Tour of regular temperaments: Difference between revisions
Wikispaces>genewardsmith **Imported revision 555729327 - Original comment: ** |
Wikispaces>hstraub **Imported revision 569682457 - 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: | : This revision was by author [[User:hstraub|hstraub]] and made on <tt>2015-12-10 02:57:37 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>569682457</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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html"><span style="display: block; text-align: right;"> | <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;white-space: pre-wrap ! important" class="old-revision-html"><span style="display: block; text-align: right;">[[xenharmonie/Reguläre Temperaturen|Deutsch]] - [[レギュラーテンペラメントとランクrテンペラメント|日本語]] | ||
</span> | </span> | ||
[[toc|flat]] | [[toc|flat]] | ||
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This tempers out the maja comma, 762939453125/753145430616. | This tempers out the maja comma, 762939453125/753145430616. | ||
===[[Pental family]]=== | ===[[Pental family]]=== | ||
The pental family tempers out the pental comma, 847288609443/838860800000 = |-28 25 -5>. | The pental family tempers out the pental comma, 847288609443/838860800000 = |-28 25 -5>. | ||
===[[Maquila family]]=== | ===[[Maquila family]]=== | ||
This tempers out the maquila comma, 562949953421312/556182861328125 = |49 -6 -17>. | This tempers out the maquila comma, 562949953421312/556182861328125 = |49 -6 -17>. | ||
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Hemimage temperaments temper out the hemimage comma, |5 -7 -1 3> = 10976/10935. | Hemimage temperaments temper out the hemimage comma, |5 -7 -1 3> = 10976/10935. | ||
===[[Cataharry temperaments]]=== | ===[[Cataharry temperaments]]=== | ||
Cataharry temperaments temper out the cataharry comma, |-4 9 -2 -2> = 19683/19600. | Cataharry temperaments temper out the cataharry comma, |-4 9 -2 -2> = 19683/19600. | ||
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These temper out the valinorsma, 176/175. | These temper out the valinorsma, 176/175. | ||
===[[Rastmic temperaments]]=== | ===[[Rastmic temperaments]]=== | ||
These temper out the rastma, 243/242. | These temper out the rastma, 243/242. | ||
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* [[@http://www.huygens-fokker.org/docs/lintemps.html|List of temperaments]] in [[@http://www.huygens-fokker.org/scala|Scala]] with ready to use values</pre></div> | * [[@http://www.huygens-fokker.org/docs/lintemps.html|List of temperaments]] in [[@http://www.huygens-fokker.org/scala|Scala]] with ready to use values</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><span style="display: block; text-align: right;"> | <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><span style="display: block; text-align: right;"><a class="wiki_link" href="http://xenharmonie.wikispaces.com/Regul%C3%A4re%20Temperaturen">Deutsch</a> - <a class="wiki_link" href="/%E3%83%AC%E3%82%AE%E3%83%A5%E3%83%A9%E3%83%BC%E3%83%86%E3%83%B3%E3%83%9A%E3%83%A9%E3%83%A1%E3%83%B3%E3%83%88%E3%81%A8%E3%83%A9%E3%83%B3%E3%82%AFr%E3%83%86%E3%83%B3%E3%83%9A%E3%83%A9%E3%83%A1%E3%83%B3%E3%83%88">日本語</a><br /> | ||
</span><br /> | </span><br /> | ||
