Breedsmic temperaments: Difference between revisions
Wikispaces>genewardsmith **Imported revision 323637958 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 337128632 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<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- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-05-18 13:51:11 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>337128632</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> | ||
| Line 18: | Line 18: | ||
By adding 243/242 (which also means 441/440, 540/539 and 896/891) to the commas, hemififths extends to a less accurate 11-limit version, but one where 11/4 is only five generator steps. [[99edo]] is an excellent tuning; one which loses little of the accuracy of the 7-limit but improves the 11-limit a bit. Now adding 144/143 brings in the 13-limit with less accuracy yet, but with very low complexity, as the generator can be taken to be 16/13. 99 remains a good tuning choice. | By adding 243/242 (which also means 441/440, 540/539 and 896/891) to the commas, hemififths extends to a less accurate 11-limit version, but one where 11/4 is only five generator steps. [[99edo]] is an excellent tuning; one which loses little of the accuracy of the 7-limit but improves the 11-limit a bit. Now adding 144/143 brings in the 13-limit with less accuracy yet, but with very low complexity, as the generator can be taken to be 16/13. 99 remains a good tuning choice. | ||
==5-limit== | |||
Comma: 858993459200/847288609443 | |||
POTE generator: ~655360/531441 = 351.476 | |||
Map: [<1 1 -5|, <0 2 25|] | |||
EDOs: 41, 58, 99, 239, 338, 915b, 1253bc | |||
Badness: 0.3728 | |||
==7-limit== | |||
Commas: 2401/2400, 5120/5103 | Commas: 2401/2400, 5120/5103 | ||
| Line 352: | Line 362: | ||
EDOs: 157, 171, 1012, 1183, 1354, 1525, 1696, 6955d | EDOs: 157, 171, 1012, 1183, 1354, 1525, 1696, 6955d | ||
Badness: 0.0283 | Badness: 0.0283 | ||
</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"><html><head><title>Breedsmic temperaments</title></head><body><!-- ws:start:WikiTextTocRule: | <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"><html><head><title>Breedsmic temperaments</title></head><body><!-- ws:start:WikiTextTocRule:72:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:72 --><!-- ws:start:WikiTextTocRule:73: --><a href="#Hemififths">Hemififths</a><!-- ws:end:WikiTextTocRule:73 --><!-- ws:start:WikiTextTocRule:74: --><!-- ws:end:WikiTextTocRule:74 --><!-- ws:start:WikiTextTocRule:75: --><!-- ws:end:WikiTextTocRule:75 --><!-- ws:start:WikiTextTocRule:76: --><!-- ws:end:WikiTextTocRule:76 --><!-- ws:start:WikiTextTocRule:77: --><!-- ws:end:WikiTextTocRule:77 --><!-- ws:start:WikiTextTocRule:78: --> | <a href="#Semihemi">Semihemi</a><!-- ws:end:WikiTextTocRule:78 --><!-- ws:start:WikiTextTocRule:79: --><!-- ws:end:WikiTextTocRule:79 --><!-- ws:start:WikiTextTocRule:80: --> | <a href="#Tertiaseptal">Tertiaseptal</a><!-- ws:end:WikiTextTocRule:80 --><!-- ws:start:WikiTextTocRule:81: --><!-- ws:end:WikiTextTocRule:81 --><!-- ws:start:WikiTextTocRule:82: --><!-- ws:end:WikiTextTocRule:82 --><!-- ws:start:WikiTextTocRule:83: --> | <a href="#Hemitert">Hemitert</a><!-- ws:end:WikiTextTocRule:83 --><!-- ws:start:WikiTextTocRule:84: --> | <a href="#Harry">Harry</a><!-- ws:end:WikiTextTocRule:84 --><!-- ws:start:WikiTextTocRule:85: --><!-- ws:end:WikiTextTocRule:85 --><!-- ws:start:WikiTextTocRule:86: --><!-- ws:end:WikiTextTocRule:86 --><!-- ws:start:WikiTextTocRule:87: --> | <a href="#Quasiorwell">Quasiorwell</a><!-- ws:end:WikiTextTocRule:87 --><!-- ws:start:WikiTextTocRule:88: --><!