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Tour of regular temperaments: Difference between revisions

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Wikispaces>spt3125
**Imported revision 474462244 - Original comment: added a few links and corrected some typos**
Wikispaces>genewardsmith
**Imported revision 505791420 - 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:spt3125|spt3125]] and made on <tt>2013-12-03 20:58:57 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-05-01 10:17:34 UTC</tt>.<br>
: The original revision id was <tt>474462244</tt>.<br>
: The original revision id was <tt>505791420</tt>.<br>
: The revision comment was: <tt>added a few links and corrected some typos</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>
<h4>Original Wikitext content:</h4>
<h4>Original Wikitext content:</h4>
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===[[Ragisma family]]===  
===[[Ragisma family]]===  
The 7-limit rank three microtemperament which tempers out the ragisma, 4375/4374, extends to various higher limit rank three temperaments such as thor.
The 7-limit rank three microtemperament which tempers out the ragisma, 4375/4374, extends to various higher limit rank three temperaments such as thor.
==[[Landscape family]]==
The 7-limit rank three microtemperament which tempers out the lanscape comma, 250047/250000, extends to various higher limit rank three temperaments such as tyr and odin.


===[[Hemifamity family]]===  
===[[Hemifamity family]]===  
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<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Tour of Regular Temperaments&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;span style="display: block; text-align: right;"&gt;Other languages: &lt;a class="wiki_link" href="http://xenharmonie.wikispaces.com/Regul%C3%A4re%20Temperaturen"&gt;Deutsch&lt;/a&gt;&lt;br /&gt;
<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Tour of Regular Temperaments&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;span style="display: block; text-align: right;"&gt;Other languages: &lt;a class="wiki_link" href="http://xenharmonie.wikispaces.com/Regul%C3%A4re%20Temperaturen"&gt;Deutsch&lt;/a&gt;&lt;br /&gt;
&lt;/span&gt;&lt;br /&gt;
&lt;/span&gt;&lt;br /&gt;
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| &lt;a href="#Temperaments for a given comma"&gt;Temperaments for a given comma&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:284 --&gt;&lt;!-- ws:start:WikiTextTocRule:285: --&gt;&lt;!-- ws:end:WikiTextTocRule:285 --&gt;&lt;!-- ws:start:WikiTextTocRule:286: --&gt;&lt;!-- ws:end:WikiTextTocRule:286 --&gt;&lt;!-- ws:start:WikiTextTocRule:287: --&gt;&lt;!-- ws:end:WikiTextTocRule:287 --&gt;&lt;!-- ws:start:WikiTextTocRule:288: --&gt;&lt;!-- ws:end:WikiTextTocRule:288 --&gt;&lt;!-- ws:start:WikiTextTocRule:289: --&gt;&lt;!-- ws:end:WikiTextTocRule:289 --&gt;&lt;!-- ws:start:WikiTextTocRule:290: --&gt;&lt;!-- ws:end:WikiTextTocRule:290 --&gt;&lt;!-- ws:start:WikiTextTocRule:291: --&gt;&lt;!-- ws:end:WikiTextTocRule:291 --&gt;&lt;!-- ws:start:WikiTextTocRule:292: --&gt;&lt;!-- ws:end:WikiTextTocRule:292 --&gt;&lt;!-- ws:start:WikiTextTocRule:293: --&gt;&lt;!-- ws:end:WikiTextTocRule:293 --&gt;&lt;!-- ws:start:WikiTextTocRule:294: --&gt;&lt;!-- ws:end:WikiTextTocRule:294 --&gt;&lt;!-- ws:start:WikiTextTocRule:295: --&gt;&lt;!-- ws:end:WikiTextTocRule:295 --&gt;&lt;!-- ws:start:WikiTextTocRule:296: --&gt;&lt;!-- ws:end:WikiTextTocRule:296 --&gt;&lt;!-- ws:start:WikiTextTocRule:297: --&gt;&lt;!-- ws:end:WikiTextTocRule:297 --&gt;&lt;!-- ws:start:WikiTextTocRule:298: --&gt;&lt;!-- ws:end:WikiTextTocRule:298 --&gt;&lt;!-- ws:start:WikiTextTocRule:299: --&gt;&lt;!-- ws:end:WikiTextTocRule:299 --&gt;&lt;!-- ws:start:WikiTextTocRule:300: --&gt;&lt;!-- ws:end:WikiTextTocRule:300 --&gt;&lt;!-- ws:start:WikiTextTocRule:301: --&gt;&lt;!-- ws:end:WikiTextTocRule:301 --&gt;&lt;!-- ws:start:WikiTextTocRule:302: --&gt;&lt;!-- ws:end:WikiTextTocRule:302 --&gt;&lt;!-- ws:start:WikiTextTocRule:303: --&gt;&lt;!-- ws:end:WikiTextTocRule:303 --&gt;&lt;!-- ws:start:WikiTextTocRule:304: --&gt;&lt;!-- ws:end:WikiTextTocRule:304 --&gt;&lt;!-- ws:start:WikiTextTocRule:305: --&gt;&lt;!-- ws:end:WikiTextTocRule:305 --&gt;&lt;!-- ws:start:WikiTextTocRule:306: --&gt;&lt;!-- ws:end:WikiTextTocRule:306 --&gt;&lt;!-- ws:start:WikiTextTocRule:307: --&gt;&lt;!-- ws:end:WikiTextTocRule:307 --&gt;&lt;!-- ws:start:WikiTextTocRule:308: --&gt; | &lt;a href="#Rank 3 temperaments"&gt;Rank 3 temperaments&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:308 --&gt;&lt;!-- ws:start:WikiTextTocRule:309: --&gt;&lt;!-- ws:end:WikiTextTocRule:309 --&gt;&lt;!-- ws:start:WikiTextTocRule:310: --&gt;&lt;!-- ws:end:WikiTextTocRule:310 --&gt;&lt;!-- ws:start:WikiTextTocRule:311: --&gt;&lt;!-- ws:end:WikiTextTocRule:311 --&gt;&lt;!-- ws:start:WikiTextTocRule:312: --&gt;&lt;!-- ws:end:WikiTextTocRule:312 --&gt;&lt;!-- ws:start:WikiTextTocRule:313: --&gt;&lt;!-- ws:end:WikiTextTocRule:313 --&gt;&lt;!-- ws:start:WikiTextTocRule:314: --&gt;&lt;!-- ws:end:WikiTextTocRule:314 --&gt;&lt;!-- ws:start:WikiTextTocRule:315: --&gt;&lt;!-- ws:end:WikiTextTocRule:315 --&gt;&lt;!-- ws:start:WikiTextTocRule:316: --&gt;&lt;!-- ws:end:WikiTextTocRule:316 --&gt;&lt;!-- ws:start:WikiTextTocRule:317: --&gt;&lt;!-- ws:end:WikiTextTocRule:317 --&gt;&lt;!-- ws:start:WikiTextTocRule:318: --&gt;&lt;!-- ws:end:WikiTextTocRule:318 --&gt;&lt;!-- ws:start:WikiTextTocRule:319: --&gt;&lt;!-- ws:end:WikiTextTocRule:319 --&gt;&lt;!-- ws:start:WikiTextTocRule:320: --&gt;&lt;!-- ws:end:WikiTextTocRule:320 --&gt;&lt;!-- ws:start:WikiTextTocRule:321: --&gt;&lt;!-- ws:end:WikiTextTocRule:321 --&gt;&lt;!-- ws:start:WikiTextTocRule:322: --&gt;&lt;!-- ws:end:WikiTextTocRule:322 --&gt;&lt;!-- ws:start:WikiTextTocRule:323: --&gt;&lt;!-- ws:end:WikiTextTocRule:323 --&gt;&lt;!-- ws:start:WikiTextTocRule:324: --&gt;&lt;!-- ws:end:WikiTextTocRule:324 --&gt;&lt;!-- ws:start:WikiTextTocRule:325: --&gt;&lt;!-- ws:end:WikiTextTocRule:325 --&gt;&lt;!-- ws:start:WikiTextTocRule:326: --&gt;&lt;!-- ws:end:WikiTextTocRule:326 --&gt;&lt;!-- ws:start:WikiTextTocRule:327: --&gt;&lt;!-- ws:end:WikiTextTocRule:327 --&gt;&lt;!-- ws:start:WikiTextTocRule:328: --&gt;&lt;!-- ws:end:WikiTextTocRule:328 --&gt;&lt;!-- ws:start:WikiTextTocRule:329: --&gt;&lt;!-- ws:end:WikiTextTocRule:329 --&gt;&lt;!-- ws:start:WikiTextTocRule:330: --&gt;&lt;!-- ws:end:WikiTextTocRule:330 --&gt;&lt;!-- ws:start:WikiTextTocRule:331: --&gt;&lt;!-- ws:end:WikiTextTocRule:331 --&gt;&lt;!-- ws:start:WikiTextTocRule:332: --&gt;&lt;!-- ws:end:WikiTextTocRule:332 --&gt;&lt;!-- ws:start:WikiTextTocRule:333: --&gt;&lt;!-- ws:end:WikiTextTocRule:333 --&gt;&lt;!-- ws:start:WikiTextTocRule:334: --&gt;&lt;!-- ws:end:WikiTextTocRule:334 --&gt;&lt;!