<!-- ws:start:WikiTextTocRule:244:&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:244 --><!-- ws:start:WikiTextTocRule:245: --><a href="#Regular temperaments">Regular temperaments</a><!-- ws:end:WikiTextTocRule:245 --><!-- ws:start:WikiTextTocRule:246: --><!-- ws:end:WikiTextTocRule:246 --><!-- ws:start:WikiTextTocRule:247: --><!-- ws:end:WikiTextTocRule:247 --><!-- ws:start:WikiTextTocRule:248: --> | <a href="#Equal temperaments">Equal temperaments</a><!-- ws:end:WikiTextTocRule:248 --><!-- ws:start:WikiTextTocRule:249: --> | <a href="#Rank 2 (including &quot;linear&quot;) temperaments">Rank 2 (including &quot;linear&quot;) temperaments</a><!-- ws:end:WikiTextTocRule:249 --><!-- ws:start:WikiTextTocRule:250: --><!-- ws:end:WikiTextTocRule:250 --><!-- ws:start:WikiTextTocRule:251: --><!-- ws:end:WikiTextTocRule:251 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ws:end:WikiTextTocRule:292 --><!-- ws:start:WikiTextTocRule:293: --><!-- ws:end:WikiTextTocRule:293 --><!-- ws:start:WikiTextTocRule:294: --><!-- ws:end:WikiTextTocRule:294 --><!-- ws:start:WikiTextTocRule:295: --><!-- ws:end:WikiTextTocRule:295 --><!-- ws:start:WikiTextTocRule:296: --><!-- ws:end:WikiTextTocRule:296 --><!-- ws:start:WikiTextTocRule:297: --><!-- ws:end:WikiTextTocRule:297 --><!-- ws:start:WikiTextTocRule:298: --> | <a href="#Temperaments for a given comma">Temperaments for a given comma</a><!-- ws:end:WikiTextTocRule:298 --><!-- ws:start:WikiTextTocRule:299: --><!-- ws:end:WikiTextTocRule:299 --><!-- ws:start:WikiTextTocRule:300: --><!-- ws:end:WikiTextTocRule:300 --><!-- ws:start:WikiTextTocRule:301: --><!-- ws:end:WikiTextTocRule:301 --><!-- ws:start:WikiTextTocRule:302: --><!-- ws:end:WikiTextTocRule:302 --><!-- ws:start:WikiTextTocRule:303: --><!-- ws:end:WikiTextTocRule:303 --><!-- ws:start:WikiTextTocRule:304: --><!-- ws:end:WikiTextTocRule:304 --><!-- 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ws:end:WikiTextTocRule:358 --><!-- ws:start:WikiTextTocRule:359: --><!-- ws:end:WikiTextTocRule:359 --><!-- ws:start:WikiTextTocRule:360: --> | <a href="#Rank 4 temperaments">Rank 4 temperaments</a><!-- ws:end:WikiTextTocRule:360 --><!-- ws:start:WikiTextTocRule:361: --> | <a href="#Subgroup temperaments">Subgroup temperaments</a><!-- ws:end:WikiTextTocRule:361 --><!-- ws:start:WikiTextTocRule:362: --> | <a href="#Commatic realms">Commatic realms</a><!-- ws:end:WikiTextTocRule:362 --><!-- ws:start:WikiTextTocRule:363: --><!-- ws:end:WikiTextTocRule:363 --><!-- ws:start:WikiTextTocRule:364: --><!-- ws:end:WikiTextTocRule:364 --><!-- ws:start:WikiTextTocRule:365: --><!-- ws:end:WikiTextTocRule:365 --><!-- ws:start:WikiTextTocRule:366: --> | <a href="#Links">Links</a><!-- ws:end:WikiTextTocRule:366 --><!-- ws:start:WikiTextTocRule:367: --> | <!-- ws:start:WikiTextTocRule:244:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of 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ws:start:WikiTextTocRule:294: --><!-- ws:end:WikiTextTocRule:294 --><!-- ws:start:WikiTextTocRule:295: --><!-- ws:end:WikiTextTocRule:295 --><!-- ws:start:WikiTextTocRule:296: --><!-- ws:end:WikiTextTocRule:296 --><!-- ws:start:WikiTextTocRule:297: --><!-- ws:end:WikiTextTocRule:297 --><!-- ws:start:WikiTextTocRule:298: --> | <a href="#Temperaments for a given comma">Temperaments for a given comma</a><!