Tour of regular temperaments: Difference between revisions

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The würschmidt (or wuerschmidt) family tempers out Würschmidt's comma, |17 1 -8&gt;. Würschmidt itself has a generator of a major third, eight of which give a 6/1 (the 6th harmonic, or a perfect 5th two octaves up); that is, (5/4)^8 * |17 1 -8&gt; = 6. It tends to generate the same MOS's as [[magic family|magic temperament]], but is tuned slightly more accurately. Both [[31edo]] and [[34edo]] can be used as würschmidt tunings, as can [[65edo]], which is quite accurate.

The semicomma (also known as **Fokker's comma),** |-21 3 7&gt; is tempered out by the members of the semicomma family. It doesn't have much independent existence as a 5-limit temperament, since its generator has a natural interpretation as 7/6, leading to [[orwell]] temperament.

&lt;span style="font-weight: normal;"&gt;The sycamore family tempers out the sycamore comma, |-16 -6 11&gt;, which is the amount by which five stacked chromatic semitones, 25/24, exceed 6/5, and hence also the amount six exceeds 5/4.&lt;/span&gt;

This tempers out the amity comma, |9 -13 5&gt;.

This tempers out the vishnuzma, |23 6 -14&gt;, or the amount by which seven chromatic semitones (25/24) fall short of a perfect fourth (4/3), or (4/3)/(25/24)^7.

This tempers out the Luna comma; |38 -2 -15&gt;

This tempers out the immunity comma, |16 -13 2&gt;.

This tempers out the ditonma, [[tel/1220703125|1220703125]]/1207959552.

This tempers out the shibboleth comma, |-5 -10 9&gt;.

This tempers out the comic comma, |13 -14 4&gt;.

This tempers out the fifive comma, |-1 -14 10&gt;.

This tempers out the maja comma, [[tel/762939453125|762939453125]]/753145430616.

The pental family tempers out the pental comma, |-28 25 -5&gt;.

This tempers out the maquila comma, |49 -6 -17&gt;.

This tempers out quince, the no-threes comma |-15 0 -2 7&gt;.

Stearnsmic temperaments temper out the stearnsma, |1 10 0 -6&gt;.

A landscape temperament is one which tempers out |-4 6 -6 3&gt;.

A wizmic temperament is one which tempers out the wizma, | -6 -8 2 5 &gt;.

The 7-limit rank three microtemperament which tempers out the lanscape comma, |-4 6 -6 3&gt;, extends to various higher limit rank three temperaments such as tyr and odin.

The dimcomp family of rank three temperaments tempers out the dimcomp comma, |-1 -4 8 -4&gt;.

These temper out the tolerma, |10 -11 2 1&gt;.

These are the rank three temperaments tempering out the porcupine comma or maximal diesis, 250/243. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth.

  The würschmidt (or wuerschmidt) family tempers out Würschmidt's comma, |17 1 -8&amp;gt;. Würschmidt itself has a generator of a major third, eight of which give a 6/1 (the 6th harmonic, or a perfect 5th two octaves up); that is, (5/4)^8 * |17 1 -8&amp;gt; = 6. It tends to generate the same MOS's as &lt;a class="wiki_link" href="/magic%20family"&gt;magic temperament&lt;/a&gt;, but is tuned slightly more accurately. Both &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; and &lt;a class="wiki_link" href="/34edo"&gt;34edo&lt;/a&gt; can be used as würschmidt tunings, as can &lt;a class="wiki_link" href="/65edo"&gt;65edo&lt;/a&gt;, which is quite accurate.&lt;br /&gt;

  The semicomma (also known as &lt;strong&gt;Fokker's comma),&lt;/strong&gt; |-21 3 7&amp;gt; is tempered out by the members of the semicomma family. It doesn't have much independent existence as a 5-limit temperament, since its generator has a natural interpretation as 7/6, leading to &lt;a class="wiki_link" href="/orwell"&gt;orwell&lt;/a&gt; temperament.&lt;br /&gt;

  &lt;span style="font-weight: normal;"&gt;The sycamore family tempers out the sycamore comma, |-16 -6 11&amp;gt;, which is the amount by which five stacked chromatic semitones, 25/24, exceed 6/5, and hence also the amount six exceeds 5/4.&lt;/span&gt;&lt;br /&gt;

  This tempers out the amity comma, |9 -13 5&amp;gt;.&lt;br /&gt;

  This tempers out the vishnuzma, |23 6 -14&amp;gt;, or the amount by which seven chromatic semitones (25/24) fall short of a perfect fourth (4/3), or (4/3)/(25/24)^7.&lt;br /&gt;

  This tempers out the Luna comma; |38 -2 -15&amp;gt;&lt;br /&gt;

  This tempers out the immunity comma, |16 -13 2&amp;gt;.&lt;br /&gt;

  This tempers out the ditonma, &lt;a class="wiki_link" href="http://tel.wikispaces.com/1220703125"&gt;1220703125&lt;/a&gt;/1207959552.&lt;br /&gt;

  This tempers out the shibboleth comma, |-5 -10 9&amp;gt;.&lt;br /&gt;

  This tempers out the comic comma, |13 -14 4&amp;gt;.&lt;br /&gt;

  This tempers out the fifive comma, |-1 -14 10&amp;gt;.&lt;br /&gt;

  This tempers out the maja comma, &lt;a class="wiki_link" href="http://tel.wikispaces.com/762939453125"&gt;762939453125&lt;/a&gt;/753145430616.&lt;br /&gt;

  The pental family tempers out the pental comma, |-28 25 -5&amp;gt;.&lt;br /&gt;

  This tempers out the maquila comma, |49 -6 -17&amp;gt;.&lt;br /&gt;

  This tempers out quince, the no-threes comma |-15 0 -2 7&amp;gt;.&lt;br /&gt;

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

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

  A wizmic temperament is one which tempers out the wizma, | -6 -8 2 5 &amp;gt;.&lt;br /&gt;

  The 7-limit rank three microtemperament which tempers out the lanscape comma, |-4 6 -6 3&amp;gt;, extends to various higher limit rank three temperaments such as tyr and odin.&lt;br /&gt;

  The dimcomp family of rank three temperaments tempers out the dimcomp comma, |-1 -4 8 -4&amp;gt;.&lt;br /&gt;

  These temper out the tolerma, |10 -11 2 1&amp;gt;.&lt;br /&gt;

  These are the rank three temperaments tempering out the porcupine comma or maximal diesis, 250/243. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth.&lt;br /&gt;