Tour of regular temperaments: Difference between revisions
Wikispaces>genewardsmith **Imported revision 541030442 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 541030568 - 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> | ||
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2015-02-15 15: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2015-02-15 15:35:42 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>541030568</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt></tt><br> | ||
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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Hemimage temperaments temper out the hemimage comma, |5 -7 -1 3> = 10976/10935. | Hemimage temperaments temper out the hemimage comma, |5 -7 -1 3> = 10976/10935. | ||
==[[Cataharry temperaments]]== | ===[[Cataharry temperaments]]=== | ||
Cataharry temperaments temper out the cataharry comma, |-4 9 -2 -2> = 19683/19600. | Cataharry temperaments temper out the cataharry comma, |-4 9 -2 -2> = 19683/19600. | ||
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Hemimage temperaments temper out the hemimage comma, |5 -7 -1 3&gt; = 10976/10935.<br /> | Hemimage temperaments temper out the hemimage comma, |5 -7 -1 3&gt; = 10976/10935.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:130:&lt; | <!-- ws:start:WikiTextHeadingRule:130:&lt;h3&gt; --><h3 id="toc65"><a name="Temperaments for a given comma--Cataharry temperaments"></a><!-- ws:end:WikiTextHeadingRule:130 --><a class="wiki_link" href="/Cataharry%20temperaments">Cataharry temperaments</a></h3> | ||
Cataharry temperaments temper out the cataharry comma, |-4 9 -2 -2&gt; = 19683/19600.<br /> | Cataharry temperaments temper out the cataharry comma, |-4 9 -2 -2&gt; = 19683/19600.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:132:&lt;h3&gt; --><h3 id="toc66"><a name="Temperaments for a given comma- | <!-- ws:start:WikiTextHeadingRule:132:&lt;h3&gt; --><h3 id="toc66"><a name="Temperaments for a given comma--Horwell temperaments"></a><!-- ws:end:WikiTextHeadingRule:132 --><a class="wiki_link" href="/Horwell%20temperaments">Horwell temperaments</a></h3> | ||
Horwell temperaments temper out the horwell comma, |-16 1 5 1&gt; = 65625/65536.<br /> | Horwell temperaments temper out the horwell comma, |-16 1 5 1&gt; = 65625/65536.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:134:&lt;h3&gt; --><h3 id="toc67"><a name="Temperaments for a given comma- | <!-- ws:start:WikiTextHeadingRule:134:&lt;h3&gt; --><h3 id="toc67"><a name="Temperaments for a given comma--Breedsmic temperaments"></a><!-- ws:end:WikiTextHeadingRule:134 --><a class="wiki_link" href="/Breedsmic%20temperaments">Breedsmic temperaments</a></h3> | ||
A breedsmic temperament is one which tempers out the breedsma, |-5 -1 -2 4&gt; = 2401/2400. Some which do not get discussed elsewhere are collected on a page <a class="wiki_link" href="/Breedsmic%20temperaments">here</a>.<br /> | A breedsmic temperament is one which tempers out the breedsma, |-5 -1 -2 4&gt; = 2401/2400. Some which do not get discussed elsewhere are collected on a page <a class="wiki_link" href="/Breedsmic%20temperaments">here</a>.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:136:&lt;h3&gt; --><h3 id="toc68"><a name="Temperaments for a given comma- | <!-- ws:start:WikiTextHeadingRule:136:&lt;h3&gt; --><h3 id="toc68"><a name="Temperaments for a given comma--Ragismic microtemperaments"></a><!-- ws:end:WikiTextHeadingRule:136 --><a class="wiki_link" href="/Ragismic%20microtemperaments">Ragismic microtemperaments</a></h3> | ||
A ragismic temperament is one which tempers out |-1 -7 4 1&gt; = 4375/4374. These are not by any means all microtemperaments, but those which are not highly accurate are probably best discussed under another heading. Accurate ones include ennealimmal, supermajor, enneadecal, amity, mitonic, parakleismic, gamera and vishnu. Pontiac belongs on the list but falls under the schismatic family rubric.<br /> | A ragismic temperament is one which tempers out |-1 -7 4 1&gt; = 4375/4374. These are not by any means all microtemperaments, but those which are not highly accurate are probably best discussed under another heading. Accurate ones include ennealimmal, supermajor, enneadecal, amity, mitonic, parakleismic, gamera and vishnu. Pontiac belongs on the list but falls under the schismatic family rubric.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:138:&lt;h3&gt; --><h3 id="toc69"><a name="Temperaments for a given comma- | <!-- ws:start:WikiTextHeadingRule:138:&lt;h3&gt; --><h3 id="toc69"><a name="Temperaments for a given comma--Landscape microtemperaments"></a><!-- ws:end:WikiTextHeadingRule:138 --><a class="wiki_link" href="/Landscape%20microtemperaments">Landscape microtemperaments</a></h3> | ||
