Magic family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 337663318 - Original comment: ** |
Wikispaces>guest **Imported revision 360079091 - 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: | : This revision was by author [[User:guest|guest]] and made on <tt>2012-08-26 21:31:04 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>360079091</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">[[toc]] | <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">[[toc]] | ||
=Five limit magic= | |||
=Five limit magic= | The 5-limit parent comma for the magic family is 3125/3072, the small diesis or magic comma. Its monzo is |-10 -1 5>, and flipping that yields <<5 1 -10|| for the wedgie. This tells us the generator is a major third, and that to get to the interval class of fifths will require five of these. In fact, (5/4)^5 = 3 * 3125/3072. 13/41 is a highly recommendable generator, though 19\60, the optimal patent val generator, also makes a lot of sense and using [[19edo]] or [[22edo]] is always possible. | ||
The 5-limit parent comma for the magic family is 3125/3072, the small diesis or magic comma. Its monzo is |-10 -1 5>, and flipping that yields <<5 1 -10|| for the wedgie. This tells us the generator is a major third, and that to get to the interval class of fifths will require five of these. In fact, (5/4)^5 = 3 * 3125/3072. 13/41 is a highly recommendable generator, though 19\60, the optimal patent val generator, also makes a lot of | |||
[[Comma]]: 3125/3072 | [[Comma]]: 3125/3072 | ||
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[[Edo|Edos]]: [[6edo|6]], [[16edo|16]], [[19edo|19]], [[22edo|22]], [[41edo|41]], [[60edo|60]], [[221edo|221c]], [[281edo|281c]] | [[Edo|Edos]]: [[6edo|6]], [[16edo|16]], [[19edo|19]], [[22edo|22]], [[41edo|41]], [[60edo|60]], [[221edo|221c]], [[281edo|281c]] | ||
==Seven limit children== | ==Seven limit children== | ||
The second comma of the [[Normal lists|normal comma list]] defines which 7-limit family member we are looking at. 875/864, the keemic comma, gives magic, and 525/512, Avicenna's enharmonic diesis, gives his annoying brother muggles. Both use the major third as a generator. | The second comma of the [[Normal lists|normal comma list]] defines which 7-limit family member we are looking at. 875/864, the keemic comma, gives magic, and 525/512, Avicenna's enharmonic diesis, gives his annoying brother muggles. Both use the major third as a generator. | ||
=Magic= | =Magic= | ||
Magic tempers out not only 3125/3072 and 875/864, but also 225/224, 245/243, and 10976/10935. [[41edo]] is a good magic tuning, and 19 or 22 note MOS are possible scales. Five major thirds approximate 3/1. Twelve major thirds, less an octave, approximate 7/1. | Magic tempers out not only 3125/3072 and 875/864, but also 225/224, 245/243, and 10976/10935. [[41edo]] is a good magic tuning, and 19 or 22 note MOS are possible scales. Five major thirds approximate 3/1. Twelve major thirds, less an octave, approximate 7/1. | ||
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EDOs: 41, 142cd, 183cd, 224cd | EDOs: 41, 142cd, 183cd, 224cd | ||
==11-limit== | ==11-limit== | ||
Commas: 225/224, 245/243, 100/99 | Commas: 225/224, 245/243, 100/99 | ||
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Badness: 0.0204 | Badness: 0.0204 | ||
==13-limit== | ==13-limit== | ||
Commas: 100/99, 105/104, 144/143, 196/195 | Commas: 100/99, 105/104, 144/143, 196/195 | ||
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Badness: 0.0215 | Badness: 0.0215 | ||
===Sorcery=== | ===Sorcery=== | ||
Commas: 65/64, 78/77, 91/90, 100/99 | Commas: 65/64, 78/77, 91/90, 100/99 | ||
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Badness: 0.0258 | Badness: 0.0258 | ||
===Necromancy=== | ===Necromancy=== | ||
Commas: 100/99, 225/224, 245/243, 275/273 | Commas: 100/99, 225/224, 245/243, 275/273 | ||
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Badness: 0.0253 | Badness: 0.0253 | ||
==Telepathy== | ==Telepathy== | ||
Commas: 55/54, 99/98, 176/175 | Commas: 55/54, 99/98, 176/175 | ||
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Badness: 0.0271 | Badness: 0.0271 | ||
