Xenharmonic Wiki

Tour of regular temperaments: Difference between revisions

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Wikispaces>genewardsmith
**Imported revision 331298724 - Original comment: **
Wikispaces>mbattaglia1
**Imported revision 337249970 - 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>2012-05-07 15:35:07 UTC</tt>.<br>
: This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2012-05-19 04:40:23 UTC</tt>.<br>
: The original revision id was <tt>331298724</tt>.<br>
: The original revision id was <tt>337249970</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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The augmented family tempers out the diesis of 128/125, the difference between three 5/4 major thirds and a 2/1 octave, and so identifies the major third with the third-octave. Hence it has the same 400-cent 5/4-approximations as [[12edo]], which is an excellent tuning for augmented. It is the temperament that results in what is commonly called the "augmented scale" (3L3s) in common 12-based music theory, as well as what is commonly called "Tcherepnin's scale" (3L6s).
The augmented family tempers out the diesis of 128/125, the difference between three 5/4 major thirds and a 2/1 octave, and so identifies the major third with the third-octave. Hence it has the same 400-cent 5/4-approximations as [[12edo]], which is an excellent tuning for augmented. It is the temperament that results in what is commonly called the "augmented scale" (3L3s) in common 12-based music theory, as well as what is commonly called "Tcherepnin's scale" (3L6s).


===[[Dimipent family]]===
===[[Dimipent family]]===  
The dimipent family tempers out the major diesis aka diminished comma, 648/625, the amount by which four 6/5 minor thirds exceed an octave, and so identifies the minor third with the quarter-octave. Hence it has the same 300-cent 6/5-approximations as [[12edo]].  
The dimipent family tempers out the major diesis aka diminished comma, 648/625, the amount by which four 6/5 minor thirds exceed an octave, and so identifies the minor third with the quarter-octave. Hence it has the same 300-cent 6/5-approximations as [[12edo]].


===[[Dicot family]]===  
===[[Dicot family]]===  
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This tempers out the escapade comma, |32 -7 -9&gt;, which is the difference between nine just major thirds and seven just fourths.
This tempers out the escapade comma, |32 -7 -9&gt;, which is the difference between nine just major thirds and seven just fourths.


===[[Amity family]]===
===[[Amity family]]===  
This tempers out the amity comma, 1600000/1594323 = |9 -13 5&gt;.
This tempers out the amity comma, 1600000/1594323 = |9 -13 5&gt;.


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This tempers out the laconic comma, 2187/2000, which is the difference between three 10/9's and one 3/2. Laconic is supported by 16-EDO, 21-EDO, and 37b-EDO, among others.
This tempers out the laconic comma, 2187/2000, which is the difference between three 10/9's and one 3/2. Laconic is supported by 16-EDO, 21-EDO, and 37b-EDO, among others.


===[[Immunity family]]===
===[[Immunity family]]===  
This tempers out the immunity comma, 1638400/1594323.
This tempers out the immunity comma, 1638400/1594323.


===[[Ditonmic family]]===
===[[Ditonmic family]]===  
This tempers out the ditonma, 1220703125/1207959552.
This tempers out the ditonma, 1220703125/1207959552.


===[[Shibboleth family]]===
===[[Shibboleth family]]===  
This tempers out the shibboleth comma, 1953125/1889568.
This tempers out the shibboleth comma, 1953125/1889568.


===[[Comic family]]===
===[[Comic family]]===  
This tempers out the comic comma, 5120000/4782969.
This tempers out the comic comma, 5120000/4782969.


===[[Wesley family]]===
===[[Wesley family]]===  
This tempers out the wesley comma, 78125/73728.
This tempers out the wesley comma, 78125/73728.


===[[Fifive family]]===
===[[Fifive family]]===  
This tempers out the fifive comme, 9765625/9565938.
This tempers out the fifive comme, 9765625/9565938.


===[[Maja family]]===
===[[Maja family]]===  
This tempers out the maja comma, 762939453125/753145430616.
This tempers out the maja comma, 762939453125/753145430616.


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


===[[Slendro clan]]===
===[[Slendro clan]]===  
This clan tempers out the slendro diesis, [[49_48|49/48]], 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.


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


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


===[[Starling temperaments]]===  
===[[Starling temperaments]]===  
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Microtemperaments which don't fit in elsewhere.
Microtemperaments which don't fit in elsewhere.


===[[High badness temperaments]]===
===[[High badness temperaments]]===  
High in badness, but worth cataloging for one reason or another.
High in badness, but worth cataloging for one reason or another.


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Jubilismic temperament tempers out 50/49 and thereby identifies the two septimal tritones, 7/5 and 10/7.
Jubilismic temperament tempers out 50/49 and thereby identifies the two septimal tritones, 7/5 and 10/7.


