Macrotonal EDO: 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:~~hstraub~~|~~hstraub~~]] and made on <tt>~~2010~~-08-~~17 07~~:35:04 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-02-28 11:26:33 UTC</tt>.<br>

: The original revision id was <tt>~~156890465~~</tt>.<br>

: The original revision id was <tt>205698236</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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==EDO Families==

Macrotonal edos (or any edo really) are available in larger edos which are multiples of them; the edos which are multiples of the same smaller edo can be thought of as being "related," perhaps even "in the same family" as one another. This becomes especially significant with linear temperaments such as [[Blackwood Temperament]] which use some division of the octave (in the case of Blackwood, a fifth of an octave) as the period. It also suggests a family of superscales that one could use to expand upon the potential of a simpler scale: for instance, [[14edo]] as a superscale containing two [[7edo]]s. Here are some edo families:

Macrotonal edos (or any edo really) are available in larger edos which are multiples of them; the edos which are multiples of the same smaller edo can be thought of as being "related," perhaps even "in the same family" as one another. This becomes especially significant with linear temperaments such as [[Archytas clan|Blackwood Temperament]] which use some division of the octave (in the case of Blackwood, a fifth of an octave) as the period. It also suggests a family of superscales that one could use to expand upon the potential of a simpler scale: for instance, [[14edo]] as a superscale containing two [[7edo]]s. Here are some edo families:

* 3n edo family: [[3edo]], [[6edo]], [[9edo]], [[12edo]], [[15edo]], [[18edo]], [[21edo]], [[24edo]], [[27edo]], [[30edo]], [[33edo]], [[36edo]], [[39edo]], [[42edo]], [[45edo]], [[48edo]]...

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<h2 id="toc1"><a name="x-EDO Families"></a>EDO Families</h2>

<br />

Macrotonal edos (or any edo really) are available in larger edos which are multiples of them; the edos which are multiples of the same smaller edo can be thought of as being &quot;related,&quot; perhaps even &quot;in the same family&quot; as one another. This becomes especially significant with linear temperaments such as <a class="wiki_link" href="/~~Blackwood~~%~~20Temperament~~">Blackwood Temperament</a> which use some division of the octave (in the case of Blackwood, a fifth of an octave) as the period. It also suggests a family of superscales that one could use to expand upon the potential of a simpler scale: for instance, <a class="wiki_link" href="/14edo">14edo</a> as a superscale containing two <a class="wiki_link" href="/7edo">7edo</a>s. Here are some edo families:<br />

Macrotonal edos (or any edo really) are available in larger edos which are multiples of them; the edos which are multiples of the same smaller edo can be thought of as being &quot;related,&quot; perhaps even &quot;in the same family&quot; as one another. This becomes especially significant with linear temperaments such as <a class="wiki_link" href="/Archytas%20clan">Blackwood Temperament</a> which use some division of the octave (in the case of Blackwood, a fifth of an octave) as the period. It also suggests a family of superscales that one could use to expand upon the potential of a simpler scale: for instance, <a class="wiki_link" href="/14edo">14edo</a> as a superscale containing two <a class="wiki_link" href="/7edo">7edo</a>s. Here are some edo families:<br />

