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Map of rank-2 temperaments: Difference between revisions

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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>
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: This revision was by author [[User:Kosmorsky|Kosmorsky]] and made on <tt>2012-04-10 14:07:11 UTC</tt>.<br>
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: The original revision id was <tt>319165762</tt>.<br>
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==Five periods per octave==  
==Five periods per octave==  
* [[Blackwood]]/[[blacksmith]] - The prime 3, and in blacksmith also 7, is represented using [[5edo]]. The generator gets you to all intervals of 5.
* [[Blackwood]]/[[blacksmith]] - The prime 3, and in blacksmith also 7, is represented using [[5edo]]. The generator gets you to all intervals of 5.
* Elderthing - generator of phi. Two generators up to 3, two down to 7, other intervals are more complex. One generator up and one down are ambiguous 13.
* Elderthing - generator of phi. Two generators up to 3, two down to 7, other primes are more complex. (One generator up or one down are ambiguous 13.)
==Six periods per octave==  
==Six periods per octave==  
* [[Hexe]] - The 2.5.7 subgroup is represented using [[6edo]], and the generator gets you to 4/3 and 3/2. Makes little sense not to additionally temper down to [[12edo]].
* [[Hexe]] - The 2.5.7 subgroup is represented using [[6edo]], and the generator gets you to 4/3 and 3/2. Makes little sense not to additionally temper down to [[12edo]].
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&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="x-Five periods per octave"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Five periods per octave&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="x-Five periods per octave"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Five periods per octave&lt;/h2&gt;
  &lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Blackwood"&gt;Blackwood&lt;/a&gt;/&lt;a class="wiki_link" href="/blacksmith"&gt;blacksmith&lt;/a&gt; - The prime 3, and in blacksmith also 7, is represented using &lt;a class="wiki_link" href="/5edo"&gt;5edo&lt;/a&gt;. The generator gets you to all intervals of 5.&lt;/li&gt;&lt;li&gt;Elderthing - generator of phi. Two generators up to 3, two down to 7, other intervals are more complex. One generator up and one down are ambiguous 13.&lt;/li&gt;&lt;/ul&gt;&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="x-Six periods per octave"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Six periods per octave&lt;/h2&gt;
  &lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Blackwood"&gt;Blackwood&lt;/a&gt;/&lt;a class="wiki_link" href="/blacksmith"&gt;blacksmith&lt;/a&gt; - The prime 3, and in blacksmith also 7, is represented using &lt;a class="wiki_link" href="/5edo"&gt;5edo&lt;/a&gt;. The generator gets you to all intervals of 5.&lt;/li&gt;&lt;li&gt;Elderthing - generator of phi. Two generators up to 3, two down to 7, other primes are more complex. (One generator up or one down are ambiguous 13.)&lt;/li&gt;&lt;/ul&gt;&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="x-Six periods per octave"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Six periods per octave&lt;/h2&gt;
  &lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Hexe"&gt;Hexe&lt;/a&gt; - The 2.5.7 subgroup is represented using &lt;a class="wiki_link" href="/6edo"&gt;6edo&lt;/a&gt;, and the generator gets you to 4/3 and 3/2. Makes little sense not to additionally temper down to &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;.&lt;/li&gt;&lt;/ul&gt;&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="x-Seven periods per octave"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Seven periods per octave&lt;/h2&gt;
  &lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Hexe"&gt;Hexe&lt;/a&gt; - The 2.5.7 subgroup is represented using &lt;a class="wiki_link" href="/6edo"&gt;6edo&lt;/a&gt;, and the generator gets you to 4/3 and 3/2. Makes little sense not to additionally temper down to &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;.&lt;/li&gt;&lt;/ul&gt;&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="x-Seven periods per octave"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Seven periods per octave&lt;/h2&gt;
  &lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Whitewood"&gt;Whitewood&lt;/a&gt; - Analogue of blackwood. The prime 3 is represented using 7edo, the generator is used for 5.&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Jamesbond"&gt;Jamesbond&lt;/a&gt;/&lt;a class="wiki_link" href="/septimal"&gt;septimal&lt;/a&gt; - The 5-limit (and in septimal the prime 11) is represented using &lt;a class="wiki_link" href="/7edo"&gt;7edo&lt;/a&gt;, and the generator is only used for intervals of 7.&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Sevond"&gt;Sevond&lt;/a&gt; - 10/9 is tempered to be exactly 1\7 of an octave. Therefore 3/2 is 1 generator sharp of a 7edo step and 5/4 is 2 generators sharp.&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Absurdity"&gt;Absurdity&lt;/a&gt; - A complex temperament (perhaps &amp;quot;absurdly&amp;quot; so).&lt;/li&gt;&lt;/ul&gt;&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="x-Eight periods per octave"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Eight periods per octave&lt;/h2&gt;
  &lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Whitewood"&gt;Whitewood&lt;/a&gt; - Analogue of blackwood. The prime 3 is represented using 7edo, the generator is used for 5.&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Jamesbond"&gt;Jamesbond&lt;/a&gt;/&lt;a class="wiki_link" href="/septimal"&gt;septimal&lt;/a&gt; - The 5-limit (and in septimal the prime 11) is represented using &lt;a class="wiki_link" href="/7edo"&gt;7edo&lt;/a&gt;, and the generator is only used for intervals of 7.&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Sevond"&gt;Sevond&lt;/a&gt; - 10/9 is tempered to be exactly 1\7 of an octave. Therefore 3/2 is 1 generator sharp of a 7edo step and 5/4 is 2 generators sharp.&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Absurdity"&gt;Absurdity&lt;/a&gt; - A complex temperament (perhaps &amp;quot;absurdly&amp;quot; so).&lt;/li&gt;&lt;/ul&gt;&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="x-Eight periods per octave"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Eight periods per octave&lt;/h2&gt;
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