Map of rank-2 temperaments: Difference between revisions

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* [[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]].

==Seven periods per octave==  

* [[Jamesbond]] - The 5-limit is represented using [[7edo]], and the generator is only used for intervals of 7.

==Eight periods per octave==  

* [[Octoid]] - 16-cent generator, sub-cent accuracy.

Temperaments in this family are interesting because they can be thought of as [[12edo]] with microtonal alterations.

* [[Compton]] - 3-limit as in 12edo; intervals of 5 are off by one generator. In the 7-limit (sometimes called [[waage]]), intervals of 7 are off by two generators. In the 11-limit, intervals of 11 are off by 3 generators. Thinking of [[72edo]] might make this more concrete.

<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;Map of rank-2 temperaments&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This is intended to be a map of all interesting linear (rank-2) temperaments that are compatible with octave equivalence. The only linear temperaments not appearing here should be ones like &lt;a class="wiki_link" href="/Bohlen-Pierce"&gt;Bohlen-Pierce&lt;/a&gt; that completely lack octaves.&lt;br /&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;/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="/Octoid"&gt;Octoid&lt;/a&gt; - 16-cent generator, sub-cent accuracy.&lt;/li&gt;&lt;/ul&gt;&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="x-Nine periods per octave"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Nine periods per octave&lt;/h2&gt;

  &lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Ennealimmal"&gt;Ennealimmal&lt;/a&gt; - The generator is 49.02 cents, and don't forget the &amp;quot;.02&amp;quot; because it really is that accurate.&lt;/li&gt;&lt;/ul&gt;&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="x-Twelve periods per octave"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Twelve periods per octave&lt;/h2&gt;

  See also: &lt;a class="wiki_link" href="/Pythagorean%20family"&gt;Pythagorean family&lt;/a&gt;&lt;br /&gt;

Temperaments in this family are interesting because they can be thought of as &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt; with microtonal alterations.&lt;br /&gt;