250 ||
|| 3025/3024 || [[2554edo]] || [[Ragismic microtemperaments#Supermajor-Semisupermajor|semisupermajor]] || 3025/3024, 4375/4374, 35156250/35153041 ||

=13 limit=
|| Comma || OPV || Temperament || Basis ||
|| 26/25 || [[12edo]] || [[Augmented family#August|augustus]] || 26/25, 36/35, 45/44, 56/55 ||
|| 27/26 || [[35edo]] || [[Avicennmic temperaments#Secund|secund]] ||  27/26, 45/44, 99/98, 385/384 ||
|| 27/26 || [[35edo]] || [[Greenwoodmic temperaments#Greenwood|greenwood]] || 27/26, 45/44, 99/98, 640/637 ||
|| 40/39 || [[15edo]] || [[Archytas clan#Blacksmith|blacksmith]] || 28/27, 40/39, 49/48, 55/54 ||
|| 65/64 || [[29edo]] || [[Marvel temperaments#Negril|negril]] || 49/48, 65/64, 91/90, 875/858 ||
|| 65/64 || [[29edo]] || [[Porcupine family#Coendou|coendou]] || 55/54, 65/64, 100/99, 105/104 ||
|| 66/65 || [[31edo]] || [[Semicomma family#Winston|winston]] || 66/65, 99/98, 105/104, 121/120 ||
|| 66/65 || [[31edo]] || [[Meantone family#Mohajira-13-limit|mohajira]] || 66/65, 81/80, 105/104, 121/120 ||
|| 66/65 || [[31edo]] || [[Meantone family#Squares-13-limit|squares]] || 66/65, 81/80, 99/98, 121/120 ||
|| 78/77 || [[43edo]] || [[Marvel temperaments#Amavil|amavil]] || 78/77, 99/98, 144/143, 176/175 ||
|| 78/77 || [[43edo]] || [[Meantone family#Jerome|jerome]] || 78/77, 81/80, 99/98, 144/143 ||
|| 91/90 || [[102edo]] || [[Diaschismic family#Echidnic|echidnic]] || 91/90, 169/168, 385/384, 441/440 ||
|| 105/104 || [[91edo]] || [[Marvel temperaments#Septimin|septimin]] || 105/104, 144/143, 196/195, 245/242 ||
|| 275/273 || [[94edo]] || [[Schismatic family#Garibaldi|garibaldi]] || 225/224, 275/273, 325/324, 385/384 ||
|| 275/273 || [[94edo]] || [[Hemifamity temperaments#Supers|supers]] || 352/351, 540/539, 729/728, 1575/1573 ||
|| 144/143 || [[84edo]] || [[Marvel temperaments#Merman|merman]] || 144/143, 225/224, 364/363, 441/440 ||
|| 144/143 || [[84edo]] || [[Orwellismic temperaments|secant]] || 144/143, 351/350, 364/363, 441/440 ||
|| 169/168 || [[152edo]] || [[Ragismic microtemperaments#Octoid-Octopus|octopus]] || 169/168, 325/324, 364/363, 540/539 ||

Original HTML content:

<html><head><title>Associated rank two temperaments</title></head><body>By an <em>associated temperament</em> to a p-limit comma is meant a p-limit temperament tempering out that comma which shares the same <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> as the <a class="wiki_link" href="/Rank%20and%20codimension">codimension one</a> temperament tempering out that comma. By definition, the optimal patent val defines the unique rank one associated temperament. For rank two temperaments, 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, the rank two temperament, and a comma basis for the rank two temperament.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x7 limit"></a><!-- ws:end:WikiTextHeadingRule:0 -->7 limit</h1>


<table class="wiki_table">
    <tr>
        <td>Comma<br />
</td>
        <td>OPV<br />
</td>
        <td>Temperament<br />
</td>
        <td>Basis<br />
</td>
    </tr>
    <tr>
        <td>28/27<br />
</td>
        <td><a class="wiki_link" href="/15edo">15edo</a><br />
</td>
        <td><a class="wiki_link" href="/blacksmith">blacksmith</a><br />
</td>
        <td>28/27, 49/48<br />
</td>
    </tr>
    <tr>
        <td>1029/1000<br />
</td>
        <td><a class="wiki_link" href="/55edo">55edo</a><br />
</td>
        <td><a class="wiki_link" href="/liese">liese</a><br />
</td>
        <td>81/80, 686/675<br />
</td>
    </tr>
    <tr>
        <td>36/35<br />
</td>
        <td><a class="wiki_link" href="/12edo">12edo</a><br />