A landscape temperament is one which tempers out |-4 6 -6 3&gt; = 250047/250000.<br /> | A landscape temperament is one which tempers out |-4 6 -6 3&gt; = 250047/250000.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:140:&lt;h3&gt; --><h3 id="toc70"><a name="Temperaments for a given comma- | <!-- ws:start:WikiTextHeadingRule:140:&lt;h3&gt; --><h3 id="toc70"><a name="Temperaments for a given comma--Wizmic microtemperaments"></a><!-- ws:end:WikiTextHeadingRule:140 --><a class="wiki_link" href="/Wizmic%20microtemperaments">Wizmic microtemperaments</a></h3> | ||
A wizmic temperament is one which tempers out the wizma, | -6 -8 2 5 &gt; = 420175/419904.<br /> | A wizmic temperament is one which tempers out the wizma, | -6 -8 2 5 &gt; = 420175/419904.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:142:&lt;h3&gt; --><h3 id="toc71"><a name="Temperaments for a given comma- | <!-- ws:start:WikiTextHeadingRule:142:&lt;h3&gt; --><h3 id="toc71"><a name="Temperaments for a given comma--31 comma temperaments"></a><!-- ws:end:WikiTextHeadingRule:142 --><a class="wiki_link" href="/31%20comma%20temperaments">31 comma temperaments</a></h3> | ||
These all have period 1/31 of an octave.<br /> | These all have period 1/31 of an octave.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:144:&lt;h3&gt; --><h3 id="toc72"><a name="Temperaments for a given comma- | <!-- ws:start:WikiTextHeadingRule:144:&lt;h3&gt; --><h3 id="toc72"><a name="Temperaments for a given comma--Turkish maqam music temperaments"></a><!-- ws:end:WikiTextHeadingRule:144 --><a class="wiki_link" href="/Turkish%20maqam%20music%20temperaments">Turkish maqam music temperaments</a></h3> | ||
Various theoretical solutions have been put forward for the vexing problem of how to indicate and define the tuning of Turkish <a class="wiki_link" href="/Arabic%2C%20Turkish%2C%20Persian">makam (maqam) music</a> in a systematic way. This includes, in effect, certain linear temperaments.<br /> | Various theoretical solutions have been put forward for the vexing problem of how to indicate and define the tuning of Turkish <a class="wiki_link" href="/Arabic%2C%20Turkish%2C%20Persian">makam (maqam) music</a> in a systematic way. This includes, in effect, certain linear temperaments.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:146:&lt;h3&gt; --><h3 id="toc73"><a name="Temperaments for a given comma- | <!-- ws:start:WikiTextHeadingRule:146:&lt;h3&gt; --><h3 id="toc73"><a name="Temperaments for a given comma--Very low accuracy temperaments"></a><!-- ws:end:WikiTextHeadingRule:146 --><a class="wiki_link" href="/Very%20low%20accuracy%20temperaments">Very low accuracy temperaments</a></h3> | ||
All hope abandon ye who enter here.<br /> | All hope abandon ye who enter here.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:148:&lt;h3&gt; --><h3 id="toc74"><a name="Temperaments for a given comma- | <!-- ws:start:WikiTextHeadingRule:148:&lt;h3&gt; --><h3 id="toc74"><a name="Temperaments for a given comma--Very high accuracy temperaments"></a><!-- ws:end:WikiTextHeadingRule:148 --><a class="wiki_link" href="/Very%20high%20accuracy%20temperaments">Very high accuracy temperaments</a></h3> | ||
Microtemperaments which don't fit in elsewhere.<br /> | Microtemperaments which don't fit in elsewhere.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:150:&lt;h3&gt; --><h3 id="toc75"><a name="Temperaments for a given comma- | <!-- ws:start:WikiTextHeadingRule:150:&lt;h3&gt; --><h3 id="toc75"><a name="Temperaments for a given comma--High badness temperaments"></a><!-- ws:end:WikiTextHeadingRule:150 --><a class="wiki_link" href="/High%20badness%20temperaments">High badness temperaments</a></h3> | ||
High in badness, but worth cataloging for one reason or another.<br /> | High in badness, but worth cataloging for one reason or another.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:152:&lt;h3&gt; --><h3 id="toc76"><a name="Temperaments for a given comma- | <!-- ws:start:WikiTextHeadingRule:152:&lt;h3&gt; --><h3 id="toc76"><a name="Temperaments for a given comma--11-limit comma temperaments"></a><!-- ws:end:WikiTextHeadingRule:152 --><a class="wiki_link" href="/11-limit%20comma%20temperaments">11-limit comma temperaments</a></h3> | ||
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<!-- ws:start:WikiTextHeadingRule:154:&lt;h1&gt; --><h1 id="toc77"><a name="Rank 3 temperaments"></a><!-- ws:end:WikiTextHeadingRule:154 -->Rank 3 temperaments</h1> | <!-- ws:start:WikiTextHeadingRule:154:&lt;h1&gt; --><h1 id="toc77"><a name="Rank 3 temperaments"></a><!-- ws:end:WikiTextHeadingRule:154 -->Rank 3 temperaments</h1> | ||