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Tour of regular temperaments: Difference between revisions

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Wikispaces>JosephRuhf
**Imported revision 602402198 - Original comment: **
Wikispaces>JosephRuhf
**Imported revision 602402660 - 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:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-17 10:50:18 UTC</tt>.<br>
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-17 11:11:38 UTC</tt>.<br>
: The original revision id was <tt>602402198</tt>.<br>
: The original revision id was <tt>602402660</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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===[[Sycamore family]]===  
===[[Sycamore family]]===  
The sycamore family tempers out the sycamore comma, |-16 -6 11&gt; = [[tel:48828125/47775744|48828125/47775744]], 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 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;


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


===[[Vulture family]]===  
===[[Vulture family]]===  
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===[[Luna Family]]===  
===[[Luna Family]]===  
This tempers out the Luna comma; |38 -2 -15&gt; ([[tel:274877906944|274877906944]]/274658203125)
This tempers out the Luna comma; |38 -2 -15&gt;


===[[Laconic Family]]===  
===[[Laconic Family]]===  
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===[[Immunity family]]===  
===[[Immunity family]]===  
This tempers out the immunity comma, [[tel:1638400/1594323|1638400/1594323]].
This tempers out the immunity comma, |16 -13 2&gt;.


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


===[[Shibboleth family]]===  
===[[Shibboleth family]]===  
This tempers out the shibboleth comma, [[tel:1953125/1889568|1953125/1889568]].
This tempers out the shibboleth comma, |-5 -10 9&gt;.


===[[Comic family]]===  
===[[Comic family]]===  
This tempers out the comic comma, [[tel:5120000/4782969|5120000/4782969]].
This tempers out the comic comma, |13 -14 4&gt;.


===[[Wesley family]]===  
===[[Wesley family]]===  
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===[[Fifive family]]===  
===[[Fifive family]]===  
This tempers out the fifive comma, [[tel:9765625/9565938|9765625/9565938]].
This tempers out the fifive comma, |-1 -14 10&gt;.


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


===[[Pental family]]===  
===[[Pental family]]===  
The pental family tempers out the pental comma, [[tel:847288609443|847288609443]]/838860800000 = |-28 25 -5&gt;.
The pental family tempers out the pental comma, |-28 25 -5&gt;.


===[[Maquila family]]===  
===[[Maquila family]]===  
This tempers out the maquila comma, [[tel:562949953421312|562949953421312]]/556182861328125 = |49 -6 -17&gt;.
This tempers out the maquila comma, |49 -6 -17&gt;.


===[[Mutt family]]===  
===[[Mutt family]]===  
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===[[Quince clan]]===  
===[[Quince clan]]===  
This tempers out quince, the no-threes comma |-15 0 -2 7&gt; = [[tel:823543/819200|823543/819200]].
This tempers out quince, the no-threes comma |-15 0 -2 7&gt;.


=Temperaments for a given comma=  
=Temperaments for a given comma=  
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===[[Stearnsmic temperaments]]===  
===[[Stearnsmic temperaments]]===  
Stearnsmic temperaments temper out the stearnsma, |1 10 0 -6&gt; = [[tel:118098/117649|118098/117649]].
Stearnsmic temperaments temper out the stearnsma, |1 10 0 -6&gt;.


===[[Hemimage temperaments]]===  
===[[Hemimage temperaments]]===  
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===[[Landscape microtemperaments]]===  
===[[Landscape microtemperaments]]===  
A landscape temperament is one which tempers out |-4 6 -6 3&gt; = [[tel:250047/250000|250047/250000]].
A landscape temperament is one which tempers out |-4 6 -6 3&gt;.


===[[Wizmic microtemperaments]]===  
===[[Wizmic microtemperaments]]===  
A wizmic temperament is one which tempers out the wizma, | -6 -8 2 5 &gt; = [[tel:420175/419904|420175/419904]].
A wizmic temperament is one which tempers out the wizma, | -6 -8 2 5 &gt;.


===[[31 comma temperaments]]===  
===[[31 comma temperaments]]===  
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===[[Landscape family]]===  
===[[Landscape family]]===  
The 7-limit rank three microtemperament which tempers out the lanscape comma, [[tel:250047/250000|250047/250000]], extends to various higher limit rank three temperaments such as tyr and odin.
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.