<br />

<ul><li>3n edo family: <a class="wiki_link" href="/3edo">3edo</a>, <a class="wiki_link" href="/6edo">6edo</a>, <a class="wiki_link" href="/9edo">9edo</a>, <a class="wiki_link" href="/12edo">12edo</a>, <a class="wiki_link" href="/15edo">15edo</a>, <a class="wiki_link" href="/18edo">18edo</a>, <a class="wiki_link" href="/21edo">21edo</a>, <a class="wiki_link" href="/24edo">24edo</a>, <a class="wiki_link" href="/27edo">27edo</a>, <a class="wiki_link" href="/30edo">30edo</a>, <a class="wiki_link" href="/33edo">33edo</a>, <a class="wiki_link" href="/36edo">36edo</a>, <a class="wiki_link" href="/39edo">39edo</a>, <a class="wiki_link" href="/42edo">42edo</a>, <a class="wiki_link" href="/45edo">45edo</a>, <a class="wiki_link" href="/48edo">48edo</a>...</li><li>4n edo family: <a class="wiki_link" href="/4edo">4edo</a>, <a class="wiki_link" href="/8edo">8edo</a>, <a class="wiki_link" href="/12edo">12edo</a>, <a class="wiki_link" href="/16edo">16edo</a>, <a class="wiki_link" href="/20edo">20edo</a>, <a class="wiki_link" href="/24edo">24edo</a>, <a class="wiki_link" href="/28edo">28edo</a>, <a class="wiki_link" href="/32edo">32edo</a>, <a class="wiki_link" href="/36edo">36edo</a>, <a class="wiki_link" href="/40edo">40edo</a>, <a class="wiki_link" href="/44edo">44edo</a>, <a class="wiki_link" href="/48edo">48edo</a>...</li><li>5n edo family: <a class="wiki_link" href="/5edo">5edo</a>, <a class="wiki_link" href="/10edo">10edo</a>, <a class="wiki_link" href="/15edo">15edo</a>, <a class="wiki_link" href="/20edo">20edo</a>, <a class="wiki_link" href="/25edo">25edo</a>, <a class="wiki_link" href="/30edo">30edo</a>, <a class="wiki_link" href="/35edo">35edo</a>, <a class="wiki_link" href="/40edo">40edo</a>...</li><li>6n edo family: <a class="wiki_link" href="/6edo">6edo</a>, <a class="wiki_link" href="/12edo">12edo</a>, <a class="wiki_link" href="/18edo">18edo</a>, <a class="wiki_link" href="/24edo">24edo</a>, <a class="wiki_link" href="/30edo">30edo</a>, <a class="wiki_link" href="/36edo">36edo</a>, <a class="wiki_link" href="/42edo">42edo</a>, <a class="wiki_link" href="/48edo">48edo</a>...</li><li>7n edo family: <a class="wiki_link" href="/7edo">7edo</a>, <a class="wiki_link" href="/14edo">14edo</a>, <a class="wiki_link" href="/21edo">21edo</a>, <a class="wiki_link" href="/28edo">28edo</a>, <a class="wiki_link" href="/35edo">35edo</a>, <a class="wiki_link" href="/42edo">42edo</a>, <a class="wiki_link" href="/49edo">49edo</a>...</li><li>8n edo family: <a class="wiki_link" href="/8edo">8edo</a>, <a class="wiki_link" href="/16edo">16edo</a>, <a class="wiki_link" href="/24edo">24edo</a>, <a class="wiki_link" href="/32edo">32edo</a>, <a class="wiki_link" href="/40edo">40edo</a>, <a class="wiki_link" href="/48edo">48edo</a>...</li><li>9n edo family: <a class="wiki_link" href="/9edo">9edo</a>, <a class="wiki_link" href="/18edo">18edo</a>, <a class="wiki_link" href="/27edo">27edo</a>, <a class="wiki_link" href="/36edo">36edo</a>, <a class="wiki_link" href="/45edo">45edo</a>...</li><li>10n edo family: <a class="wiki_link" href="/10edo">10edo</a>, <a class="wiki_link" href="/20edo">20edo</a>, <a class="wiki_link" href="/30edo">30edo</a>, <a class="wiki_link" href="/40edo">40edo</a>, <a class="wiki_link" href="/50edo">50edo</a>...</li><li>11n edo family: <a class="wiki_link" href="/11edo">11edo</a>, <a class="wiki_link" href="/22edo">22edo</a>, <a class="wiki_link" href="/33edo">33edo</a>, <a class="wiki_link" href="/44edo">44edo</a>...</li><li>12n edo family: <a class="wiki_link" href="/12edo">12edo</a>, <a class="wiki_link" href="/24edo">24edo</a>, <a class="wiki_link" href="/36edo">36edo</a>, <a class="wiki_link" href="/48edo">48edo</a>...</li><li>...</li></ul><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:hstraub|hstraub]] and made on <tt>2010-08-17 07:35:04 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-02-28 11:26:33 UTC</tt>.<br>
-: The original revision id was <tt>156890465</tt>.<br>
+: The original revision id was <tt>205698236</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 31: / Line 31: @@
