Semicomma family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 301295888 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 303360246 - 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- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-02-20 11:32:48 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>303360246</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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Orwell has MOS of size 9, 13, 22 and 31. The 9-note MOS is small enough to be retained in the mind as a genuine scale, is pleasing melodically, and has [[Retuning 12edo to Orwell9|considerable harmonic resources]] despite its absence of 5-limit triads. The 13 note MOS has those, and of course the 22 and 31 note MOS are very well supplied with everything. | Orwell has MOS of size 9, 13, 22 and 31. The 9-note MOS is small enough to be retained in the mind as a genuine scale, is pleasing melodically, and has [[Retuning 12edo to Orwell9|considerable harmonic resources]] despite its absence of 5-limit triads. The 13 note MOS has those, and of course the 22 and 31 note MOS are very well supplied with everything. | ||
= | =Orwell= | ||
[[Comma|Commas]]: 225/224, 1728/1715 | [[Comma|Commas]]: 225/224, 1728/1715 | ||
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[[Eigenmonzo|Eigenmonzos]]: 2, 10/9 | [[Eigenmonzo|Eigenmonzos]]: 2, 10/9 | ||
[[POTE tuning|POTE generator]]: 271.509 | [[POTE tuning|POTE generator]]: ~7/6 = 271.509 | ||
Algebraic generators: Sabra3, the real root of 12x^3-7x-48. | Algebraic generators: Sabra3, the real root of 12x^3-7x-48. | ||
Map: [<1 0 3 1|, <0 7 -3 8|] | Map: [<1 0 3 1|, <0 7 -3 8|] | ||
Wedgie: <<7 -3 8 -21 -7 27|| | |||
EDOs: 22, 31, 53, 84, 137, 221d, 358d | EDOs: 22, 31, 53, 84, 137, 221d, 358d | ||
Badness: 0.0207 | |||
=11-limit= | ==11-limit== | ||
[[Comma|Commas]]: 99/98, 121/120, 176/175 | [[Comma|Commas]]: 99/98, 121/120, 176/175 | ||
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Badness: 0.0152 | Badness: 0.0152 | ||
=Newspeak= | ==13-limit== | ||
Commas: 99/98, 121/120, 176/175, 275/273 | |||
[[POTE tuning|POTE generator]]: ~7/6 = 271.546 | |||
Map: [<1 0 3 1 3 8|, <0 7 -3 8 2 -19|] | |||
EDOs: 22, 31, 53, 84e, 137e | |||
Badness: 0.0197 | |||
==Blair== | |||
Commas: 65/64, 78/77, 91/90, 99/98 | |||
POTE generator: ~7/6 = 271.301 | |||
Map: [<1 0 3 1 3 3|, <0 7 -3 8 2 3|] | |||
EDOs: 9, 22, 31f | |||
Badness: 0.0231 | |||
==Newspeak== | |||
Commas: 225/224, 441/440, 1728/1715 | Commas: 225/224, 441/440, 1728/1715 | ||
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Badness: 0.0314 | Badness: 0.0314 | ||
=Winston= | ==Winston== | ||
Commas: 66/65, 99/98, 105/104, 121/120 | Commas: 66/65, 99/98, 105/104, 121/120 | ||
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EDOs: 22f, 31 | EDOs: 22f, 31 | ||
Badness: 0.0199 | Badness: 0.0199 | ||
=Doublethink= | =Doublethink= | ||
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<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>Semicomma family</title></head><body><!-- ws:start:WikiTextTocRule:26:&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:26 --><!-- ws:start:WikiTextTocRule:27: --><div style="margin-left: 1em;"><a href="#Seven limit children">Seven limit children</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>Semicomma family</title></head><body><!-- ws:start:WikiTextTocRule:26:&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:26 --><!-- ws:start:WikiTextTocRule:27: --><div style="margin-left: 1em;"><a href="#Seven limit children">Seven limit children</a></div> | ||
<!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --><div style="margin-left: 2em;"><a href="#Seven limit children-Orwell">Orwell</a></div> | <!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --><div style="margin-left: 2em;"><a href="#Seven limit children-Orwell">Orwell</a></div> | ||
<!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --><div style="margin-left: | <!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --><div style="margin-left: 1em;"><a href="#Orwell">Orwell</a></div> | ||
<!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --><div style="margin-left: | <!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --><div style="margin-left: 2em;"><a href="#Orwell-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --><div style="margin-left: | <!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --><div style="margin-left: 2em;"><a href="#Orwell-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --><div style="margin-left: | <!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --><div style="margin-left: 2em;"><a href="#Orwell-Blair">Blair</a></div> | ||
<!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --><div style="margin-left: | <!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --><div style="margin-left: 2em;"><a href="#Orwell-Newspeak">Newspeak</a></div> | ||