</td>
        <td><a class="wiki_link" href="/diminished">diminished</a><br />
</td>
        <td>36/35, 50/49<br />
</td>
    </tr>
    <tr>
        <td>36/35<br />
</td>
        <td><a class="wiki_link" href="/12edo">12edo</a><br />
</td>
        <td><a class="wiki_link" href="/august">august</a><br />
</td>
        <td>36/35, 128/125<br />
</td>
    </tr>
    <tr>
        <td>36/35<br />
</td>
        <td><a class="wiki_link" href="/12edo">12edo</a><br />
</td>
        <td><a class="wiki_link" href="/dominant">dominant</a><br />
</td>
        <td>36/35, 64/63<br />
</td>
    </tr>
    <tr>
        <td>525/512<br />
</td>
        <td><a class="wiki_link" href="/45edo">45edo</a><br />
</td>
        <td><a class="wiki_link" href="/flattone">flattone</a><br />
</td>
        <td>81/80, 525/512<br />
</td>
    </tr>
    <tr>
        <td>49/48<br />
</td>
        <td><a class="wiki_link" href="/19edo">19edo</a><br />
</td>
        <td><a class="wiki_link" href="/keemun">keemun</a><br />
</td>
        <td>49/48, 126/125<br />
</td>
    </tr>
    <tr>
        <td>49/48<br />
</td>
        <td><a class="wiki_link" href="/19edo">19edo</a><br />
</td>
        <td><a class="wiki_link" href="/godzilla">godzilla</a><br />
</td>
        <td>49/48, 81/80<br />
</td>
    </tr>
    <tr>
        <td>50/49<br />
</td>
        <td><a class="wiki_link" href="/48edo">48edo</a><br />
</td>
        <td><a class="wiki_link" href="/doublewide">doublewide</a><br />
</td>
        <td>50/49, 875/864<br />
</td>
    </tr>
    <tr>
        <td>64/63<br />
</td>
        <td><a class="wiki_link" href="/49edo">49edo</a><br />
</td>
        <td><a class="wiki_link" href="/superpyth">superpyth</a><br />
</td>
        <td>64/63, 245/243<br />
</td>
    </tr>
    <tr>
        <td>875/864<br />
</td>
        <td><a class="wiki_link" href="/41edo">41edo</a><br />
</td>
        <td><a class="wiki_link" href="/magic">magic</a><br />
</td>
        <td>225/224, 245/243<br />
</td>
    </tr>
    <tr>
        <td>875/864<br />
</td>
        <td><a class="wiki_link" href="/41edo">41edo</a><br />
</td>
        <td><a class="wiki_link" href="/superkleismic">superkleismic</a><br />
</td>
        <td>875/864, 1029/1024<br />
</td>
    </tr>
    <tr>
        <td>3125/3087<br />
</td>
        <td><a class="wiki_link" href="/94edo">94edo</a><br />
</td>
        <td><a class="wiki_link" href="/garibaldi">garibaldi</a><br />
</td>
        <td>225/224, 3125/3087<br />
</td>
    </tr>
    <tr>
        <td>2430/2401<br />
</td>
        <td><a class="wiki_link" href="/137edo">137edo</a><br />
</td>
        <td><a class="wiki_link" href="/orwell">orwell</a><br />
</td>
        <td>225/224, 1728/1715<br />
</td>
    </tr>
    <tr>
        <td>245/243<br />
</td>
        <td><a class="wiki_link" href="/283edo">283edo</a><br />
</td>
        <td><a class="wiki_link" href="/Escapade%20family#Escaped">escaped</a><br />
</td>
        <td>245/243, 65625/65536<br />
</td>
    </tr>
    <tr>
        <td>126/125<br />
</td>
        <td><a class="wiki_link" href="/185edo">185edo</a><br />
</td>
        <td><a class="wiki_link" href="/valentine">valentine</a><br />
</td>
        <td>126/125, 1029/1024<br />
</td>
    </tr>
    <tr>
        <td>1728/1715<br />
</td>
        <td><a class="wiki_link" href="/111edo">111edo</a><br />
</td>
        <td><a class="wiki_link" href="/Hemifamity%20temperaments#Buzzard">buzzard</a><br />
</td>
        <td>1728/1715, 5120/5103<br />
</td>
    </tr>
    <tr>
        <td>1728/1715<br />
</td>
        <td><a class="wiki_link" href="/111edo">111edo</a><br />
</td>