-- ws:end:WikiTextTocRule:88 --><!-- ws:start:WikiTextTocRule:89: --><!-- ws:end:WikiTextTocRule:89 --><!-- ws:start:WikiTextTocRule:90: --> | <a href="#Decoid">Decoid</a><!-- ws:end:WikiTextTocRule:90 --><!-- ws:start:WikiTextTocRule:91: --><!-- ws:end:WikiTextTocRule:91 --><!-- ws:start:WikiTextTocRule:92: --><!-- ws:end:WikiTextTocRule:92 --><!-- ws:start:WikiTextTocRule:93: --> | <a href="#Neominor">Neominor</a><!-- ws:end:WikiTextTocRule:93 --><!-- ws:start:WikiTextTocRule:94: --><!-- ws:end:WikiTextTocRule:94 --><!-- ws:start:WikiTextTocRule:95: --><!-- ws:end:WikiTextTocRule:95 --><!-- ws:start:WikiTextTocRule:96: --> | <a href="#Emmthird">Emmthird</a><!-- ws:end:WikiTextTocRule:96 --><!-- ws:start:WikiTextTocRule:97: --> | <a href="#Quinmite">Quinmite</a><!-- ws:end:WikiTextTocRule:97 --><!-- ws:start:WikiTextTocRule:98: --> | <a href="#Unthirds">Unthirds</a><!-- ws:end:WikiTextTocRule:98 --><!-- ws:start:WikiTextTocRule:99: --><!-- ws:end:WikiTextTocRule:99 --><!-- ws:start:WikiTextTocRule:100: --><!-- ws:end:WikiTextTocRule:100 --><!-- ws:start:WikiTextTocRule:101: --> | <a href="#Newt">Newt</a><!-- ws:end:WikiTextTocRule:101 --><!-- ws:start:WikiTextTocRule:102: --><!-- ws:end:WikiTextTocRule:102 --><!-- ws:start:WikiTextTocRule:103: --><!-- ws:end:WikiTextTocRule:103 --><!-- ws:start:WikiTextTocRule:104: --> | <a href="#Amicable">Amicable</a><!-- ws:end:WikiTextTocRule:104 --><!-- ws:start:WikiTextTocRule:105: --> | <a href="#Septidiasemi">Septidiasemi</a><!-- ws:end:WikiTextTocRule:105 --><!-- ws:start:WikiTextTocRule:106: --> | <a href="#Maviloid">Maviloid</a><!-- ws:end:WikiTextTocRule:106 --><!-- ws:start:WikiTextTocRule:107: --> | <a href="#Subneutral">Subneutral</a><!-- ws:end:WikiTextTocRule:107 --><!-- ws:start:WikiTextTocRule:108: --> | <a href="#Osiris">Osiris</a><!-- ws:end:WikiTextTocRule:108 --><!-- ws:start:WikiTextTocRule:109: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:109 --><br /> | ||
<br /> | <br /> | ||
Breedsmic temperaments are rank two temperaments tempering out the breedsma, |-5 -1 -2 4&gt; = 2401/2400. This is the amount by which two 49/40 intervals exceed 3/2, and by which two 60/49 intervals fall short. Either of these represent a neutral third interval which is highly characteristic of breedsmic tempering; any tuning system (12edo, for example) which does not possess a neutral third cannot be tempering out the breedsma.<br /> | Breedsmic temperaments are rank two temperaments tempering out the breedsma, |-5 -1 -2 4&gt; = 2401/2400. This is the amount by which two 49/40 intervals exceed 3/2, and by which two 60/49 intervals fall short. Either of these represent a neutral third interval which is highly characteristic of breedsmic tempering; any tuning system (12edo, for example) which does not possess a neutral third cannot be tempering out the breedsma.<br /> | ||
| Line 367: | Line 376: | ||
By adding 243/242 (which also means 441/440, 540/539 and 896/891) to the commas, hemififths extends to a less accurate 11-limit version, but one where 11/4 is only five generator steps. <a class="wiki_link" href="/99edo">99edo</a> is an excellent tuning; one which loses little of the accuracy of the 7-limit but improves the 11-limit a bit. Now adding 144/143 brings in the 13-limit with less accuracy yet, but with very low complexity, as the generator can be taken to be 16/13. 99 remains a good tuning choice.<br /> | By adding 243/242 (which also means 441/440, 540/539 and 896/891) to the commas, hemififths extends to a less accurate 11-limit version, but one where 11/4 is only five generator steps. <a class="wiki_link" href="/99edo">99edo</a> is an excellent tuning; one which loses little of the accuracy of the 7-limit but improves the 11-limit a bit. Now adding 144/143 brings in the 13-limit with less accuracy yet, but with very low complexity, as the generator can be taken to be 16/13. 99 remains a good tuning choice.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="Hemififths-5-limit"></a><!-- ws:end:WikiTextHeadingRule:2 -->5-limit</h2> | |||
