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- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-01 06:00:06 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>205992840</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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===[[Semaphore family]]=== | ===[[Semaphore 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". | 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". | ||
===[[Quartonic family]]=== | |||
The quartonic temperament tempers out 36/35, identifying both 7/6 with 6/5 and 5/4 with 9/7. | |||
===[[Werckismic temperaments]]=== | ===[[Werckismic temperaments]]=== | ||
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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:142:&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:142 --><!-- ws:start:WikiTextTocRule:143: --><a href="#Equal temperaments">Equal temperaments</a><!-- ws:end:WikiTextTocRule:143 --><!-- ws:start:WikiTextTocRule:144: --> | <a href="#Rank 2 (including &quot;linear&quot;) temperaments">Rank 2 (including &quot;linear&quot;) temperaments</a><!-- ws:end:WikiTextTocRule:144 --><!-- ws:start:WikiTextTocRule:145: --><!-- ws:end:WikiTextTocRule:145 --><!-- ws:start:WikiTextTocRule:146: --><!-- 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: --><!-- 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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: --> | <a href="#Rank 3 temperaments">Rank 3 temperaments</a><!-- ws:end:WikiTextTocRule:180 --><!-- ws:start:WikiTextTocRule:181: --><!-- ws:end:WikiTextTocRule:181 --><!-- ws:start:WikiTextTocRule:182: --><!-- 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: --><!-- 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ws:start:WikiTextTocRule:208: --><!-- ws:end:WikiTextTocRule:208 --><!-- ws:start:WikiTextTocRule:209: --> | <a href="#Rank 4 temperaments">Rank 4 temperaments</a><!-- ws:end:WikiTextTocRule:209 --><!-- ws:start:WikiTextTocRule:210: --> | <a href="#Subgroup temperaments">Subgroup temperaments</a><!-- ws:end:WikiTextTocRule:210 --><!-- ws:start:WikiTextTocRule:211: --> | <a href="#Miscellaneous">Miscellaneous</a><!-- ws:end:WikiTextTocRule:211 --><!-- ws:start:WikiTextTocRule:212: --><!-- ws:end:WikiTextTocRule:212 --><!-- ws:start:WikiTextTocRule:213: --><!-- ws:end:WikiTextTocRule:213 --><!-- ws:start:WikiTextTocRule:214: --> | ||
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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:215:&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:215 --></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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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:122:&lt;h3&gt; --><h3 id="toc61"><a name="Rank 3 temperaments--Werckismic temperaments"></a><!-- ws:end:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:122:&lt;h3&gt; --><h3 id="toc61"><a name="Rank 3 temperaments--Quartonic family"></a><!-- ws:end:WikiTextHeadingRule:122 --><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 /> | |||
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<!-- ws:start:WikiTextHeadingRule:124:&lt;h3&gt; --><h3 id="toc62"><a name="Rank 3 temperaments--Werckismic temperaments"></a><!-- ws:end:WikiTextHeadingRule:124 --><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:126:&lt;h3&gt; --><h3 id="toc63"><a name="Rank 3 temperaments--Swetismic temperaments"></a><!-- ws:end:WikiTextHeadingRule:126 --><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:128:&lt;h3&gt; --><h3 id="toc64"><a name="Rank 3 temperaments--Lehmerismic temperaments"></a><!-- ws:end:WikiTextHeadingRule:128 --><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:130:&lt;h3&gt; --><h3 id="toc65"><a name="Rank 3 temperaments--Kalismic temperaments"></a><!-- ws:end:WikiTextHeadingRule:130 --><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:132:&lt;h1&gt; --><h1 id="toc66"><a name="Rank 4 temperaments"></a><!-- ws:end:WikiTextHeadingRule:132 --><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:134:&lt;h1&gt; --><h1 id="toc67"><a name="Subgroup temperaments"></a><!-- ws:end:WikiTextHeadingRule:134 --><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:136:&lt;h1&gt; --><h1 id="toc68"><a name="Miscellaneous"></a><!-- ws:end:WikiTextHeadingRule:136 -->Miscellaneous</h1> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:138:&lt;h2&gt; --><h2 id="toc69"><a name="Miscellaneous-The Archipelago"></a><!-- ws:end:WikiTextHeadingRule:138 --><a class="wiki_link" href="/The%20Archipelago">The Archipelago</a></h2> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:140:&lt;h2&gt; --><h2 id="toc70"><a name="Miscellaneous-Links"></a><!-- ws:end:WikiTextHeadingRule:140 -->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> | ||