Marvel temperaments: Difference between revisions
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<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">[[toc]] | <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">[[toc]] | ||
This page discusses some of the temperaments tempering out |-5 2 2 -1> =[[225_224| 225/224]], the [[marvel | This page discusses some of the temperaments tempering out |-5 2 2 -1> =[[225_224| 225/224]], the [[Marvel family|marvel]] comma or septimal kleisma. These include negri, wizard, tritonic, septimin, slender, triton, merman and marvo. Considered elsewhere are [[Meantone family|meantone]], [[Miracle|miracle]], [[Magic family|magic]], [[Pajara|pajara]], [[Orwell|orwell]], [[Kleismic family|catakleismic]], [[Garibaldi temperament|garibaldi]], [[Augmented family|august]], [[Pythagorean family|compton]], sharp [where?], [[Escapade family|escapade]] and [[Pelogic family|mavila]]. | ||
Since (5/4)^2 = 225/224 * 14/9, these temperaments tend to have a relatively small complexity for 5/4. They also possess 5/4-9/7 versions of the augmented triad. Since this is a chord of meantone temperament in wide use in Western common practice harmony long before 12edo established itself as the standard tuning, it is arguably more authentic to tune it as two stacked major thirds and a diminished fourth, which is what it is in meantone, than as the modern version of three stacked very sharp major thirds. | Since (5/4)^2 = 225/224 * 14/9, these temperaments tend to have a relatively small complexity for 5/4. They also possess 5/4-9/7 versions of the augmented triad. Since this is a chord of meantone temperament in wide use in Western common practice harmony long before 12edo established itself as the standard tuning, it is arguably more authentic to tune it as two stacked major thirds and a diminished fourth, which is what it is in meantone, than as the modern version of three stacked very sharp major thirds. | ||
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Badness: 0.0353 | Badness: 0.0353 | ||
==13-limit== | ==13-limit== | ||
Commas: 49/48, 55/54, 65/64, 91/90 | Commas: 49/48, 55/54, 65/64, 91/90 | ||
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<!-- ws:end:WikiTextTocRule:170 --><!-- ws:start:WikiTextTocRule:171: --><div style="margin-left: 2em;"><a href="#Alphorn-11-limit">11-limit</a></div> | <!-- ws:end:WikiTextTocRule:170 --><!-- ws:start:WikiTextTocRule:171: --><div style="margin-left: 2em;"><a href="#Alphorn-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule:171 --><!-- ws:start:WikiTextTocRule:172: --></div> | <!-- ws:end:WikiTextTocRule:171 --><!-- ws:start:WikiTextTocRule:172: --></div> | ||
<!-- ws:end:WikiTextTocRule:172 -->This page discusses some of the temperaments tempering out |-5 2 2 -1&gt; =<a class="wiki_link" href="/225_224"> 225/224</a>, the <a class="wiki_link" href="/ | <!-- ws:end:WikiTextTocRule:172 -->This page discusses some of the temperaments tempering out |-5 2 2 -1&gt; =<a class="wiki_link" href="/225_224"> 225/224</a>, the <a class="wiki_link" href="/Marvel%20family">marvel</a> comma or septimal kleisma. These include negri, wizard, tritonic, septimin, slender, triton, merman and marvo. Considered elsewhere are <a class="wiki_link" href="/Meantone%20family">meantone</a>, <a class="wiki_link" href="/Miracle">miracle</a>, <a class="wiki_link" href="/Magic%20family">magic</a>, <a class="wiki_link" href="/Pajara">pajara</a>, <a class="wiki_link" href="/Orwell">orwell</a>, <a class="wiki_link" href="/Kleismic%20family">catakleismic</a>, <a class="wiki_link" href="/Garibaldi%20temperament">garibaldi</a>, <a class="wiki_link" href="/Augmented%20family">august</a>, <a class="wiki_link" href="/Pythagorean%20family">compton</a>, sharp [where?], <a class="wiki_link" href="/Escapade%20family">escapade</a> and <a class="wiki_link" href="/Pelogic%20family">mavila</a>.<br /> | ||
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Since (5/4)^2 = 225/224 * 14/9, these temperaments tend to have a relatively small complexity for 5/4. They also possess 5/4-9/7 versions of the augmented triad. Since this is a chord of meantone temperament in wide use in Western common practice harmony long before 12edo established itself as the standard tuning, it is arguably more authentic to tune it as two stacked major thirds and a diminished fourth, which is what it is in meantone, than as the modern version of three stacked very sharp major thirds.<br /> | Since (5/4)^2 = 225/224 * 14/9, these temperaments tend to have a relatively small complexity for 5/4. They also possess 5/4-9/7 versions of the augmented triad. Since this is a chord of meantone temperament in wide use in Western common practice harmony long before 12edo established itself as the standard tuning, it is arguably more authentic to tune it as two stacked major thirds and a diminished fourth, which is what it is in meantone, than as the modern version of three stacked very sharp major thirds.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="Negroni-13-limit"></a><!-- ws:end:WikiTextHeadingRule:16 -->13-limit</h2> | <!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="Negroni-13-limit"></a><!-- ws:end:WikiTextHeadingRule:16 -->13-limit</h2> | ||
Commas: 49/48, 55/54, 65/64, 91/90<br /> | Commas: 49/48, 55/54, 65/64, 91/90<br /> | ||
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POTE generator: ~15/14 = 124.545<br /> | POTE generator: ~15/14 = 124.545<br /> | ||