4L 2s: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>

: This revision was by author [[User:~~guest~~|~~guest~~]] and made on <tt>2011-08-29 05:01:34 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-08-29 14:07:58 UTC</tt>.<br>

: The original revision id was <tt>~~249053409~~</tt>.<br>

: The original revision id was <tt>249162149</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>

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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.

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 first is [[Chromatic pairs#Antikythera|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.

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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 />

<br />

The first is ~~&quot;~~<a class="wiki_link" href="/~~antikythera~~">antikythera</a&gt~~;&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 />

The first is <a class="wiki_link" href="/Chromatic%20pairs#Antikythera">antikythera</a>, 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 />

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 />

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:guest|guest]] and made on <tt>2011-08-29 05:01:34 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-08-29 14:07:58 UTC</tt>.<br>
-: The original revision id was <tt>249053409</tt>.<br>
+: The original revision id was <tt>249162149</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>
@@ Line 8: / Line 8: @@
 <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 "[[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 first is [[Chromatic pairs#Antikythera|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.
@@ Line 41: / Line 41: @@
 <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">&lt;html&gt;&lt;head&gt;&lt;title&gt;4L 2s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;There are three scales with this &lt;a class="wiki_link" href="/MOSScales"&gt;MOS&lt;/a&gt; pattern that are significant minima of harmonic entropy.&lt;br /&gt;
 &lt;br /&gt;
-The first is &amp;quot;&lt;a class="wiki_link" href="/antikythera"&gt;antikythera&lt;/a&gt;&amp;quot;, or no-3's &lt;a class="wiki_link" href="/Diaschismic%20family"&gt;srutal/pajara&lt;/a&gt;, 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 &amp;quot;whole tone&amp;quot; scale, but made uneven so some 2-step intervals are 5/4 and others are 9/7.&lt;br /&gt;
+The first is &lt;a class="wiki_link" href="/Chromatic%20pairs#Antikythera"&gt;antikythera&lt;/a&gt;, or no-3's &lt;a class="wiki_link" href="/Diaschismic%20family"&gt;srutal/pajara&lt;/a&gt;, 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 &amp;quot;whole tone&amp;quot; scale, but made uneven so some 2-step intervals are 5/4 and others are 9/7.&lt;br /&gt;
 &lt;br /&gt;
 The second is &lt;a class="wiki_link" href="/Dicot%20family"&gt;decimal&lt;/a&gt;, in which two generators make a 4/3, and the third is &lt;a class="wiki_link" href="/Jubilismic%20clan"&gt;Doublewide&lt;/a&gt;, in which the generator is 7/6 so the period minus the generator is 6/5.&lt;br /&gt;