Comma: 858993459200/847288609443<br /> | |||
<br /> | |||
POTE generator: ~655360/531441 = 351.476<br /> | |||
<br /> | |||
Map: [&lt;1 1 -5|, &lt;0 2 25|]<br /> | |||
EDOs: 41, 58, 99, 239, 338, 915b, 1253bc<br /> | |||
Badness: 0.3728<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Hemififths-7-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->7-limit</h2> | |||
Commas: 2401/2400, 5120/5103<br /> | Commas: 2401/2400, 5120/5103<br /> | ||
<br /> | <br /> | ||
| Line 379: | Line 398: | ||
Badness: 0.0222<br /> | Badness: 0.0222<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Hemififths-11-limit"></a><!-- ws:end:WikiTextHeadingRule:6 -->11-limit</h2> | ||
Commas: 243/242, 441/440, 896/891<br /> | Commas: 243/242, 441/440, 896/891<br /> | ||
<br /> | <br /> | ||
| Line 388: | Line 407: | ||
Badness: 0.0235<br /> | Badness: 0.0235<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Hemififths-13-limit"></a><!-- ws:end:WikiTextHeadingRule:8 -->13-limit</h2> | ||
Commas: 144/143, 196/195, 243/242, 364/363<br /> | Commas: 144/143, 196/195, 243/242, 364/363<br /> | ||
<br /> | <br /> | ||
| Line 397: | Line 416: | ||
Badness: 0.0191<br /> | Badness: 0.0191<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="Semihemi"></a><!-- ws:end:WikiTextHeadingRule:10 -->Semihemi</h1> | ||
Commas: 2401/2400, 3388/3375, 9801/9800<br /> | Commas: 2401/2400, 3388/3375, 9801/9800<br /> | ||
<br /> | <br /> | ||
| Line 406: | Line 425: | ||
Badness: 42.487<br /> | Badness: 42.487<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Semihemi-13-limit"></a><!-- ws:end:WikiTextHeadingRule:12 -->13-limit</h2> | ||
Commas: 352/351, 676/675, 847/845, 1716/1715<br /> | Commas: 352/351, 676/675, 847/845, 1716/1715<br /> | ||
<br /> | <br /> | ||
| Line 415: | Line 434: | ||
Badness: 0.0212<br /> | Badness: 0.0212<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:14:&lt;h1&gt; --><h1 id="toc7"><a name="Tertiaseptal"></a><!-- ws:end:WikiTextHeadingRule:14 -->Tertiaseptal</h1> | ||
Aside from the breedsma, tertiaseptal tempers out 65625/65536, the horwell comma, 703125/702464, the meter, and 2100875/2097152. It can be described as the 140&amp;171 temperament, and 256/245, 1029/1024 less than 21/20, serves as its generator. Three of these fall short of 8/7 by 2100875/2097152, and the generator can be taken as 1/3 of an 8/7 flattened by a fraction of a cent. <a class="wiki_link" href="/171edo">171edo</a> makes for an excellent tuning. The 15 or 16 note MOS can be used to explore no-threes harmony, and the 31 note MOS gives plenty of room for those as well.<br /> | Aside from the breedsma, tertiaseptal tempers out 65625/65536, the horwell comma, 703125/702464, the meter, and 2100875/2097152. It can be described as the 140&amp;171 temperament, and 256/245, 1029/1024 less than 21/20, serves as its generator. Three of these fall short of 8/7 by 2100875/2097152, and the generator can be taken as 1/3 of an 8/7 flattened by a fraction of a cent. <a class="wiki_link" href="/171edo">171edo</a> makes for an excellent tuning. The 15 or 16 note MOS can be used to explore no-threes harmony, and the 31 note MOS gives plenty of room for those as well.<br /> | ||