        <td><a class="wiki_link" href="/semisept">semisept</a><br />
</td>
        <td>1728/1715, 3136/3125<br />
</td>
    </tr>
    <tr>
        <td>1029/1024<br />
</td>
        <td><a class="wiki_link" href="/190edo">190edo</a><br />
</td>
        <td><a class="wiki_link" href="/unidec">unidec</a><br />
</td>
        <td>1029/1024, 4375/4374<br />
</td>
    </tr>
    <tr>
        <td>225/224<br />
</td>
        <td><a class="wiki_link" href="/197edo">197edo</a><br />
</td>
        <td><a class="wiki_link" href="/catakleismic">catakleismic</a><br />
</td>
        <td>225/224, 4375/4374<br />
</td>
    </tr>
    <tr>
        <td>3136/3125<br />
</td>
        <td><a class="wiki_link" href="/446edo">446edo</a><br />
</td>
        <td><a class="wiki_link" href="/Hemimean%20clan#Sengagen">sengagen</a><br />
</td>
        <td>3136/3125, 420175/419904<br />
</td>
    </tr>
    <tr>
        <td>5120/5103<br />
</td>
        <td><a class="wiki_link" href="/391edo">391edo</a><br />
</td>
        <td><a class="wiki_link" href="/Hemifamity%20temperaments#Alphaquarter">alphaquarter</a><br />
</td>
        <td>5120/5103, 29360128/29296875<br />
</td>
    </tr>
    <tr>
        <td>5120/5103<br />
</td>
        <td><a class="wiki_link" href="/391edo">391edo</a><br />
</td>
        <td><a class="wiki_link" href="/Hemifamity%20temperaments#Septiquarter">septiquarter</a><br />
</td>
        <td>5120/5103, 420175/419904<br />
</td>
    </tr>
    <tr>
        <td>6144/6125<br />
</td>
        <td><a class="wiki_link" href="/381edo">381edo</a><br />
</td>
        <td><a class="wiki_link" href="/Porwell%20temperaments#Nessafof">nessafof</a><br />
</td>
        <td>6144/6125, 250047/250000<br />
</td>
    </tr>
    <tr>
        <td>65625/65536<br />
</td>
        <td><a class="wiki_link" href="/171edo">171edo</a><br />
</td>
        <td><a class="wiki_link" href="/Breedsmic%20temperaments#Tertiaseptal">tertiaseptal</a><br />
</td>
        <td>2401/2400, 65625/65536<br />
</td>
    </tr>
    <tr>
        <td>703125/702464<br />
</td>
        <td><a class="wiki_link" href="/2185edo">2185edo</a><br />
</td>
        <td><a class="wiki_link" href="/Ragismic%20microtemperaments#Enneadecal">enneadecal</a><br />
</td>
        <td>4375/4374, 703125/702464<br />
</td>
    </tr>
    <tr>
        <td>4375/4374<br />
</td>
        <td><a class="wiki_link" href="/8419edo">8419edo</a><br />
</td>
        <td><a class="wiki_link" href="/Ragismic%20microtemperaments#Semidimi">semidimi</a><br />
</td>
        <td>4375/4374, 3955078125/3954653486<br />
</td>
    </tr>
    <tr>
        <td>250047/250000<br />
</td>
        <td><a class="wiki_link" href="/12555edo">12555edo</a><br />
</td>
        <td><br />
</td>
        <td>250047/250000, 281484423828125/281474976710656<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="x11 limit"></a><!-- ws:end:WikiTextHeadingRule:2 -->11 limit</h1>


<table class="wiki_table">
    <tr>
        <td>Comma<br />
</td>
        <td>OPV<br />
</td>
        <td>Temperament<br />
</td>
        <td>Basis<br />
</td>
    </tr>
    <tr>
        <td>33/32<br />
</td>
        <td><a class="wiki_link" href="/16edo">16edo</a><br />
</td>
        <td><a class="wiki_link" href="/Pelogic%20family#Armodue">armodue</a><br />
</td>
        <td>33/32, 36/35, 45/44<br />
</td>
    </tr>
    <tr>
        <td>77/75<br />
</td>
        <td><a class="wiki_link" href="/39edo">39edo</a><br />
</td>
        <td><a class="wiki_link" href="/triforce">triforce</a><br />
</td>
        <td>49/48, 56/55, 77/75<br />
</td>
    </tr>
    <tr>
        <td>352/343<br />
