Meantone family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 191257462 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 191261592 - 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>2011-01-05 18: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-01-05 18:44:35 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>191261592</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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Badness: 0.0170 | Badness: 0.0170 | ||
===Meanpop=== | |||
Commas: 81/80, 126/125, 385/384 | Commas: 81/80, 126/125, 385/384 | ||
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Badness: 0.0207 | Badness: 0.0207 | ||
==Sharptone== | |||
Commas: 21/20, 28/27 | Commas: 21/20, 28/27 | ||
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Badness: 0.0248 | Badness: 0.0248 | ||
==Injera== | |||
Commas: 50/49, 81/80 | Commas: 50/49, 81/80 | ||
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Godzilla has wedgie <<2 8 1 8 -4 -20||, and tempers out 49/48, equating 8/7 with 7/6. Two of the step-and-a-half intervals these represent give a fourth, and so step-and-a-half generators generate godzilla. [[19edo]] is the perfect godzilla tuning, so much so that's there's not much point in looking elsewhere. Hence it can be more or less equated with taking 4/19 as a generator. Godzilla is not well supplied with good [[MOSScales|MOS scales]], though it has a pentatonic scale which could serve as an alternative to [[5edo]], but other options exist for those wanting to explore it. | Godzilla has wedgie <<2 8 1 8 -4 -20||, and tempers out 49/48, equating 8/7 with 7/6. Two of the step-and-a-half intervals these represent give a fourth, and so step-and-a-half generators generate godzilla. [[19edo]] is the perfect godzilla tuning, so much so that's there's not much point in looking elsewhere. Hence it can be more or less equated with taking 4/19 as a generator. Godzilla is not well supplied with good [[MOSScales|MOS scales]], though it has a pentatonic scale which could serve as an alternative to [[5edo]], but other options exist for those wanting to explore it. | ||
[[POTE tuning|POTE generator]]: | [[POTE tuning|POTE generator]]: 252.635 | ||
Map: [<1 0 -4 2|, <0 2 8 1|] | |||
Wedgie: <<2 8 1 8 -4 -20|| | |||
EDOs: 5, 14, 19 | |||
Badness: 0.0267 | |||
==Mohajira== | |||
Commas: 81/80, 6144/6125 | Commas: 81/80, 6144/6125 | ||
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Map: [<1 1 0 6|, <0 2 8 -11|] | Map: [<1 1 0 6|, <0 2 8 -11|] | ||
Generators: 2, 128/105 | Generators: 2, 128/105 | ||
Wedgie: <<2 8 -11 8 -23 -48|| | |||
EDOs: 7, 24, 31 | |||
Badness: 0.0557 | |||
===11 limit mohajira=== | |||
Commas: 81/80, 121/120, 176/175 | Commas: 81/80, 121/120, 176/175 | ||
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Map: [<1 1 0 6 2|, <0 2 8 -11 5|] | Map: [<1 1 0 6 2|, <0 2 8 -11 5|] | ||
Generators: 2, 11/9 | Generators: 2, 11/9 | ||
EDOs: 7, 24, 31 | |||
Badness: 0.0261 | |||
==Mothra== | |||
Commas: 81/80, 1029/1024 | Commas: 81/80, 1029/1024 | ||
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Badness: 0.0170<br /> | Badness: 0.0170<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:6:&lt; | <!-- ws:start:WikiTextHeadingRule:6:&lt;h3&gt; --><h3 id="toc3"><a name="x-Septimal meantone-Meanpop"></a><!-- ws:end:WikiTextHeadingRule:6 -->Meanpop</h3> | ||
Commas: 81/80, 126/125, 385/384<br /> | Commas: 81/80, 126/125, 385/384<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0207<br /> | Badness: 0.0207<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:12:&lt; | <!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="x-Sharptone"></a><!-- ws:end:WikiTextHeadingRule:12 -->Sharptone</h2> | ||
Commas: 21/20, 28/27<br /> | Commas: 21/20, 28/27<br /> | ||
<br /> | <br /> | ||
| Line 341: | Line 351: | ||
Badness: 0.0248<br /> | Badness: 0.0248<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:14:&lt; | <!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="x-Injera"></a><!-- ws:end:WikiTextHeadingRule:14 -->Injera</h2> | ||
Commas: 50/49, 81/80<br /> | |||
<br /> | <br /> | ||
The wedgie for injera is &lt;&lt;2 8 8 8 7 -4||, which tells us it has a half-octave period and a generator which can be taken as a fifth or fourth, but also as a 15/14 semitone difference between a half-octave and a perfect fifth. Injera tempers out 50/49, equating 7/5 with 10/7 and giving a tritone of half an octave. A major third up from this tritone is the 7/4. <a class="wiki_link" href="/38edo">38edo</a>, which is two parallel 19edos, is an excellent tuning for injera.<br /> | The wedgie for injera is &lt;&lt;2 8 8 8 7 -4||, which tells us it has a half-octave period and a generator which can be taken as a fifth or fourth, but also as a 15/14 semitone difference between a half-octave and a perfect fifth. Injera tempers out 50/49, equating 7/5 with 10/7 and giving a tritone of half an octave. A major third up from this tritone is the 7/4. <a class="wiki_link" href="/38edo">38edo</a>, which is two parallel 19edos, is an excellent tuning for injera.<br /> | ||