<br /> | <br /> | ||
| Line 426: | Line 445: | ||
Badness: 0.0130<br /> | Badness: 0.0130<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="Tertiaseptal-11-limit"></a><!-- ws:end:WikiTextHeadingRule:16 -->11-limit</h2> | ||
Commas: 243/242, 441/440, 65625/65536<br /> | Commas: 243/242, 441/440, 65625/65536<br /> | ||
<br /> | <br /> | ||
| Line 435: | Line 454: | ||
Badness: 0.0356<br /> | Badness: 0.0356<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="Tertiaseptal-Tertia"></a><!-- ws:end:WikiTextHeadingRule:18 -->Tertia</h2> | ||
Commas: 385/384, 1331/1323, 1375/1372<br /> | Commas: 385/384, 1331/1323, 1375/1372<br /> | ||
<br /> | <br /> | ||
| Line 444: | Line 463: | ||
Badness: 0.0302<br /> | Badness: 0.0302<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc10"><a name="Hemitert"></a><!-- ws:end:WikiTextHeadingRule:20 -->Hemitert</h1> | ||
Commas: 2401/2400 3025/3024 65625/65536<br /> | Commas: 2401/2400 3025/3024 65625/65536<br /> | ||
<br /> | <br /> | ||
| Line 453: | Line 472: | ||
Badness: 0.0156<br /> | Badness: 0.0156<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:22:&lt;h1&gt; --><h1 id="toc11"><a name="Harry"></a><!-- ws:end:WikiTextHeadingRule:22 -->Harry</h1> | ||
Commas: 2401/2400, 19683/19600<br /> | Commas: 2401/2400, 19683/19600<br /> | ||
<br /> | <br /> | ||
| Line 469: | Line 488: | ||
Badness: 0.0341<br /> | Badness: 0.0341<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:24:&lt;h2&gt; --><h2 id="toc12"><a name="Harry-11-limit"></a><!-- ws:end:WikiTextHeadingRule:24 -->11-limit</h2> | ||
Commas: 243/242, 441/440, 4000/3993<br /> | Commas: 243/242, 441/440, 4000/3993<br /> | ||
<br /> | <br /> | ||
| Line 478: | Line 497: | ||
Badness: 0.0159<br /> | Badness: 0.0159<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:26:&lt;h2&gt; --><h2 id="toc13"><a name="Harry-13-limit"></a><!-- ws:end:WikiTextHeadingRule:26 -->13-limit</h2> | ||
Commas: 243/242, 351/350, 441/440, 676/675<br /> | Commas: 243/242, 351/350, 441/440, 676/675<br /> | ||
<br /> | <br /> | ||
| Line 487: | Line 506: | ||
Badness: 0.0130<br /> | Badness: 0.0130<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:28:&lt;h1&gt; --><h1 id="toc14"><a name="Quasiorwell"></a><!-- ws:end:WikiTextHeadingRule:28 -->Quasiorwell</h1> | ||
In addition to 2401/2400, quasiorwell tempers out 29360128/29296875 = |22 -1 -10 1&gt;. It has a wedgie &lt;&lt;38 -3 8 -93 -94 27||. It has a generator 1024/875, which is 6144/6125 more than 7/6. It may be described as the 31&amp;270 temperament, and as one might expect, 61/270 makes for an excellent tuning choice. Other possibilities are (7/2)^(1/8), giving just 7s, or 384^(1/38), giving pure fifths.<br /> | In addition to 2401/2400, quasiorwell tempers out 29360128/29296875 = |22 -1 -10 1&gt;. It has a wedgie &lt;&lt;38 -3 8 -93 -94 27||. It has a generator 1024/875, which is 6144/6125 more than 7/6. It may be described as the 31&amp;270 temperament, and as one might expect, 61/270 makes for an excellent tuning choice. Other possibilities are (7/2)^(1/8), giving just 7s, or 384^(1/38), giving pure fifths.<br /> | ||
<br /> | <br /> | ||
| Line 500: | Line 519: | ||
Badness: 0.0358<br /> | Badness: 0.0358<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:30:&lt;h2&gt; --><h2 id="toc15"><a name="Quasiorwell-11-limit"></a><!-- ws:end:WikiTextHeadingRule:30 -->11-limit</h2> | ||
Commas: 2401/2400, 3025/3024, 5632/5625<br /> | Commas: 2401/2400, 3025/3024, 5632/5625<br /> | ||
<br /> | <br /> | ||
| Line 509: | Line 528: | ||