-- ws:start:WikiTextTocRule:335: --&gt;&lt;!-- ws:end:WikiTextTocRule:335 --&gt;&lt;!-- ws:start:WikiTextTocRule:336: --&gt;&lt;!-- ws:end:WikiTextTocRule:336 --&gt;&lt;!-- ws:start:WikiTextTocRule:337: --&gt;&lt;!-- ws:end:WikiTextTocRule:337 --&gt;&lt;!-- ws:start:WikiTextTocRule:338: --&gt;&lt;!-- ws:end:WikiTextTocRule:338 --&gt;&lt;!-- ws:start:WikiTextTocRule:339: --&gt;&lt;!-- ws:end:WikiTextTocRule:339 --&gt;&lt;!-- ws:start:WikiTextTocRule:340: --&gt;&lt;!-- ws:end:WikiTextTocRule:340 --&gt;&lt;!-- ws:start:WikiTextTocRule:341: --&gt;&lt;!-- ws:end:WikiTextTocRule:341 --&gt;&lt;!-- ws:start:WikiTextTocRule:342: --&gt; | &lt;a href="#Rank 4 temperaments"&gt;Rank 4 temperaments&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:342 --&gt;&lt;!-- ws:start:WikiTextTocRule:343: --&gt; | &lt;a href="#Subgroup temperaments"&gt;Subgroup temperaments&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:343 --&gt;&lt;!-- ws:start:WikiTextTocRule:344: --&gt; | &lt;a href="#Commatic realms"&gt;Commatic realms&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:344 --&gt;&lt;!-- ws:start:WikiTextTocRule:345: --&gt;&lt;!-- ws:end:WikiTextTocRule:345 --&gt;&lt;!-- ws:start:WikiTextTocRule:346: --&gt;&lt;!-- ws:end:WikiTextTocRule:346 --&gt;&lt;!-- ws:start:WikiTextTocRule:347: --&gt;&lt;!-- ws:end:WikiTextTocRule:347 --&gt;&lt;!-- ws:start:WikiTextTocRule:348: --&gt; | &lt;a href="#Links"&gt;Links&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:348 --&gt;&lt;!-- ws:start:WikiTextTocRule:349: --&gt;
&lt;!-- ws:start:WikiTextTocRule:234:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:234 --&gt;&lt;!-- ws:start:WikiTextTocRule:235: --&gt;&lt;a href="#Regular temperaments"&gt;Regular temperaments&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:235 --&gt;&lt;!-- ws:start:WikiTextTocRule:236: --&gt;&lt;!-- ws:end:WikiTextTocRule:236 --&gt;&lt;!-- ws:start:WikiTextTocRule:237: --&gt;&lt;!-- ws:end:WikiTextTocRule:237 --&gt;&lt;!-- ws:start:WikiTextTocRule:238: --&gt; | &lt;a href="#Equal temperaments"&gt;Equal temperaments&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:238 --&gt;&lt;!-- ws:start:WikiTextTocRule:239: --&gt; | &lt;a href="#Rank 2 (including &amp;quot;linear&amp;quot;) temperaments"&gt;Rank 2 (including &amp;quot;linear&amp;quot;) temperaments&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:239 --&gt;&lt;!-- ws:start:WikiTextTocRule:240: --&gt;&lt;!-- ws:end:WikiTextTocRule:240 --&gt;&lt;!-- ws:start:WikiTextTocRule:241: --&gt;&lt;!-- ws:end:WikiTextTocRule:241 --&gt;&lt;!-- ws:start:WikiTextTocRule:242: --&gt;&lt;!-- ws:end:WikiTextTocRule:242 --&gt;&lt;!-- ws:start:WikiTextTocRule:243: --&gt;&lt;!-- ws:end:WikiTextTocRule:243 --&gt;&lt;!-- ws:start:WikiTextTocRule:244: --&gt;&lt;!-- ws:end:WikiTextTocRule:244 --&gt;&lt;!-- ws:start:WikiTextTocRule:245: --&gt;&lt;!-- ws:end:WikiTextTocRule:245 --&gt;&lt;!-- ws:start:WikiTextTocRule:246: --&gt;&lt;!-- ws:end:WikiTextTocRule:246 --&gt;&lt;!-- ws:start:WikiTextTocRule:247: --&gt;&lt;!-- ws:end:WikiTextTocRule:247 --&gt;&lt;!-- ws:start:WikiTextTocRule:248: --&gt;&lt;!-- ws:end:WikiTextTocRule:248 --&gt;&lt;!-- ws:start:WikiTextTocRule:249: --&gt;&lt;!-- ws:end:WikiTextTocRule:249 --&gt;&lt;!-- ws:start:WikiTextTocRule:250: --&gt;&lt;!-- ws:end:WikiTextTocRule:250 --&gt;&lt;!-- ws:start:WikiTextTocRule:251: --&gt;&lt;!-- ws:end:WikiTextTocRule:251 --&gt;&lt;!-- ws:start:WikiTextTocRule:252: --&gt;&lt;!-- ws:end:WikiTextTocRule:252 --&gt;&lt;!-- ws:start:WikiTextTocRule:253: --&gt;&lt;!-- ws:end:WikiTextTocRule:253 --&gt;&lt;!-- ws:start:WikiTextTocRule:254: --&gt;&lt;!-- ws:end:WikiTextTocRule:254 --&gt;&lt;!-- ws:start:WikiTextTocRule:255: --&gt;&lt;!-- ws:end:WikiTextTocRule:255 --&gt;&lt;!-- ws:start:WikiTextTocRule:256: --&gt;&lt;!-- ws:end:WikiTextTocRule:256 --&gt;&lt;!-- ws:start:WikiTextTocRule:257: --&gt;&lt;!-- ws:end:WikiTextTocRule:257 --&gt;&lt;!-- ws:start:WikiTextTocRule:258: --&gt;&lt;!-- ws:end:WikiTextTocRule:258 --&gt;&lt;!-- ws:start:WikiTextTocRule:259: --&gt;&lt;!-- ws:end:WikiTextTocRule:259 --&gt;&lt;!-- ws:start:WikiTextTocRule:260: --&gt;&lt;!-- ws:end:WikiTextTocRule:260 --&gt;&lt;!-- ws:start:WikiTextTocRule:261: --&gt;&lt;!-- ws:end:WikiTextTocRule:261 --&gt;&lt;!-- ws:start:WikiTextTocRule:262: --&gt;&lt;!-- ws:end:WikiTextTocRule:262 --&gt;&lt;!-- ws:start:WikiTextTocRule:263: --&gt;&lt;!-- ws:end:WikiTextTocRule:263 --&gt;&lt;!-- ws:start:WikiTextTocRule:264: --&gt;&lt;!-- ws:end:WikiTextTocRule:264 --&gt;&lt;!-- ws:start:WikiTextTocRule:265: --&gt;&lt;!-- ws:end:WikiTextTocRule:265 --&gt;&lt;!-- ws:start:WikiTextTocRule:266: --&gt;&lt;!-- ws:end:WikiTextTocRule:266 --&gt;&lt;!-- ws:start:WikiTextTocRule:267: --&gt;&lt;!-- ws:end:WikiTextTocRule:267 --&gt;&lt;!-- ws:start:WikiTextTocRule:268: --&gt;&lt;!-- ws:end:WikiTextTocRule:268 --&gt;&lt;!-- ws:start:WikiTextTocRule:269: --&gt;&lt;!-- ws:end:WikiTextTocRule:269 --&gt;&lt;!-- ws:start:WikiTextTocRule:270: --&gt;&lt;!-- ws:end:WikiTextTocRule:270 --&gt;&lt;!-- ws:start:WikiTextTocRule:271: --&gt;&lt;!-- ws:end:WikiTextTocRule:271 --&gt;&lt;!-- ws:start:WikiTextTocRule:272: --&gt;&lt;!-- ws:end:WikiTextTocRule:272 --&gt;&lt;!-- ws:start:WikiTextTocRule:273: --&gt;&lt;!-- ws:end:WikiTextTocRule:273 --&gt;&lt;!-- ws:start:WikiTextTocRule:274: --&gt;&lt;!-- ws:end:WikiTextTocRule:274 --&gt;&lt;!-- ws:start:WikiTextTocRule:275: --&gt;&lt;!-- ws:end:WikiTextTocRule:275 --&gt;&lt;!-- ws:start:WikiTextTocRule:276: --&gt;&lt;!-- ws:end:WikiTextTocRule:276 --&gt;&lt;!-- ws:start:WikiTextTocRule:277: --&gt;&lt;!-- ws:end:WikiTextTocRule:277 --&gt;&lt;!-- ws:start:WikiTextTocRule:278: --&gt;&lt;!-- ws:end:WikiTextTocRule:278 --&gt;&lt;!-- ws:start:WikiTextTocRule:279: --&gt;&lt;!-- ws:end:WikiTextTocRule:279 --&gt;&lt;!-- ws:start:WikiTextTocRule:280: --&gt;&lt;!-- ws:end:WikiTextTocRule:280 --&gt;&lt;!-- ws:start:WikiTextTocRule:281: --&gt;&lt;!-- ws:end:WikiTextTocRule:281 --&gt;&lt;!-- ws:start:WikiTextTocRule:282: --&gt;&lt;!-- ws:end:WikiTextTocRule:282 --&gt;&lt;!-- ws:start:WikiTextTocRule:283: --&gt;&lt;!-- ws:end:WikiTextTocRule:283 --&gt;&lt;!-- ws:start:WikiTextTocRule:284: --&gt;&lt;!-- ws:end:WikiTextTocRule:284 --&gt;&lt;!-- ws:start:WikiTextTocRule:285: --&gt;&lt;!-- ws:end:WikiTextTocRule:285 --&gt;&lt;!-- ws:start:WikiTextTocRule:286: --&gt; | &lt;a href="#Temperaments for a given comma"&gt;Temperaments for a given comma&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:286 --&gt;&lt;!-- ws:start:WikiTextTocRule:287: --&gt;&lt;!-- ws:end:WikiTextTocRule:287 --&gt;&lt;!-- ws:start:WikiTextTocRule:288: --&gt;&lt;!-- ws:end:WikiTextTocRule:288 --&gt;&lt;!-- ws:start:WikiTextTocRule:289: --&gt;&lt;!-- ws:end:WikiTextTocRule:289 --&gt;&lt;!-- ws:start:WikiTextTocRule:290: --&gt;&lt;!