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Godzilla has wedgie &lt;&lt;2 8 1 8 -4 -20||, and tempers out 49/48, equating 8/7 with 7/6. Two of the step-and-a-half intervals these represent give a fourth, and so step-and-a-half generators generate godzilla. <a class="wiki_link" href="/19edo">19edo</a> is the perfect godzilla tuning, so much so that's there's not much point in looking elsewhere. Hence it can be more or less equated with taking 4/19 as a generator. Godzilla is not well supplied with good <a class="wiki_link" href="/MOSScales">MOS scales</a>, though it has a pentatonic scale which could serve as an alternative to <a class="wiki_link" href="/5edo">5edo</a>, but other options exist for those wanting to explore it.<br /> | Godzilla has wedgie &lt;&lt;2 8 1 8 -4 -20||, and tempers out 49/48, equating 8/7 with 7/6. Two of the step-and-a-half intervals these represent give a fourth, and so step-and-a-half generators generate godzilla. <a class="wiki_link" href="/19edo">19edo</a> is the perfect godzilla tuning, so much so that's there's not much point in looking elsewhere. Hence it can be more or less equated with taking 4/19 as a generator. Godzilla is not well supplied with good <a class="wiki_link" href="/MOSScales">MOS scales</a>, though it has a pentatonic scale which could serve as an alternative to <a class="wiki_link" href="/5edo">5edo</a>, but other options exist for those wanting to explore it.<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 252.635<br /> | ||
<br /> | |||
Map: [&lt;1 0 -4 2|, &lt;0 2 8 1|]<br /> | |||
Wedgie: &lt;&lt;2 8 1 8 -4 -20||<br /> | |||
EDOs: 5, 14, 19<br /> | |||
Badness: 0.0267<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:18:&lt; | <!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="x-Mohajira"></a><!-- ws:end:WikiTextHeadingRule:18 -->Mohajira</h2> | ||
Commas: 81/80, 6144/6125<br /> | Commas: 81/80, 6144/6125<br /> | ||
<br /> | <br /> | ||
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Map: [&lt;1 1 0 6|, &lt;0 2 8 -11|]<br /> | Map: [&lt;1 1 0 6|, &lt;0 2 8 -11|]<br /> | ||
Generators: 2, 128/105<br /> | Generators: 2, 128/105<br /> | ||
Wedgie: &lt;&lt;2 8 -11 8 -23 -48||<br /> | |||
EDOs: 7, 24, 31<br /> | |||
Badness: 0.0557<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:20:&lt; | <!-- ws:start:WikiTextHeadingRule:20:&lt;h3&gt; --><h3 id="toc10"><a name="x-Mohajira-11 limit mohajira"></a><!-- ws:end:WikiTextHeadingRule:20 -->11 limit mohajira</h3> | ||
Commas: 81/80, 121/120, 176/175<br /> | Commas: 81/80, 121/120, 176/175<br /> | ||
<br /> | <br /> | ||
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Map: [&lt;1 1 0 6 2|, &lt;0 2 8 -11 5|]<br /> | Map: [&lt;1 1 0 6 2|, &lt;0 2 8 -11 5|]<br /> | ||
Generators: 2, 11/9<br /> | Generators: 2, 11/9<br /> | ||
EDOs: 7, 24, 31<br /> | |||
Badness: 0.0261<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:22:&lt; | <!-- ws:start:WikiTextHeadingRule:22:&lt;h2&gt; --><h2 id="toc11"><a name="x-Mothra"></a><!-- ws:end:WikiTextHeadingRule:22 -->Mothra</h2> | ||
Commas: 81/80, 1029/1024<br /> | Commas: 81/80, 1029/1024<br /> | ||
<br /> | <br /> | ||
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Generators: 2, 8/7<br /> | Generators: 2, 8/7<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:24:&lt;h3&gt; --><h3 id="toc12"><a name="x- | <!-- ws:start:WikiTextHeadingRule:24:&lt;h3&gt; --><h3 id="toc12"><a name="x-Mothra-Squares"></a><!-- ws:end:WikiTextHeadingRule:24 -->Squares</h3> | ||
Commas: 81/80, 2401/2400<br /> | Commas: 81/80, 2401/2400<br /> | ||
<br /> | <br /> | ||
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Music:<br /> | Music:<br /> | ||
By Chris Vaisvil<br /> | By Chris Vaisvil<br /> | ||
<!-- ws:start:WikiTextUrlRule: | <!-- ws:start:WikiTextUrlRule:294:http://tinyurl.com/25kv7cq --><a class="wiki_link_ext" href="http://tinyurl.com/25kv7cq" rel="nofollow">http://tinyurl.com/25kv7cq</a><!-- ws:end:WikiTextUrlRule:294 --><br /> | ||
<!-- ws:start:WikiTextUrlRule: | <!-- ws:start:WikiTextUrlRule:295:http://tinyurl.com/24cbxse --><a class="wiki_link_ext" href="http://tinyurl.com/24cbxse" rel="nofollow">http://tinyurl.com/24cbxse</a><!-- ws:end:WikiTextUrlRule:295 --><br /> | ||
<br /> | <br /> | ||
11-limit<br /> | 11-limit<br /> | ||
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EDOs: 14, 31, 200<br /> | EDOs: 14, 31, 200<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:26:&lt;h3&gt; --><h3 id="toc13"><a name="x- | <!-- ws:start:WikiTextHeadingRule:26:&lt;h3&gt; --><h3 id="toc13"><a name="x-Mothra-Liese"></a><!-- ws:end:WikiTextHeadingRule:26 -->Liese</h3> | ||
Commas: 81/80, 686/675<br /> | Commas: 81/80, 686/675<br /> | ||
<br /> | <br /> | ||