Map of rank-2 temperaments: Difference between revisions
Wikispaces>keenanpepper **Imported revision 250724014 - Original comment: ** |
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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:keenanpepper|keenanpepper]] and made on <tt>2011-09-04 22: | : This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-09-04 22:35:41 UTC</tt>.<br> | ||
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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> | ||
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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. | ||
==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]]. | |||
==Seven periods per octave== | |||
* [[Jamesbond]] - The 5-limit is represented using [[7edo]], and the generator is only used for intervals of 7. | |||
==Nine periods per octave== | |||
* [[Ennealimmal]] - The generator is 49.02 cents, and don't forget the ".02" because it really is that accurate. | |||
==Twelve periods per octave== | |||
See also: [[Pythagorean family]] | |||
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. | |||
* [[Catler]] - 5-limit as in 12edo; intervals of 7 are off by one generator.</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"><html><head><title>Map of rank-2 temperaments</title></head><body>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 <a class="wiki_link" href="/Bohlen-Pierce">Bohlen-Pierce</a> that completely lack octaves.<br /> | <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"><html><head><title>Map of rank-2 temperaments</title></head><body>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 <a class="wiki_link" href="/Bohlen-Pierce">Bohlen-Pierce</a> that completely lack octaves.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="x-Five periods per octave"></a><!-- ws:end:WikiTextHeadingRule:8 -->Five periods per octave</h2> | <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="x-Five periods per octave"></a><!-- ws:end:WikiTextHeadingRule:8 -->Five periods per octave</h2> | ||
<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="x- | <ul><li><a class="wiki_link" href="/Blackwood">Blackwood</a>/<a class="wiki_link" href="/blacksmith">blacksmith</a> - The prime 3, and in blacksmith also 7, is represented using <a class="wiki_link" href="/5edo">5edo</a>. The generator gets you to all intervals of 5.</li></ul><!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="x-Six periods per octave"></a><!-- ws:end:WikiTextHeadingRule:10 -->Six periods per octave</h2> | ||
</body></html></pre></div> | <ul><li><a class="wiki_link" href="/Hexe">Hexe</a> - The 2.5.7 subgroup is represented using <a class="wiki_link" href="/6edo">6edo</a>, and the generator gets you to 4/3 and 3/2. Makes little sense not to additionally temper down to <a class="wiki_link" href="/12edo">12edo</a>.</li></ul><!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="x-Seven periods per octave"></a><!-- ws:end:WikiTextHeadingRule:12 -->Seven periods per octave</h2> | ||
<ul><li><a class="wiki_link" href="/Jamesbond">Jamesbond</a> - The 5-limit is represented using <a class="wiki_link" href="/7edo">7edo</a>, and the generator is only used for intervals of 7.</li></ul><!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="x-Nine periods per octave"></a><!-- ws:end:WikiTextHeadingRule:14 -->Nine periods per octave</h2> | |||
<ul><li><a class="wiki_link" href="/Ennealimmal">Ennealimmal</a> - The generator is 49.02 cents, and don't forget the &quot;.02&quot; because it really is that accurate.</li></ul><!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="x-Twelve periods per octave"></a><!-- ws:end:WikiTextHeadingRule:16 -->Twelve periods per octave</h2> | |||
See also: <a class="wiki_link" href="/Pythagorean%20family">Pythagorean family</a><br /> | |||
Temperaments in this family are interesting because they can be thought of as <a class="wiki_link" href="/12edo">12edo</a> with microtonal alterations.<br /> | |||
<ul><li><a class="wiki_link" href="/Compton">Compton</a> - 3-limit as in 12edo; intervals of 5 are off by one generator. In the 7-limit (sometimes called <a class="wiki_link" href="/waage">waage</a>), intervals of 7 are off by two generators. In the 11-limit, intervals of 11 are off by 3 generators. Thinking of <a class="wiki_link" href="/72edo">72edo</a> might make this more concrete.</li><li><a class="wiki_link" href="/Catler">Catler</a> - 5-limit as in 12edo; intervals of 7 are off by one generator.</li></ul></body></html></pre></div> | |||