-- ws:end:WikiTextTocRule:290 --&gt;&lt;!-- ws:start:WikiTextTocRule:291: --&gt;&lt;!-- ws:end:WikiTextTocRule:291 --&gt;&lt;!-- ws:start:WikiTextTocRule:292: --&gt;&lt;!-- ws:end:WikiTextTocRule:292 --&gt;&lt;!-- ws:start:WikiTextTocRule:293: --&gt;&lt;!-- ws:end:WikiTextTocRule:293 --&gt;&lt;!-- ws:start:WikiTextTocRule:294: --&gt;&lt;!-- ws:end:WikiTextTocRule:294 --&gt;&lt;!-- ws:start:WikiTextTocRule:295: --&gt;&lt;!-- ws:end:WikiTextTocRule:295 --&gt;&lt;!-- ws:start:WikiTextTocRule:296: --&gt;&lt;!-- ws:end:WikiTextTocRule:296 --&gt;&lt;!-- ws:start:WikiTextTocRule:297: --&gt;&lt;!-- ws:end:WikiTextTocRule:297 --&gt;&lt;!-- ws:start:WikiTextTocRule:298: --&gt;&lt;!-- ws:end:WikiTextTocRule:298 --&gt;&lt;!-- ws:start:WikiTextTocRule:299: --&gt;&lt;!-- ws:end:WikiTextTocRule:299 --&gt;&lt;!-- ws:start:WikiTextTocRule:300: --&gt;&lt;!-- ws:end:WikiTextTocRule:300 --&gt;&lt;!-- ws:start:WikiTextTocRule:301: --&gt;&lt;!-- ws:end:WikiTextTocRule:301 --&gt;&lt;!-- ws:start:WikiTextTocRule:302: --&gt;&lt;!-- ws:end:WikiTextTocRule:302 --&gt;&lt;!-- ws:start:WikiTextTocRule:303: --&gt;&lt;!-- ws:end:WikiTextTocRule:303 --&gt;&lt;!-- ws:start:WikiTextTocRule:304: --&gt;&lt;!-- ws:end:WikiTextTocRule:304 --&gt;&lt;!-- ws:start:WikiTextTocRule:305: --&gt;&lt;!-- ws:end:WikiTextTocRule:305 --&gt;&lt;!-- ws:start:WikiTextTocRule:306: --&gt;&lt;!-- ws:end:WikiTextTocRule:306 --&gt;&lt;!-- ws:start:WikiTextTocRule:307: --&gt;&lt;!-- ws:end:WikiTextTocRule:307 --&gt;&lt;!-- ws:start:WikiTextTocRule:308: --&gt;&lt;!-- ws:end:WikiTextTocRule:308 --&gt;&lt;!-- ws:start:WikiTextTocRule:309: --&gt;&lt;!-- ws:end:WikiTextTocRule:309 --&gt;&lt;!-- ws:start:WikiTextTocRule:310: --&gt; | &lt;a href="#Rank 3 temperaments"&gt;Rank 3 temperaments&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:310 --&gt;&lt;!-- ws:start:WikiTextTocRule:311: --&gt;&lt;!-- ws:end:WikiTextTocRule:311 --&gt;&lt;!-- ws:start:WikiTextTocRule:312: --&gt;&lt;!-- ws:end:WikiTextTocRule:312 --&gt;&lt;!-- ws:start:WikiTextTocRule:313: --&gt;&lt;!-- ws:end:WikiTextTocRule:313 --&gt;&lt;!-- ws:start:WikiTextTocRule:314: --&gt;&lt;!-- ws:end:WikiTextTocRule:314 --&gt;&lt;!-- ws:start:WikiTextTocRule:315: --&gt;&lt;!-- ws:end:WikiTextTocRule:315 --&gt;&lt;!-- ws:start:WikiTextTocRule:316: --&gt;&lt;!-- ws:end:WikiTextTocRule:316 --&gt;&lt;!-- ws:start:WikiTextTocRule:317: --&gt;&lt;!-- ws:end:WikiTextTocRule:317 --&gt;&lt;!-- ws:start:WikiTextTocRule:318: --&gt;&lt;!-- ws:end:WikiTextTocRule:318 --&gt;&lt;!-- ws:start:WikiTextTocRule:319: --&gt;&lt;!-- ws:end:WikiTextTocRule:319 --&gt;&lt;!-- ws:start:WikiTextTocRule:320: --&gt;&lt;!-- ws:end:WikiTextTocRule:320 --&gt;&lt;!-- ws:start:WikiTextTocRule:321: --&gt;&lt;!-- ws:end:WikiTextTocRule:321 --&gt;&lt;!-- ws:start:WikiTextTocRule:322: --&gt;&lt;!-- ws:end:WikiTextTocRule:322 --&gt;&lt;!-- ws:start:WikiTextTocRule:323: --&gt;&lt;!-- ws:end:WikiTextTocRule:323 --&gt;&lt;!-- ws:start:WikiTextTocRule:324: --&gt;&lt;!-- ws:end:WikiTextTocRule:324 --&gt;&lt;!-- ws:start:WikiTextTocRule:325: --&gt;&lt;!-- ws:end:WikiTextTocRule:325 --&gt;&lt;!-- ws:start:WikiTextTocRule:326: --&gt;&lt;!-- ws:end:WikiTextTocRule:326 --&gt;&lt;!-- ws:start:WikiTextTocRule:327: --&gt;&lt;!-- ws:end:WikiTextTocRule:327 --&gt;&lt;!-- ws:start:WikiTextTocRule:328: --&gt;&lt;!-- ws:end:WikiTextTocRule:328 --&gt;&lt;!-- ws:start:WikiTextTocRule:329: --&gt;&lt;!-- ws:end:WikiTextTocRule:329 --&gt;&lt;!-- ws:start:WikiTextTocRule:330: --&gt;&lt;!-- ws:end:WikiTextTocRule:330 --&gt;&lt;!-- ws:start:WikiTextTocRule:331: --&gt;&lt;!-- ws:end:WikiTextTocRule:331 --&gt;&lt;!-- ws:start:WikiTextTocRule:332: --&gt;&lt;!-- ws:end:WikiTextTocRule:332 --&gt;&lt;!-- ws:start:WikiTextTocRule:333: --&gt;&lt;!-- ws:end:WikiTextTocRule:333 --&gt;&lt;!-- ws:start:WikiTextTocRule:334: --&gt;&lt;!-- ws:end:WikiTextTocRule:334 --&gt;&lt;!-- ws:start:WikiTextTocRule:335: --&gt;&lt;!-- ws:end:WikiTextTocRule:335 --&gt;&lt;!-- ws:start:WikiTextTocRule:336: --&gt;&lt;!-- ws:end:WikiTextTocRule:336 --&gt;&lt;!-- ws:start:WikiTextTocRule:337: --&gt;&lt;!-- ws:end:WikiTextTocRule:337 --&gt;&lt;!-- ws:start:WikiTextTocRule:338: --&gt;&lt;!-- ws:end:WikiTextTocRule:338 --&gt;&lt;!-- ws:start:WikiTextTocRule:339: --&gt;&lt;!-- ws:end:WikiTextTocRule:339 --&gt;&lt;!-- ws:start:WikiTextTocRule:340: --&gt;&lt;!-- ws:end:WikiTextTocRule:340 --&gt;&lt;!-- ws:start:WikiTextTocRule:341: --&gt;&lt;!-- ws:end:WikiTextTocRule:341 --&gt;&lt;!-- ws:start:WikiTextTocRule:342: --&gt;&lt;!-- ws:end:WikiTextTocRule:342 --&gt;&lt;!-- ws:start:WikiTextTocRule:343: --&gt;&lt;!-- ws:end:WikiTextTocRule:343 --&gt;&lt;!-- ws:start:WikiTextTocRule:344: --&gt;&lt;!-- ws:end:WikiTextTocRule:344 --&gt;&lt;!-- ws:start:WikiTextTocRule:345: --&gt; | &lt;a href="#Rank 4 temperaments"&gt;Rank 4 temperaments&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:345 --&gt;&lt;!-- ws:start:WikiTextTocRule:346: --&gt; | &lt;a href="#Subgroup temperaments"&gt;Subgroup temperaments&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:346 --&gt;&lt;!-- ws:start:WikiTextTocRule:347: --&gt; | &lt;a href="#Commatic realms"&gt;Commatic realms&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:347 --&gt;&lt;!-- ws:start:WikiTextTocRule:348: --&gt;&lt;!-- ws:end:WikiTextTocRule:348 --&gt;&lt;!-- ws:start:WikiTextTocRule:349: --&gt;&lt;!-- ws:end:WikiTextTocRule:349 --&gt;&lt;!-- ws:start:WikiTextTocRule:350: --&gt;&lt;!-- ws:end:WikiTextTocRule:350 --&gt;&lt;!-- ws:start:WikiTextTocRule:351: --&gt; | &lt;a href="#Links"&gt;Links&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:351 --&gt;&lt;!-- ws:start:WikiTextTocRule:352: --&gt;
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&lt;a class="wiki_link" href="/Equal%20Temperaments"&gt;Equal temperaments&lt;/a&gt; (abbreviated ET or tET) and equal divisions of the octave (abbreviated EDO or ED2) are similar concepts, although there are distinctions in the way these terms are used. A p-limit ET is simply a p-limit temperament that uses a single generator (making it a &amp;quot;Rank 1&amp;quot;) temperament, which thus maps the set of n-limit JI intervals using one-dimensional coordinates. An ET thus does not have to be thought of as an &amp;quot;equal division&amp;quot; of any interval (let alone the octave), and in fact many ETs do not divide the pure octave at all. On the other hand, an n-EDO is a division of the octave into n equal parts, with no consideration given to mapping of JI intervals. An EDO can be treated as an ET by applying a temperament mapping to the intervals of the EDO, typically by using a val for a temperament supported by that EDO (although one can also use unsupported vals or poorly-supported vals to achieve &amp;quot;fun&amp;quot; results). 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, although there are other temperaments supported by 12-tET.&lt;br /&gt;
