Tour of regular temperaments: Difference between revisions
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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>2011-03-01 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-01 07:14:28 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>206003116</tt>.<br> | ||
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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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===[[Keemic family]]=== | ===[[Keemic family]]=== | ||
These temper out 875/864. | These temper out 875/864. | ||
===[[Sengic family]]=== | |||
These temper out the senga, 686/675. | |||
===[[Orwellismic family]]=== | ===[[Orwellismic family]]=== | ||
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* [[http://en.wikipedia.org/wiki/Regular_temperament|Regular temperaments - Wikipedia]]</pre></div> | * [[http://en.wikipedia.org/wiki/Regular_temperament|Regular temperaments - Wikipedia]]</pre></div> | ||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Tour of Regular Temperaments</title></head><body><!-- ws:start:WikiTextTocRule: | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Tour of Regular Temperaments</title></head><body><!-- ws:start:WikiTextTocRule:144:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:144 --><!-- ws:start:WikiTextTocRule:145: --><a href="#Equal temperaments">Equal temperaments</a><!-- ws:end:WikiTextTocRule:145 --><!-- ws:start:WikiTextTocRule:146: --> | <a href="#Rank 2 (including &quot;linear&quot;) temperaments">Rank 2 (including &quot;linear&quot;) temperaments</a><!-- ws:end:WikiTextTocRule:146 --><!-- ws:start:WikiTextTocRule:147: --><!-- ws:end:WikiTextTocRule:147 --><!-- ws:start:WikiTextTocRule:148: --><!-- ws:end:WikiTextTocRule:148 --><!-- ws:start:WikiTextTocRule:149: --><!-- ws:end:WikiTextTocRule:149 --><!-- ws:start:WikiTextTocRule:150: --><!-- ws:end:WikiTextTocRule:150 --><!-- ws:start:WikiTextTocRule:151: --><!-- ws:end:WikiTextTocRule:151 --><!-- ws:start:WikiTextTocRule:152: --><!-- ws:end:WikiTextTocRule:152 --><!-- ws:start:WikiTextTocRule:153: --><!-- ws:end:WikiTextTocRule:153 --><!-- ws:start:WikiTextTocRule:154: --><!-- ws:end:WikiTextTocRule:154 --><!-- ws:start:WikiTextTocRule:155: --><!-- ws:end:WikiTextTocRule:155 --><!-- ws:start:WikiTextTocRule:156: --><!-- ws:end:WikiTextTocRule:156 --><!-- ws:start:WikiTextTocRule:157: --><!-- ws:end:WikiTextTocRule:157 --><!-- ws:start:WikiTextTocRule:158: --><!-- ws:end:WikiTextTocRule:158 --><!-- ws:start:WikiTextTocRule:159: --><!-- ws:end:WikiTextTocRule:159 --><!-- ws:start:WikiTextTocRule:160: --><!-- ws:end:WikiTextTocRule:160 --><!-- ws:start:WikiTextTocRule:161: --><!-- ws:end:WikiTextTocRule:161 --><!-- ws:start:WikiTextTocRule:162: --><!-- ws:end:WikiTextTocRule:162 --><!-- ws:start:WikiTextTocRule:163: --><!-- ws:end:WikiTextTocRule:163 --><!-- ws:start:WikiTextTocRule:164: --><!-- ws:end:WikiTextTocRule:164 --><!-- ws:start:WikiTextTocRule:165: --><!-- ws:end:WikiTextTocRule:165 --><!-- ws:start:WikiTextTocRule:166: --><!-- ws:end:WikiTextTocRule:166 --><!-- ws:start:WikiTextTocRule:167: --><!-- ws:end:WikiTextTocRule:167 --><!-- ws:start:WikiTextTocRule:168: --><!-- ws:end:WikiTextTocRule:168 --><!-- ws:start:WikiTextTocRule:169: --><!-- ws:end:WikiTextTocRule:169 --><!-- ws:start:WikiTextTocRule:170: --><!-- ws:end:WikiTextTocRule:170 --><!-- ws:start:WikiTextTocRule:171: --><!-- ws:end:WikiTextTocRule:171 --><!-- ws:start:WikiTextTocRule:172: --><!-- ws:end:WikiTextTocRule:172 --><!-- ws:start:WikiTextTocRule:173: --><!-- ws:end:WikiTextTocRule:173 --><!