===13-limit telepathy=== | ===13-limit telepathy=== | ||
Commas: 55/54, 65/64, 91/90, 99/98 | Commas: 55/54, 65/64, 91/90, 99/98 | ||
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Badness: 0.0255 | Badness: 0.0255 | ||
==Horcrux== | ==Horcrux== | ||
Commas: 45/44, 56/55, 245/243 | Commas: 45/44, 56/55, 245/243 | ||
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Badness: 0.0393 | Badness: 0.0393 | ||
=Divination= | =Divination= | ||
Commas: 121/120, 225/224, 245/243 | Commas: 121/120, 225/224, 245/243 | ||
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Badness: 0.0359 | Badness: 0.0359 | ||
==13-limit== | ==13-limit== | ||
Commas: 105/104, 121/120, 196/195, 245/243 | Commas: 105/104, 121/120, 196/195, 245/243 | ||
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Badness: 0.0346 | Badness: 0.0346 | ||
=Soothsaying= | =Soothsaying= | ||
Commas: 100/99, 225/224, 245/243, 1352/1331 | Commas: 100/99, 225/224, 245/243, 1352/1331 | ||
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Badness: 0.0554 | Badness: 0.0554 | ||
=Witchcraft= | =Witchcraft= | ||
Commas: 225/224, 245/243, 441/440 | Commas: 225/224, 245/243, 441/440 | ||
POTE generator: ~5/4 = 380.232 | POTE generator: ~5/4 = 380.232 | ||
Map: [<1 0 2 -1 -7|, | Map: [<1 0 2 -1 -7|, <0 5 1 12 33|] | ||
EDOs: 41, 60e, 101cd, 243cde | EDOs: 41, 60e, 101cd, 243cde | ||
Badness: 0.0307 | Badness: 0.0307 | ||
==13-limit== | ==13-limit== | ||
Commas: 105/104, 196/195, 245/243, 275/273 | Commas: 105/104, 196/195, 245/243, 275/273 | ||
POTE generator: ~5/4 = | POTE generator: ~5/4 = 380.189 | ||
Map: [<1 0 2 -1 -7 -2|, | Map: [<1 0 2 -1 -7 -2|, <0 5 1 12 33 18|] | ||
EDOs: 41, 60e, 101cd | EDOs: 41, 60e, 101cd | ||
Badness: 0.0235 | Badness: 0.0235 | ||
=Muggles= | =Muggles= | ||
Aside from 3125/3072 and 525/512 muggles also tempers out 126/125 and 1323/1280. A good muggles tuning is [[19edo]], in which tuning it's the same thing as magic. Muggles works better for small scales than magic in the sense that 7 or 10 note MOS are reasonable choices. The muggles wedgie is <<5 1 -7 -10 -25 -19||. | Aside from 3125/3072 and 525/512 muggles also tempers out 126/125 and 1323/1280. A good muggles tuning is [[19edo]], in which tuning it's the same thing as magic. Muggles works better for small scales than magic in the sense that 7 or 10 note MOS are reasonable choices. The muggles wedgie is <<5 1 -7 -10 -25 -19||. | ||
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EDOs: 19, 73bcd, 92bcd | EDOs: 19, 73bcd, 92bcd | ||
=Astrology= | =Astrology= | ||
Commas: 50/49, 3125/3072 | Commas: 50/49, 3125/3072 | ||
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Badness: 0.0827 | Badness: 0.0827 | ||
==11-limit== | ==11-limit== | ||
Commas: 50/49, 121/120, 176/175 | Commas: 50/49, 121/120, 176/175 | ||
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Badness: 0.0392 | Badness: 0.0392 | ||
==13-limit== | ==13-limit== | ||
Commas: 50/49, 65/64, 78/77, 121/120 | Commas: 50/49, 65/64, 78/77, 121/120 | ||
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Badness: 0.0344 | Badness: 0.0344 | ||
==Horoscope== | ==Horoscope== | ||
Commas: 50/49, 66/65, 105/104, 121/120 | Commas: 50/49, 66/65, 105/104, 121/120 | ||
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Badness: 0.0353 | Badness: 0.0353 | ||
=Spell= | =Spell= | ||
Commas: 49/48, 3125/3072 | Commas: 49/48, 3125/3072 | ||
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Badness: 0.0810 | Badness: 0.0810 | ||
==11-limit== | ==11-limit== | ||
Commas: 49/48, 56/55, 125/121 | Commas: 49/48, 56/55, 125/121 | ||
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Badness: 0.0598 | Badness: 0.0598 | ||
==13-limit== | ==13-limit== | ||
Commas: 49/48, 56/55, 78/77, 125/121 | Commas: 49/48, 56/55, 78/77, 125/121 | ||
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Badness: 0.0456 | Badness: 0.0456 | ||
==Cantrip== | ==Cantrip== | ||
Commas: 49/48, 56/55, 91/90, 125/121 | Commas: 49/48, 56/55, 91/90, 125/121 | ||
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Badness: 0.0416 | Badness: 0.0416 | ||
=Hocum= | =Hocum= | ||