&lt;a class="wiki_link" href="/Equal%20Temperaments"&gt;Equal temperaments&lt;/a&gt; (abbreviated ET or tET) and equal divisions of the octave (abbreviated EDO or ED2) are similar concepts, although there are distinctions in the way these terms are used. A p-limit ET is simply a p-limit temperament that uses a single generator (making it a &amp;quot;Rank 1&amp;quot;) temperament, which thus maps the set of n-limit JI intervals using one-dimensional coordinates. An ET thus does not have to be thought of as an &amp;quot;equal division&amp;quot; of any interval (let alone the octave), and in fact many ETs do not divide the pure octave at all. On the other hand, an n-EDO is a division of the octave into n equal parts, with no consideration given to mapping of JI intervals. An EDO can be treated as an ET by applying a temperament mapping to the intervals of the EDO, typically by using a val for a temperament supported by that EDO (although one can also use unsupported vals or poorly-supported vals to achieve &amp;quot;fun&amp;quot; results). 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, although there are other temperaments supported by 12-tET.&lt;br /&gt;
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&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Rank 2 (including &amp;quot;linear&amp;quot;) temperaments&lt;!-- ws:start:WikiTextAnchorRule:350:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@lineartemperaments&amp;quot; title=&amp;quot;Anchor: lineartemperaments&amp;quot;/&amp;gt; --&gt;&lt;a name="lineartemperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:350 --&gt;&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Rank 2 (including &amp;quot;linear&amp;quot;) temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Rank 2 (including &amp;quot;linear&amp;quot;) temperaments&lt;!-- ws:start:WikiTextAnchorRule:353:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@lineartemperaments&amp;quot; title=&amp;quot;Anchor: lineartemperaments&amp;quot;/&amp;gt; --&gt;&lt;a name="lineartemperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:353 --&gt;&lt;/h1&gt;
  &lt;br /&gt;
  &lt;br /&gt;
Regular temperaments of ranks two and three are cataloged &lt;a class="wiki_link" href="/Optimal%20patent%20val"&gt;here&lt;/a&gt;. Other pages listing them are &lt;a class="wiki_link" href="/Paul%20Erlich"&gt;Paul Erlich&lt;/a&gt;'s &lt;a class="wiki_link" href="/Catalog%20of%20five-limit%20rank%20two%20temperaments"&gt;catalog of 5-limit rank two temperaments&lt;/a&gt;, and a &lt;a class="wiki_link" href="/Proposed%20names%20for%20rank%202%20temperaments"&gt;page&lt;/a&gt; listing higher limit rank two temperaments. There is also &lt;a class="wiki_link" href="/Graham%20Breed"&gt;Graham Breed&lt;/a&gt;'s &lt;a class="wiki_link_ext" href="http://x31eq.com/catalog2.html" rel="nofollow"&gt;giant list of regular temperaments&lt;/a&gt;.&lt;br /&gt;
Regular temperaments of ranks two and three are cataloged &lt;a class="wiki_link" href="/Optimal%20patent%20val"&gt;here&lt;/a&gt;. Other pages listing them are &lt;a class="wiki_link" href="/Paul%20Erlich"&gt;Paul Erlich&lt;/a&gt;'s &lt;a class="wiki_link" href="/Catalog%20of%20five-limit%20rank%20two%20temperaments"&gt;catalog of 5-limit rank two temperaments&lt;/a&gt;, and a &lt;a class="wiki_link" href="/Proposed%20names%20for%20rank%202%20temperaments"&gt;page&lt;/a&gt; listing higher limit rank two temperaments. There is also &lt;a class="wiki_link" href="/Graham%20Breed"&gt;Graham Breed&lt;/a&gt;'s &lt;a class="wiki_link_ext" href="http://x31eq.com/catalog2.html" rel="nofollow"&gt;giant list of regular temperaments&lt;/a&gt;.&lt;br /&gt;
Line 645: Line 648:
  The 7-limit rank three microtemperament which tempers out the ragisma, 4375/4374, extends to various higher limit rank three temperaments such as thor.&lt;br /&gt;
  The 7-limit rank three microtemperament which tempers out the ragisma, 4375/4374, extends to various higher limit rank three temperaments such as thor.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:162:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc81"&gt;&lt;a name="Rank 3 temperaments--Hemifamity family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:162 --&gt;&lt;a class="wiki_link" href="/Hemifamity%20family"&gt;Hemifamity family&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:162:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc81"&gt;&lt;a name="Rank 3 temperaments-Landscape family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:162 --&gt;&lt;a class="wiki_link" href="/Landscape%20family"&gt;Landscape family&lt;/a&gt;&lt;/h2&gt;
The 7-limit rank three microtemperament which tempers out the lanscape comma, 250047/250000, extends to various higher limit rank three temperaments such as tyr and odin.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:164:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc82"&gt;&lt;a name="Rank 3 temperaments-Landscape family-Hemifamity family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:164 --&gt;&lt;a class="wiki_link" href="/Hemifamity%20family"&gt;Hemifamity family&lt;/a&gt;&lt;/h3&gt;
  The hemifamity family of rank three temperaments tempers out the hemifamity comma, 5120/5103.&lt;br /&gt;
  The hemifamity family of rank three temperaments tempers out the hemifamity comma, 5120/5103.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:164:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc82"&gt;&lt;a name="Rank 3 temperaments--Porwell family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:164 --&gt;&lt;a class="wiki_link" href="/Porwell%20family"&gt;Porwell family&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:166:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc83"&gt;&lt;a name="Rank 3 temperaments-Landscape family-Porwell family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:166 --&gt;&lt;a class="wiki_link" href="/Porwell%20family"&gt;Porwell family&lt;/a&gt;&lt;/h3&gt;
  The porwell family of rank three temperaments tempers out the porwell comma, 6144/6125.&lt;br /&gt;
  The porwell family of rank three temperaments tempers out the porwell comma, 6144/6125.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:166:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc83"&gt;&lt;a name="Rank 3 temperaments--Horwell family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:166 --&gt;&lt;a class="wiki_link" href="/Horwell%20family"&gt;Horwell family&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:168:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc84"&gt;&lt;a name="Rank 3 temperaments-Landscape family-Horwell family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:168 --&gt;&lt;a class="wiki_link" href="/Horwell%20family"&gt;Horwell family&lt;/a&gt;&lt;/h3&gt;