===[[Hemifamity family]]===  
===[[Hemifamity family]]===  
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===[[Dimcomp family]]===  
===[[Dimcomp family]]===  
The dimcomp family of rank three temperaments tempers out the dimcomp comma, [[tel:390625/388962|390625/388962]].
The dimcomp family of rank three temperaments tempers out the dimcomp comma, |-1 -4 8 -4&gt;.


===[[Tolermic family]]===  
===[[Tolermic family]]===  
These temper out the tolerma, [[tel:179200/177147|179200/177147]].
These temper out the tolerma, |10 -11 2 1&gt;.


===[[Kleismic rank three family]]===  
===[[Kleismic rank three family]]===  
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===[[Porcupine rank three family]]===  
===[[Porcupine rank three family]]===  
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.
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.


===[[Archytas family]]===  
===[[Archytas family]]===  
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&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:52:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc26"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments-Families-Sycamore family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:52 --&gt;&lt;a class="wiki_link" href="/Sycamore%20family"&gt;Sycamore family&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:52:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc26"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments-Families-Sycamore family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:52 --&gt;&lt;a class="wiki_link" href="/Sycamore%20family"&gt;Sycamore family&lt;/a&gt;&lt;/h3&gt;
  The sycamore family tempers out the sycamore comma, |-16 -6 11&amp;gt; = [[tel:48828125/47775744|48828125/47775744]], 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;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;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:54:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc27"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments-Families-Escapade family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:54 --&gt;&lt;a class="wiki_link" href="/Escapade%20family"&gt;Escapade family&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:54:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc27"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments-Families-Escapade family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:54 --&gt;&lt;a class="wiki_link" href="/Escapade%20family"&gt;Escapade 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, [[tel:1600000/1594323|1600000/1594323]] = |9 -13 5&amp;gt;.&lt;br /&gt;
  This tempers out the amity comma, |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:62:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc31"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments-Families-Luna Family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:62 --&gt;&lt;a class="wiki_link" href="/Luna%20Family"&gt;Luna Family&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:62:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc31"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments-Families-Luna Family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:62 --&gt;&lt;a class="wiki_link" href="/Luna%20Family"&gt;Luna Family&lt;/a&gt;&lt;/h3&gt;
  This tempers out the Luna comma; |38 -2 -15&amp;gt; (&lt;a class="wiki_link" href="http://tel.wikispaces.com/274877906944"&gt;274877906944&lt;/a&gt;/274658203125)&lt;br /&gt;
  This tempers out the Luna comma; |38 -2 -15&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:64:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc32"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments-Families-Laconic Family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:64 --&gt;&lt;a class="wiki_link" href="/Laconic%20Family"&gt;Laconic Family&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:64:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc32"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments-Families-Laconic Family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:64 --&gt;&lt;a class="wiki_link" href="/Laconic%20Family"&gt;Laconic 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, [[tel:1638400/1594323|1638400/1594323]].&lt;br /&gt;
  This tempers out the immunity comma, |16 -13 2&amp;gt;.&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;
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&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, [[tel:1953125/1889568|1953125/1889568]].&lt;br /&gt;
  This tempers out the shibboleth comma, |-5 -10 9&amp;gt;.&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, [[tel:5120000/4782969|5120000/4782969]].&lt;br /&gt;
  This tempers out the comic comma, |13 -14 4&amp;gt;.&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;
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&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 comma, [[tel:9765625/9565938|9765625/9565938]].&lt;br /&gt;
  This tempers out the fifive comma, |-1 -14 10&amp;gt;.&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;
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&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-Pental family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:80 --&gt;&lt;a class="wiki_link" href="/Pental%20family"&gt;Pental 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-Pental family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:80 --&gt;&lt;a class="wiki_link" href="/Pental%20family"&gt;Pental family&lt;/a&gt;&lt;/h3&gt;
  The pental family tempers out the pental comma, &lt;a class="wiki_link" href="http://tel.wikispaces.com/847288609443"&gt;847288609443&lt;/a&gt;/838860800000 = |-28 25 -5&amp;gt;.&lt;br /&gt;