</td>
        <td><a class="wiki_link" href="/22edo">22edo</a><br />
</td>
        <td><a class="wiki_link" href="/hedgehog">hedgehog</a><br />
</td>
        <td>50/49, 55/54, 99/98<br />
</td>
    </tr>
    <tr>
        <td>45/44<br />
</td>
        <td><a class="wiki_link" href="/45edo">45edo</a><br />
</td>
        <td><a class="wiki_link" href="/flattone">flattone</a><br />
</td>
        <td>45/44, 81/80, 385/384<br />
</td>
    </tr>
    <tr>
        <td>55/54<br />
</td>
        <td><a class="wiki_link" href="/51edo">51edo</a><br />
</td>
        <td><a class="wiki_link" href="/porky">porky</a><br />
</td>
        <td>55/54, 100/99, 225/224<br />
</td>
    </tr>
    <tr>
        <td>56/55<br />
</td>
        <td><a class="wiki_link" href="/36edo">36edo</a><br />
</td>
        <td><a class="wiki_link" href="/Pythagorean%20family#Catler temperament">catcall</a><br />
</td>
        <td>56/55, 81/80, 128/125<br />
</td>
    </tr>
    <tr>
        <td>245/242<br />
</td>
        <td><a class="wiki_link" href="/91edo">91edo</a><br />
</td>
        <td><a class="wiki_link" href="/septimin">septimin</a><br />
</td>
        <td>225/224, 245/242, 385/384<br />
</td>
    </tr>
    <tr>
        <td>99/98<br />
</td>
        <td><a class="wiki_link" href="/127edo">127edo</a><br />
</td>
        <td><a class="wiki_link" href="/W%C3%BCrschmidt%20family#Würschmidt">würschmidt</a><br />
</td>
        <td>99/98, 176/175, 243/242<br />
</td>
    </tr>
    <tr>
        <td>100/99<br />
</td>
        <td><a class="wiki_link" href="/104edo">104edo</a><br />
</td>
        <td><a class="wiki_link" href="/magic">magic</a><br />
</td>
        <td>100/99, 225/224, 245/243<br />
</td>
    </tr>
    <tr>
        <td>121/120<br />
</td>
        <td><a class="wiki_link" href="/99edo">99edo</a><br />
</td>
        <td><a class="wiki_link" href="/hitchcock">hitchcock</a><br />
</td>
        <td>121/120, 176/175, 2200/2187<br />
</td>
    </tr>
    <tr>
        <td>121/120<br />
</td>
        <td><a class="wiki_link" href="/99edo">99edo</a><br />
</td>
        <td><a class="wiki_link" href="/W%C3%BCrschmidt%20family#Hemiwürschmidt">hemiwur</a><br />
</td>
        <td>121/120, 176/175, 1375/1372<br />
</td>
    </tr>
    <tr>
        <td>176/175<br />
</td>
        <td><a class="wiki_link" href="/111edo">111edo</a><br />
</td>
        <td><a class="wiki_link" href="/semisept">semisept</a><br />
</td>
        <td>176/175, 540/539, 1331/1323<br />
</td>
    </tr>
    <tr>
        <td>896/891<br />
</td>
        <td><a class="wiki_link" href="/208edo">208edo</a><br />
</td>
        <td><a class="wiki_link" href="/Kleismic%20family#Metakleismic">metakleismic</a><br />
</td>
        <td>896/891, 2200/2187, 14700/14641<br />
</td>
    </tr>
    <tr>
        <td>65536/65219<br />
</td>
        <td><a class="wiki_link" href="/282edo">282edo</a><br />
</td>
        <td><a class="wiki_link" href="/Porwell%20temperaments#Septisuperfourth">septisuperfourth</a><br />
</td>
        <td>540/539, 4000/3993, 5632/5625<br />
</td>
    </tr>
    <tr>
        <td>243/242<br />
</td>
        <td><a class="wiki_link" href="/202edo">202edo</a><br />
</td>
        <td><a class="wiki_link" href="/harry">harry</a><br />
</td>
        <td>243/242, 441/440, 4000/3993<br />
</td>
    </tr>
    <tr>
        <td>243/242<br />
</td>
        <td><a class="wiki_link" href="/202edo">202edo</a><br />
</td>
        <td><a class="wiki_link" href="/Breedsmic%20temperaments#Tertiaseptal">tertiaseptal</a><br />
</td>
        <td>243/242, 441/440, 65625/65536<br />
</td>
    </tr>
    <tr>