  The horwell family of rank three temperaments tempers out the horwell comma, 65625/65536.&lt;br /&gt;
  The horwell family of rank three temperaments tempers out the horwell comma, 65625/65536.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:168:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc84"&gt;&lt;a name="Rank 3 temperaments--Hemimage family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:168 --&gt;&lt;a class="wiki_link" href="/Hemimage%20family"&gt;Hemimage family&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:170:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc85"&gt;&lt;a name="Rank 3 temperaments-Landscape family-Hemimage family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:170 --&gt;&lt;a class="wiki_link" href="/Hemimage%20family"&gt;Hemimage family&lt;/a&gt;&lt;/h3&gt;
  The hemimage family of rank three temperaments tempers out the hemimage comma, 10976/10935.&lt;br /&gt;
  The hemimage family of rank three temperaments tempers out the hemimage comma, 10976/10935.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:170:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc85"&gt;&lt;a name="Rank 3 temperaments--Sensamagic family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:170 --&gt;&lt;a class="wiki_link" href="/Sensamagic%20family"&gt;Sensamagic family&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:172:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc86"&gt;&lt;a name="Rank 3 temperaments-Landscape family-Sensamagic family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:172 --&gt;&lt;a class="wiki_link" href="/Sensamagic%20family"&gt;Sensamagic family&lt;/a&gt;&lt;/h3&gt;
  These temper out 245/243.&lt;br /&gt;
  These temper out 245/243.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:172:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc86"&gt;&lt;a name="Rank 3 temperaments--Keemic family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:172 --&gt;&lt;a class="wiki_link" href="/Keemic%20family"&gt;Keemic family&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:174:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc87"&gt;&lt;a name="Rank 3 temperaments-Landscape family-Keemic family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:174 --&gt;&lt;a class="wiki_link" href="/Keemic%20family"&gt;Keemic family&lt;/a&gt;&lt;/h3&gt;
  These temper out 875/864.&lt;br /&gt;
  These temper out 875/864.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:174:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc87"&gt;&lt;a name="Rank 3 temperaments--Sengic family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:174 --&gt;&lt;a class="wiki_link" href="/Sengic%20family"&gt;Sengic family&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:176:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc88"&gt;&lt;a name="Rank 3 temperaments-Landscape family-Sengic family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:176 --&gt;&lt;a class="wiki_link" href="/Sengic%20family"&gt;Sengic family&lt;/a&gt;&lt;/h3&gt;
  These temper out the senga, 686/675.&lt;br /&gt;
  These temper out the senga, 686/675.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:176:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc88"&gt;&lt;a name="Rank 3 temperaments--Orwellismic family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:176 --&gt;&lt;a class="wiki_link" href="/Orwellismic%20family"&gt;Orwellismic family&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:178:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc89"&gt;&lt;a name="Rank 3 temperaments-Landscape family-Orwellismic family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:178 --&gt;&lt;a class="wiki_link" href="/Orwellismic%20family"&gt;Orwellismic family&lt;/a&gt;&lt;/h3&gt;
  These temper out 1728/1715.&lt;br /&gt;
  These temper out 1728/1715.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:178:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc89"&gt;&lt;a name="Rank 3 temperaments--Nuwell family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:178 --&gt;&lt;a class="wiki_link" href="/Nuwell%20family"&gt;Nuwell family&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:180:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc90"&gt;&lt;a name="Rank 3 temperaments-Landscape family-Nuwell family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:180 --&gt;&lt;a class="wiki_link" href="/Nuwell%20family"&gt;Nuwell family&lt;/a&gt;&lt;/h3&gt;
  These temper out the nuwell comma, 2430/2401.&lt;br /&gt;
  These temper out the nuwell comma, 2430/2401.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:180:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc90"&gt;&lt;a name="Rank 3 temperaments--Octagar family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:180 --&gt;&lt;a class="wiki_link" href="/Octagar%20family"&gt;Octagar family&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:182:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc91"&gt;&lt;a name="Rank 3 temperaments-Landscape family-Octagar family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:182 --&gt;&lt;a class="wiki_link" href="/Octagar%20family"&gt;Octagar family&lt;/a&gt;&lt;/h3&gt;
  The octagar family of rank three temperaments tempers out the octagar comma, 4000/3969.&lt;br /&gt;
  The octagar family of rank three temperaments tempers out the octagar comma, 4000/3969.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:182:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc91"&gt;&lt;a name="Rank 3 temperaments--Mirkwai family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:182 --&gt;&lt;a class="wiki_link" href="/Mirkwai%20family"&gt;Mirkwai family&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:184:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc92"&gt;&lt;a name="Rank 3 temperaments-Landscape family-Mirkwai family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:184 --&gt;&lt;a class="wiki_link" href="/Mirkwai%20family"&gt;Mirkwai family&lt;/a&gt;&lt;/h3&gt;
  The mirkwai family of rank three temperaments tempers out the mirkwai comma, 16875/16807.&lt;br /&gt;
  The mirkwai family of rank three temperaments tempers out the mirkwai comma, 16875/16807.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:184:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc92"&gt;&lt;a name="Rank 3 temperaments--Hemimean family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:184 --&gt;&lt;a class="wiki_link" href="/Hemimean%20family"&gt;Hemimean family&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:186:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc93"&gt;&lt;a name="Rank 3 temperaments-Landscape family-Hemimean family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:186 --&gt;&lt;a class="wiki_link" href="/Hemimean%20family"&gt;Hemimean family&lt;/a&gt;&lt;/h3&gt;