-- ws:start:WikiTextTocRule:174: --><!-- ws:end:WikiTextTocRule:174 --><!-- ws:start:WikiTextTocRule:175: --><!-- ws:end:WikiTextTocRule:175 --><!-- ws:start:WikiTextTocRule:176: --><!-- ws:end:WikiTextTocRule:176 --><!-- ws:start:WikiTextTocRule:177: --><!-- ws:end:WikiTextTocRule:177 --><!-- ws:start:WikiTextTocRule:178: --><!-- ws:end:WikiTextTocRule:178 --><!-- ws:start:WikiTextTocRule:179: --><!-- ws:end:WikiTextTocRule:179 --><!-- ws:start:WikiTextTocRule:180: --><!-- ws:end:WikiTextTocRule:180 --><!-- ws:start:WikiTextTocRule:181: --><!-- ws:end:WikiTextTocRule:181 --><!-- ws:start:WikiTextTocRule:182: --> | <a href="#Rank 3 temperaments">Rank 3 temperaments</a><!-- ws:end:WikiTextTocRule:182 --><!-- ws:start:WikiTextTocRule:183: --><!-- ws:end:WikiTextTocRule:183 --><!-- ws:start:WikiTextTocRule:184: --><!-- ws:end:WikiTextTocRule:184 --><!-- ws:start:WikiTextTocRule:185: --><!-- ws:end:WikiTextTocRule:185 --><!-- ws:start:WikiTextTocRule:186: --><!-- ws:end:WikiTextTocRule:186 --><!-- ws:start:WikiTextTocRule:187: --><!-- ws:end:WikiTextTocRule:187 --><!-- ws:start:WikiTextTocRule:188: --><!-- ws:end:WikiTextTocRule:188 --><!-- ws:start:WikiTextTocRule:189: --><!-- ws:end:WikiTextTocRule:189 --><!-- ws:start:WikiTextTocRule:190: --><!-- ws:end:WikiTextTocRule:190 --><!-- ws:start:WikiTextTocRule:191: --><!-- ws:end:WikiTextTocRule:191 --><!-- ws:start:WikiTextTocRule:192: --><!-- ws:end:WikiTextTocRule:192 --><!-- ws:start:WikiTextTocRule:193: --><!-- ws:end:WikiTextTocRule:193 --><!-- ws:start:WikiTextTocRule:194: --><!-- ws:end:WikiTextTocRule:194 --><!-- ws:start:WikiTextTocRule:195: --><!-- ws:end:WikiTextTocRule:195 --><!-- ws:start:WikiTextTocRule:196: --><!-- ws:end:WikiTextTocRule:196 --><!-- ws:start:WikiTextTocRule:197: --><!-- ws:end:WikiTextTocRule:197 --><!-- ws:start:WikiTextTocRule:198: --><!-- ws:end:WikiTextTocRule:198 --><!-- ws:start:WikiTextTocRule:199: --><!-- ws:end:WikiTextTocRule:199 --><!-- ws:start:WikiTextTocRule:200: --><!-- ws:end:WikiTextTocRule:200 --><!-- ws:start:WikiTextTocRule:201: --><!-- ws:end:WikiTextTocRule:201 --><!-- ws:start:WikiTextTocRule:202: --><!-- ws:end:WikiTextTocRule:202 --><!-- ws:start:WikiTextTocRule:203: --><!-- ws:end:WikiTextTocRule:203 --><!-- ws:start:WikiTextTocRule:204: --><!-- ws:end:WikiTextTocRule:204 --><!-- ws:start:WikiTextTocRule:205: --><!-- ws:end:WikiTextTocRule:205 --><!-- ws:start:WikiTextTocRule:206: --><!-- ws:end:WikiTextTocRule:206 --><!-- ws:start:WikiTextTocRule:207: --><!-- ws:end:WikiTextTocRule:207 --><!-- ws:start:WikiTextTocRule:208: --><!-- ws:end:WikiTextTocRule:208 --><!-- ws:start:WikiTextTocRule:209: --><!-- ws:end:WikiTextTocRule:209 --><!-- ws:start:WikiTextTocRule:210: --><!-- ws:end:WikiTextTocRule:210 --><!-- ws:start:WikiTextTocRule:211: --><!-- ws:end:WikiTextTocRule:211 --><!-- ws:start:WikiTextTocRule:212: --> | <a href="#Rank 4 temperaments">Rank 4 temperaments</a><!-- ws:end:WikiTextTocRule:212 --><!-- ws:start:WikiTextTocRule:213: --> | <a href="#Subgroup temperaments">Subgroup temperaments</a><!-- ws:end:WikiTextTocRule:213 --><!-- ws:start:WikiTextTocRule:214: --> | <a href="#Miscellaneous">Miscellaneous</a><!-- ws:end:WikiTextTocRule:214 --><!-- ws:start:WikiTextTocRule:215: --><!-- ws:end:WikiTextTocRule:215 --><!-- ws:start:WikiTextTocRule:216: --><!-- ws:end:WikiTextTocRule:216 --><!-- ws:start:WikiTextTocRule:217: --> | ||
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<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Equal temperaments"></a><!-- ws:end:WikiTextHeadingRule:0 --><a class="wiki_link" href="/edo">Equal temperaments</a></h1> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Equal temperaments"></a><!-- ws:end:WikiTextHeadingRule:0 --><a class="wiki_link" href="/edo">Equal temperaments</a></h1> | ||
