Marvel family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 489828228 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 543471786 - 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> | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2015-03-09 13:22:52 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>543471786</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> | ||
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Scales: [[spectacle31]] | Scales: [[spectacle31]] | ||
==13-limit== | |||
Commas: 225/224, 243/242, 351/350 | |||
Map: [<1 1 0 -3 2 -5|, <0 2 0 4 5 -2|, <0 0 1 2 0 4|] | |||
EDOs: 31, 72, 103, 175f, 209, 240 | |||
Badness: 0.001009 | |||
=Apollo= | =Apollo= | ||
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Map: [<1 0 0 -5 -13 -4|, <0 1 0 2 6 -1|, <0 0 1 2 3 4|] | Map: [<1 0 0 -5 -13 -4|, <0 1 0 2 6 -1|, <0 0 1 2 3 4|] | ||
EDOs: 31, 72, 103, 175f | EDOs: 31, 72, 103, 175f | ||
Badness: 0.000889 | Badness: 0.000889</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>Marvel family</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>Marvel family</title></head><body><!-- ws:start:WikiTextTocRule:74:&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:74 --><!-- ws:start:WikiTextTocRule:75: --><a href="#Marvel">Marvel</a><!-- ws:end:WikiTextTocRule:75 --><!-- ws:start:WikiTextTocRule:76: --><!-- ws:end:WikiTextTocRule:76 --><!-- ws:start:WikiTextTocRule:77: --><!-- ws:end:WikiTextTocRule:77 --><!-- ws:start:WikiTextTocRule:78: --><!-- ws:end:WikiTextTocRule:78 --><!-- ws:start:WikiTextTocRule:79: --><!-- ws:end:WikiTextTocRule:79 --><!-- ws:start:WikiTextTocRule:80: --><!-- ws:end:WikiTextTocRule:80 --><!-- ws:start:WikiTextTocRule:81: --><!-- ws:end:WikiTextTocRule:81 --><!-- ws:start:WikiTextTocRule:82: --> | <a href="#Hecate">Hecate</a><!-- ws:end:WikiTextTocRule:82 --><!-- ws:start:WikiTextTocRule:83: --><!-- ws:end:WikiTextTocRule:83 --><!-- ws:start:WikiTextTocRule:84: --><!-- ws:end:WikiTextTocRule:84 --><!-- ws:start:WikiTextTocRule:85: --> | <a href="#Marvelcat">Marvelcat</a><!-- ws:end:WikiTextTocRule:85 --><!-- ws:start:WikiTextTocRule:86: --> | <a href="#Marvell">Marvell</a><!-- ws:end:WikiTextTocRule:86 --><!-- ws:start:WikiTextTocRule:87: --> | <a href="#Isis">Isis</a><!-- ws:end:WikiTextTocRule:87 --><!-- ws:start:WikiTextTocRule:88: --> | <a href="#Deecee">Deecee</a><!-- ws:end:WikiTextTocRule:88 --><!-- ws:start:WikiTextTocRule:89: --> | <a href="#Mirage">Mirage</a><!-- ws:end:WikiTextTocRule:89 --><!-- ws:start:WikiTextTocRule:90: --> | <a href="#Minerva">Minerva</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="#Spectacle">Spectacle</a><!-- ws:end:WikiTextTocRule:93 --><!-- ws:start:WikiTextTocRule:94: --><!-- ws:end:WikiTextTocRule:94 --><!-- ws:start:WikiTextTocRule:95: --> | <a href="#Apollo">Apollo</a><!-- ws:end:WikiTextTocRule:95 --><!-- ws:start:WikiTextTocRule:96: --><!-- ws:end:WikiTextTocRule:96 --><!-- ws:start:WikiTextTocRule:97: --> | <a href="#Potassium">Potassium</a><!-- ws:end:WikiTextTocRule:97 --><!-- ws:start:WikiTextTocRule:98: --><!-- ws:end:WikiTextTocRule:98 --><!-- ws:start:WikiTextTocRule:99: --> | <a href="#Fantastic">Fantastic</a><!-- ws:end:WikiTextTocRule:99 --><!-- ws:start:WikiTextTocRule:100: --> | <a href="#Catakleismoid">Catakleismoid</a><!-- ws:end:WikiTextTocRule:100 --><!-- ws:start:WikiTextTocRule:101: --><!-- ws:end:WikiTextTocRule:101 --><!-- ws:start:WikiTextTocRule:102: --> | <a href="#Hestia">Hestia</a><!-- ws:end:WikiTextTocRule:102 --><!