Commas: 3125/3072, 4000/3969 | Commas: 3125/3072, 4000/3969 | ||
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Badness: 0.1071 | Badness: 0.1071 | ||
=Hocus= | =Hocus= | ||
Commas: 225/224, 243/242, 245/242 | Commas: 225/224, 243/242, 245/242 | ||
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Badness: 0.0385 | Badness: 0.0385 | ||
==13-limit== | ==13-limit== | ||
Commas: 105/104, 196/195, 243/242, 245/242 | Commas: 105/104, 196/195, 243/242, 245/242 | ||
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Badness: 0.0303 | Badness: 0.0303 | ||
=Trismegistus= | =Trismegistus= | ||
Commas: 3125/3072, 1029/1024 | Commas: 3125/3072, 1029/1024 | ||
POTE generator: ~147/100 = 673.290 | POTE generator: ~147/100 = 673.290 | ||
Map: [<1 10 4 0|, | Map: [<1 10 4 0|, <0 -15 -3 5|] | ||
Wedgie: <<15 3 -5 -30 -50 -20|| | Wedgie: <<15 3 -5 -30 -50 -20|| | ||
EDOs: 16, 25, 41, 139c, 180c, 221c, 262c | EDOs: 16, 25, 41, 139c, 180c, 221c, 262c | ||
Badness: 0.0983 | Badness: 0.0983 | ||
==11-limit== | ==11-limit== | ||
Commas: 385/384, 441/440, 625/616 | Commas: 385/384, 441/440, 625/616 | ||
POTE generator: ~22/15 = 673.340 | POTE generator: ~22/15 = 673.340 | ||
Map: [<1 10 4 0 13|, | Map: [<1 10 4 0 13|, <0 -15 -3 5 -17|] | ||
EDOs: 16, 25e, 41, 98c, 139c, 180c | EDOs: 16, 25e, 41, 98c, 139c, 180c | ||
Badness: 0.0456 | Badness: 0.0456 | ||
==13-limit== | ==13-limit== | ||
Commas: 105/104, 144/143, 275/273, 625/616 | Commas: 105/104, 144/143, 275/273, 625/616 | ||
POTE generator: ~22/15 = 673.359 | POTE generator: ~22/15 = 673.359 | ||
Map: [<1 10 4 0 13 11|, | Map: [<1 10 4 0 13 11|, <0 -15 -3 5 -17 -13|] | ||
EDOs: 16, 25e, 41, 98c, 139cf | EDOs: 16, 25e, 41, 98c, 139cf | ||
Badness: 0.0331 | Badness: 0.0331 | ||
=Quadrimage= | =Quadrimage= | ||
Commas: 2401/2400, 3125/3072 | Commas: 2401/2400, 3125/3072 | ||
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Badness: 0.1274 | Badness: 0.1274 | ||
==11-limit== | ==11-limit== | ||
Commas: 245/242, 385/384, 625/616 | Commas: 245/242, 385/384, 625/616 | ||
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Badness: 0.0616 | Badness: 0.0616 | ||
==13-limit== | ==13-limit== | ||
Commas: 105/104, 144/143, 245/242, 625/616 | Commas: 105/104, 144/143, 245/242, 625/616 | ||
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Map: [<1 5 3 4 5 9|, <0 -20 -4 -7 -9 -31|] | Map: [<1 5 3 4 5 9|, <0 -20 -4 -7 -9 -31|] | ||
EDOs: 41, 117c, 158cd, 199cdef | EDOs: 41, 117c, 158cd, 199cdef | ||
Badness: 0.0440 | Badness: 0.0440</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>Magic family</title></head><body><!-- ws:start:WikiTextTocRule:66:&lt;img id=&quot;wikitext@@toc@@normal&quot; class=&quot;WikiMedia WikiMediaToc&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/normal?w=225&amp;h=100&quot;/&gt; --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:66 --><!-- ws:start:WikiTextTocRule:67: --><div style="margin-left: 1em;"><a href="#Five limit magic">Five limit magic</a></div> | <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>Magic family</title></head><body><!-- ws:start:WikiTextTocRule:66:&lt;img id=&quot;wikitext@@toc@@normal&quot; class=&quot;WikiMedia WikiMediaToc&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/normal?w=225&amp;h=100&quot;/&gt; --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:66 --><!-- ws:start:WikiTextTocRule:67: --><div style="margin-left: 1em;"><a href="#Five limit magic">Five limit magic</a></div> | ||
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<!-- ws:end:WikiTextTocRule:98 --><!-- ws:start:WikiTextTocRule:99: --><div style="margin-left: 2em;"><a href="#Quadrimage-13-limit">13-limit</a></div> | <!-- ws:end:WikiTextTocRule:98 --><!-- ws:start:WikiTextTocRule:99: --><div style="margin-left: 2em;"><a href="#Quadrimage-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule:99 --><!-- ws:start:WikiTextTocRule:100: --></div> | <!-- ws:end:WikiTextTocRule:99 --><!-- ws:start:WikiTextTocRule:100: --></div> | ||