 ==EDO Families==
-Macrotonal edos (or any edo really) are available in larger edos which are multiples of them; the edos which are multiples of the same smaller edo can be thought of as being "related," perhaps even "in the same family" as one another. This becomes especially significant with linear temperaments such as [[Blackwood Temperament]] which use some division of the octave (in the case of Blackwood, a fifth of an octave) as the period. It also suggests a family of superscales that one could use to expand upon the potential of a simpler scale: for instance, [[14edo]] as a superscale containing two [[7edo]]s. Here are some edo families:
+Macrotonal edos (or any edo really) are available in larger edos which are multiples of them; the edos which are multiples of the same smaller edo can be thought of as being "related," perhaps even "in the same family" as one another. This becomes especially significant with linear temperaments such as [[Archytas clan|Blackwood Temperament]] which use some division of the octave (in the case of Blackwood, a fifth of an octave) as the period. It also suggests a family of superscales that one could use to expand upon the potential of a simpler scale: for instance, [[14edo]] as a superscale containing two [[7edo]]s. Here are some edo families:
 * 3n edo family: [[3edo]], [[6edo]], [[9edo]], [[12edo]], [[15edo]], [[18edo]], [[21edo]], [[24edo]], [[27edo]], [[30edo]], [[33edo]], [[36edo]], [[39edo]], [[42edo]], [[45edo]], [[48edo]]...
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   &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x-EDO Families"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;EDO Families&lt;/h2&gt;
   &lt;br /&gt;
-Macrotonal edos (or any edo really) are available in larger edos which are multiples of them; the edos which are multiples of the same smaller edo can be thought of as being &amp;quot;related,&amp;quot; perhaps even &amp;quot;in the same family&amp;quot; as one another. This becomes especially significant with linear temperaments such as &lt;a class="wiki_link" href="/Blackwood%20Temperament"&gt;Blackwood Temperament&lt;/a&gt; which use some division of the octave (in the case of Blackwood, a fifth of an octave) as the period. It also suggests a family of superscales that one could use to expand upon the potential of a simpler scale: for instance, &lt;a class="wiki_link" href="/14edo"&gt;14edo&lt;/a&gt; as a superscale containing two &lt;a class="wiki_link" href="/7edo"&gt;7edo&lt;/a&gt;s. Here are some edo families:&lt;br /&gt;
+Macrotonal edos (or any edo really) are available in larger edos which are multiples of them; the edos which are multiples of the same smaller edo can be thought of as being &amp;quot;related,&amp;quot; perhaps even &amp;quot;in the same family&amp;quot; as one another. This becomes especially significant with linear temperaments such as &lt;a class="wiki_link" href="/Archytas%20clan"&gt;Blackwood Temperament&lt;/a&gt; which use some division of the octave (in the case of Blackwood, a fifth of an octave) as the period. It also suggests a family of superscales that one could use to expand upon the potential of a simpler scale: for instance, &lt;a class="wiki_link" href="/14edo"&gt;14edo&lt;/a&gt; as a superscale containing two &lt;a class="wiki_link" href="/7edo"&gt;7edo&lt;/a&gt;s. Here are some edo families:&lt;br /&gt;
 &lt;br /&gt;
 &lt;ul&gt;&lt;li&gt;3n edo family: &lt;a class="wiki_link" href="/3edo"&gt;3edo&lt;/a&gt;, &lt;a class="wiki_link" href="/6edo"&gt;6edo&lt;/a&gt;, &lt;a class="wiki_link" href="/9edo"&gt;9edo&lt;/a&gt;, &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;, &lt;a class="wiki_link" href="/15edo"&gt;15edo&lt;/a&gt;, &lt;a class="wiki_link" href="/18edo"&gt;18edo&lt;/a&gt;, &lt;a class="wiki_link" href="/21edo"&gt;21edo&lt;/a&gt;, &lt;a class="wiki_link" href="/24edo"&gt;24edo&lt;/a&gt;, &lt;a class="wiki_link" href="/27edo"&gt;27edo&lt;/a&gt;, &lt;a class="wiki_link" href="/30edo"&gt;30edo&lt;/a&gt;, &lt;a class="wiki_link" href="/33edo"&gt;33edo&lt;/a&gt;, &lt;a class="wiki_link" href="/36edo"&gt;36edo&lt;/a&gt;, &lt;a class="wiki_link" href="/39edo"&gt;39edo&lt;/a&gt;, &lt;a class="wiki_link" href="/42edo"&gt;42edo&lt;/a&gt;, &lt;a class="wiki_link" href="/45edo"&gt;45edo&lt;/a&gt;, &lt;a class="wiki_link" href="/48edo"&gt;48edo&lt;/a&gt;...