  The hemimean family of rank three temperaments tempers out the hemimean comma, 3136/3125.&lt;br /&gt;
  The hemimean family of rank three temperaments tempers out the hemimean comma, 3136/3125.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:186:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc93"&gt;&lt;a name="Rank 3 temperaments--Mirwomo family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:186 --&gt;&lt;a class="wiki_link" href="/Mirwomo%20family"&gt;Mirwomo family&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:188:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc94"&gt;&lt;a name="Rank 3 temperaments-Landscape family-Mirwomo family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:188 --&gt;&lt;a class="wiki_link" href="/Mirwomo%20family"&gt;Mirwomo family&lt;/a&gt;&lt;/h3&gt;
  The mirwomo family of rank three temperaments tempers out the mirwomo comma, 33075/32768.&lt;br /&gt;
  The mirwomo family of rank three temperaments tempers out the mirwomo comma, 33075/32768.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:188:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc94"&gt;&lt;a name="Rank 3 temperaments--Dimcomp family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:188 --&gt;&lt;a class="wiki_link" href="/Dimcomp%20family"&gt;Dimcomp family&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:190:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc95"&gt;&lt;a name="Rank 3 temperaments-Landscape family-Dimcomp family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:190 --&gt;&lt;a class="wiki_link" href="/Dimcomp%20family"&gt;Dimcomp family&lt;/a&gt;&lt;/h3&gt;
  The dimcomp family of rank three temperaments tempers out the dimcomp comma, 390625/388962.&lt;br /&gt;
  The dimcomp family of rank three temperaments tempers out the dimcomp comma, 390625/388962.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:190:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc95"&gt;&lt;a name="Rank 3 temperaments--Tolermic family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:190 --&gt;&lt;a class="wiki_link" href="/Tolermic%20family"&gt;Tolermic family&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:192:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc96"&gt;&lt;a name="Rank 3 temperaments-Landscape family-Tolermic family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:192 --&gt;&lt;a class="wiki_link" href="/Tolermic%20family"&gt;Tolermic family&lt;/a&gt;&lt;/h3&gt;
  These temper out the tolerma, 179200/177147.&lt;br /&gt;
  These temper out the tolerma, 179200/177147.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:192:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc96"&gt;&lt;a name="Rank 3 temperaments--Kleismic rank three family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:192 --&gt;&lt;a class="wiki_link" href="/Kleismic%20rank%20three%20family"&gt;Kleismic rank three family&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:194:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc97"&gt;&lt;a name="Rank 3 temperaments-Landscape family-Kleismic rank three family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:194 --&gt;&lt;a class="wiki_link" href="/Kleismic%20rank%20three%20family"&gt;Kleismic rank three family&lt;/a&gt;&lt;/h3&gt;
  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.&lt;br /&gt;
  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.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:194:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc97"&gt;&lt;a name="Rank 3 temperaments--Diaschismic rank three family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:194 --&gt;&lt;a class="wiki_link" href="/Diaschismic%20rank%20three%20family"&gt;Diaschismic rank three family&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:196:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc98"&gt;&lt;a name="Rank 3 temperaments-Landscape family-Diaschismic rank three family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:196 --&gt;&lt;a class="wiki_link" href="/Diaschismic%20rank%20three%20family"&gt;Diaschismic rank three family&lt;/a&gt;&lt;/h3&gt;
  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.&lt;br /&gt;
  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.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:196:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc98"&gt;&lt;a name="Rank 3 temperaments--Didymus rank three family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:196 --&gt;&lt;a class="wiki_link" href="/Didymus%20rank%20three%20family"&gt;Didymus rank three family&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:198:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc99"&gt;&lt;a name="Rank 3 temperaments-Landscape family-Didymus rank three family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:198 --&gt;&lt;a class="wiki_link" href="/Didymus%20rank%20three%20family"&gt;Didymus rank three family&lt;/a&gt;&lt;/h3&gt;
  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.&lt;br /&gt;
  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.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:198:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc99"&gt;&lt;a name="Rank 3 temperaments--Porcupine rank three family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:198 --&gt;&lt;a class="wiki_link" href="/Porcupine%20rank%20three%20family"&gt;Porcupine rank three family&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:200:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc100"&gt;&lt;a name="Rank 3 temperaments-Landscape family-Porcupine rank three family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:200 --&gt;&lt;a class="wiki_link" href="/Porcupine%20rank%20three%20family"&gt;Porcupine rank three family&lt;/a&gt;&lt;/h3&gt;
  These are the rank three temperaments tempering out the porcupine comma or maximal 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.&lt;br /&gt;
  These are the rank three temperaments tempering out the porcupine comma or maximal 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.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:200:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc100"&gt;&lt;a name="Rank 3 temperaments--Archytas family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:200 --&gt;&lt;a class="wiki_link" href="/Archytas%20family"&gt;Archytas family&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:202:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc101"&gt;&lt;a name="Rank 3 temperaments-Landscape family-Archytas family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:202 --&gt;&lt;a class="wiki_link" href="/Archytas%20family"&gt;Archytas family&lt;/a&gt;&lt;/h3&gt;