<!-- ws:end:WikiTextTocRule:100 --> | <!-- ws:end:WikiTextTocRule:100 --><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Five limit magic"></a><!-- ws:end:WikiTextHeadingRule:0 -->Five limit magic</h1> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Five limit magic"></a><!-- ws:end:WikiTextHeadingRule:0 -->Five limit magic</h1> | The 5-limit parent comma for the magic family is 3125/3072, the small diesis or magic comma. Its monzo is |-10 -1 5&gt;, and flipping that yields &lt;&lt;5 1 -10|| for the wedgie. This tells us the generator is a major third, and that to get to the interval class of fifths will require five of these. In fact, (5/4)^5 = 3 * 3125/3072. 13/41 is a highly recommendable generator, though 19\60, the optimal patent val generator, also makes a lot of sense and using <a class="wiki_link" href="/19edo">19edo</a> or <a class="wiki_link" href="/22edo">22edo</a> is always possible.<br /> | ||
The 5-limit parent comma for the magic family is 3125/3072, the small diesis or magic comma. Its monzo is |-10 -1 5&gt;, and flipping that yields &lt;&lt;5 1 -10|| for the wedgie. This tells us the generator is a major third, and that to get to the interval class of fifths will require five of these. In fact, (5/4)^5 = 3 * 3125/3072. 13/41 is a highly recommendable generator, though 19\60, the optimal patent val generator, also makes a lot of | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/Comma">Comma</a>: 3125/3072<br /> | <a class="wiki_link" href="/Comma">Comma</a>: 3125/3072<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="Five limit magic-Seven limit children"></a><!-- ws:end:WikiTextHeadingRule:2 -->Seven limit children</h2> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="Five limit magic-Seven limit children"></a><!-- ws:end:WikiTextHeadingRule:2 -->Seven limit children</h2> | ||
The second comma of the <a class="wiki_link" href="/Normal%20lists">normal comma list</a> defines which 7-limit family member we are looking at. 875/864, the keemic comma, gives magic, and 525/512, Avicenna's enharmonic diesis, gives his annoying brother muggles. Both use the major third as a generator.<br /> | The second comma of the <a class="wiki_link" href="/Normal%20lists">normal comma list</a> defines which 7-limit family member we are looking at. 875/864, the keemic comma, gives magic, and 525/512, Avicenna's enharmonic diesis, gives his annoying brother muggles. Both use the major third as a generator.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Magic"></a><!-- ws:end:WikiTextHeadingRule:4 -->Magic</h1> | <!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Magic"></a><!-- ws:end:WikiTextHeadingRule:4 -->Magic</h1> | ||
Magic tempers out not only 3125/3072 and 875/864, but also 225/224, 245/243, and 10976/10935. <a class="wiki_link" href="/41edo">41edo</a> is a good magic tuning, and 19 or 22 note MOS are possible scales. Five major thirds approximate 3/1. Twelve major thirds, less an octave, approximate 7/1.<br /> | Magic tempers out not only 3125/3072 and 875/864, but also 225/224, 245/243, and 10976/10935. <a class="wiki_link" href="/41edo">41edo</a> is a good magic tuning, and 19 or 22 note MOS are possible scales. Five major thirds approximate 3/1. Twelve major thirds, less an octave, approximate 7/1.<br /> | ||
<br /> | <br /> | ||
Magic, with its accurate fifths, works well with 9-limit harmony. It's more accurate than meantone and simpler than garibaldi. It's a little tricky to work with because in it fifths are a relatively complex interval and it doesn't naturally work with scales of around seven notes to the octave. Its wedgie is &lt;&lt;5 1 12 -10 5 25||.<br /> | Magic, with its accurate fifths, works well with 9-limit harmony. It's more accurate than meantone and simpler than garibaldi. It's a little tricky to work with because in it fifths are a relatively complex interval and it doesn't naturally work with scales of around seven notes to the octave. Its wedgie is &lt;&lt;5 1 12 -10 5 25||.<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Magic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:6 -->11-limit</h2> | <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Magic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:6 -->11-limit</h2> | ||
