Tour of regular temperaments: Difference between revisions
Wikispaces>genewardsmith **Imported revision 195736138 - 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- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-02-03 21:41:03 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>198598402</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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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 [[Hobbits|hobbit scales]] can be constructed for them. | 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 [[Hobbits|hobbit scales]] can be constructed for them. | ||
=Miscellaneous= | |||
==The Archipelago== | |||
---- | ---- | ||
==Links== | ==Links== | ||
* [[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:124:&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:124 --><!-- ws:start:WikiTextTocRule:125: --><a href="#Equal temperaments">Equal temperaments</a><!-- ws:end:WikiTextTocRule:125 --><!-- ws:start:WikiTextTocRule:126: --> | <a href="#Rank 2 (including &quot;linear&quot;) temperaments">Rank 2 (including &quot;linear&quot;) temperaments</a><!-- ws:end:WikiTextTocRule:126 --><!-- ws:start:WikiTextTocRule:127: --><!-- ws:end:WikiTextTocRule:127 --><!-- ws:start:WikiTextTocRule:128: --><!-- ws:end:WikiTextTocRule:128 --><!-- ws:start:WikiTextTocRule:129: --><!-- ws:end:WikiTextTocRule:129 --><!-- ws:start:WikiTextTocRule:130: --><!-- ws:end:WikiTextTocRule:130 --><!-- ws:start:WikiTextTocRule:131: --><!-- ws:end:WikiTextTocRule:131 --><!-- ws:start:WikiTextTocRule:132: --><!-- ws:end:WikiTextTocRule:132 --><!-- ws:start:WikiTextTocRule:133: --><!-- ws:end:WikiTextTocRule:133 --><!-- ws:start:WikiTextTocRule:134: --><!-- ws:end:WikiTextTocRule:134 --><!-- ws:start:WikiTextTocRule:135: --><!-- ws:end:WikiTextTocRule:135 --><!-- ws:start:WikiTextTocRule:136: --><!-- ws:end:WikiTextTocRule:136 --><!-- ws:start:WikiTextTocRule:137: --><!-- ws:end:WikiTextTocRule:137 --><!-- ws:start:WikiTextTocRule:138: --><!-- ws:end:WikiTextTocRule:138 --><!-- ws:start:WikiTextTocRule:139: --><!-- ws:end:WikiTextTocRule:139 --><!-- ws:start:WikiTextTocRule:140: --><!-- ws:end:WikiTextTocRule:140 --><!-- ws:start:WikiTextTocRule:141: --><!-- ws:end:WikiTextTocRule:141 --><!-- ws:start:WikiTextTocRule:142: --><!-- ws:end:WikiTextTocRule:142 --><!-- ws:start:WikiTextTocRule:143: --><!-- ws:end:WikiTextTocRule:143 --><!-- ws:start:WikiTextTocRule:144: --><!-- 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: --><!-- 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: --> | <a href="#Rank 3 temperaments">Rank 3 temperaments</a><!-- 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: --><!-- ws:end:WikiTextTocRule:182 --><!-- ws:start:WikiTextTocRule:183: --> | <a href="#Rank 4 temperaments">Rank 4 temperaments</a><!-- ws:end:WikiTextTocRule:183 --><!-- ws:start:WikiTextTocRule:184: --> | <a href="#Miscellaneous">Miscellaneous</a><!-- ws:end:WikiTextTocRule:184 --><!-- ws:start:WikiTextTocRule:185: --><!-- ws:end:WikiTextTocRule:185 --><!-- ws:start:WikiTextTocRule:186: --><!-- ws:end:WikiTextTocRule:186 --><!-- ws:start:WikiTextTocRule:187: --> | ||
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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:188:&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:188 --></h1> | ||
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<a class="wiki_link" href="/Paul%20Erlich">Paul Erlich</a> has given us a <a class="wiki_link" href="/Catalog%20of%20five-limit%20rank%20two%20temperaments">catalog of 5-limit rank two temperaments</a>, and we also have a <a class="wiki_link" href="/Proposed%20names%20for%20rank%202%20temperaments">page</a> listing higher limit temperaments.<br /> | <a class="wiki_link" href="/Paul%20Erlich">Paul Erlich</a> has given us a <a class="wiki_link" href="/Catalog%20of%20five-limit%20rank%20two%20temperaments">catalog of 5-limit rank two temperaments</a>, and we also have a <a class="wiki_link" href="/Proposed%20names%20for%20rank%202%20temperaments">page</a> listing higher limit temperaments.<br /> | ||
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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 /> | ||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:118:&lt;h1&gt; --><h1 id="toc59"><a name="Miscellaneous"></a><!-- ws:end:WikiTextHeadingRule:118 -->Miscellaneous</h1> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:120:&lt;h2&gt; --><h2 id="toc60"><a name="Miscellaneous-The Archipelago"></a><!-- ws:end:WikiTextHeadingRule:120 -->The Archipelago</h2> | |||
<hr /> | <hr /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:122:&lt;h2&gt; --><h2 id="toc61"><a name="Miscellaneous-Links"></a><!-- ws:end:WikiTextHeadingRule:122 -->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> | ||