        <td>3388/3375<br />
</td>
        <td><a class="wiki_link" href="/316edo">316edo</a><br />
</td>
        <td><a class="wiki_link" href="/Ragismic%20microtemperaments#Semiparakleismic">semiparakleismic</a><br />
</td>
        <td>3025/3024, 3136/3125, 4375/4374<br />
</td>
    </tr>
    <tr>
        <td>385/384<br />
</td>
        <td><a class="wiki_link" href="/284edo">284edo</a><br />
</td>
        <td><a class="wiki_link" href="/quadritikleismic">quadritikleismic</a><br />
</td>
        <td>385/384, 1375/1372, 6250/6237<br />
</td>
    </tr>
    <tr>
        <td>441/400<br />
</td>
        <td><a class="wiki_link" href="/320edo">320edo</a><br />
</td>
        <td><a class="wiki_link" href="/octowerck">octowerck</a><br />
</td>
        <td>441/440, 8019/8000, 41503/41472<br />
</td>
    </tr>
    <tr>
        <td>540/539<br />
</td>
        <td><a class="wiki_link" href="/578edo">578edo</a><br />
</td>
        <td><a class="wiki_link" href="/Schismatic%20family#Pogo">pogo</a><br />
</td>
        <td>540/539, 4000/3993, 32805/32768<br />
</td>
    </tr>
    <tr>
        <td>4000/3993<br />
</td>
        <td><a class="wiki_link" href="/665edo">665edo</a><br />
</td>
        <td><a class="wiki_link" href="/Ragismic%20microtemperaments#Brahmagupta">brahmagupta</a><br />
</td>
        <td>4000/3993, 4375/4374, 131072/130977<br />
</td>
    </tr>
    <tr>
        <td>5632/5625<br />
</td>
        <td><a class="wiki_link" href="/1092edo">1092edo</a><br />
</td>
        <td><a class="wiki_link" href="/Landscape%20microtemperaments#Sextile">sextile</a><br />
</td>
        <td>5632/5625, 9801/9800, 151263/151250<br />
</td>
    </tr>
    <tr>
        <td>3025/3024<br />
</td>
        <td><a class="wiki_link" href="/2554edo">2554edo</a><br />
</td>
        <td><a class="wiki_link" href="/Ragismic%20microtemperaments#Supermajor-Semisupermajor">semisupermajor</a><br />
</td>
        <td>3025/3024, 4375/4374, 35156250/35153041<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="x13 limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->13 limit</h1>


<table class="wiki_table">
    <tr>
        <td>Comma<br />
</td>
        <td>OPV<br />
</td>
        <td>Temperament<br />
</td>
        <td>Basis<br />
</td>
    </tr>
    <tr>
        <td>26/25<br />
</td>
        <td><a class="wiki_link" href="/12edo">12edo</a><br />
</td>
        <td><a class="wiki_link" href="/Augmented%20family#August">augustus</a><br />
</td>
        <td>26/25, 36/35, 45/44, 56/55<br />
</td>
    </tr>
    <tr>
        <td>27/26<br />
</td>
        <td><a class="wiki_link" href="/35edo">35edo</a><br />
</td>
        <td><a class="wiki_link" href="/Avicennmic%20temperaments#Secund">secund</a><br />
</td>
        <td>27/26, 45/44, 99/98, 385/384<br />
</td>
    </tr>
    <tr>
        <td>27/26<br />
</td>
        <td><a class="wiki_link" href="/35edo">35edo</a><br />
</td>
        <td><a class="wiki_link" href="/Greenwoodmic%20temperaments#Greenwood">greenwood</a><br />
</td>
        <td>27/26, 45/44, 99/98, 640/637<br />
</td>
    </tr>
    <tr>
        <td>40/39<br />
</td>
        <td><a class="wiki_link" href="/15edo">15edo</a><br />
</td>
        <td><a class="wiki_link" href="/Archytas%20clan#Blacksmith">blacksmith</a><br />
</td>
        <td>28/27, 40/39, 49/48, 55/54<br />
</td>
    </tr>
    <tr>
        <td>65/64<br />
</td>
        <td><a class="wiki_link" href="/29edo">29edo</a><br />
</td>
        <td><a class="wiki_link" href="/Marvel%20temperaments#Negril">negril</a><br />
</td>
        <td>49/48, 65/64, 91/90, 875/858<br />
</td>
    </tr>
    <tr>
