Macrotonal EDO: Difference between revisions
Wikispaces>xenwolf **Imported revision 148684475 - Original comment: ** |
Wikispaces>Andrew_Heathwaite **Imported revision 155751129 - 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> | ||
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Note that "macrotonal edos" is a finite set containing 11 members. "Xenharmonic macrotonal edos" would exclude those which are subsets of 12edo (1-4 & 6), & would thus contain 6 members (5, 7, 8, 9, 10, 11). | Note that "macrotonal edos" is a finite set containing 11 members. "Xenharmonic macrotonal edos" would exclude those which are subsets of 12edo (1-4 & 6), & would thus contain 6 members (5, 7, 8, 9, 10, 11). | ||
== == | |||
==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: | |||
* 3n edo family: [[3edo]], [[6edo]], [[9edo]], [[12edo]], [[15edo]], [[18edo]], [[21edo]], [[24edo]], [[27edo]], [[30edo]], [[33edo]], [[36edo]], [[39edo]], [[42edo]], [[45edo]], [[48edo]]... | |||
* 4n edo family: [[4edo]], [[8edo]], [[12edo]], [[16edo]], [[20edo]], [[24edo]], [[28edo]], [[32edo]], [[36edo]], [[40edo]], [[44edo]], [[48edo]]... | |||
* 5n edo family: [[5edo]], [[10edo]], [[15edo]], [[20edo]], [[25edo]], [[30edo]], [[35edo]], [[40edo]]... | |||
* 6n edo family: [[6edo]], [[12edo]], [[18edo]], [[24edo]], [[30edo]], [[36edo]], [[42edo]], [[48edo]]... | |||
* 7n edo family: [[7edo]], [[14edo]], [[21edo]], [[28edo]], [[35edo]], [[42edo]], [[49edo]]... | |||
* 8n edo family: [[8edo]], [[16edo]], [[24edo]], [[32edo]], [[40edo]], [[48edo]]... | |||
* 9n edo family: [[9edo]], [[18edo]], [[27edo]], [[36edo]], [[45edo]]... | |||
* 10n edo family: [[10edo]], [[20edo]], [[30edo]], [[40edo]], [[50edo]]... | |||
* 11n edo family: [[11edo]], [[22edo]], [[33edo]], [[44edo]]... | |||
* 12n edo family: [[12edo]], [[24edo]], [[36edo]], [[48edo]]... | |||
* ... | |||
[[image:macrotonal_edos.jpg]] | [[image:macrotonal_edos.jpg]] | ||
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Note that &quot;macrotonal edos&quot; is a finite set containing 11 members. &quot;Xenharmonic macrotonal edos&quot; would exclude those which are subsets of 12edo (1-4 &amp; 6), &amp; would thus contain 6 members (5, 7, 8, 9, 10, 11).<br /> | Note that &quot;macrotonal edos&quot; is a finite set containing 11 members. &quot;Xenharmonic macrotonal edos&quot; would exclude those which are subsets of 12edo (1-4 &amp; 6), &amp; would thus contain 6 members (5, 7, 8, 9, 10, 11).<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><!-- ws:end:WikiTextHeadingRule:0 --> </h2> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-EDO Families"></a><!-- ws:end:WikiTextHeadingRule:2 -->EDO Families</h2> | |||
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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 /> | |||
<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 /> | |||
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