Tour of regular temperaments: Difference between revisions
Wikispaces>genewardsmith **Imported revision 286990864 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 286990978 - 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>2011-12-16 19: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-12-16 19:14:10 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>286990978</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 hemimean family of rank three temperaments tempers out the hemimean comma, 3136/3125. | The hemimean family of rank three temperaments tempers out the hemimean comma, 3136/3125. | ||
===[[Mirwomo family]]== | ===[[Mirwomo family]]=== | ||
The mirwomo family of rank three temperaments tempers out the mirwomo comma, 33075/32768. | The mirwomo family of rank three temperaments tempers out the mirwomo comma, 33075/32768. | ||
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The hemimean family of rank three temperaments tempers out the hemimean comma, 3136/3125.<br /> | The hemimean family of rank three temperaments tempers out the hemimean comma, 3136/3125.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:130:&lt; | <!-- ws:start:WikiTextHeadingRule:130:&lt;h3&gt; --><h3 id="toc65"><a name="Rank 3 temperaments--Mirwomo family"></a><!-- ws:end:WikiTextHeadingRule:130 --><a class="wiki_link" href="/Mirwomo%20family">Mirwomo family</a></h3> | ||
The mirwomo family of rank three temperaments tempers out the mirwomo comma, 33075/32768.<br /> | The mirwomo family of rank three temperaments tempers out the mirwomo comma, 33075/32768.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:132:&lt;h3&gt; --><h3 id="toc66"><a name="Rank 3 temperaments- | <!-- ws:start:WikiTextHeadingRule:132:&lt;h3&gt; --><h3 id="toc66"><a name="Rank 3 temperaments--Dimcomp family"></a><!-- ws:end:WikiTextHeadingRule:132 --><a class="wiki_link" href="/Dimcomp%20family">Dimcomp family</a></h3> | ||
The dimcomp family of rank three temperaments tempers out the dimcomp comma, 390625/388962.<br /> | The dimcomp family of rank three temperaments tempers out the dimcomp comma, 390625/388962.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:134:&lt;h3&gt; --><h3 id="toc67"><a name="Rank 3 temperaments- | <!-- ws:start:WikiTextHeadingRule:134:&lt;h3&gt; --><h3 id="toc67"><a name="Rank 3 temperaments--Kleismic rank three family"></a><!-- ws:end:WikiTextHeadingRule:134 --><a class="wiki_link" href="/Kleismic%20rank%20three%20family">Kleismic rank three family</a></h3> | ||
These are the rank three temperaments tempering out the kleisma, 15625/15552. 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.<br /> | These are the rank three temperaments tempering out the kleisma, 15625/15552. 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.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:136:&lt;h3&gt; --><h3 id="toc68"><a name="Rank 3 temperaments- | <!-- ws:start:WikiTextHeadingRule:136:&lt;h3&gt; --><h3 id="toc68"><a name="Rank 3 temperaments--Diaschismic rank three family"></a><!-- ws:end:WikiTextHeadingRule:136 --><a class="wiki_link" href="/Diaschismic%20rank%20three%20family">Diaschismic rank three family</a></h3> | ||
These are the rank three temperaments tempering out the dischisma, 2048/2025. 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.<br /> | These are the rank three temperaments tempering out the dischisma, 2048/2025. 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.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:138:&lt;h3&gt; --><h3 id="toc69"><a name="Rank 3 temperaments- | <!-- ws:start:WikiTextHeadingRule:138:&lt;h3&gt; --><h3 id="toc69"><a name="Rank 3 temperaments--Didymus rank three family"></a><!-- ws:end:WikiTextHeadingRule:138 --><a class="wiki_link" href="/Didymus%20rank%20three%20family">Didymus rank three family</a></h3> | ||
These are the rank three temperaments tempering out the didymus comma, 81/80. 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.<br /> | These are the rank three temperaments tempering out the didymus comma, 81/80. 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.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:140:&lt;h3&gt; --><h3 id="toc70"><a name="Rank 3 temperaments- | <!-- ws:start:WikiTextHeadingRule:140:&lt;h3&gt; --><h3 id="toc70"><a name="Rank 3 temperaments--Porcupine rank three family"></a><!-- ws:end:WikiTextHeadingRule:140 --><a class="wiki_link" href="/Porcupine%20rank%20three%20family">Porcupine rank three family</a></h3> | ||