-- ws:start:WikiTextTocRule:103: --><!-- ws:end:WikiTextTocRule:103 --><!-- ws:start:WikiTextTocRule:104: --> | <a href="#Malcolm">Malcolm</a><!-- ws:end:WikiTextTocRule:104 --><!-- ws:start:WikiTextTocRule:105: --><!-- ws:end:WikiTextTocRule:105 --><!-- ws:start:WikiTextTocRule:106: --> | <a href="#Tripod">Tripod</a><!-- ws:end:WikiTextTocRule:106 --><!-- ws:start:WikiTextTocRule:107: --> | <a href="#Prodigy">Prodigy</a><!-- ws:end:WikiTextTocRule:107 --><!-- ws:start:WikiTextTocRule:108: --><!-- ws:end:WikiTextTocRule:108 --><!-- ws:start:WikiTextTocRule:109: --><!-- ws:end:WikiTextTocRule:109 --><!-- ws:start:WikiTextTocRule:110: --><!-- ws:end:WikiTextTocRule:110 --><!-- ws:start:WikiTextTocRule:111: --><!-- ws:end:WikiTextTocRule:111 --><!-- ws:start:WikiTextTocRule:112: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:112 --><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Marvel"></a><!-- ws:end:WikiTextHeadingRule:0 -->Marvel</h1> | ||
The head of the marvel family is marvel, which tempers out <a class="wiki_link" href="/225_224">225/224</a>, the <a class="wiki_link" href="/septimal%20kleisma">septimal kleisma</a> or <a class="wiki_link" href="/marvel%20comma">marvel comma</a>. Marvel has a <a class="wiki_link" href="/Normal%20lists">normal list basis</a> of [2, 3, 5]; hence a <a class="wiki_link" href="/Harmonic%20Limit">5-limit</a> scale can be converted to marvel simply by tempering it. One way to do that, and an excellent marvel tuning, is given by <a class="wiki_link" href="/197edo">197edo</a>.<br /> | The head of the marvel family is marvel, which tempers out <a class="wiki_link" href="/225_224">225/224</a>, the <a class="wiki_link" href="/septimal%20kleisma">septimal kleisma</a> or <a class="wiki_link" href="/marvel%20comma">marvel comma</a>. Marvel has a <a class="wiki_link" href="/Normal%20lists">normal list basis</a> of [2, 3, 5]; hence a <a class="wiki_link" href="/Harmonic%20Limit">5-limit</a> scale can be converted to marvel simply by tempering it. One way to do that, and an excellent marvel tuning, is given by <a class="wiki_link" href="/197edo">197edo</a>.<br /> | ||
<br /> | <br /> | ||
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Scales: <a class="wiki_link" href="/spectacle31">spectacle31</a><br /> | Scales: <a class="wiki_link" href="/spectacle31">spectacle31</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:38:&lt;h1&gt; --><h1 id=" | <!-- ws:start:WikiTextHeadingRule:38:&lt;h2&gt; --><h2 id="toc19"><a name="Spectacle-13-limit"></a><!-- ws:end:WikiTextHeadingRule:38 -->13-limit</h2> | ||
Commas: 225/224, 243/242, 351/350<br /> | |||
<br /> | |||
Map: [&lt;1 1 0 -3 2 -5|, &lt;0 2 0 4 5 -2|, &lt;0 0 1 2 0 4|]<br /> | |||
EDOs: 31, 72, 103, 175f, 209, 240<br /> | |||
Badness: 0.001009<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:40:&lt;h1&gt; --><h1 id="toc20"><a name="Apollo"></a><!-- ws:end:WikiTextHeadingRule:40 -->Apollo</h1> | |||
<a class="wiki_link" href="/Comma">Commas</a>: 100/99, 225/224<br /> | <a class="wiki_link" href="/Comma">Commas</a>: 100/99, 225/224<br /> | ||
Related linear temperament: <a class="wiki_link" href="/Magic%20family">Magic</a><br /> | Related linear temperament: <a class="wiki_link" href="/Magic%20family">Magic</a><br /> | ||
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Projection pairs: 7 225/32 11 100/9<br /> | Projection pairs: 7 225/32 11 100/9<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:42:&lt;h2&gt; --><h2 id="toc21"><a name="Apollo-13-limit"></a><!-- ws:end:WikiTextHeadingRule:42 -->13-limit</h2> | ||