Badness: 0.0175<br /> | Badness: 0.0175<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:32:&lt;h2&gt; --><h2 id="toc16"><a name="Quasiorwell-13-limit"></a><!-- ws:end:WikiTextHeadingRule:32 -->13-limit</h2> | ||
Commas: 1001/1000, 1716/1715, 3025/3024, 4096/4095<br /> | Commas: 1001/1000, 1716/1715, 3025/3024, 4096/4095<br /> | ||
<br /> | <br /> | ||
| Line 518: | Line 537: | ||
Badness: 0.0179<br /> | Badness: 0.0179<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:34:&lt;h1&gt; --><h1 id="toc17"><a name="Decoid"></a><!-- ws:end:WikiTextHeadingRule:34 -->Decoid</h1> | ||
Commas: 2401/2400, 67108864/66976875<br /> | Commas: 2401/2400, 67108864/66976875<br /> | ||
<br /> | <br /> | ||
| Line 528: | Line 547: | ||
Badness: 0.0339<br /> | Badness: 0.0339<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:36:&lt;h2&gt; --><h2 id="toc18"><a name="Decoid-11-limit"></a><!-- ws:end:WikiTextHeadingRule:36 -->11-limit</h2> | ||
Commas: 2401/2400, 5832/5825, 9801/9800<br /> | Commas: 2401/2400, 5832/5825, 9801/9800<br /> | ||
<br /> | <br /> | ||
| Line 537: | Line 556: | ||
Badness: 0.0187<br /> | Badness: 0.0187<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:38:&lt;h2&gt; --><h2 id="toc19"><a name="Decoid-13-limit"></a><!-- ws:end:WikiTextHeadingRule:38 -->13-limit</h2> | ||
Commas: 676/675, 1001/1000, 1716/1715, 4225/4224<br /> | Commas: 676/675, 1001/1000, 1716/1715, 4225/4224<br /> | ||
<br /> | <br /> | ||
| Line 546: | Line 565: | ||
Badness: 0.0135<br /> | Badness: 0.0135<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:40:&lt;h1&gt; --><h1 id="toc20"><a name="Neominor"></a><!-- ws:end:WikiTextHeadingRule:40 -->Neominor</h1> | ||
Commas: 2401/2400, 177147/175616<br /> | Commas: 2401/2400, 177147/175616<br /> | ||
<br /> | <br /> | ||
| Line 556: | Line 575: | ||
Badness: 0.0882<br /> | Badness: 0.0882<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:42:&lt;h2&gt; --><h2 id="toc21"><a name="Neominor-11-limit"></a><!-- ws:end:WikiTextHeadingRule:42 -->11-limit</h2> | ||
Commas: 243/242, 441/440, 35937/35840<br /> | Commas: 243/242, 441/440, 35937/35840<br /> | ||
<br /> | <br /> | ||
| Line 565: | Line 584: | ||
Badness: 0.0280<br /> | Badness: 0.0280<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:44:&lt;h2&gt; --><h2 id="toc22"><a name="Neominor-13-limit"></a><!-- ws:end:WikiTextHeadingRule:44 -->13-limit</h2> | ||
Commas: 169/168, 243/242, 364/363, 441/440<br /> | Commas: 169/168, 243/242, 364/363, 441/440<br /> | ||
<br /> | <br /> | ||
| Line 574: | Line 593: | ||
Badness: 0.0269<br /> | Badness: 0.0269<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:46:&lt;h1&gt; --><h1 id="toc23"><a name="Emmthird"></a><!-- ws:end:WikiTextHeadingRule:46 -->Emmthird</h1> | ||
The generator for emmthird temperament is the hemimage third, sharper than 5/4 by the hemimage comma, 10976/10935.<br /> | The generator for emmthird temperament is the hemimage third, sharper than 5/4 by the hemimage comma, 10976/10935.<br /> | ||
<br /> | <br /> | ||
| Line 586: | Line 605: | ||
Badness: 0.0167<br /> | Badness: 0.0167<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:48:&lt;h1&gt; --><h1 id="toc24"><a name="Quinmite"></a><!-- ws:end:WikiTextHeadingRule:48 -->Quinmite</h1> | ||
Commas: 2401/2400, 1959552/1953125<br /> | Commas: 2401/2400, 1959552/1953125<br /> | ||
<br /> | <br /> | ||
| Line 596: | Line 615: | ||
Badness: 0.0373<br /> | Badness: 0.0373<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:50:&lt;h1&gt; --><h1 id="toc25"><a name="Unthirds"></a><!-- ws:end:WikiTextHeadingRule:50 -->Unthirds</h1> | ||
Commas: 2401/2400, 68359375/68024448<br /> | Commas: 2401/2400, 68359375/68024448<br /> | ||
<br /> | <br /> | ||