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<a class="wiki_link" href="/Equal%20Temperaments">Equal temperaments</a> (abbreviated ET or tET) and equal divisions of the octave (abbreviated EDO) are similar concepts, although there are distinctions in the way these terms are used. An EDO is simply a division of the octave into equal steps (specifically, steps of equal size in cents). An ET, on the other hand, is a temperament, an altered representation of some subset of the intervals of just intonation. The familiar 12-note equal temperament (12-ET) reduces the size of the perfect fifth (about 701.955 cents) by 1/12 of the Pythagorean comma, resulting in a fifth of 700.0 cents.<br /> | <a class="wiki_link" href="/Equal%20Temperaments">Equal temperaments</a> (abbreviated ET or tET) and equal divisions of the octave (abbreviated EDO) are similar concepts, although there are distinctions in the way these terms are used. An EDO is simply a division of the octave into equal steps (specifically, steps of equal size in cents). An ET, on the other hand, is a temperament, an altered representation of some subset of the intervals of just intonation. The familiar 12-note equal temperament (12-ET) reduces the size of the perfect fifth (about 701.955 cents) by 1/12 of the Pythagorean comma, resulting in a fifth of 700.0 cents.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Rank 2 (including &quot;linear&quot;) temperaments"></a><!-- ws:end:WikiTextHeadingRule:2 -->Rank 2 (including &quot;linear&quot;) temperaments<!-- ws:start:WikiTextAnchorRule: | <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Rank 2 (including &quot;linear&quot;) temperaments"></a><!-- ws:end:WikiTextHeadingRule:2 -->Rank 2 (including &quot;linear&quot;) temperaments<!-- ws:start:WikiTextAnchorRule:218:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@lineartemperaments&quot; title=&quot;Anchor: lineartemperaments&quot;/&gt; --><a name="lineartemperaments"></a><!-- ws:end:WikiTextAnchorRule:218 --></h1> | ||
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Regular temperaments of ranks two and three are cataloged <a class="wiki_link" href="/Optimal%20patent%20val">here</a>. Other pages listing them are <a class="wiki_link" href="/Paul%20Erlich">Paul Erlich</a>'s <a class="wiki_link" href="/Catalog%20of%20five-limit%20rank%20two%20temperaments">catalog of 5-limit rank two temperaments</a>, and a <a class="wiki_link" href="/Proposed%20names%20for%20rank%202%20temperaments">page</a> listing higher limit rank two temperaments.<br /> | Regular temperaments of ranks two and three are cataloged <a class="wiki_link" href="/Optimal%20patent%20val">here</a>. Other pages listing them are <a class="wiki_link" href="/Paul%20Erlich">Paul Erlich</a>'s <a class="wiki_link" href="/Catalog%20of%20five-limit%20rank%20two%20temperaments">catalog of 5-limit rank two temperaments</a>, and a <a class="wiki_link" href="/Proposed%20names%20for%20rank%202%20temperaments">page</a> listing higher limit rank two temperaments.<br /> | ||
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These temper out 875/864.<br /> | These temper out 875/864.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:98:&lt;h3&gt; --><h3 id="toc49"><a name="Rank 3 temperaments--Orwellismic family"></a><!-- ws:end:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:98:&lt;h3&gt; --><h3 id="toc49"><a name="Rank 3 temperaments--Sengic family"></a><!-- ws:end:WikiTextHeadingRule:98 --><a class="wiki_link" href="/Sengic%20family">Sengic family</a></h3> | ||