<a class="wiki_link" href="/Comma">Commas</a>: 100/99, 225/224, 245/243<br /> | <a class="wiki_link" href="/Comma">Commas</a>: 100/99, 225/224, 245/243<br /> | ||
<br /> | <br /> | ||
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Projection pairs: 7 225/32 11 100/9 13 3200/243<br /> | Projection pairs: 7 225/32 11 100/9 13 3200/243<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:44:&lt;h1&gt; --><h1 id="toc22"><a name="Potassium"></a><!-- ws:end:WikiTextHeadingRule:44 -->Potassium</h1> | ||
Commas: 45/44, 56/55<br /> | Commas: 45/44, 56/55<br /> | ||
<br /> | <br /> | ||
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Projection pairs: 7 225/32 11 45/4<br /> | Projection pairs: 7 225/32 11 45/4<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:46:&lt;h2&gt; --><h2 id="toc23"><a name="Potassium-13-limit"></a><!-- ws:end:WikiTextHeadingRule:46 -->13-limit</h2> | ||
Commas: 45/44, 56/55, 78/77<br /> | Commas: 45/44, 56/55, 78/77<br /> | ||
<br /> | <br /> | ||
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Projection pairs: 7 225/32 11 45/4 13 3375/256<br /> | Projection pairs: 7 225/32 11 45/4 13 3375/256<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:48:&lt;h1&gt; --><h1 id="toc24"><a name="Fantastic"></a><!-- ws:end:WikiTextHeadingRule:48 -->Fantastic</h1> | ||
Commas: 225/224, 4375/4356<br /> | Commas: 225/224, 4375/4356<br /> | ||
<br /> | <br /> | ||
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Badness: 0.000743<br /> | Badness: 0.000743<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:50:&lt;h1&gt; --><h1 id="toc25"><a name="Catakleismoid"></a><!-- ws:end:WikiTextHeadingRule:50 -->Catakleismoid</h1> | ||
Commas: 225/224, 4375/4374<br /> | Commas: 225/224, 4375/4374<br /> | ||
<br /> | <br /> | ||
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Badness: 0.001275<br /> | Badness: 0.001275<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:52:&lt;h2&gt; --><h2 id="toc26"><a name="Catakleismoid-13-limit"></a><!-- ws:end:WikiTextHeadingRule:52 -->13-limit</h2> | ||
Commas: 169/168, 225/224, 325/324<br /> | Commas: 169/168, 225/224, 325/324<br /> | ||
<br /> | <br /> | ||
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Badness: 0.000916<br /> | Badness: 0.000916<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:54:&lt;h1&gt; --><h1 id="toc27"><a name="Hestia"></a><!-- ws:end:WikiTextHeadingRule:54 -->Hestia</h1> | ||
Commas: 225/224, 125000/124509<br /> | Commas: 225/224, 125000/124509<br /> | ||
<br /> | <br /> | ||
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Badness: 0.00154<br /> | Badness: 0.00154<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:56:&lt;h2&gt; --><h2 id="toc28"><a name="Hestia-13-limit"></a><!-- ws:end:WikiTextHeadingRule:56 -->13-limit</h2> | ||
Commas: 169/168, 225/224, 1001/1000<br /> | Commas: 169/168, 225/224, 1001/1000<br /> | ||
<br /> | <br /> | ||
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Badness: 0.001062<br /> | Badness: 0.001062<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:58:&lt;h1&gt; --><h1 id="toc29"><a name="Malcolm"></a><!-- ws:end:WikiTextHeadingRule:58 -->Malcolm</h1> | ||
Commas: 225/224, 2200/2187<br /> | Commas: 225/224, 2200/2187<br /> | ||
<br /> | <br /> | ||
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Badness: 0.001250<br /> | Badness: 0.001250<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:60:&lt;h2&gt; --><h2 id="toc30"><a name="Malcolm-13-limit"></a><!-- ws:end:WikiTextHeadingRule:60 -->13-limit</h2> | ||