These are the rank three temperaments tempering out the porcupine comma or aximal 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.<br /> | These are the rank three temperaments tempering out the porcupine comma or aximal 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.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:142:&lt;h3&gt; --><h3 id="toc71"><a name="Rank 3 temperaments- | <!-- ws:start:WikiTextHeadingRule:142:&lt;h3&gt; --><h3 id="toc71"><a name="Rank 3 temperaments--Archytas family"></a><!-- ws:end:WikiTextHeadingRule:142 --><a class="wiki_link" href="/Archytas%20family">Archytas family</a></h3> | ||
Archytas temperament tempers out 64/63, and thereby identifies the otonal tetrad with the dominant seventh chord.<br /> | Archytas temperament tempers out 64/63, and thereby identifies the otonal tetrad with the dominant seventh chord.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:144:&lt;h3&gt; --><h3 id="toc72"><a name="Rank 3 temperaments- | <!-- ws:start:WikiTextHeadingRule:144:&lt;h3&gt; --><h3 id="toc72"><a name="Rank 3 temperaments--Jubilismic family"></a><!-- ws:end:WikiTextHeadingRule:144 --><a class="wiki_link" href="/Jubilismic%20family">Jubilismic family</a></h3> | ||
Jubilismic temperament tempers out 50/49 and thereby identifies the two septimal tritones, 7/5 and 10/7.<br /> | Jubilismic temperament tempers out 50/49 and thereby identifies the two septimal tritones, 7/5 and 10/7.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:146:&lt;h3&gt; --><h3 id="toc73"><a name="Rank 3 temperaments- | <!-- ws:start:WikiTextHeadingRule:146:&lt;h3&gt; --><h3 id="toc73"><a name="Rank 3 temperaments--Semaphore family"></a><!-- ws:end:WikiTextHeadingRule:146 --><a class="wiki_link" href="/Semaphore%20family">Semaphore family</a></h3> | ||
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 &quot;semi-fourth&quot;.<br /> | 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 &quot;semi-fourth&quot;.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:148:&lt;h3&gt; --><h3 id="toc74"><a name="Rank 3 temperaments- | <!-- ws:start:WikiTextHeadingRule:148:&lt;h3&gt; --><h3 id="toc74"><a name="Rank 3 temperaments--Quartonic family"></a><!-- ws:end:WikiTextHeadingRule:148 --><a class="wiki_link" href="/Quartonic%20family">Quartonic family</a></h3> | ||
The quartonic temperament tempers out 36/35, identifying both 7/6 with 6/5 and 5/4 with 9/7.<br /> | The quartonic temperament tempers out 36/35, identifying both 7/6 with 6/5 and 5/4 with 9/7.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:150:&lt;h3&gt; --><h3 id="toc75"><a name="Rank 3 temperaments- | <!-- ws:start:WikiTextHeadingRule:150:&lt;h3&gt; --><h3 id="toc75"><a name="Rank 3 temperaments--Valinorismic temperaments"></a><!-- ws:end:WikiTextHeadingRule:150 --><a class="wiki_link" href="/Valinorismic%20temperaments">Valinorismic temperaments</a></h3> | ||
These temper out the valinorsma, 176/175.<br /> | These temper out the valinorsma, 176/175.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:152:&lt;h3&gt; --><h3 id="toc76"><a name="Rank 3 temperaments- | <!-- ws:start:WikiTextHeadingRule:152:&lt;h3&gt; --><h3 id="toc76"><a name="Rank 3 temperaments--Werckismic temperaments"></a><!-- ws:end:WikiTextHeadingRule:152 --><a class="wiki_link" href="/Werckismic%20temperaments">Werckismic temperaments</a></h3> | ||
These temper out the werckisma, 441/440.<br /> | These temper out the werckisma, 441/440.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:154:&lt;h3&gt; --><h3 id="toc77"><a name="Rank 3 temperaments- | <!-- ws:start:WikiTextHeadingRule:154:&lt;h3&gt; --><h3 id="toc77"><a name="Rank 3 temperaments--Swetismic temperaments"></a><!-- ws:end:WikiTextHeadingRule:154 --><a class="wiki_link" href="/Swetismic%20temperaments">Swetismic temperaments</a></h3> | ||
These temper out the swetisma, 540/539.<br /> | These temper out the swetisma, 540/539.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:156:&lt;h3&gt; --><h3 id="toc78"><a name="Rank 3 temperaments- | <!-- ws:start:WikiTextHeadingRule:156:&lt;h3&gt; --><h3 id="toc78"><a name="Rank 3 temperaments--Lehmerismic temperaments"></a><!-- ws:end:WikiTextHeadingRule:156 --><a class="wiki_link" href="/Lehmerismic%20temperaments">Lehmerismic temperaments</a></h3> | ||
These temper out the lehmerisma, 3025/3024.<br /> | These temper out the lehmerisma, 3025/3024.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:158:&lt;h3&gt; --><h3 id="toc79"><a name="Rank 3 temperaments- | <!-- ws:start:WikiTextHeadingRule:158:&lt;h3&gt; --><h3 id="toc79"><a name="Rank 3 temperaments--Kalismic temperaments"></a><!-- ws:end:WikiTextHeadingRule:158 --><a class="wiki_link" href="/Kalismic%20temperaments">Kalismic temperaments</a></h3> | ||
These temper out the kalisma, 9801/9800.<br /> | These temper out the kalisma, 9801/9800.<br /> | ||
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