===[[Semaphore family]]===  
===[[Semiphore family]]===  
Semaphore temperament tempers out 49/48 and thereby identifies the septimal minor third, 7/6 and the septimal whole tone, 8/7. It also splits the fourth into two of these intervals; hence the name, which sounds like "semi-fourth".
Semiphore temperament tempers out 49/48 and thereby identifies the septimal minor third, 7/6 and the septimal whole tone, 8/7. It also splits the fourth into two of these intervals; hence the name, which sounds like "semi-fourth".


===[[Mint family]]===  
===[[Mint family]]===  
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&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc15"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments-Families-Dimipent family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;&lt;a class="wiki_link" href="/Dimipent%20family"&gt;Dimipent family&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc15"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments-Families-Dimipent family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;&lt;a class="wiki_link" href="/Dimipent%20family"&gt;Dimipent family&lt;/a&gt;&lt;/h3&gt;
The dimipent family tempers out the major diesis aka diminished comma, 648/625, the amount by which four 6/5 minor thirds exceed an octave, and so identifies the minor third with the quarter-octave. Hence it has the same 300-cent 6/5-approximations as &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;. &lt;br /&gt;
The dimipent family tempers out the major diesis aka diminished comma, 648/625, the amount by which four 6/5 minor thirds exceed an octave, and so identifies the minor third with the quarter-octave. Hence it has the same 300-cent 6/5-approximations as &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc16"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments-Families-Dicot family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;&lt;a class="wiki_link" href="/Dicot%20family"&gt;Dicot family&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc16"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments-Families-Dicot family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;&lt;a class="wiki_link" href="/Dicot%20family"&gt;Dicot family&lt;/a&gt;&lt;/h3&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:56:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc28"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments-Families-Amity family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:56 --&gt;&lt;a class="wiki_link" href="/Amity%20family"&gt;Amity family&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:56:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc28"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments-Families-Amity family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:56 --&gt;&lt;a class="wiki_link" href="/Amity%20family"&gt;Amity family&lt;/a&gt;&lt;/h3&gt;
This tempers out the amity comma, 1600000/1594323 = |9 -13 5&amp;gt;.&lt;br /&gt;
This tempers out the amity comma, 1600000/1594323 = |9 -13 5&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:58:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc29"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments-Families-Vulture family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:58 --&gt;&lt;a class="wiki_link" href="/Vulture%20family"&gt;Vulture family&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:58:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc29"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments-Families-Vulture family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:58 --&gt;&lt;a class="wiki_link" href="/Vulture%20family"&gt;Vulture family&lt;/a&gt;&lt;/h3&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:66:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc33"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments-Families-Immunity family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:66 --&gt;&lt;a class="wiki_link" href="/Immunity%20family"&gt;Immunity family&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:66:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc33"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments-Families-Immunity family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:66 --&gt;&lt;a class="wiki_link" href="/Immunity%20family"&gt;Immunity family&lt;/a&gt;&lt;/h3&gt;
This tempers out the immunity comma, 1638400/1594323.&lt;br /&gt;
This tempers out the immunity comma, 1638400/1594323.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:68:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc34"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments-Families-Ditonmic family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:68 --&gt;&lt;a class="wiki_link" href="/Ditonmic%20family"&gt;Ditonmic family&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:68:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc34"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments-Families-Ditonmic family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:68 --&gt;&lt;a class="wiki_link" href="/Ditonmic%20family"&gt;Ditonmic family&lt;/a&gt;&lt;/h3&gt;
This tempers out the ditonma, 1220703125/1207959552.&lt;br /&gt;
This tempers out the ditonma, 1220703125/1207959552.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:70:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc35"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments-Families-Shibboleth family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:70 --&gt;&lt;a class="wiki_link" href="/Shibboleth%20family"&gt;Shibboleth family&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:70:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc35"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments-Families-Shibboleth family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:70 --&gt;&lt;a class="wiki_link" href="/Shibboleth%20family"&gt;Shibboleth family&lt;/a&gt;&lt;/h3&gt;
This tempers out the shibboleth comma, 1953125/1889568.&lt;br /&gt;
This tempers out the shibboleth comma, 1953125/1889568.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:72:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc36"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments-Families-Comic family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:72 --&gt;&lt;a class="wiki_link" href="/Comic%20family"&gt;Comic family&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:72:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc36"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments-Families-Comic family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:72 --&gt;&lt;a class="wiki_link" href="/Comic%20family"&gt;Comic family&lt;/a&gt;&lt;/h3&gt;
This tempers out the comic comma, 5120000/4782969.&lt;br /&gt;
