Tour of regular temperaments: Difference between revisions
Wikispaces>genewardsmith **Imported revision 232426176 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 232453738 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<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>2011-05-27 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-05-27 13:55:58 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>232453738</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> | ||
| Line 242: | Line 242: | ||
By a //commatic realm// is meant the whole collection of regular temperaments of various ranks and for both full groups and [[Just intonation subgroups|subgroups]] tempering out a given comma. For some commas, looking at the full commatic realm seems the best approach to discussing associated temperaments. | By a //commatic realm// is meant the whole collection of regular temperaments of various ranks and for both full groups and [[Just intonation subgroups|subgroups]] tempering out a given comma. For some commas, looking at the full commatic realm seems the best approach to discussing associated temperaments. | ||
==[[Orgonia]]== | |||
By //Orgonia// is meant the commatic realm of the [[11-limit]] comma 65536/65219 = |16 0 0 -2 -3>, the orgonisma. | |||
==[[The Biosphere]]== | |||
The Biosphere is the name given to the commatic realm of the 13-limit comma 91/90. | |||
==[[The Archipelago]]== | ==[[The Archipelago]]== | ||
The Archipelago is a name which has been given to the commatic realm of the [[13-limit]] comma 676/675. | The Archipelago is a name which has been given to the commatic realm of the [[13-limit]] comma 676/675. | ||
---- | ---- | ||
| Line 253: | Line 258: | ||
* [[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:154:&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:154 --><!-- ws:start:WikiTextTocRule:155: --><a href="#Regular temperaments">Regular temperaments</a><!-- ws:end:WikiTextTocRule:155 --><!-- ws:start:WikiTextTocRule:156: --> | <a href="#Equal temperaments">Equal temperaments</a><!-- ws:end:WikiTextTocRule:156 --><!-- ws:start:WikiTextTocRule:157: --> | <a href="#Rank 2 (including &quot;linear&quot;) temperaments">Rank 2 (including &quot;linear&quot;) temperaments</a><!-- 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: --><!-- 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: --> | <a href="#Rank 3 temperaments">Rank 3 temperaments</a><!-- 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: --><!-- ws:end:WikiTextTocRule:212 --><!-- ws:start:WikiTextTocRule:213: --><!-- ws:end:WikiTextTocRule:213 --><!-- ws:start:WikiTextTocRule:214: --><!-- ws:end:WikiTextTocRule:214 --><!-- ws:start:WikiTextTocRule:215: --><!-- ws:end:WikiTextTocRule:215 --><!-- ws:start:WikiTextTocRule:216: --><!-- ws:end:WikiTextTocRule:216 --><!-- ws:start:WikiTextTocRule:217: --><!-- ws:end:WikiTextTocRule:217 --><!-- ws:start:WikiTextTocRule:218: --><!-- ws:end:WikiTextTocRule:218 --><!-- ws:start:WikiTextTocRule:219: --><!-- ws:end:WikiTextTocRule:219 --><!-- ws:start:WikiTextTocRule:220: --><!-- ws:end:WikiTextTocRule:220 --><!-- ws:start:WikiTextTocRule:221: --><!-- ws:end:WikiTextTocRule:221 --><!-- ws:start:WikiTextTocRule:222: --><!-- ws:end:WikiTextTocRule:222 --><!-- ws:start:WikiTextTocRule:223: --><!-- ws:end:WikiTextTocRule:223 --><!-- ws:start:WikiTextTocRule:224: --><!-- ws:end:WikiTextTocRule:224 --><!-- ws:start:WikiTextTocRule:225: --> | <a href="#Rank 4 temperaments">Rank 4 temperaments</a><!-- ws:end:WikiTextTocRule:225 --><!-- ws:start:WikiTextTocRule:226: --> | <a href="#Subgroup temperaments">Subgroup temperaments</a><!-- ws:end:WikiTextTocRule:226 --><!-- ws:start:WikiTextTocRule:227: --> | <a href="#Commatic realms">Commatic realms</a><!-- ws:end:WikiTextTocRule:227 --><!-- ws:start:WikiTextTocRule:228: --><!