Commas: 225/224, 245/243, 100/99<br /> | Commas: 225/224, 245/243, 100/99<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 380.696<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 380.696<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Magic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:8 -->13-limit</h2> | <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Magic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:8 -->13-limit</h2> | ||
Commas: 100/99, 105/104, 144/143, 196/195<br /> | Commas: 100/99, 105/104, 144/143, 196/195<br /> | ||
<br /> | <br /> | ||
POTE generator: ~5/4 = 380.427<br /> | POTE generator: ~5/4 = 380.427<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><h3 id="toc5"><a name="Magic-13-limit-Sorcery"></a><!-- ws:end:WikiTextHeadingRule:10 -->Sorcery</h3> | <!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><h3 id="toc5"><a name="Magic-13-limit-Sorcery"></a><!-- ws:end:WikiTextHeadingRule:10 -->Sorcery</h3> | ||
Commas: 65/64, 78/77, 91/90, 100/99<br /> | Commas: 65/64, 78/77, 91/90, 100/99<br /> | ||
<br /> | <br /> | ||
POTE generator: ~5/4 = 380.477<br /> | POTE generator: ~5/4 = 380.477<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:12:&lt;h3&gt; --><h3 id="toc6"><a name="Magic-13-limit-Necromancy"></a><!-- ws:end:WikiTextHeadingRule:12 -->Necromancy</h3> | <!-- ws:start:WikiTextHeadingRule:12:&lt;h3&gt; --><h3 id="toc6"><a name="Magic-13-limit-Necromancy"></a><!-- ws:end:WikiTextHeadingRule:12 -->Necromancy</h3> | ||
Commas: 100/99, 225/224, 245/243, 275/273<br /> | Commas: 100/99, 225/224, 245/243, 275/273<br /> | ||
<br /> | <br /> | ||
POTE generator: ~5/4 = 380.787<br /> | POTE generator: ~5/4 = 380.787<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="Magic-Telepathy"></a><!-- ws:end:WikiTextHeadingRule:14 -->Telepathy</h2> | <!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="Magic-Telepathy"></a><!-- ws:end:WikiTextHeadingRule:14 -->Telepathy</h2> | ||
Commas: 55/54, 99/98, 176/175<br /> | Commas: 55/54, 99/98, 176/175<br /> | ||
<br /> | <br /> | ||
POTE generator: ~5/4 = 381.019<br /> | POTE generator: ~5/4 = 381.019<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:16:&lt;h3&gt; --><h3 id="toc8"><a name="Magic-Telepathy-13-limit telepathy"></a><!-- ws:end:WikiTextHeadingRule:16 -->13-limit telepathy</h3> | <!-- ws:start:WikiTextHeadingRule:16:&lt;h3&gt; --><h3 id="toc8"><a name="Magic-Telepathy-13-limit telepathy"></a><!-- ws:end:WikiTextHeadingRule:16 -->13-limit telepathy</h3> | ||
Commas: 55/54, 65/64, 91/90, 99/98<br /> | Commas: 55/54, 65/64, 91/90, 99/98<br /> | ||
<br /> | <br /> | ||
POTE generator: ~5/4 = 380.520<br /> | POTE generator: ~5/4 = 380.520<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="Magic-Horcrux"></a><!-- ws:end:WikiTextHeadingRule:18 -->Horcrux</h2> | <!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="Magic-Horcrux"></a><!-- ws:end:WikiTextHeadingRule:18 -->Horcrux</h2> | ||
Commas: 45/44, 56/55, 245/243<br /> | Commas: 45/44, 56/55, 245/243<br /> | ||
<br /> | <br /> | ||
POTE generator: ~5/4 = 379.642<br /> | POTE generator: ~5/4 = 379.642<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc10"><a name="Divination"></a><!-- ws:end:WikiTextHeadingRule:20 -->Divination</h1> | <!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc10"><a name="Divination"></a><!-- ws:end:WikiTextHeadingRule:20 -->Divination</h1> | ||
Commas: 121/120, 225/224, 245/243<br /> | Commas: 121/120, 225/224, 245/243<br /> | ||
<br /> | <br /> | ||
POTE generator: ~5/4 = 380.233<br /> | POTE generator: ~5/4 = 380.233<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:22:&lt;h2&gt; --><h2 id="toc11"><a name="Divination-13-limit"></a><!-- ws:end:WikiTextHeadingRule:22 -->13-limit</h2> | <!-- ws:start:WikiTextHeadingRule:22:&lt;h2&gt; --><h2 id="toc11"><a name="Divination-13-limit"></a><!-- ws:end:WikiTextHeadingRule:22 -->13-limit</h2> | ||
Commas: 105/104, 121/120, 196/195, 245/243<br /> | Commas: 105/104, 121/120, 196/195, 245/243<br /> | ||
<br /> | <br /> | ||