  The pental family tempers out the pental comma, |-28 25 -5&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:82:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc41"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments-Families-Maquila family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:82 --&gt;&lt;a class="wiki_link" href="/Maquila%20family"&gt;Maquila family&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:82:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc41"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments-Families-Maquila family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:82 --&gt;&lt;a class="wiki_link" href="/Maquila%20family"&gt;Maquila family&lt;/a&gt;&lt;/h3&gt;
  This tempers out the maquila comma, &lt;a class="wiki_link" href="http://tel.wikispaces.com/562949953421312"&gt;562949953421312&lt;/a&gt;/556182861328125 = |49 -6 -17&amp;gt;.&lt;br /&gt;
  This tempers out the maquila comma, |49 -6 -17&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:84:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc42"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments-Families-Mutt family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:84 --&gt;&lt;a class="wiki_link" href="/Mutt%20family"&gt;Mutt family&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:84:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc42"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments-Families-Mutt family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:84 --&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:104:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc52"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments-Clans-Quince clan"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:104 --&gt;&lt;a class="wiki_link" href="/Quince%20clan"&gt;Quince clan&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:104:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc52"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments-Clans-Quince clan"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:104 --&gt;&lt;a class="wiki_link" href="/Quince%20clan"&gt;Quince clan&lt;/a&gt;&lt;/h3&gt;
  This tempers out quince, the no-threes comma |-15 0 -2 7&amp;gt; = [[tel:823543/819200|823543/819200]].&lt;br /&gt;
  This tempers out quince, the no-threes comma |-15 0 -2 7&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:106:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc53"&gt;&lt;a name="Temperaments for a given comma"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:106 --&gt;Temperaments for a given comma&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:106:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc53"&gt;&lt;a name="Temperaments for a given comma"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:106 --&gt;Temperaments for a given comma&lt;/h1&gt;
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&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:130:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc65"&gt;&lt;a name="Temperaments for a given comma--Stearnsmic temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:130 --&gt;&lt;a class="wiki_link" href="/Stearnsmic%20temperaments"&gt;Stearnsmic temperaments&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:130:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc65"&gt;&lt;a name="Temperaments for a given comma--Stearnsmic temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:130 --&gt;&lt;a class="wiki_link" href="/Stearnsmic%20temperaments"&gt;Stearnsmic temperaments&lt;/a&gt;&lt;/h3&gt;
  Stearnsmic temperaments temper out the stearnsma, |1 10 0 -6&amp;gt; = [[tel:118098/117649|118098/117649]].&lt;br /&gt;
  Stearnsmic temperaments temper out the stearnsma, |1 10 0 -6&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:132:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc66"&gt;&lt;a name="Temperaments for a given comma--Hemimage temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:132 --&gt;&lt;a class="wiki_link" href="/Hemimage%20temperaments"&gt;Hemimage temperaments&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:132:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc66"&gt;&lt;a name="Temperaments for a given comma--Hemimage temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:132 --&gt;&lt;a class="wiki_link" href="/Hemimage%20temperaments"&gt;Hemimage temperaments&lt;/a&gt;&lt;/h3&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:142:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc71"&gt;&lt;a name="Temperaments for a given comma--Landscape microtemperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:142 --&gt;&lt;a class="wiki_link" href="/Landscape%20microtemperaments"&gt;Landscape microtemperaments&lt;/a&gt;&lt;/h3&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--Landscape microtemperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:142 --&gt;&lt;a class="wiki_link" href="/Landscape%20microtemperaments"&gt;Landscape microtemperaments&lt;/a&gt;&lt;/h3&gt;
  A landscape temperament is one which tempers out |-4 6 -6 3&amp;gt; = [[tel:250047/250000|250047/250000]].&lt;br /&gt;
  A landscape temperament is one which tempers out |-4 6 -6 3&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:144:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc72"&gt;&lt;a name="Temperaments for a given comma--Wizmic microtemperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:144 --&gt;&lt;a class="wiki_link" href="/Wizmic%20microtemperaments"&gt;Wizmic microtemperaments&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:144:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc72"&gt;&lt;a name="Temperaments for a given comma--Wizmic microtemperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:144 --&gt;&lt;a class="wiki_link" href="/Wizmic%20microtemperaments"&gt;Wizmic microtemperaments&lt;/a&gt;&lt;/h3&gt;
  A wizmic temperament is one which tempers out the wizma, | -6 -8 2 5 &amp;gt; = [[tel:420175/419904|420175/419904]].&lt;br /&gt;
