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> | 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 23: | : This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-09-04 23:34:56 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>250744802</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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|| || || || || || || || || 6\87 || 82.759 || [[Tritikleismic]] || | |||
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|| || || || || 2\27 || || || || || 88.889 || [[Augmented]]/[[augene]] || | || || || || || 2\27 || || || || || 88.889 || [[Augmented]]/[[augene]] || | ||
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==Seven periods per octave== | ==Seven periods per octave== | ||
* [[Jamesbond]] - The 5-limit is represented using [[7edo]], and the generator is only used for intervals of 7. | * [[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. | |||
==Nine periods per octave== | ==Nine periods per octave== | ||
* [[Ennealimmal]] - The generator is 49.02 cents, and don't forget the ".02" because it really is that accurate. | * [[Ennealimmal]] - The generator is 49.02 cents, and don't forget the ".02" because it really is that accurate. | ||
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<td>6\87<br /> | |||
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<td><a class="wiki_link" href="/Tritikleismic">Tritikleismic</a><br /> | |||
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<td>5\72<br /> | |||
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<td>83.333<br /> | |||
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<td>Tritikleismic<br /> | |||
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<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> | <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> | ||
<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="/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: | <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-Eight periods per octave"></a><!-- ws:end:WikiTextHeadingRule:14 -->Eight 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: | <ul><li><a class="wiki_link" href="/Octoid">Octoid</a> - 16-cent generator, sub-cent accuracy.</li></ul><!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="x-Nine periods per octave"></a><!-- ws:end:WikiTextHeadingRule:16 -->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:18:&lt;h2&gt; --><h2 id="toc9"><a name="x-Twelve periods per octave"></a><!-- ws:end:WikiTextHeadingRule:18 -->Twelve periods per octave</h2> | |||
See also: <a class="wiki_link" href="/Pythagorean%20family">Pythagorean family</a><br /> | 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 /> | 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> | <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> | ||