commas: 225/224, 275/273, 325/324<br /> | commas: 225/224, 275/273, 325/324<br /> | ||
<br /> | <br /> | ||
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Badness: 0.001075<br /> | Badness: 0.001075<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:62:&lt;h1&gt; --><h1 id="toc31"><a name="Tripod"></a><!-- ws:end:WikiTextHeadingRule:62 -->Tripod</h1> | ||
Commas: 105/104, 144/143, 196/195<br /> | Commas: 105/104, 144/143, 196/195<br /> | ||
<br /> | <br /> | ||
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Projection pairs: 7 225/32 11 4096/375 13 3375/256<br /> | Projection pairs: 7 225/32 11 4096/375 13 3375/256<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:64:&lt;h1&gt; --><h1 id="toc32"><a name="Prodigy"></a><!-- ws:end:WikiTextHeadingRule:64 -->Prodigy</h1> | ||
Prodigy shrinks 1024/1029, 243/242, 384/385 and 2400/2401 down to the same tiny interval. Hence in practice it probably makes the most sense to temper this out as well, leading to <a class="wiki_link" href="/Gamelismic%20clan">miracle temperament</a>. This, however, does not render it pointless to consider prodigy; for one thing, scales in prodigy such as hobbit scales translate into interesting scales for miracle.<br /> | Prodigy shrinks 1024/1029, 243/242, 384/385 and 2400/2401 down to the same tiny interval. Hence in practice it probably makes the most sense to temper this out as well, leading to <a class="wiki_link" href="/Gamelismic%20clan">miracle temperament</a>. This, however, does not render it pointless to consider prodigy; for one thing, scales in prodigy such as hobbit scales translate into interesting scales for miracle.<br /> | ||
<br /> | <br /> | ||
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Scales: <a class="wiki_link" href="/prodigy11">prodigy11</a>, <a class="wiki_link" href="/prodigy12">prodigy12</a>, <a class="wiki_link" href="/prodigy29">prodigy29</a><br /> | Scales: <a class="wiki_link" href="/prodigy11">prodigy11</a>, <a class="wiki_link" href="/prodigy12">prodigy12</a>, <a class="wiki_link" href="/prodigy29">prodigy29</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:66:&lt;h2&gt; --><h2 id="toc33"><a name="Prodigy-Hobbit bases"></a><!-- ws:end:WikiTextHeadingRule:66 -->Hobbit bases</h2> | ||
{2, 3, 5} subgroup<br /> | {2, 3, 5} subgroup<br /> | ||
<br /> | <br /> | ||
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41: 34171875/33554432, 32805/32768<br /> | 41: 34171875/33554432, 32805/32768<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:68:&lt;h2&gt; --><h2 id="toc34"><a name="Prodigy-13-limit"></a><!-- ws:end:WikiTextHeadingRule:68 -->13-limit</h2> | ||
Commas: 105/104, 196/195, 352/351<br /> | Commas: 105/104, 196/195, 352/351<br /> | ||
<br /> | <br /> | ||
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Badness: 0.000736<br /> | Badness: 0.000736<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:70:&lt;h2&gt; --><h2 id="toc35"><a name="Prodigy-Prodigious"></a><!-- ws:end:WikiTextHeadingRule:70 -->Prodigious</h2> | ||
Commas: 225/224, 441/440, 364/363<br /> | Commas: 225/224, 441/440, 364/363<br /> | ||
<br /> | <br /> | ||
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Badness: 0.000900<br /> | Badness: 0.000900<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:72:&lt;h2&gt; --><h2 id="toc36"><a name="Prodigy-Prodigal"></a><!-- ws:end:WikiTextHeadingRule:72 -->Prodigal</h2> | ||
Commas: 225/224, 441/440, 351/350<br /> | Commas: 225/224, 441/440, 351/350<br /> | ||
<br /> | <br /> | ||