POTE generator: ~5/4 = 379.920<br /> | POTE generator: ~5/4 = 379.920<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:24:&lt;h1&gt; --><h1 id="toc12"><a name="Soothsaying"></a><!-- ws:end:WikiTextHeadingRule:24 -->Soothsaying</h1> | <!-- ws:start:WikiTextHeadingRule:24:&lt;h1&gt; --><h1 id="toc12"><a name="Soothsaying"></a><!-- ws:end:WikiTextHeadingRule:24 -->Soothsaying</h1> | ||
Commas: 100/99, 225/224, 245/243, 1352/1331<br /> | Commas: 100/99, 225/224, 245/243, 1352/1331<br /> | ||
<br /> | <br /> | ||
POTE generator: ~5/4 = 380.508<br /> | POTE generator: ~5/4 = 380.508<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:26:&lt;h1&gt; --><h1 id="toc13"><a name="Witchcraft"></a><!-- ws:end:WikiTextHeadingRule:26 -->Witchcraft</h1> | <!-- ws:start:WikiTextHeadingRule:26:&lt;h1&gt; --><h1 id="toc13"><a name="Witchcraft"></a><!-- ws:end:WikiTextHeadingRule:26 -->Witchcraft</h1> | ||
Commas: 225/224, 245/243, 441/440<br /> | Commas: 225/224, 245/243, 441/440<br /> | ||
<br /> | <br /> | ||
POTE generator: ~5/4 = 380.232<br /> | POTE generator: ~5/4 = 380.232<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 0 2 -1 -7|, | Map: [&lt;1 0 2 -1 -7|, &lt;0 5 1 12 33|]<br /> | ||
EDOs: 41, 60e, 101cd, 243cde<br /> | EDOs: 41, 60e, 101cd, 243cde<br /> | ||
Badness: 0.0307<br /> | Badness: 0.0307<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:28:&lt;h2&gt; --><h2 id="toc14"><a name="Witchcraft-13-limit"></a><!-- ws:end:WikiTextHeadingRule:28 -->13-limit</h2> | <!-- ws:start:WikiTextHeadingRule:28:&lt;h2&gt; --><h2 id="toc14"><a name="Witchcraft-13-limit"></a><!-- ws:end:WikiTextHeadingRule:28 -->13-limit</h2> | ||
Commas: 105/104, 196/195, 245/243, 275/273<br /> | Commas: 105/104, 196/195, 245/243, 275/273<br /> | ||
<br /> | <br /> | ||
POTE generator: ~5/4 = | POTE generator: ~5/4 = 380.189<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 0 2 -1 -7 -2|, | Map: [&lt;1 0 2 -1 -7 -2|, &lt;0 5 1 12 33 18|]<br /> | ||
EDOs: 41, 60e, 101cd<br /> | EDOs: 41, 60e, 101cd<br /> | ||
Badness: 0.0235<br /> | Badness: 0.0235<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:30:&lt;h1&gt; --><h1 id="toc15"><a name="Muggles"></a><!-- ws:end:WikiTextHeadingRule:30 -->Muggles</h1> | <!-- ws:start:WikiTextHeadingRule:30:&lt;h1&gt; --><h1 id="toc15"><a name="Muggles"></a><!-- ws:end:WikiTextHeadingRule:30 -->Muggles</h1> | ||
Aside from 3125/3072 and 525/512 muggles also tempers out 126/125 and 1323/1280. A good muggles tuning is <a class="wiki_link" href="/19edo">19edo</a>, in which tuning it's the same thing as magic. Muggles works better for small scales than magic in the sense that 7 or 10 note MOS are reasonable choices. The muggles wedgie is &lt;&lt;5 1 -7 -10 -25 -19||.<br /> | Aside from 3125/3072 and 525/512 muggles also tempers out 126/125 and 1323/1280. A good muggles tuning is <a class="wiki_link" href="/19edo">19edo</a>, in which tuning it's the same thing as magic. Muggles works better for small scales than magic in the sense that 7 or 10 note MOS are reasonable choices. The muggles wedgie is &lt;&lt;5 1 -7 -10 -25 -19||.<br /> | ||
<br /> | <br /> | ||
Commas: 126/125, 525/512<br /> | Commas: 126/125, 525/512<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:32:&lt;h1&gt; --><h1 id="toc16"><a name="Astrology"></a><!-- ws:end:WikiTextHeadingRule:32 -->Astrology</h1> | <!-- ws:start:WikiTextHeadingRule:32:&lt;h1&gt; --><h1 id="toc16"><a name="Astrology"></a><!-- ws:end:WikiTextHeadingRule:32 -->Astrology</h1> | ||
Commas: 50/49, 3125/3072<br /> | Commas: 50/49, 3125/3072<br /> | ||
<br /> | <br /> | ||
POTE generator: ~5/4 = 380.578<br /> | POTE generator: ~5/4 = 380.578<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:34:&lt;h2&gt; --><h2 id="toc17"><a name="Astrology-11-limit"></a><!-- ws:end:WikiTextHeadingRule:34 -->11-limit</h2> | <!-- ws:start:WikiTextHeadingRule:34:&lt;h2&gt; --><h2 id="toc17"><a name="Astrology-11-limit"></a><!-- ws:end:WikiTextHeadingRule:34 -->11-limit</h2> | ||
Commas: 50/49, 121/120, 176/175<br /> | Commas: 50/49, 121/120, 176/175<br /> | ||