  A wizmic temperament is one which tempers out the wizma, | -6 -8 2 5 &amp;gt;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:146:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc73"&gt;&lt;a name="Temperaments for a given comma--31 comma temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:146 --&gt;&lt;a class="wiki_link" href="/31%20comma%20temperaments"&gt;31 comma temperaments&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:146:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc73"&gt;&lt;a name="Temperaments for a given comma--31 comma temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:146 --&gt;&lt;a class="wiki_link" href="/31%20comma%20temperaments"&gt;31 comma temperaments&lt;/a&gt;&lt;/h3&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:170:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc85"&gt;&lt;a name="Rank 3 temperaments--Landscape family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:170 --&gt;&lt;a class="wiki_link" href="/Landscape%20family"&gt;Landscape family&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:170:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc85"&gt;&lt;a name="Rank 3 temperaments--Landscape family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:170 --&gt;&lt;a class="wiki_link" href="/Landscape%20family"&gt;Landscape family&lt;/a&gt;&lt;/h3&gt;
  The 7-limit rank three microtemperament which tempers out the lanscape comma, [[tel:250047/250000|250047/250000]], extends to various higher limit rank three temperaments such as tyr and odin.&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;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:172:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc86"&gt;&lt;a name="Rank 3 temperaments--Hemifamity family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:172 --&gt;&lt;a class="wiki_link" href="/Hemifamity%20family"&gt;Hemifamity family&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:172:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc86"&gt;&lt;a name="Rank 3 temperaments--Hemifamity family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:172 --&gt;&lt;a class="wiki_link" href="/Hemifamity%20family"&gt;Hemifamity family&lt;/a&gt;&lt;/h3&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:198:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc99"&gt;&lt;a name="Rank 3 temperaments--Dimcomp family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:198 --&gt;&lt;a class="wiki_link" href="/Dimcomp%20family"&gt;Dimcomp family&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:198:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc99"&gt;&lt;a name="Rank 3 temperaments--Dimcomp family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:198 --&gt;&lt;a class="wiki_link" href="/Dimcomp%20family"&gt;Dimcomp family&lt;/a&gt;&lt;/h3&gt;
  The dimcomp family of rank three temperaments tempers out the dimcomp comma, [[tel:390625/388962|390625/388962]].&lt;br /&gt;
  The dimcomp family of rank three temperaments tempers out the dimcomp comma, |-1 -4 8 -4&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:200:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc100"&gt;&lt;a name="Rank 3 temperaments--Tolermic family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:200 --&gt;&lt;a class="wiki_link" href="/Tolermic%20family"&gt;Tolermic family&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:200:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc100"&gt;&lt;a name="Rank 3 temperaments--Tolermic family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:200 --&gt;&lt;a class="wiki_link" href="/Tolermic%20family"&gt;Tolermic family&lt;/a&gt;&lt;/h3&gt;
  These temper out the tolerma, [[tel:179200/177147|179200/177147]].&lt;br /&gt;
  These temper out the tolerma, |10 -11 2 1&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:202:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc101"&gt;&lt;a name="Rank 3 temperaments--Kleismic rank three family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:202 --&gt;&lt;a class="wiki_link" href="/Kleismic%20rank%20three%20family"&gt;Kleismic rank three family&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:202:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc101"&gt;&lt;a name="Rank 3 temperaments--Kleismic rank three family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:202 --&gt;&lt;a class="wiki_link" href="/Kleismic%20rank%20three%20family"&gt;Kleismic rank three family&lt;/a&gt;&lt;/h3&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:208:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc104"&gt;&lt;a name="Rank 3 temperaments--Porcupine rank three family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:208 --&gt;&lt;a class="wiki_link" href="/Porcupine%20rank%20three%20family"&gt;Porcupine rank three family&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:208:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc104"&gt;&lt;a name="Rank 3 temperaments--Porcupine rank three family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:208 --&gt;&lt;a class="wiki_link" href="/Porcupine%20rank%20three%20family"&gt;Porcupine rank three family&lt;/a&gt;&lt;/h3&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;
  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;
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&lt;!-- ws:start:WikiTextHeadingRule:210:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc105"&gt;&lt;a name="Rank 3 temperaments--Archytas family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:210 --&gt;&lt;a class="wiki_link" href="/Archytas%20family"&gt;Archytas family&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:210:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc105"&gt;&lt;a name="Rank 3 temperaments--Archytas family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:210 --&gt;&lt;a class="wiki_link" href="/Archytas%20family"&gt;Archytas family&lt;/a&gt;&lt;/h3&gt;
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