Maximal evenness: Difference between revisions
Wikispaces>keenanpepper **Imported revision 284372374 - Original comment: ** |
Wikispaces>hstraub **Imported revision 479367202 - 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:hstraub|hstraub]] and made on <tt>2013-12-25 12:07:40 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>479367202</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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The ME 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 ME 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> | 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. | ||
Maximally even sets tend to be familiar and musically relevant scale collections. The maximally even heptatonic set of [[19edo]] is, like the one in 12edo, a diatonic scale. The maximally even heptatonic sets of [[17edo]] and [[24edo]], in contrary, are Maqamic[7]. The maximally even heptatonic set of [[22edo]] is Porcupine[7] (the diatonic scale in 22edo is not maximally even), the maximally even octatonic set of 22edo is Porcupine[8], while the maximally even decatonic set of 22edo is the symmetric decatonic scale of Pajara.</pre></div> | |||
<h4>Original HTML content:</h4> | <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;maximally even&quot; (ME) or &quot;quasi-equal&quot; scale for every smaller edo. The maximally even scale is the closest the parent edo can get to representing the smaller edo.<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>Maximal evenness</title></head><body>Within every <a class="wiki_link" href="/edo">edo</a> one can specify a &quot;maximally even&quot; (ME) or &quot;quasi-equal&quot; scale for every smaller edo. The maximally even scale is the closest the parent edo can get to representing the smaller edo.<br /> | ||
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The ME 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 /> | The ME 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 /> | ||
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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> | 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.<br /> | ||
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Maximally even sets tend to be familiar and musically relevant scale collections. The maximally even heptatonic set of <a class="wiki_link" href="/19edo">19edo</a> is, like the one in 12edo, a diatonic scale. The maximally even heptatonic sets of <a class="wiki_link" href="/17edo">17edo</a> and <a class="wiki_link" href="/24edo">24edo</a>, in contrary, are Maqamic[7]. The maximally even heptatonic set of <a class="wiki_link" href="/22edo">22edo</a> is Porcupine[7] (the diatonic scale in 22edo is not maximally even), the maximally even octatonic set of 22edo is Porcupine[8], while the maximally even decatonic set of 22edo is the symmetric decatonic scale of Pajara.</body></html></pre></div> | |||