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POTE generator: ~5/4 = 380.530<br /> | POTE generator: ~5/4 = 380.530<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:36:&lt;h2&gt; --><h2 id="toc18"><a name="Astrology-13-limit"></a><!-- ws:end:WikiTextHeadingRule:36 -->13-limit</h2> | <!-- ws:start:WikiTextHeadingRule:36:&lt;h2&gt; --><h2 id="toc18"><a name="Astrology-13-limit"></a><!-- ws:end:WikiTextHeadingRule:36 -->13-limit</h2> | ||
Commas: 50/49, 65/64, 78/77, 121/120<br /> | Commas: 50/49, 65/64, 78/77, 121/120<br /> | ||
<br /> | <br /> | ||
POTE generator: ~5/4 = 379.787<br /> | POTE generator: ~5/4 = 379.787<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:38:&lt;h2&gt; --><h2 id="toc19"><a name="Astrology-Horoscope"></a><!-- ws:end:WikiTextHeadingRule:38 -->Horoscope</h2> | <!-- ws:start:WikiTextHeadingRule:38:&lt;h2&gt; --><h2 id="toc19"><a name="Astrology-Horoscope"></a><!-- ws:end:WikiTextHeadingRule:38 -->Horoscope</h2> | ||
Commas: 50/49, 66/65, 105/104, 121/120<br /> | Commas: 50/49, 66/65, 105/104, 121/120<br /> | ||
<br /> | <br /> | ||
POTE generator: ~5/4 = 379.837<br /> | POTE generator: ~5/4 = 379.837<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:40:&lt;h1&gt; --><h1 id="toc20"><a name="Spell"></a><!-- ws:end:WikiTextHeadingRule:40 -->Spell</h1> | <!-- ws:start:WikiTextHeadingRule:40:&lt;h1&gt; --><h1 id="toc20"><a name="Spell"></a><!-- ws:end:WikiTextHeadingRule:40 -->Spell</h1> | ||
Commas: 49/48, 3125/3072<br /> | Commas: 49/48, 3125/3072<br /> | ||
<br /> | <br /> | ||
POTE generator: ~28/25 = 189.927<br /> | POTE generator: ~28/25 = 189.927<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:42:&lt;h2&gt; --><h2 id="toc21"><a name="Spell-11-limit"></a><!-- ws:end:WikiTextHeadingRule:42 -->11-limit</h2> | <!-- ws:start:WikiTextHeadingRule:42:&lt;h2&gt; --><h2 id="toc21"><a name="Spell-11-limit"></a><!-- ws:end:WikiTextHeadingRule:42 -->11-limit</h2> | ||
Commas: 49/48, 56/55, 125/121<br /> | Commas: 49/48, 56/55, 125/121<br /> | ||
<br /> | <br /> | ||
POTE generator: ~11/10 = 190.285<br /> | POTE generator: ~11/10 = 190.285<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:44:&lt;h2&gt; --><h2 id="toc22"><a name="Spell-13-limit"></a><!-- ws:end:WikiTextHeadingRule:44 -->13-limit</h2> | <!-- ws:start:WikiTextHeadingRule:44:&lt;h2&gt; --><h2 id="toc22"><a name="Spell-13-limit"></a><!-- ws:end:WikiTextHeadingRule:44 -->13-limit</h2> | ||
Commas: 49/48, 56/55, 78/77, 125/121<br /> | Commas: 49/48, 56/55, 78/77, 125/121<br /> | ||
<br /> | <br /> | ||
POTE generator: ~11/10 = 189.928<br /> | POTE generator: ~11/10 = 189.928<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:46:&lt;h2&gt; --><h2 id="toc23"><a name="Spell-Cantrip"></a><!-- ws:end:WikiTextHeadingRule:46 -->Cantrip</h2> | <!-- ws:start:WikiTextHeadingRule:46:&lt;h2&gt; --><h2 id="toc23"><a name="Spell-Cantrip"></a><!-- ws:end:WikiTextHeadingRule:46 -->Cantrip</h2> | ||
Commas: 49/48, 56/55, 91/90, 125/121<br /> | Commas: 49/48, 56/55, 91/90, 125/121<br /> | ||
<br /> | <br /> | ||
POTE generator: ~11/10 = 190.360<br /> | POTE generator: ~11/10 = 190.360<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:48:&lt;h1&gt; --><h1 id="toc24"><a name="Hocum"></a><!-- ws:end:WikiTextHeadingRule:48 -->Hocum</h1> | <!-- ws:start:WikiTextHeadingRule:48:&lt;h1&gt; --><h1 id="toc24"><a name="Hocum"></a><!-- ws:end:WikiTextHeadingRule:48 -->Hocum</h1> | ||
Commas: 3125/3072, 4000/3969<br /> | Commas: 3125/3072, 4000/3969<br /> | ||
<br /> | <br /> | ||
POTE generator: ~63/50 = 400.108<br /> | POTE generator: ~63/50 = 400.108<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:50:&lt;h1&gt; --><h1 id="toc25"><a name="Hocus"></a><!-- ws:end:WikiTextHeadingRule:50 -->Hocus</h1> | <!-- ws:start:WikiTextHeadingRule:50:&lt;h1&gt; --><h1 id="toc25"><a name="Hocus"></a><!-- ws:end:WikiTextHeadingRule:50 -->Hocus</h1> | ||
Commas: 225/224, 243/242, 245/242<br /> | Commas: 225/224, 243/242, 245/242<br /> | ||
<br /> | <br /> | ||
POTE generator: ~14/11 = 409.910<br /> | POTE generator: ~14/11 = 409.910<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:52:&lt;h2&gt; --><h2 id="toc26"><a name="Hocus-13-limit"></a><!-- ws:end:WikiTextHeadingRule:52 -->13-limit</h2> | <!-- ws:start:WikiTextHeadingRule:52:&lt;h2&gt; --><h2 id="toc26"><a name="Hocus-13-limit"></a><!-- ws:end:WikiTextHeadingRule:52 -->13-limit</h2> | ||