These temper out the senga, 686/675.<br /> | |||
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<!-- ws:start:WikiTextHeadingRule:100:&lt;h3&gt; --><h3 id="toc50"><a name="Rank 3 temperaments--Orwellismic family"></a><!-- ws:end:WikiTextHeadingRule:100 --><a class="wiki_link" href="/Orwellismic%20family">Orwellismic family</a></h3> | |||
These temper out 1728/1715.<br /> | These temper out 1728/1715.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:102:&lt;h3&gt; --><h3 id="toc51"><a name="Rank 3 temperaments--Nuwell family"></a><!-- ws:end:WikiTextHeadingRule:102 --><a class="wiki_link" href="/Nuwell%20family">Nuwell family</a></h3> | ||
These temper out the nuwell comma, 2430/2401.<br /> | These temper out the nuwell comma, 2430/2401.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:104:&lt;h3&gt; --><h3 id="toc52"><a name="Rank 3 temperaments--Octagar family"></a><!-- ws:end:WikiTextHeadingRule:104 --><a class="wiki_link" href="/Octagar%20family">Octagar family</a></h3> | ||
The octagar family of rank three temperaments tempers out the octagar comma, 4000/3969.<br /> | The octagar family of rank three temperaments tempers out the octagar comma, 4000/3969.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:106:&lt;h3&gt; --><h3 id="toc53"><a name="Rank 3 temperaments--Mirkwai family"></a><!-- ws:end:WikiTextHeadingRule:106 --><a class="wiki_link" href="/Mirkwai%20family">Mirkwai family</a></h3> | ||
The mirkwai family of rank three temperaments tempers out the mirkwai comma, 16875/16807.<br /> | The mirkwai family of rank three temperaments tempers out the mirkwai comma, 16875/16807.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:108:&lt;h3&gt; --><h3 id="toc54"><a name="Rank 3 temperaments--Hemimean family"></a><!-- ws:end:WikiTextHeadingRule:108 --><a class="wiki_link" href="/Hemimean%20family">Hemimean family</a></h3> | ||
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: | <!-- ws:start:WikiTextHeadingRule:110:&lt;h3&gt; --><h3 id="toc55"><a name="Rank 3 temperaments--Kleismic rank three family"></a><!-- ws:end:WikiTextHeadingRule:110 --><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: | <!-- ws:start:WikiTextHeadingRule:112:&lt;h3&gt; --><h3 id="toc56"><a name="Rank 3 temperaments--Diaschismic rank three family"></a><!-- ws:end:WikiTextHeadingRule:112 --><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: | <!-- ws:start:WikiTextHeadingRule:114:&lt;h3&gt; --><h3 id="toc57"><a name="Rank 3 temperaments--Didymus rank three family"></a><!-- ws:end:WikiTextHeadingRule:114 --><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: | <!-- ws:start:WikiTextHeadingRule:116:&lt;h3&gt; --><h3 id="toc58"><a name="Rank 3 temperaments--Porcupine rank three family"></a><!-- ws:end:WikiTextHeadingRule:116 --><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: | <!-- ws:start:WikiTextHeadingRule:118:&lt;h3&gt; --><h3 id="toc59"><a name="Rank 3 temperaments--Archytas family"></a><!-- ws:end:WikiTextHeadingRule:118 --><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: | <!-- ws:start:WikiTextHeadingRule:120:&lt;h3&gt; --><h3 id="toc60"><a name="Rank 3 temperaments--Jubilismic family"></a><!-- ws:end:WikiTextHeadingRule:120 --><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: | <!-- ws:start:WikiTextHeadingRule:122:&lt;h3&gt; --><h3 id="toc61"><a name="Rank 3 temperaments--Semaphore family"></a><!-- ws:end:WikiTextHeadingRule:122 --><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: | <!