4L 2s: Difference between revisions
Wikispaces>guest **Imported revision 248861579 - Original comment: ** |
Wikispaces>keenanpepper **Imported revision 248977817 - 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:keenanpepper|keenanpepper]] and made on <tt>2011-08-28 20:15:27 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>248977817</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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<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">There are three scales with this [[MOSScales|MOS]] pattern that are significant minima of harmonic entropy. | <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">There are three scales with this [[MOSScales|MOS]] pattern that are significant minima of harmonic entropy. | ||
The first is no-3's [[Diaschismic family|srutal/pajara]], which is srutal/pajara without any intervals containing 3 in their prime factorization, so it becomes a 2.5.9 or 2.5.7.9 subgroup temperament. This means that the generator is twice that of srutal/pajara (210-220 cents rather than 105-110), since odd numbers of generators are only needed for intervals with 3. So this is a basically "whole tone" scale, but made uneven so some 2-step intervals are 5/4 and others are 9/7. | The first is "[[antikythera]]", or no-3's [[Diaschismic family|srutal/pajara]], which is srutal/pajara without any intervals containing 3 in their prime factorization, so it becomes a 2.5.9 or 2.5.7.9 subgroup temperament. This means that the generator is twice that of srutal/pajara (210-220 cents rather than 105-110), since odd numbers of generators are only needed for intervals with 3. So this is a basically "whole tone" scale, but made uneven so some 2-step intervals are 5/4 and others are 9/7. | ||
The second is [[Dicot family|decimal]], in which two generators make a 4/3, and the third is [[Jubilismic clan|Doublewide]], in which the generator is 7/6 so the period minus the generator is 6/5. | The second is [[Dicot family|decimal]], in which two generators make a 4/3, and the third is [[Jubilismic clan|Doublewide]], in which the generator is 7/6 so the period minus the generator is 6/5. | ||
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|| 1\6 || || || || || || || || || || || 200 || || | || 1\6 || || || || || || || || || || || 200 || || | ||
|| || || || || || 6\34 || || || || || || 211.76 || || | || || || || || || 6\34 || || || || || || 211.76 || || | ||
|| || || || || 5\28 || || || || || || || 214.29 || | || || || || || 5\28 || || || || || || || 214.29 || Antikythera is around here || | ||
|| || || || 4\22 || || || || || || || || 218.18 || || | || || || || 4\22 || || || || || || || || 218.18 || || | ||
|| || || 3\16 || || || || || || || || || 225 || || | || || || 3\16 || || || || || || || || || 225 || || | ||
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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>4L 2s</title></head><body>There are three scales with this <a class="wiki_link" href="/MOSScales">MOS</a> pattern that are significant minima of harmonic entropy.<br /> | <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>4L 2s</title></head><body>There are three scales with this <a class="wiki_link" href="/MOSScales">MOS</a> pattern that are significant minima of harmonic entropy.<br /> | ||
<br /> | <br /> | ||
The first is no-3's <a class="wiki_link" href="/Diaschismic%20family">srutal/pajara</a>, which is srutal/pajara without any intervals containing 3 in their prime factorization, so it becomes a 2.5.9 or 2.5.7.9 subgroup temperament. This means that the generator is twice that of srutal/pajara (210-220 cents rather than 105-110), since odd numbers of generators are only needed for intervals with 3. So this is a basically &quot;whole tone&quot; scale, but made uneven so some 2-step intervals are 5/4 and others are 9/7.<br /> | The first is &quot;<a class="wiki_link" href="/antikythera">antikythera</a>&quot;, or no-3's <a class="wiki_link" href="/Diaschismic%20family">srutal/pajara</a>, which is srutal/pajara without any intervals containing 3 in their prime factorization, so it becomes a 2.5.9 or 2.5.7.9 subgroup temperament. This means that the generator is twice that of srutal/pajara (210-220 cents rather than 105-110), since odd numbers of generators are only needed for intervals with 3. So this is a basically &quot;whole tone&quot; scale, but made uneven so some 2-step intervals are 5/4 and others are 9/7.<br /> | ||
<br /> | <br /> | ||
The second is <a class="wiki_link" href="/Dicot%20family">decimal</a>, in which two generators make a 4/3, and the third is <a class="wiki_link" href="/Jubilismic%20clan">Doublewide</a>, in which the generator is 7/6 so the period minus the generator is 6/5.<br /> | The second is <a class="wiki_link" href="/Dicot%20family">decimal</a>, in which two generators make a 4/3, and the third is <a class="wiki_link" href="/Jubilismic%20clan">Doublewide</a>, in which the generator is 7/6 so the period minus the generator is 6/5.<br /> | ||
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<td>214.29<br /> | <td>214.29<br /> | ||
</td> | </td> | ||
<td> | <td>Antikythera is around here<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||