  Archytas temperament tempers out 64/63, and thereby identifies the otonal tetrad with the dominant seventh chord.&lt;br /&gt;
  Archytas temperament tempers out 64/63, and thereby identifies the otonal tetrad with the dominant seventh chord.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:202:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc101"&gt;&lt;a name="Rank 3 temperaments--Jubilismic family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:202 --&gt;&lt;a class="wiki_link" href="/Jubilismic%20family"&gt;Jubilismic family&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:204:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc102"&gt;&lt;a name="Rank 3 temperaments-Landscape family-Jubilismic family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:204 --&gt;&lt;a class="wiki_link" href="/Jubilismic%20family"&gt;Jubilismic family&lt;/a&gt;&lt;/h3&gt;
  Jubilismic temperament tempers out 50/49 and thereby identifies the two septimal tritones, 7/5 and 10/7.&lt;br /&gt;
  Jubilismic temperament tempers out 50/49 and thereby identifies the two septimal tritones, 7/5 and 10/7.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:204:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc102"&gt;&lt;a name="Rank 3 temperaments--Semiphore family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:204 --&gt;&lt;a class="wiki_link" href="/Semiphore%20family"&gt;Semiphore family&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:206:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc103"&gt;&lt;a name="Rank 3 temperaments-Landscape family-Semiphore family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:206 --&gt;&lt;a class="wiki_link" href="/Semiphore%20family"&gt;Semiphore family&lt;/a&gt;&lt;/h3&gt;
  Semiphore 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 &amp;quot;semi-fourth&amp;quot;.&lt;br /&gt;
  Semiphore 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 &amp;quot;semi-fourth&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:206:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc103"&gt;&lt;a name="Rank 3 temperaments--Mint family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:206 --&gt;&lt;a class="wiki_link" href="/Mint%20family"&gt;Mint family&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:208:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc104"&gt;&lt;a name="Rank 3 temperaments-Landscape family-Mint family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:208 --&gt;&lt;a class="wiki_link" href="/Mint%20family"&gt;Mint family&lt;/a&gt;&lt;/h3&gt;
  The mint temperament tempers out 36/35, identifying both 7/6 with 6/5 and 5/4 with 9/7.&lt;br /&gt;
  The mint temperament tempers out 36/35, identifying both 7/6 with 6/5 and 5/4 with 9/7.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:208:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc104"&gt;&lt;a name="Rank 3 temperaments--Valinorismic temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:208 --&gt;&lt;a class="wiki_link" href="/Valinorismic%20temperaments"&gt;Valinorismic temperaments&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:210:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc105"&gt;&lt;a name="Rank 3 temperaments-Landscape family-Valinorismic temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:210 --&gt;&lt;a class="wiki_link" href="/Valinorismic%20temperaments"&gt;Valinorismic temperaments&lt;/a&gt;&lt;/h3&gt;
  These temper out the valinorsma, 176/175.&lt;br /&gt;
  These temper out the valinorsma, 176/175.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:210:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc105"&gt;&lt;a name="Rank 3 temperaments--Werckismic temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:210 --&gt;&lt;a class="wiki_link" href="/Werckismic%20temperaments"&gt;Werckismic temperaments&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:212:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc106"&gt;&lt;a name="Rank 3 temperaments-Landscape family-Werckismic temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:212 --&gt;&lt;a class="wiki_link" href="/Werckismic%20temperaments"&gt;Werckismic temperaments&lt;/a&gt;&lt;/h3&gt;
  These temper out the werckisma, 441/440.&lt;br /&gt;
  These temper out the werckisma, 441/440.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:212:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc106"&gt;&lt;a name="Rank 3 temperaments--Swetismic temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:212 --&gt;&lt;a class="wiki_link" href="/Swetismic%20temperaments"&gt;Swetismic temperaments&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:214:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc107"&gt;&lt;a name="Rank 3 temperaments-Landscape family-Swetismic temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:214 --&gt;&lt;a class="wiki_link" href="/Swetismic%20temperaments"&gt;Swetismic temperaments&lt;/a&gt;&lt;/h3&gt;
  These temper out the swetisma, 540/539.&lt;br /&gt;
  These temper out the swetisma, 540/539.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:214:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc107"&gt;&lt;a name="Rank 3 temperaments--Lehmerismic temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:214 --&gt;&lt;a class="wiki_link" href="/Lehmerismic%20temperaments"&gt;Lehmerismic temperaments&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:216:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc108"&gt;&lt;a name="Rank 3 temperaments-Landscape family-Lehmerismic temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:216 --&gt;&lt;a class="wiki_link" href="/Lehmerismic%20temperaments"&gt;Lehmerismic temperaments&lt;/a&gt;&lt;/h3&gt;
  These temper out the lehmerisma, 3025/3024.&lt;br /&gt;
  These temper out the lehmerisma, 3025/3024.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:216:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc108"&gt;&lt;a name="Rank 3 temperaments--Kalismic temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:216 --&gt;&lt;a class="wiki_link" href="/Kalismic%20temperaments"&gt;Kalismic temperaments&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:218:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc109"&gt;&lt;a name="Rank 3 temperaments-Landscape family-Kalismic temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:218 --&gt;&lt;a class="wiki_link" href="/Kalismic%20temperaments"&gt;Kalismic temperaments&lt;/a&gt;&lt;/h3&gt;
  These temper out the kalisma, 9801/9800.&lt;br /&gt;
  These temper out the kalisma, 9801/9800.&lt;br /&gt;