-- ws:end:WikiTextTocRule:298 --><!-- ws:start:WikiTextTocRule:299: --><!-- ws:end:WikiTextTocRule:299 --><!-- ws:start:WikiTextTocRule:300: --><!-- ws:end:WikiTextTocRule:300 --><!-- ws:start:WikiTextTocRule:301: --><!-- ws:end:WikiTextTocRule:301 --><!-- ws:start:WikiTextTocRule:302: --><!-- ws:end:WikiTextTocRule:302 --><!-- ws:start:WikiTextTocRule:303: --><!-- ws:end:WikiTextTocRule:303 --><!-- ws:start:WikiTextTocRule:304: --><!-- ws:end:WikiTextTocRule:304 --><!-- ws:start:WikiTextTocRule:305: --><!-- ws:end:WikiTextTocRule:305 --><!-- ws:start:WikiTextTocRule:306: --><!-- ws:end:WikiTextTocRule:306 --><!-- ws:start:WikiTextTocRule:307: --><!-- ws:end:WikiTextTocRule:307 --><!-- ws:start:WikiTextTocRule:308: --><!-- ws:end:WikiTextTocRule:308 --><!-- ws:start:WikiTextTocRule:309: --><!-- ws:end:WikiTextTocRule:309 --><!-- ws:start:WikiTextTocRule:310: --><!-- ws:end:WikiTextTocRule:310 --><!-- ws:start:WikiTextTocRule:311: --><!-- ws:end:WikiTextTocRule:311 --><!-- ws:start:WikiTextTocRule:312: --><!-- ws:end:WikiTextTocRule:312 --><!-- ws:start:WikiTextTocRule:313: --><!-- ws:end:WikiTextTocRule:313 --><!-- ws:start:WikiTextTocRule:314: --><!-- ws:end:WikiTextTocRule:314 --><!-- ws:start:WikiTextTocRule:315: --><!-- ws:end:WikiTextTocRule:315 --><!-- ws:start:WikiTextTocRule:316: --><!-- ws:end:WikiTextTocRule:316 --><!-- ws:start:WikiTextTocRule:317: --><!-- ws:end:WikiTextTocRule:317 --><!-- ws:start:WikiTextTocRule:318: --><!-- ws:end:WikiTextTocRule:318 --><!-- ws:start:WikiTextTocRule:319: --><!-- ws:end:WikiTextTocRule:319 --><!-- ws:start:WikiTextTocRule:320: --><!-- ws:end:WikiTextTocRule:320 --><!-- ws:start:WikiTextTocRule:321: --><!-- ws:end:WikiTextTocRule:321 --><!-- ws:start:WikiTextTocRule:322: --><!-- ws:end:WikiTextTocRule:322 --><!-- ws:start:WikiTextTocRule:323: --><!-- ws:end:WikiTextTocRule:323 --><!-- ws:start:WikiTextTocRule:324: --> | <a href="#Rank 3 temperaments">Rank 3 temperaments</a><!-- ws:end:WikiTextTocRule:324 --><!-- ws:start:WikiTextTocRule:325: --><!-- ws:end:WikiTextTocRule:325 --><!-- ws:start:WikiTextTocRule:326: --><!-- ws:end:WikiTextTocRule:326 --><!-- ws:start:WikiTextTocRule:327: --><!-- ws:end:WikiTextTocRule:327 --><!-- ws:start:WikiTextTocRule:328: --><!-- ws:end:WikiTextTocRule:328 --><!-- ws:start:WikiTextTocRule:329: --><!-- ws:end:WikiTextTocRule:329 --><!-- ws:start:WikiTextTocRule:330: --><!-- ws:end:WikiTextTocRule:330 --><!-- ws:start:WikiTextTocRule:331: --><!-- ws:end:WikiTextTocRule:331 --><!-- ws:start:WikiTextTocRule:332: --><!-- ws:end:WikiTextTocRule:332 --><!-- ws:start:WikiTextTocRule:333: --><!-- ws:end:WikiTextTocRule:333 --><!-- ws:start:WikiTextTocRule:334: --><!-- ws:end:WikiTextTocRule:334 --><!-- ws:start:WikiTextTocRule:335: --><!-- ws:end:WikiTextTocRule:335 --><!-- ws:start:WikiTextTocRule:336: --><!-- ws:end:WikiTextTocRule:336 --><!-- ws:start:WikiTextTocRule:337: --><!-- ws:end:WikiTextTocRule:337 --><!-- ws:start:WikiTextTocRule:338: --><!-- ws:end:WikiTextTocRule:338 --><!-- ws:start:WikiTextTocRule:339: --><!-- ws:end:WikiTextTocRule:339 --><!-- ws:start:WikiTextTocRule:340: --><!-- ws:end:WikiTextTocRule:340 --><!-- ws:start:WikiTextTocRule:341: --><!-- ws:end:WikiTextTocRule:341 --><!