Tour of regular temperaments: Difference between revisions

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This clan tempers out the septimal third-tone, [[28_27|28/27]], a triprime comma with factors of 2, 3 and 7.

This clan tempers out the slendro diesis, [[49_48|49/48]], a triprime comma with factors of 2, 3 and 7.

These temper out the avicennma, |-9 1 2 1&gt; = 525/512, also known as Avicenna's enharmonic diesis.

These temper out the keema, |-5 -3 3 1&gt;  = 875/864.

  This clan tempers out the septimal third-tone, &lt;a class="wiki_link" href="/28_27"&gt;28/27&lt;/a&gt;, a triprime comma with factors of 2, 3 and 7.&lt;br /&gt;

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This clan tempers out the slendro diesis, &lt;a class="wiki_link" href="/49_48"&gt;49/48&lt;/a&gt;, a triprime comma with factors of 2, 3 and 7.&lt;br /&gt;

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  This tempers out the jubilisma, &lt;a class="wiki_link" href="/50_49"&gt;50/49&lt;/a&gt;, E.A. the difference between 10/7 and 7/5.&lt;br /&gt;

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  This clan tempers out the Archytas comma, &lt;a class="wiki_link" href="/64_63"&gt;64/63&lt;/a&gt;, which is a triprime comma with factors of 2, 3 and 7. The clan consists of rank two temperaments, and should not be confused with the &lt;a class="wiki_link" href="/Archytas%20family"&gt;Archytas family&lt;/a&gt; of rank three temperaments.&lt;br /&gt;

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  This clan tempers out 245/243, the sensamagic comma.&lt;br /&gt;

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  This tempers out the hemimean comma, 3136/3125, a no-threes comma.&lt;br /&gt;

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  This tempers out the mirkwai comma, |0 3 4 -5&amp;gt; = 16875/16807, a no-twos comma (ratio of odd numbers.)&lt;br /&gt;

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  These temper out the avicennma, |-9 1 2 1&amp;gt; = 525/512, also known as Avicenna's enharmonic diesis.&lt;br /&gt;

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These temper out the keema, |-5 -3 3 1&amp;gt;  = 875/864.&lt;br /&gt;

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  Not a family or clan, but related by the fact that 126/125, the septimal semicomma or starling comma (&lt;span class="commentBody"&gt;The difference between three 6/5s, one 7/6, and an octave) &lt;/span&gt;is tempered out, are myna, sensi, valentine, casablanca and nusecond temperaments, not to mention meantone, keemun, muggles and opossum.&lt;br /&gt;

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  These temper out |-5 2 2 -1&amp;gt; = 225/224, the marvel comma, and include negri, sharp, mavila, wizard, tritonic, septimin, slender, triton, escapade and marvo. Considered elsewhere are meantone, miracle, magic, pajara, orwell, catakleismic, garibaldi, august and compton.&lt;br /&gt;

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  These temper out |6 3 -1 -3&amp;gt; = 1728/1715, the orwellisma.&lt;br /&gt;

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  Hemifamity temperaments temper out the hemifamity comma, |10 -6 1 -1&amp;gt; = 5120/5103.&lt;br /&gt;

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  Porwell temperaments temper out the porwell comma, |11 1 -3 -2&amp;gt; = 6144/6125.&lt;br /&gt;

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  Stearnsmic temperaments temper out the stearnsma, |1 10 0 -6&amp;gt; = 118098/117649.&lt;br /&gt;

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  Hemimage temperaments temper out the hemimage comma, |5 -7 -1 3&amp;gt; = 10976/10935.&lt;br /&gt;

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  Horwell temperaments temper out the horwell comma, |-16 1 5 1&amp;gt; = 65625/65536.&lt;br /&gt;

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  A breedsmic temperament is one which tempers out the breedsma, |-5 -1 -2 4&amp;gt; = 2401/2400. Some which do not get discussed elsewhere are collected on a page &lt;a class="wiki_link" href="/Breedsmic%20temperaments"&gt;here&lt;/a&gt;.&lt;br /&gt;

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  A ragismic temperament is one which tempers out |-1 -7 4 1&amp;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.&lt;br /&gt;

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  A landscape temperament is one which tempers out |-4 6 -6 3&amp;gt; = 250047/250000.&lt;br /&gt;

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  These all have period 1/31 of an octave.&lt;br /&gt;

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Vsrious theoretical solutions have been put forward for the vexing problem of how to indicate and define the tuning of Turkish &lt;a class="wiki_link" href="/Arabic%2C%20Turkish%2C%20Persian"&gt;maqam music&lt;/a&gt; in a systematic way. This includes, in effect, certain linear temperaments.&lt;br /&gt;

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  All hope abandon ye who enter here.&lt;br /&gt;

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  Microtemperaments which don't fit in elsewhere.&lt;br /&gt;

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High in badness, but worth cataloging for one reason or another.&lt;br /&gt;

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&lt;!-- ws:start:WikiTextHeadingRule:138:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc69"&gt;&lt;a name="Rank 3 temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:138 --&gt;Rank 3 temperaments&lt;/h1&gt;