<!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --><div style="margin-left: | <!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --><div style="margin-left: 2em;"><a href="#Orwell-Winston">Winston</a></div> | ||
<!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --><div style="margin-left: 1em;"><a href="#Doublethink">Doublethink</a></div> | <!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --><div style="margin-left: 1em;"><a href="#Doublethink">Doublethink</a></div> | ||
<!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --><div style="margin-left: 1em;"><a href="#Borwell">Borwell</a></div> | <!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --><div style="margin-left: 1em;"><a href="#Borwell">Borwell</a></div> | ||
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Orwell has MOS of size 9, 13, 22 and 31. The 9-note MOS is small enough to be retained in the mind as a genuine scale, is pleasing melodically, and has <a class="wiki_link" href="/Retuning%2012edo%20to%20Orwell9">considerable harmonic resources</a> despite its absence of 5-limit triads. The 13 note MOS has those, and of course the 22 and 31 note MOS are very well supplied with everything.<br /> | Orwell has MOS of size 9, 13, 22 and 31. The 9-note MOS is small enough to be retained in the mind as a genuine scale, is pleasing melodically, and has <a class="wiki_link" href="/Retuning%2012edo%20to%20Orwell9">considerable harmonic resources</a> despite its absence of 5-limit triads. The 13 note MOS has those, and of course the 22 and 31 note MOS are very well supplied with everything.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt; | <!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Orwell"></a><!-- ws:end:WikiTextHeadingRule:4 -->Orwell</h1> | ||
<a class="wiki_link" href="/Comma">Commas</a>: 225/224, 1728/1715<br /> | |||
<br /> | <br /> | ||
7-limit<br /> | 7-limit<br /> | ||
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<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 10/9<br /> | <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 10/9<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 271.509<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~7/6 = 271.509<br /> | ||
Algebraic generators: Sabra3, the real root of 12x^3-7x-48.<br /> | Algebraic generators: Sabra3, the real root of 12x^3-7x-48.<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 0 3 1|, &lt;0 7 -3 8|]<br /> | Map: [&lt;1 0 3 1|, &lt;0 7 -3 8|]<br /> | ||
Wedgie: &lt;&lt;7 -3 8 -21 -7 27||<br /> | |||
EDOs: 22, 31, 53, 84, 137, 221d, 358d<br /> | EDOs: 22, 31, 53, 84, 137, 221d, 358d<br /> | ||
Badness: 0.0207<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:6:&lt; | <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Orwell-11-limit"></a><!-- ws:end:WikiTextHeadingRule:6 -->11-limit</h2> | ||
<a class="wiki_link" href="/Comma">Commas</a>: 99/98, 121/120, 176/175<br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a><br /> | <a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a><br /> | ||
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Badness: 0.0152<br /> | Badness: 0.0152<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:8:&lt; | <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Orwell-13-limit"></a><!-- ws:end:WikiTextHeadingRule:8 -->13-limit</h2> | ||
Commas: 99/98, 121/120, 176/175, 275/273<br /> | |||
<br /> | |||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~7/6 = 271.546<br /> | |||
<br /> | |||
Map: [&lt;1 0 3 1 3 8|, &lt;0 7 -3 8 2 -19|]<br /> | |||
EDOs: 22, 31, 53, 84e, 137e<br /> | |||
Badness: 0.0197<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="Orwell-Blair"></a><!-- ws:end:WikiTextHeadingRule:10 -->Blair</h2> | |||
Commas: 65/64, 78/77, 91/90, 99/98<br /> | |||
<br /> | |||
POTE generator: ~7/6 = 271.301<br /> | |||
<br /> | |||
Map: [&lt;1 0 3 1 3 3|, &lt;0 7 -3 8 2 3|]<br /> | |||
EDOs: 9, 22, 31f<br /> | |||
Badness: 0.0231<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Orwell-Newspeak"></a><!-- ws:end:WikiTextHeadingRule:12 -->Newspeak</h2> | |||
Commas: 225/224, 441/440, 1728/1715<br /> | Commas: 225/224, 441/440, 1728/1715<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0314<br /> | Badness: 0.0314<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="Orwell-Winston"></a><!-- ws:end:WikiTextHeadingRule:14 -->Winston</h2> | ||
Commas: 66/65, 99/98, 105/104, 121/120<br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~7/6 = 271.088<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~7/6 = 271.088<br /> | ||
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EDOs: 22f, 31<br /> | EDOs: 22f, 31<br /> | ||
Badness: 0.0199<br /> | Badness: 0.0199<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc8"><a name="Doublethink"></a><!-- ws:end:WikiTextHeadingRule:16 -->Doublethink</h1> | <!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc8"><a name="Doublethink"></a><!-- ws:end:WikiTextHeadingRule:16 -->Doublethink</h1> | ||