&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:218:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc109"&gt;&lt;a name="Rank 4 temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:218 --&gt;&lt;a class="wiki_link" href="/Rank%20four%20temperaments"&gt;Rank 4 temperaments&lt;/a&gt;&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:220:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc110"&gt;&lt;a name="Rank 4 temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:220 --&gt;&lt;a class="wiki_link" href="/Rank%20four%20temperaments"&gt;Rank 4 temperaments&lt;/a&gt;&lt;/h1&gt;
  &lt;br /&gt;
  &lt;br /&gt;
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 &lt;a class="wiki_link" href="/Hobbits"&gt;hobbit scales&lt;/a&gt; can be constructed for them.&lt;br /&gt;
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 &lt;a class="wiki_link" href="/Hobbits"&gt;hobbit scales&lt;/a&gt; can be constructed for them.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:220:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc110"&gt;&lt;a name="Subgroup temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:220 --&gt;&lt;a class="wiki_link" href="/Subgroup%20temperaments"&gt;Subgroup temperaments&lt;/a&gt;&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:222:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc111"&gt;&lt;a name="Subgroup temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:222 --&gt;&lt;a class="wiki_link" href="/Subgroup%20temperaments"&gt;Subgroup temperaments&lt;/a&gt;&lt;/h1&gt;
  &lt;br /&gt;
  &lt;br /&gt;
A wide-open field. These are regular temperaments of various ranks which temper &lt;a class="wiki_link" href="/just%20intonation%20subgroups"&gt;just intonation subgroups&lt;/a&gt;.&lt;br /&gt;
A wide-open field. These are regular temperaments of various ranks which temper &lt;a class="wiki_link" href="/just%20intonation%20subgroups"&gt;just intonation subgroups&lt;/a&gt;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:222:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc111"&gt;&lt;a name="Commatic realms"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:222 --&gt;Commatic realms&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:224:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc112"&gt;&lt;a name="Commatic realms"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:224 --&gt;Commatic realms&lt;/h1&gt;
  &lt;br /&gt;
  &lt;br /&gt;
By a &lt;em&gt;commatic realm&lt;/em&gt; is meant the whole collection of regular temperaments of various ranks and for both full groups and &lt;a class="wiki_link" href="/Just%20intonation%20subgroups"&gt;subgroups&lt;/a&gt; tempering out a given comma. For some commas, looking at the full commatic realm seems the best approach to discussing associated temperaments.&lt;br /&gt;
By a &lt;em&gt;commatic realm&lt;/em&gt; is meant the whole collection of regular temperaments of various ranks and for both full groups and &lt;a class="wiki_link" href="/Just%20intonation%20subgroups"&gt;subgroups&lt;/a&gt; tempering out a given comma. For some commas, looking at the full commatic realm seems the best approach to discussing associated temperaments.&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:224:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc112"&gt;&lt;a name="Commatic realms-Orgonia"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:224 --&gt;&lt;a class="wiki_link" href="/Orgonia"&gt;Orgonia&lt;/a&gt;&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:226:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc113"&gt;&lt;a name="Commatic realms-Orgonia"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:226 --&gt;&lt;a class="wiki_link" href="/Orgonia"&gt;Orgonia&lt;/a&gt;&lt;/h2&gt;
  Orgonia is the commatic realm of the &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt; comma 65536/65219 = |16 0 0 -2 -3&amp;gt;, the orgonisma.&lt;br /&gt;
  Orgonia is the commatic realm of the &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt; comma 65536/65219 = |16 0 0 -2 -3&amp;gt;, the orgonisma.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:226:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc113"&gt;&lt;a name="Commatic realms-The Biosphere"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:226 --&gt;&lt;a class="wiki_link" href="/The%20Biosphere"&gt;The Biosphere&lt;/a&gt;&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:228:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc114"&gt;&lt;a name="Commatic realms-The Biosphere"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:228 --&gt;&lt;a class="wiki_link" href="/The%20Biosphere"&gt;The Biosphere&lt;/a&gt;&lt;/h2&gt;
  The Biosphere is the name given to the commatic realm of the 13-limit comma 91/90.&lt;br /&gt;
  The Biosphere is the name given to the commatic realm of the 13-limit comma 91/90.&lt;br /&gt;
&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:228:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc114"&gt;&lt;a name="Commatic realms-The Archipelago"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:228 --&gt;&lt;a class="wiki_link" href="/The%20Archipelago"&gt;The Archipelago&lt;/a&gt;&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:230:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc115"&gt;&lt;a name="Commatic realms-The Archipelago"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:230 --&gt;&lt;a class="wiki_link" href="/The%20Archipelago"&gt;The Archipelago&lt;/a&gt;&lt;/h2&gt;
  The Archipelago is a name which has been given to the commatic realm of the &lt;a class="wiki_link" href="/13-limit"&gt;13-limit&lt;/a&gt; comma 676/675.&lt;br /&gt;
  The Archipelago is a name which has been given to the commatic realm of the &lt;a class="wiki_link" href="/13-limit"&gt;13-limit&lt;/a&gt; comma 676/675.&lt;br /&gt;
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Line 753: Line 759:
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&lt;!-- ws:start:WikiTextHeadingRule:230:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc115"&gt;&lt;a name="Links"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:230 --&gt;Links&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:232:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc116"&gt;&lt;a name="Links"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:232 --&gt;Links&lt;/h1&gt;
  &lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Regular_temperament" rel="nofollow"&gt;Regular temperaments - Wikipedia&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
  &lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Regular_temperament" rel="nofollow"&gt;Regular temperaments - Wikipedia&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
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