This tempers out the comic comma, 5120000/4782969.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:74:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc37"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments-Families-Wesley family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:74 --&gt;&lt;a class="wiki_link" href="/Wesley%20family"&gt;Wesley family&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:74:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc37"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments-Families-Wesley family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:74 --&gt;&lt;a class="wiki_link" href="/Wesley%20family"&gt;Wesley family&lt;/a&gt;&lt;/h3&gt;
This tempers out the wesley comma, 78125/73728.&lt;br /&gt;
This tempers out the wesley comma, 78125/73728.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:76:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc38"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments-Families-Fifive family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:76 --&gt;&lt;a class="wiki_link" href="/Fifive%20family"&gt;Fifive family&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:76:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc38"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments-Families-Fifive family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:76 --&gt;&lt;a class="wiki_link" href="/Fifive%20family"&gt;Fifive family&lt;/a&gt;&lt;/h3&gt;
This tempers out the fifive comme, 9765625/9565938.&lt;br /&gt;
This tempers out the fifive comme, 9765625/9565938.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:78:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc39"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments-Families-Maja family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:78 --&gt;&lt;a class="wiki_link" href="/Maja%20family"&gt;Maja family&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:78:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc39"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments-Families-Maja family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:78 --&gt;&lt;a class="wiki_link" href="/Maja%20family"&gt;Maja family&lt;/a&gt;&lt;/h3&gt;
This tempers out the maja comma, 762939453125/753145430616.&lt;br /&gt;
This tempers out the maja comma, 762939453125/753145430616.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:80:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc40"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments-Families-Mutt family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:80 --&gt;&lt;a class="wiki_link" href="/Mutt%20family"&gt;Mutt family&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:80:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc40"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments-Families-Mutt family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:80 --&gt;&lt;a class="wiki_link" href="/Mutt%20family"&gt;Mutt family&lt;/a&gt;&lt;/h3&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:88:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc44"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments-Clans-Slendro clan"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:88 --&gt;&lt;a class="wiki_link" href="/Slendro%20clan"&gt;Slendro clan&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:88:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc44"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments-Clans-Slendro clan"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:88 --&gt;&lt;a class="wiki_link" href="/Slendro%20clan"&gt;Slendro clan&lt;/a&gt;&lt;/h3&gt;
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;
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;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:90:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc45"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments-Clans-Jubilismic clan"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:90 --&gt;&lt;a class="wiki_link" href="/Jubilismic%20clan"&gt;Jubilismic clan&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:90:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc45"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments-Clans-Jubilismic clan"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:90 --&gt;&lt;a class="wiki_link" href="/Jubilismic%20clan"&gt;Jubilismic clan&lt;/a&gt;&lt;/h3&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:110:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc55"&gt;&lt;a name="Temperaments for a given comma--Keemic temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:110 --&gt;&lt;a class="wiki_link" href="/Keemic%20temperaments"&gt;Keemic temperaments&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:110:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc55"&gt;&lt;a name="Temperaments for a given comma--Keemic temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:110 --&gt;&lt;a class="wiki_link" href="/Keemic%20temperaments"&gt;Keemic temperaments&lt;/a&gt;&lt;/h3&gt;
These temper out the keema, |-5 -3 3 1&amp;gt; = 875/864.&lt;br /&gt;
These temper out the keema, |-5 -3 3 1&amp;gt; = 875/864.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:112:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc56"&gt;&lt;a name="Temperaments for a given comma--Starling temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:112 --&gt;&lt;a class="wiki_link" href="/Starling%20temperaments"&gt;Starling temperaments&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:112:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc56"&gt;&lt;a name="Temperaments for a given comma--Starling temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:112 --&gt;&lt;a class="wiki_link" href="/Starling%20temperaments"&gt;Starling temperaments&lt;/a&gt;&lt;/h3&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:142:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc71"&gt;&lt;a name="Temperaments for a given comma--High badness temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:142 --&gt;&lt;a class="wiki_link" href="/High%20badness%20temperaments"&gt;High badness temperaments&lt;/a&gt;&lt;/h3&gt;
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High in badness, but worth cataloging for one reason or another.&lt;br /&gt;
High in badness, but worth cataloging for one reason or another.&lt;br /&gt;
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  Jubilismic temperament tempers out 50/49 and thereby identifies the two septimal tritones, 7/5 and 10/7.&lt;br /&gt;
  Jubilismic temperament tempers out 50/49 and thereby identifies the two septimal tritones, 7/5 and 10/7.&lt;br /&gt;
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  Semaphore temperament tempers out 49/48 and thereby identifies the septimal minor third, 7/6 and the septimal whole tone, 8/7. It also splits the fourth into two of these intervals; hence the name, which sounds like &amp;quot;semi-fourth&amp;quot;.&lt;br /&gt;
  Semiphore temperament tempers out 49/48 and thereby identifies the septimal minor third, 7/6 and the septimal whole tone, 8/7. It also splits the fourth into two of these intervals; hence the name, which sounds like &amp;quot;semi-fourth&amp;quot;.&lt;br /&gt;
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