-- ws:end:WikiTextTocRule:228 --><!-- ws:start:WikiTextTocRule:229: --><!-- ws:end:WikiTextTocRule:229 --><!-- ws:start:WikiTextTocRule:230: --><!-- ws:end:WikiTextTocRule:230 --><!-- ws:start:WikiTextTocRule:231: --><!-- ws:end:WikiTextTocRule:231 --><!-- ws:start:WikiTextTocRule:232: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:232 --><hr /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Regular temperaments"></a><!-- ws:end:WikiTextHeadingRule:0 -->Regular temperaments</h1> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Regular temperaments"></a><!-- ws:end:WikiTextHeadingRule:0 -->Regular temperaments</h1> | ||
<br /> | <br /> | ||
| Line 263: | Line 268: | ||
<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 /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Rank 2 (including &quot;linear&quot;) temperaments"></a><!-- ws:end:WikiTextHeadingRule:4 -->Rank 2 (including &quot;linear&quot;) temperaments<!-- ws:start:WikiTextAnchorRule: | <!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Rank 2 (including &quot;linear&quot;) temperaments"></a><!-- ws:end:WikiTextHeadingRule:4 -->Rank 2 (including &quot;linear&quot;) temperaments<!-- ws:start:WikiTextAnchorRule:233:&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:233 --></h1> | ||
<br /> | <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 /> | 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 /> | ||
| Line 490: | Line 495: | ||
By a <em>commatic realm</em> is meant the whole collection of regular temperaments of various ranks and for both full groups and <a class="wiki_link" href="/Just%20intonation%20subgroups">subgroups</a> tempering out a given comma. For some commas, looking at the full commatic realm seems the best approach to discussing associated temperaments.<br /> | By a <em>commatic realm</em> is meant the whole collection of regular temperaments of various ranks and for both full groups and <a class="wiki_link" href="/Just%20intonation%20subgroups">subgroups</a> tempering out a given comma. For some commas, looking at the full commatic realm seems the best approach to discussing associated temperaments.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:146:&lt;h2&gt; --><h2 id="toc73"><a name="Commatic realms-The Archipelago"></a><!-- ws:end:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:146:&lt;h2&gt; --><h2 id="toc73"><a name="Commatic realms-Orgonia"></a><!-- ws:end:WikiTextHeadingRule:146 --><a class="wiki_link" href="/Orgonia">Orgonia</a></h2> | ||
By <em>Orgonia</em> is meant the commatic realm of the <a class="wiki_link" href="/11-limit">11-limit</a> comma 65536/65219 = |16 0 0 -2 -3&gt;, the orgonisma.<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:148:&lt;h2&gt; --><h2 id="toc74"><a name="Commatic realms-The Biosphere"></a><!-- ws:end:WikiTextHeadingRule:148 --><a class="wiki_link" href="/The%20Biosphere">The Biosphere</a></h2> | |||
The Biosphere is the name given to the commatic realm of the 13-limit comma 91/90.<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:150:&lt;h2&gt; --><h2 id="toc75"><a name="Commatic realms-The Archipelago"></a><!-- ws:end:WikiTextHeadingRule:150 --><a class="wiki_link" href="/The%20Archipelago">The Archipelago</a></h2> | |||
The Archipelago is a name which has been given to the commatic realm of the <a class="wiki_link" href="/13-limit">13-limit</a> comma 676/675.<br /> | The Archipelago is a name which has been given to the commatic realm of the <a class="wiki_link" href="/13-limit">13-limit</a> comma 676/675.<br /> | ||
<br /> | <br /> | ||
<br /> | |||
<br /> | <br /> | ||
<hr /> | <hr /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:152:&lt;h2&gt; --><h2 id="toc76"><a name="Commatic realms-Links"></a><!-- ws:end:WikiTextHeadingRule:152 -->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> | ||