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Macrotonal edonois: Difference between revisions

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Wikispaces>seraph57
**Imported revision 111024993 - Original comment: added link**
Wikispaces>Andrew_Heathwaite
**Imported revision 111025587 - 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:seraph57|seraph57]] and made on <tt>2009-12-24 18:34:49 UTC</tt>.<br>
: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2009-12-24 19:10:00 UTC</tt>.<br>
: The original revision id was <tt>111024993</tt>.<br>
: The original revision id was <tt>111025587</tt>.<br>
: The revision comment was: <tt>added link</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>
<h4>Original Wikitext content:</h4>
<h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">EDONOI is short for "equal divisions of a non-octave interval".
<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">A macrotonal edonoi would be, by definition, a scale which meets two constraints:
* [[macrotonal]] - all steps are larger than a semitone
* [[edonoi]] - it consists of a single step stacked over and over which does not repeat at an octave


Examples include the equal-tempered [[BP|Bohlen-Pierce scale]] (a.k.a. the 13th root of 3), [[Carlos Alpha]], [[Carlos Beta]], [[Carlos Gamma]], the [[19ED3|19th root of 3]], the [[6edf|6th root of 3:2]] , [[88cET]] and the [[square root of 13 over 10|square root of 13:10]] .
Examples include equal-tempered [[BP|Bohlen Pierce]] (a.k.a. the 13th root of 3), the [[square root of 13 over 10|square root of 13:10]], the [[12edt|12th root of 3]], the [[4edf|4th root of 3:2]], and the [[6edf|6th root of 3:2]].


Some EDONOI contain an interval close to a 2:1 that might function like a stretched or squashed octave. They can thus be considered variations on [[edo]]s.
They are related, in step-size and equality of steps, to [[macrotonal edos]], but while macrotonal edos are a finite set, macrotonal edonoi are theoretically infinite.


Other EDONOI contain no approximation of an octave or a compound octave (at least, not for a while), and continue generating new tones as they continue upward or downward. Such scales lack a very familiar compositional [[redundancy]], that of octave equivalence, and thus require special attention.
==equal divisions of compound octaves==


==EDONOI Forum==
What about dividing a compound octave, say, 4:1 or 8:1? Examples of this kind of scale would include the 15th root of 4 and the 22nd root of 8. Do they count as edonoi?</pre></div>
[[http://xenharmonic.ning.com/group/equaldivisionofnonoctaveintervals|EDONOI Forum at Xenharmonic Alliance]]</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">&lt;html&gt;&lt;head&gt;&lt;title&gt;macrotonal edonois&lt;/title&gt;&lt;/head&gt;&lt;body&gt;EDONOI is short for &amp;quot;equal divisions of a non-octave interval&amp;quot;.&lt;br /&gt;
<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;macrotonal edonois&lt;/title&gt;&lt;/head&gt;&lt;body&gt;A macrotonal edonoi would be, by definition, a scale which meets two constraints:&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link" href="/macrotonal"&gt;macrotonal&lt;/a&gt; - all steps are larger than a semitone&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/edonoi"&gt;edonoi&lt;/a&gt; - it consists of a single step stacked over and over which does not repeat at an octave&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
Examples include equal-tempered &lt;a class="wiki_link" href="/BP"&gt;Bohlen Pierce&lt;/a&gt; (a.k.a. the 13th root of 3), the &lt;a class="wiki_link" href="/square%20root%20of%2013%20over%2010"&gt;square root of 13:10&lt;/a&gt;, the &lt;a class="wiki_link" href="/12edt"&gt;12th root of 3&lt;/a&gt;, the &lt;a class="wiki_link" href="/4edf"&gt;4th root of 3:2&lt;/a&gt;, and the &lt;a class="wiki_link" href="/6edf"&gt;6th root of 3:2&lt;/a&gt;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Examples include the equal-tempered &lt;a class="wiki_link" href="/BP"&gt;Bohlen-Pierce scale&lt;/a&gt; (a.k.a. the 13th root of 3), &lt;a class="wiki_link" href="/Carlos%20Alpha"&gt;Carlos Alpha&lt;/a&gt;, &lt;a class="wiki_link" href="/Carlos%20Beta"&gt;Carlos Beta&lt;/a&gt;, &lt;a class="wiki_link" href="/Carlos%20Gamma"&gt;Carlos Gamma&lt;/a&gt;, the &lt;a class="wiki_link" href="/19ED3"&gt;19th root of 3&lt;/a&gt;, the &lt;a class="wiki_link" href="/6edf"&gt;6th root of 3:2&lt;/a&gt; , &lt;a class="wiki_link" href="/88cET"&gt;88cET&lt;/a&gt; and the &lt;a class="wiki_link" href="/square%20root%20of%2013%20over%2010"&gt;square root of 13:10&lt;/a&gt; .&lt;br /&gt;
They are related, in step-size and equality of steps, to &lt;a class="wiki_link" href="/macrotonal%20edos"&gt;macrotonal edos&lt;/a&gt;, but while macrotonal edos are a finite set, macrotonal edonoi are theoretically infinite.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Some EDONOI contain an interval close to a 2:1 that might function like a stretched or squashed octave. They can thus be considered variations on &lt;a class="wiki_link" href="/edo"&gt;edo&lt;/a&gt;s.&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-equal divisions of compound octaves"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;equal divisions of compound octaves&lt;/h2&gt;
&lt;br /&gt;
  &lt;br /&gt;
Other EDONOI contain no approximation of an octave or a compound octave (at least, not for a while), and continue generating new tones as they continue upward or downward. Such scales lack a very familiar compositional &lt;a class="wiki_link" href="/redundancy"&gt;redundancy&lt;/a&gt;, that of octave equivalence, and thus require special attention.&lt;br /&gt;
What about dividing a compound octave, say, 4:1 or 8:1? Examples of this kind of scale would include the 15th root of 4 and the 22nd root of 8. Do they count as edonoi?&lt;/body&gt;&lt;/html&gt;</pre></div>
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-EDONOI Forum"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;EDONOI Forum&lt;/h2&gt;
  &lt;a class="wiki_link_ext" href="http://xenharmonic.ning.com/group/equaldivisionofnonoctaveintervals" rel="nofollow"&gt;EDONOI Forum at Xenharmonic Alliance&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
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