| Line 606: | Line 625: | ||
Badness: 0.0753<br /> | Badness: 0.0753<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:52:&lt;h2&gt; --><h2 id="toc26"><a name="Unthirds-11-limit"></a><!-- ws:end:WikiTextHeadingRule:52 -->11-limit</h2> | ||
Commas: 2401/2400, 3025/3024, 4000/3993<br /> | Commas: 2401/2400, 3025/3024, 4000/3993<br /> | ||
<br /> | <br /> | ||
| Line 615: | Line 634: | ||
Badness: 0.0229<br /> | Badness: 0.0229<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:54:&lt;h2&gt; --><h2 id="toc27"><a name="Unthirds-13-limit"></a><!-- ws:end:WikiTextHeadingRule:54 -->13-limit</h2> | ||
Commas: 625/624, 1575/1573, 2080/2079, 2401/2400<br /> | Commas: 625/624, 1575/1573, 2080/2079, 2401/2400<br /> | ||
<br /> | <br /> | ||
| Line 624: | Line 643: | ||
Badness: 0.0209<br /> | Badness: 0.0209<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:56:&lt;h1&gt; --><h1 id="toc28"><a name="Newt"></a><!-- ws:end:WikiTextHeadingRule:56 -->Newt</h1> | ||
Commas: 2401/2400, 33554432/33480783<br /> | Commas: 2401/2400, 33554432/33480783<br /> | ||
<br /> | <br /> | ||
| Line 634: | Line 653: | ||
Badness: 0.0419<br /> | Badness: 0.0419<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:58:&lt;h2&gt; --><h2 id="toc29"><a name="Newt-11-limit"></a><!-- ws:end:WikiTextHeadingRule:58 -->11-limit</h2> | ||
Commas: 2401/2400, 3025/3024, 19712/19683<br /> | Commas: 2401/2400, 3025/3024, 19712/19683<br /> | ||
<br /> | <br /> | ||
| Line 643: | Line 662: | ||
Badness: 0.0195<br /> | Badness: 0.0195<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:60:&lt;h2&gt; --><h2 id="toc30"><a name="Newt-13-limit"></a><!-- ws:end:WikiTextHeadingRule:60 -->13-limit</h2> | ||
Commas: 2080/2079, 2401/2400, 3025/3024, 4096/4095<br /> | Commas: 2080/2079, 2401/2400, 3025/3024, 4096/4095<br /> | ||
<br /> | <br /> | ||
| Line 652: | Line 671: | ||
Badness: 0.0138<br /> | Badness: 0.0138<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:62:&lt;h1&gt; --><h1 id="toc31"><a name="Amicable"></a><!-- ws:end:WikiTextHeadingRule:62 -->Amicable</h1> | ||
Commas: 2401/2400, 1600000/1594323<br /> | Commas: 2401/2400, 1600000/1594323<br /> | ||
<br /> | <br /> | ||
| Line 662: | Line 681: | ||
Badness: 0.0455<br /> | Badness: 0.0455<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:64:&lt;h1&gt; --><h1 id="toc32"><a name="Septidiasemi"></a><!-- ws:end:WikiTextHeadingRule:64 -->Septidiasemi</h1> | ||
Commas: 2401/2400, 2152828125/2147483648<br /> | Commas: 2401/2400, 2152828125/2147483648<br /> | ||
<br /> | <br /> | ||
| Line 672: | Line 691: | ||
Badness: 0.0441<br /> | Badness: 0.0441<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:66:&lt;h1&gt; --><h1 id="toc33"><a name="Maviloid"></a><!-- ws:end:WikiTextHeadingRule:66 -->Maviloid</h1> | ||
Commas: 2401/2400, 1224440064/1220703125<br /> | Commas: 2401/2400, 1224440064/1220703125<br /> | ||
<br /> | <br /> | ||
| Line 682: | Line 701: | ||
Badness: 0.0576<br /> | Badness: 0.0576<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:68:&lt;h1&gt; --><h1 id="toc34"><a name="Subneutral"></a><!-- ws:end:WikiTextHeadingRule:68 -->Subneutral</h1> | ||
Commas: 2401/2400, 274877906944/274658203125<br /> | Commas: 2401/2400, 274877906944/274658203125<br /> | ||
<br /> | <br /> | ||
| Line 692: | Line 711: | ||
Badness: 0.0458<br /> | Badness: 0.0458<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:70:&lt;h1&gt; --><h1 id="toc35"><a name="Osiris"></a><!-- ws:end:WikiTextHeadingRule:70 -->Osiris</h1> | ||
Commas: 2401/2400, 31381059609/31360000000<br /> | Commas: 2401/2400, 31381059609/31360000000<br /> | ||
<br /> | <br /> | ||