Maximal evenness: 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:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2009-11-05 00:11:15 UTC</tt>.<br>

: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2009-11-05 00:14:29 UTC</tt>.<br>

: The original revision id was <tt>~~100334941~~</tt>.<br>

: The original revision id was <tt>100335277</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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28 . 2 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1

29 . 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1

31 . 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2

30 . 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2

</span>

And here are all the quasi-equal scales available in [[13edo]]:

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12 . 1 1 1 1 1 1 1 1 1 1 1 2 </span>

The quasi-equal scales in 31edo will be closer to equal than those in 13edo, since the two step sizes used to approximate equal will differ by a smaller interval (one 31th of an octave instead of one 13th).</pre></div>

The quasi-equal scales in 31edo will be closer to equal than those in 13edo, since the two step sizes used to approximate equal will differ by a smaller interval (one 31th of an octave instead of one 13th).

The parent edo will better represent smaller edos than larger ones. With edos larger than 1/2 of the parent edo, the step sizes will be 2 and 1, which are, proportionally speaking, far from equal. So 13edo's 3 3 3 4 will sound more like 4edo than its 1 1 1 1 1 1 1 1 1 1 1 2 will sound like 12edo. </pre></div>

<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>Maximal evenness</title></head><body>Within every <a class="wiki_link" href="/edo">edo</a> one can specify a &quot;quasi-equal scale&quot; for every smaller edo. The quasi-equal scale would be the closest the parent edo can get to representing the smaller edo.<br />

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28 . 2 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1<br />

29 . 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1<br />

31 . 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2<br />

30 . 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2<br />

</span><br />

And here are all the quasi-equal scales available in <a class="wiki_link" href="/13edo">13edo</a>:<br />

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12 . 1 1 1 1 1 1 1 1 1 1 1 2 </span><br />

<br />

The quasi-equal scales in 31edo will be closer to equal than those in 13edo, since the two step sizes used to approximate equal will differ by a smaller interval (one 31th of an octave instead of one 13th).</body></html></pre></div>

The quasi-equal scales in 31edo will be closer to equal than those in 13edo, since the two step sizes used to approximate equal will differ by a smaller interval (one 31th of an octave instead of one 13th).<br />

<br />

The parent edo will better represent smaller edos than larger ones. With edos larger than 1/2 of the parent edo, the step sizes will be 2 and 1, which are, proportionally speaking, far from equal. So 13edo's 3 3 3 4 will sound more like 4edo than its 1 1 1 1 1 1 1 1 1 1 1 2 will sound like 12edo.</body></html></pre></div>

@@ 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:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2009-11-05 00:11:15 UTC</tt>.<br>
+: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2009-11-05 00:14:29 UTC</tt>.<br>
-: The original revision id was <tt>100334941</tt>.<br>
+: The original revision id was <tt>100335277</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 43: / Line 43: @@
 . 2 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1
 . 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 . 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2
 &lt;/span&gt;
 And here are all the quasi-equal scales available in [[13edo]]:
@@ Line 59: / Line 59: @@
 . 1 1 1 1 1 1 1 1 1 1 1 2 &lt;/span&gt;
-The quasi-equal scales in 31edo will be closer to equal than those in 13edo, since the two step sizes used to approximate equal will differ by a smaller interval (one 31th of an octave instead of one 13th).</pre></div>
+The quasi-equal scales in 31edo will be closer to equal than those in 13edo, since the two step sizes used to approximate equal will differ by a smaller interval (one 31th of an octave instead of one 13th).
+The parent edo will better represent smaller edos than larger ones. With edos larger than 1/2 of the parent edo, the step sizes will be 2 and 1, which are, proportionally speaking, far from equal. So 13edo's 3 3 3 4 will sound more like 4edo than its 1 1 1 1 1 1 1 1 1 1 1 2 will sound like 12edo. </pre></div>
 <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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Maximal evenness&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Within every &lt;a class="wiki_link" href="/edo"&gt;edo&lt;/a&gt; one can specify a &amp;quot;quasi-equal scale&amp;quot; for every smaller edo. The quasi-equal scale would be the closest the parent edo can get to representing the smaller edo.&lt;br /&gt;
@@ Line 98: / Line 100: @@
 . 2 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1&lt;br /&gt;
 . 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1&lt;br /&gt;
 . 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2&lt;br /&gt;
 &lt;/span&gt;&lt;br /&gt;
 And here are all the quasi-equal scales available in &lt;a class="wiki_link" href="/13edo"&gt;13edo&lt;/a&gt;:&lt;br /&gt;
@@ Line 114: / Line 116: @@
 . 1 1 1 1 1 1 1 1 1 1 1 2 &lt;/span&gt;&lt;br /&gt;
 &lt;br /&gt;
-The quasi-equal scales in 31edo will be closer to equal than those in 13edo, since the two step sizes used to approximate equal will differ by a smaller interval (one 31th of an octave instead of one 13th).&lt;/body&gt;&lt;/html&gt;</pre></div>
+The quasi-equal scales in 31edo will be closer to equal than those in 13edo, since the two step sizes used to approximate equal will differ by a smaller interval (one 31th of an octave instead of one 13th).&lt;br /&gt;
+&lt;br /&gt;
+The parent edo will better represent smaller edos than larger ones. With edos larger than 1/2 of the parent edo, the step sizes will be 2 and 1, which are, proportionally speaking, far from equal. So 13edo's 3 3 3 4 will sound more like 4edo than its 1 1 1 1 1 1 1 1 1 1 1 2 will sound like 12edo.&lt;/body&gt;&lt;/html&gt;</pre></div>