-- ws:start:WikiTextHeadingRule:124:&lt;h3&gt; --><h3 id="toc62"><a name="Rank 3 temperaments--Quartonic family"></a><!-- ws:end:WikiTextHeadingRule:124 --><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: | <!-- ws:start:WikiTextHeadingRule:126:&lt;h3&gt; --><h3 id="toc63"><a name="Rank 3 temperaments--Werckismic temperaments"></a><!-- ws:end:WikiTextHeadingRule:126 --><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: | <!-- ws:start:WikiTextHeadingRule:128:&lt;h3&gt; --><h3 id="toc64"><a name="Rank 3 temperaments--Swetismic temperaments"></a><!-- ws:end:WikiTextHeadingRule:128 --><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: | <!-- ws:start:WikiTextHeadingRule:130:&lt;h3&gt; --><h3 id="toc65"><a name="Rank 3 temperaments--Lehmerismic temperaments"></a><!-- ws:end:WikiTextHeadingRule:130 --><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: | <!-- ws:start:WikiTextHeadingRule:132:&lt;h3&gt; --><h3 id="toc66"><a name="Rank 3 temperaments--Kalismic temperaments"></a><!-- ws:end:WikiTextHeadingRule:132 --><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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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:134:&lt;h1&gt; --><h1 id="toc67"><a name="Rank 4 temperaments"></a><!-- ws:end:WikiTextHeadingRule:134 --><a class="wiki_link" href="/Rank%20four%20temperaments">Rank 4 temperaments</a></h1> | ||
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Even less explored than rank three temperaments are rank four temperaments. In fact, unless one counts 7-limit JI they don't seem to have been explored at all. However, they could be used; for example <a class="wiki_link" href="/Hobbits">hobbit scales</a> can be constructed for them.<br /> | Even less explored than rank three temperaments are rank four temperaments. In fact, unless one counts 7-limit JI they don't seem to have been explored at all. However, they could be used; for example <a class="wiki_link" href="/Hobbits">hobbit scales</a> can be constructed for them.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:136:&lt;h1&gt; --><h1 id="toc68"><a name="Subgroup temperaments"></a><!-- ws:end:WikiTextHeadingRule:136 --><a class="wiki_link" href="/Subgroup%20temperaments">Subgroup temperaments</a></h1> | ||
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A wide-open field. These are regular temperaments of various ranks which temper <a class="wiki_link" href="/just%20intonation%20subgroups">just intonation subgroups</a>.<br /> | A wide-open field. These are regular temperaments of various ranks which temper <a class="wiki_link" href="/just%20intonation%20subgroups">just intonation subgroups</a>.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:138:&lt;h1&gt; --><h1 id="toc69"><a name="Miscellaneous"></a><!-- ws:end:WikiTextHeadingRule:138 -->Miscellaneous</h1> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:140:&lt;h2&gt; --><h2 id="toc70"><a name="Miscellaneous-The Archipelago"></a><!-- ws:end:WikiTextHeadingRule:140 --><a class="wiki_link" href="/The%20Archipelago">The Archipelago</a></h2> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:142:&lt;h2&gt; --><h2 id="toc71"><a name="Miscellaneous-Links"></a><!-- ws:end:WikiTextHeadingRule:142 -->Links</h2> | ||
<ul><li><a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Regular_temperament" rel="nofollow">Regular temperaments - Wikipedia</a></li></ul></body></html></pre></div> | <ul><li><a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Regular_temperament" rel="nofollow">Regular temperaments - Wikipedia</a></li></ul></body></html></pre></div> | ||