Commas: 105/104, 196/195, 243/242, 245/242<br /> | Commas: 105/104, 196/195, 243/242, 245/242<br /> | ||
<br /> | <br /> | ||
POTE generator: ~14/11 = 410.004<br /> | POTE generator: ~14/11 = 410.004<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:54:&lt;h1&gt; --><h1 id="toc27"><a name="Trismegistus"></a><!-- ws:end:WikiTextHeadingRule:54 -->Trismegistus</h1> | <!-- ws:start:WikiTextHeadingRule:54:&lt;h1&gt; --><h1 id="toc27"><a name="Trismegistus"></a><!-- ws:end:WikiTextHeadingRule:54 -->Trismegistus</h1> | ||
Commas: 3125/3072, 1029/1024<br /> | Commas: 3125/3072, 1029/1024<br /> | ||
<br /> | <br /> | ||
POTE generator: ~147/100 = 673.290<br /> | POTE generator: ~147/100 = 673.290<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 10 4 0|, | Map: [&lt;1 10 4 0|, &lt;0 -15 -3 5|]<br /> | ||
Wedgie: &lt;&lt;15 3 -5 -30 -50 -20||<br /> | Wedgie: &lt;&lt;15 3 -5 -30 -50 -20||<br /> | ||
EDOs: 16, 25, 41, 139c, 180c, 221c, 262c<br /> | EDOs: 16, 25, 41, 139c, 180c, 221c, 262c<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:56:&lt;h2&gt; --><h2 id="toc28"><a name="Trismegistus-11-limit"></a><!-- ws:end:WikiTextHeadingRule:56 -->11-limit</h2> | <!-- ws:start:WikiTextHeadingRule:56:&lt;h2&gt; --><h2 id="toc28"><a name="Trismegistus-11-limit"></a><!-- ws:end:WikiTextHeadingRule:56 -->11-limit</h2> | ||
Commas: 385/384, 441/440, 625/616<br /> | Commas: 385/384, 441/440, 625/616<br /> | ||
<br /> | <br /> | ||
POTE generator: ~22/15 = 673.340<br /> | POTE generator: ~22/15 = 673.340<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 10 4 0 13|, | Map: [&lt;1 10 4 0 13|, &lt;0 -15 -3 5 -17|]<br /> | ||
EDOs: 16, 25e, 41, 98c, 139c, 180c<br /> | EDOs: 16, 25e, 41, 98c, 139c, 180c<br /> | ||
Badness: 0.0456<br /> | Badness: 0.0456<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:58:&lt;h2&gt; --><h2 id="toc29"><a name="Trismegistus-13-limit"></a><!-- ws:end:WikiTextHeadingRule:58 -->13-limit</h2> | <!-- ws:start:WikiTextHeadingRule:58:&lt;h2&gt; --><h2 id="toc29"><a name="Trismegistus-13-limit"></a><!-- ws:end:WikiTextHeadingRule:58 -->13-limit</h2> | ||
Commas: 105/104, 144/143, 275/273, 625/616<br /> | Commas: 105/104, 144/143, 275/273, 625/616<br /> | ||
<br /> | <br /> | ||
POTE generator: ~22/15 = 673.359<br /> | POTE generator: ~22/15 = 673.359<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 10 4 0 13 11|, | Map: [&lt;1 10 4 0 13 11|, &lt;0 -15 -3 5 -17 -13|]<br /> | ||
EDOs: 16, 25e, 41, 98c, 139cf<br /> | EDOs: 16, 25e, 41, 98c, 139cf<br /> | ||
Badness: 0.0331<br /> | Badness: 0.0331<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:60:&lt;h1&gt; --><h1 id="toc30"><a name="Quadrimage"></a><!-- ws:end:WikiTextHeadingRule:60 -->Quadrimage</h1> | <!-- ws:start:WikiTextHeadingRule:60:&lt;h1&gt; --><h1 id="toc30"><a name="Quadrimage"></a><!-- ws:end:WikiTextHeadingRule:60 -->Quadrimage</h1> | ||
Commas: 2401/2400, 3125/3072<br /> | Commas: 2401/2400, 3125/3072<br /> | ||
<br /> | <br /> | ||
POTE generator: ~28/25 = 204.987<br /> | POTE generator: ~28/25 = 204.987<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:62:&lt;h2&gt; --><h2 id="toc31"><a name="Quadrimage-11-limit"></a><!-- ws:end:WikiTextHeadingRule:62 -->11-limit</h2> | <!-- ws:start:WikiTextHeadingRule:62:&lt;h2&gt; --><h2 id="toc31"><a name="Quadrimage-11-limit"></a><!-- ws:end:WikiTextHeadingRule:62 -->11-limit</h2> | ||
Commas: 245/242, 385/384, 625/616<br /> | Commas: 245/242, 385/384, 625/616<br /> | ||
<br /> | <br /> | ||
POTE generator: ~28/25 = 204.956<br /> | POTE generator: ~28/25 = 204.956<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:64:&lt;h2&gt; --><h2 id="toc32"><a name="Quadrimage-13-limit"></a><!-- ws:end:WikiTextHeadingRule:64 -->13-limit</h2> | <!-- ws:start:WikiTextHeadingRule:64:&lt;h2&gt; --><h2 id="toc32"><a name="Quadrimage-13-limit"></a><!-- ws:end:WikiTextHeadingRule:64 -->13-limit</h2> | ||
Commas: 105/104, 144/143, 245/242, 625/616<br /> | Commas: 105/104, 144/143, 245/242, 625/616<br /> | ||
<br /> | <br /> | ||
POTE generator: ~28/25 = 205.028<br /> | POTE generator: ~28/25 = 205.028<br /> | ||