&lt;/li&gt;&lt;li&gt;4n edo family: &lt;a class="wiki_link" href="/4edo"&gt;4edo&lt;/a&gt;, &lt;a class="wiki_link" href="/8edo"&gt;8edo&lt;/a&gt;, &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;, &lt;a class="wiki_link" href="/16edo"&gt;16edo&lt;/a&gt;, &lt;a class="wiki_link" href="/20edo"&gt;20edo&lt;/a&gt;, &lt;a class="wiki_link" href="/24edo"&gt;24edo&lt;/a&gt;, &lt;a class="wiki_link" href="/28edo"&gt;28edo&lt;/a&gt;, &lt;a class="wiki_link" href="/32edo"&gt;32edo&lt;/a&gt;, &lt;a class="wiki_link" href="/36edo"&gt;36edo&lt;/a&gt;, &lt;a class="wiki_link" href="/40edo"&gt;40edo&lt;/a&gt;, &lt;a class="wiki_link" href="/44edo"&gt;44edo&lt;/a&gt;, &lt;a class="wiki_link" href="/48edo"&gt;48edo&lt;/a&gt;...&lt;/li&gt;&lt;li&gt;5n edo family: &lt;a class="wiki_link" href="/5edo"&gt;5edo&lt;/a&gt;, &lt;a class="wiki_link" href="/10edo"&gt;10edo&lt;/a&gt;, &lt;a class="wiki_link" href="/15edo"&gt;15edo&lt;/a&gt;, &lt;a class="wiki_link" href="/20edo"&gt;20edo&lt;/a&gt;, &lt;a class="wiki_link" href="/25edo"&gt;25edo&lt;/a&gt;, &lt;a class="wiki_link" href="/30edo"&gt;30edo&lt;/a&gt;, &lt;a class="wiki_link" href="/35edo"&gt;35edo&lt;/a&gt;, &lt;a class="wiki_link" href="/40edo"&gt;40edo&lt;/a&gt;...&lt;/li&gt;&lt;li&gt;6n edo family: &lt;a class="wiki_link" href="/6edo"&gt;6edo&lt;/a&gt;, &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;, &lt;a class="wiki_link" href="/18edo"&gt;18edo&lt;/a&gt;, &lt;a class="wiki_link" href="/24edo"&gt;24edo&lt;/a&gt;, &lt;a class="wiki_link" href="/30edo"&gt;30edo&lt;/a&gt;, &lt;a class="wiki_link" href="/36edo"&gt;36edo&lt;/a&gt;, &lt;a class="wiki_link" href="/42edo"&gt;42edo&lt;/a&gt;, &lt;a class="wiki_link" href="/48edo"&gt;48edo&lt;/a&gt;...&lt;/li&gt;&lt;li&gt;7n edo family: &lt;a class="wiki_link" href="/7edo"&gt;7edo&lt;/a&gt;, &lt;a class="wiki_link" href="/14edo"&gt;14edo&lt;/a&gt;, &lt;a class="wiki_link" href="/21edo"&gt;21edo&lt;/a&gt;, &lt;a class="wiki_link" href="/28edo"&gt;28edo&lt;/a&gt;, &lt;a class="wiki_link" href="/35edo"&gt;35edo&lt;/a&gt;, &lt;a class="wiki_link" href="/42edo"&gt;42edo&lt;/a&gt;, &lt;a class="wiki_link" href="/49edo"&gt;49edo&lt;/a&gt;...&lt;/li&gt;&lt;li&gt;8n edo family: &lt;a class="wiki_link" href="/8edo"&gt;8edo&lt;/a&gt;, &lt;a class="wiki_link" href="/16edo"&gt;16edo&lt;/a&gt;, &lt;a class="wiki_link" href="/24edo"&gt;24edo&lt;/a&gt;, &lt;a class="wiki_link" href="/32edo"&gt;32edo&lt;/a&gt;, &lt;a class="wiki_link" href="/40edo"&gt;40edo&lt;/a&gt;, &lt;a class="wiki_link" href="/48edo"&gt;48edo&lt;/a&gt;...&lt;/li&gt;&lt;li&gt;9n edo family: &lt;a class="wiki_link" href="/9edo"&gt;9edo&lt;/a&gt;, &lt;a class="wiki_link" href="/18edo"&gt;18edo&lt;/a&gt;, &lt;a class="wiki_link" href="/27edo"&gt;27edo&lt;/a&gt;, &lt;a class="wiki_link" href="/36edo"&gt;36edo&lt;/a&gt;, &lt;a class="wiki_link" href="/45edo"&gt;45edo&lt;/a&gt;...&lt;/li&gt;&lt;li&gt;10n edo family: &lt;a class="wiki_link" href="/10edo"&gt;10edo&lt;/a&gt;, &lt;a class="wiki_link" href="/20edo"&gt;20edo&lt;/a&gt;, &lt;a class="wiki_link" href="/30edo"&gt;30edo&lt;/a&gt;, &lt;a class="wiki_link" href="/40edo"&gt;40edo&lt;/a&gt;, &lt;a class="wiki_link" href="/50edo"&gt;50edo&lt;/a&gt;...&lt;/li&gt;&lt;li&gt;11n edo family: &lt;a class="wiki_link" href="/11edo"&gt;11edo&lt;/a&gt;, &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt;, &lt;a class="wiki_link" href="/33edo"&gt;33edo&lt;/a&gt;, &lt;a class="wiki_link" href="/44edo"&gt;44edo&lt;/a&gt;...&lt;/li&gt;&lt;li&gt;12n edo family: &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;, &lt;a class="wiki_link" href="/24edo"&gt;24edo&lt;/a&gt;, &lt;a class="wiki_link" href="/36edo"&gt;36edo&lt;/a&gt;, &lt;a class="wiki_link" href="/48edo"&gt;48edo&lt;/a&gt;...&lt;/li&gt;&lt;li&gt;...&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;