-- ws:start:WikiTextTocRule:342: --><!-- ws:end:WikiTextTocRule:342 --><!-- ws:start:WikiTextTocRule:343: --><!-- ws:end:WikiTextTocRule:343 --><!-- ws:start:WikiTextTocRule:344: --><!-- ws:end:WikiTextTocRule:344 --><!-- ws:start:WikiTextTocRule:345: --><!-- ws:end:WikiTextTocRule:345 --><!-- ws:start:WikiTextTocRule:346: --><!-- ws:end:WikiTextTocRule:346 --><!-- ws:start:WikiTextTocRule:347: --><!-- ws:end:WikiTextTocRule:347 --><!-- ws:start:WikiTextTocRule:348: --><!-- ws:end:WikiTextTocRule:348 --><!-- ws:start:WikiTextTocRule:349: --><!-- ws:end:WikiTextTocRule:349 --><!-- ws:start:WikiTextTocRule:350: --><!-- ws:end:WikiTextTocRule:350 --><!-- ws:start:WikiTextTocRule:351: --><!-- ws:end:WikiTextTocRule:351 --><!-- ws:start:WikiTextTocRule:352: --><!-- ws:end:WikiTextTocRule:352 --><!-- ws:start:WikiTextTocRule:353: --><!-- ws:end:WikiTextTocRule:353 --><!-- ws:start:WikiTextTocRule:354: --><!-- ws:end:WikiTextTocRule:354 --><!-- ws:start:WikiTextTocRule:355: --><!-- ws:end:WikiTextTocRule:355 --><!-- ws:start:WikiTextTocRule:356: --><!-- ws:end:WikiTextTocRule:356 --><!-- ws:start:WikiTextTocRule:357: --><!-- ws:end:WikiTextTocRule:357 --><!-- ws:start:WikiTextTocRule:358: --><!-- ws:end:WikiTextTocRule:358 --><!-- ws:start:WikiTextTocRule:359: --><!-- ws:end:WikiTextTocRule:359 --><!-- ws:start:WikiTextTocRule:360: --> | <a href="#Rank 4 temperaments">Rank 4 temperaments</a><!-- ws:end:WikiTextTocRule:360 --><!-- ws:start:WikiTextTocRule:361: --> | <a href="#Subgroup temperaments">Subgroup temperaments</a><!-- ws:end:WikiTextTocRule:361 --><!-- ws:start:WikiTextTocRule:362: --> | <a href="#Commatic realms">Commatic realms</a><!-- ws:end:WikiTextTocRule:362 --><!-- ws:start:WikiTextTocRule:363: --><!-- ws:end:WikiTextTocRule:363 --><!-- ws:start:WikiTextTocRule:364: --><!-- ws:end:WikiTextTocRule:364 --><!-- ws:start:WikiTextTocRule:365: --><!-- ws:end:WikiTextTocRule:365 --><!-- ws:start:WikiTextTocRule:366: --> | <a href="#Links">Links</a><!-- ws:end:WikiTextTocRule:366 --><!-- ws:start:WikiTextTocRule:367: --> | ||
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<!-- ws:start:WikiTextHeadingRule:80:&lt;h3&gt; --><h3 id="toc40"><a name="Rank 2 (including &quot;linear&quot;) temperaments-Families-Pental family"></a><!-- ws:end:WikiTextHeadingRule:80 --><a class="wiki_link" href="/Pental%20family">Pental family</a></h3> | <!-- ws:start:WikiTextHeadingRule:80:&lt;h3&gt; --><h3 id="toc40"><a name="Rank 2 (including &quot;linear&quot;) temperaments-Families-Pental family"></a><!-- ws:end:WikiTextHeadingRule:80 --><a class="wiki_link" href="/Pental%20family">Pental family</a></h3> | ||
The pental family tempers out the pental comma, 847288609443/838860800000 = |-28 25 -5&gt;.<br /> | The pental family tempers out the pental comma, 847288609443/838860800000 = |-28 25 -5&gt;.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:82:&lt;h3&gt; --><h3 id="toc41"><a name="Rank 2 (including &quot;linear&quot;) temperaments-Families-Maquila family"></a><!-- ws:end:WikiTextHeadingRule:82 --><a class="wiki_link" href="/Maquila%20family">Maquila family</a></h3> | <!-- ws:start:WikiTextHeadingRule:82:&lt;h3&gt; --><h3 id="toc41"><a name="Rank 2 (including &quot;linear&quot;) temperaments-Families-Maquila family"></a><!-- ws:end:WikiTextHeadingRule:82 --><a class="wiki_link" href="/Maquila%20family">Maquila family</a></h3> | ||