        <td>65/64<br />
</td>
        <td><a class="wiki_link" href="/29edo">29edo</a><br />
</td>
        <td><a class="wiki_link" href="/Porcupine%20family#Coendou">coendou</a><br />
</td>
        <td>55/54, 65/64, 100/99, 105/104<br />
</td>
    </tr>
    <tr>
        <td>66/65<br />
</td>
        <td><a class="wiki_link" href="/31edo">31edo</a><br />
</td>
        <td><a class="wiki_link" href="/Semicomma%20family#Winston">winston</a><br />
</td>
        <td>66/65, 99/98, 105/104, 121/120<br />
</td>
    </tr>
    <tr>
        <td>66/65<br />
</td>
        <td><a class="wiki_link" href="/31edo">31edo</a><br />
</td>
        <td><a class="wiki_link" href="/Meantone%20family#Mohajira-13-limit">mohajira</a><br />
</td>
        <td>66/65, 81/80, 105/104, 121/120<br />
</td>
    </tr>
    <tr>
        <td>66/65<br />
</td>
        <td><a class="wiki_link" href="/31edo">31edo</a><br />
</td>
        <td><a class="wiki_link" href="/Meantone%20family#Squares-13-limit">squares</a><br />
</td>
        <td>66/65, 81/80, 99/98, 121/120<br />
</td>
    </tr>
    <tr>
        <td>78/77<br />
</td>
        <td><a class="wiki_link" href="/43edo">43edo</a><br />
</td>
        <td><a class="wiki_link" href="/Marvel%20temperaments#Amavil">amavil</a><br />
</td>
        <td>78/77, 99/98, 144/143, 176/175<br />
</td>
    </tr>
    <tr>
        <td>78/77<br />
</td>
        <td><a class="wiki_link" href="/43edo">43edo</a><br />
</td>
        <td><a class="wiki_link" href="/Meantone%20family#Jerome">jerome</a><br />
</td>
        <td>78/77, 81/80, 99/98, 144/143<br />
</td>
    </tr>
    <tr>
        <td>91/90<br />
</td>
        <td><a class="wiki_link" href="/102edo">102edo</a><br />
</td>
        <td><a class="wiki_link" href="/Diaschismic%20family#Echidnic">echidnic</a><br />
</td>
        <td>91/90, 169/168, 385/384, 441/440<br />
</td>
    </tr>
    <tr>
        <td>105/104<br />
</td>
        <td><a class="wiki_link" href="/91edo">91edo</a><br />
</td>
        <td><a class="wiki_link" href="/Marvel%20temperaments#Septimin">septimin</a><br />
</td>
        <td>105/104, 144/143, 196/195, 245/242<br />
</td>
    </tr>
    <tr>
        <td>275/273<br />
</td>
        <td><a class="wiki_link" href="/94edo">94edo</a><br />
</td>
        <td><a class="wiki_link" href="/Schismatic%20family#Garibaldi">garibaldi</a><br />
</td>
        <td>225/224, 275/273, 325/324, 385/384<br />
</td>
    </tr>
    <tr>
        <td>275/273<br />
</td>
        <td><a class="wiki_link" href="/94edo">94edo</a><br />
</td>
        <td><a class="wiki_link" href="/Hemifamity%20temperaments#Supers">supers</a><br />
</td>
        <td>352/351, 540/539, 729/728, 1575/1573<br />
</td>
    </tr>
    <tr>
        <td>144/143<br />
</td>
        <td><a class="wiki_link" href="/84edo">84edo</a><br />
</td>
        <td><a class="wiki_link" href="/Marvel%20temperaments#Merman">merman</a><br />
</td>
        <td>144/143, 225/224, 364/363, 441/440<br />
</td>
    </tr>
    <tr>
        <td>144/143<br />
</td>
        <td><a class="wiki_link" href="/84edo">84edo</a><br />
</td>
        <td><a class="wiki_link" href="/Orwellismic%20temperaments">secant</a><br />
</td>
        <td>144/143, 351/350, 364/363, 441/440<br />
</td>
    </tr>
    <tr>
        <td>169/168<br />
</td>
        <td><a class="wiki_link" href="/152edo">152edo</a><br />
</td>
        <td><a class="wiki_link" href="/Ragismic%20microtemperaments#Octoid-Octopus">octopus</a><br />
</td>
        <td>169/168, 325/324, 364/363, 540/539<br />
</td>
    </tr>
</table>

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