This tempers out the maquila comma, 562949953421312/556182861328125 = |49 -6 -17&gt;.<br /> | This tempers out the maquila comma, 562949953421312/556182861328125 = |49 -6 -17&gt;.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:84:&lt;h3&gt; --><h3 id="toc42"><a name="Rank 2 (including &quot;linear&quot;) temperaments-Families-Mutt family"></a><!-- ws:end:WikiTextHeadingRule:84 --><a class="wiki_link" href="/Mutt%20family">Mutt family</a></h3> | <!-- ws:start:WikiTextHeadingRule:84:&lt;h3&gt; --><h3 id="toc42"><a name="Rank 2 (including &quot;linear&quot;) temperaments-Families-Mutt family"></a><!-- ws:end:WikiTextHeadingRule:84 --><a class="wiki_link" href="/Mutt%20family">Mutt family</a></h3> | ||
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<!-- ws:start:WikiTextHeadingRule:134:&lt;h3&gt; --><h3 id="toc67"><a name="Temperaments for a given comma--Cataharry temperaments"></a><!-- ws:end:WikiTextHeadingRule:134 --><a class="wiki_link" href="/Cataharry%20temperaments">Cataharry temperaments</a></h3> | <!-- ws:start:WikiTextHeadingRule:134:&lt;h3&gt; --><h3 id="toc67"><a name="Temperaments for a given comma--Cataharry temperaments"></a><!-- ws:end:WikiTextHeadingRule:134 --><a class="wiki_link" href="/Cataharry%20temperaments">Cataharry temperaments</a></h3> | ||
Cataharry temperaments temper out the cataharry comma, |-4 9 -2 -2&gt; = 19683/19600.<br /> | Cataharry temperaments temper out the cataharry comma, |-4 9 -2 -2&gt; = 19683/19600.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:136:&lt;h3&gt; --><h3 id="toc68"><a name="Temperaments for a given comma--Horwell temperaments"></a><!-- ws:end:WikiTextHeadingRule:136 --><a class="wiki_link" href="/Horwell%20temperaments">Horwell temperaments</a></h3> | <!-- ws:start:WikiTextHeadingRule:136:&lt;h3&gt; --><h3 id="toc68"><a name="Temperaments for a given comma--Horwell temperaments"></a><!-- ws:end:WikiTextHeadingRule:136 --><a class="wiki_link" href="/Horwell%20temperaments">Horwell temperaments</a></h3> | ||
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<!-- ws:start:WikiTextHeadingRule:220:&lt;h3&gt; --><h3 id="toc110"><a name="Rank 3 temperaments--Rastmic temperaments"></a><!-- ws:end:WikiTextHeadingRule:220 --><a class="wiki_link" href="/Rastmic%20temperaments">Rastmic temperaments</a></h3> | <!-- ws:start:WikiTextHeadingRule:220:&lt;h3&gt; --><h3 id="toc110"><a name="Rank 3 temperaments--Rastmic temperaments"></a><!-- ws:end:WikiTextHeadingRule:220 --><a class="wiki_link" href="/Rastmic%20temperaments">Rastmic temperaments</a></h3> | ||
These temper out the rastma, 243/242.<br /> | These temper out the rastma, 243/242.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:222:&lt;h3&gt; --><h3 id="toc111"><a name="Rank 3 temperaments--Werckismic temperaments"></a><!-- ws:end:WikiTextHeadingRule:222 --><a class="wiki_link" href="/Werckismic%20temperaments">Werckismic temperaments</a></h3> | <!-- ws:start:WikiTextHeadingRule:222:&lt;h3&gt; --><h3 id="toc111"><a name="Rank 3 temperaments--Werckismic temperaments"></a><!-- ws:end:WikiTextHeadingRule:222 --><a class="wiki_link" href="/Werckismic%20temperaments">Werckismic temperaments</a></h3> | ||