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Wikispaces>genewardsmith **Imported revision 203968408 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 213446802 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-23 22:40:03 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>213446802</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">This page discusses some of the temperaments tempering out 225/224, the marvel comma or septimal kleisma. These include negri, wizard, tritonic, septimin, slender, triton and marvo. Considered elsewhere are meantone, miracle, magic, pajara, orwell, catakleismic, garibaldi, august, compton, sharp, escapade and mavila. | <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|flat]] | ||
This page discusses some of the temperaments tempering out 225/224, the marvel comma or septimal kleisma. These include negri, wizard, tritonic, septimin, slender, triton and marvo. Considered elsewhere are meantone, miracle, magic, pajara, orwell, catakleismic, garibaldi, august, compton, sharp, escapade and mavila. | |||
Since (5/4)^3 = 225/224 * 14/9, these temperaments tend to have a relatively small complexity for 5/4. They also possess 5/4-5/4-9/7 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)^3 = 225/224 * 14/9, these temperaments tend to have a relatively small complexity for 5/4. They also possess 5/4-5/4-9/7 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. | ||
=Negri= | |||
Commas: 49/48, 225/224 | Commas: 49/48, 225/224 | ||
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EDOs: 9, 10, 19, 86 | EDOs: 9, 10, 19, 86 | ||
==11-limit== | |||
Commas: 45/44, 49/48, 56/55 | Commas: 45/44, 49/48, 56/55 | ||
| Line 27: | Line 29: | ||
EDOs: 9, 10, 19 | EDOs: 9, 10, 19 | ||
==13-limit== | |||
Commas: 45/44, 49/48, 56/55, 78/77 | Commas: 45/44, 49/48, 56/55, 78/77 | ||
| Line 35: | Line 37: | ||
EDOs: 9, 10, 19 | EDOs: 9, 10, 19 | ||
=Negric= | |||
Commas: 33/32, 49/48, 77/75 | Commas: 33/32, 49/48, 77/75 | ||
| Line 45: | Line 46: | ||
Badness: 0.0306 | Badness: 0.0306 | ||
==13-limit== | |||
Commas: 33/32, 49/48, 65/64, 91/90 | Commas: 33/32, 49/48, 65/64, 91/90 | ||
| Line 54: | Line 55: | ||
Badness: 0.0202 | Badness: 0.0202 | ||
=Wizard= | |||
Commas: 225/224, 118098/117649 | Commas: 225/224, 118098/117649 | ||
| Line 63: | Line 64: | ||
EDOs: 22, 50, 72, 382, 454 | EDOs: 22, 50, 72, 382, 454 | ||
==11-limit== | |||
Commas: 225/224, 385/384, 4000/3993 | Commas: 225/224, 385/384, 4000/3993 | ||
| Line 71: | Line 72: | ||
EDOs: 22, 50, 72, 166, 310 | EDOs: 22, 50, 72, 166, 310 | ||
==13-limit== | |||
Commas: 225/224, 351/350, 364/363, 385/384 | Commas: 225/224, 351/350, 364/363, 385/384 | ||
| Line 79: | Line 80: | ||
EDOs: 22, 50, 72 | EDOs: 22, 50, 72 | ||
==17-limit== | |||
Commas: 221/220, 273/272, 289/288, 351/350, 375/374 | Commas: 221/220, 273/272, 289/288, 351/350, 375/374 | ||
| Line 87: | Line 88: | ||
EDOs: 22, 50, 72 | EDOs: 22, 50, 72 | ||
==19-limit== | |||
Commas: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342 | Commas: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342 | ||
| Line 95: | Line 96: | ||
EDOs: 22, 50, 72, 194, 460 | EDOs: 22, 50, 72, 194, 460 | ||
=Tritonic= | |||
Commas: 225/224, 50421/50000 | Commas: 225/224, 50421/50000 | ||
| Line 104: | Line 105: | ||
EDOs: 29, 31, 60, 91, 122, 213 | EDOs: 29, 31, 60, 91, 122, 213 | ||
==11-limit== | |||
Commas: 225/224, 385/384, 27783/27500 | Commas: 225/224, 385/384, 27783/27500 | ||
| Line 112: | Line 113: | ||
EDOs: 29, 31, 60, 91, 122, 153 | EDOs: 29, 31, 60, 91, 122, 153 | ||
=Septimin= | |||
Commas: 225/224, 84035/82944 | Commas: 225/224, 84035/82944 | ||
| Line 121: | Line 122: | ||
EDOs: 9, 32, 41, 91, 132 | EDOs: 9, 32, 41, 91, 132 | ||
==11-limit== | |||
Commas: 225/224, 385/384, 2401/2376 | Commas: 225/224, 385/384, 2401/2376 | ||
| Line 129: | Line 130: | ||
EDOs: 9, 32, 41, 91 | EDOs: 9, 32, 41, 91 | ||
==13-limit== | |||
Commas: 105/104, 144/143, 196/195, 245/242 | Commas: 105/104, 144/143, 196/195, 245/242 | ||
| Line 137: | Line 138: | ||
EDOs: 9, 41, 91 | EDOs: 9, 41, 91 | ||
=Slender= | |||
Commas: 225/225, 589824/588245 | Commas: 225/225, 589824/588245 | ||
| Line 146: | Line 147: | ||
EDOs: 31, 94, 125 | EDOs: 31, 94, 125 | ||
==11-limit== | |||
Commas: 225/224, 385/384, 1331/1323 | Commas: 225/224, 385/384, 1331/1323 | ||
| Line 154: | Line 155: | ||
EDOs: 31, 63, 94, 125 | EDOs: 31, 63, 94, 125 | ||
=Triton= | |||
Commas: 225/224, 1029/1000 | Commas: 225/224, 1029/1000 | ||
| Line 163: | Line 164: | ||
EDOs: 19, 135, 289 | EDOs: 19, 135, 289 | ||
=Marvo= | |||
Commas: 225/224, 78125000/78121827 | Commas: 225/224, 78125000/78121827 | ||
| Line 172: | Line 173: | ||
EDOs: 65, 72 | EDOs: 65, 72 | ||
==11-limit== | |||
Commas: 225/224, 243/242, 4000/3993 | Commas: 225/224, 243/242, 4000/3993 | ||
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EDOs: 65, 72, 281, 497</pre></div> | EDOs: 65, 72, 281, 497</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>Marvel temperaments</title></head><body>This page discusses some of the temperaments tempering out 225/224, the marvel comma or septimal kleisma. These include negri, wizard, tritonic, septimin, slender, triton and marvo. Considered elsewhere are meantone, miracle, magic, pajara, orwell, catakleismic, garibaldi, august, compton, sharp, escapade and mavila.<br /> | <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>Marvel temperaments</title></head><body><!-- ws:start:WikiTextTocRule:40:&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:40 --><!-- ws:start:WikiTextTocRule:41: --><a href="#Negri">Negri</a><!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --><!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --><!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextTocRule:44: --> | <a href="#Negric">Negric</a><!-- ws:end:WikiTextTocRule:44 --><!-- ws:start:WikiTextTocRule:45: --><!-- ws:end:WikiTextTocRule:45 --><!-- ws:start:WikiTextTocRule:46: --> | <a href="#Wizard">Wizard</a><!-- ws:end:WikiTextTocRule:46 --><!-- ws:start:WikiTextTocRule:47: --><!-- ws:end:WikiTextTocRule:47 --><!-- ws:start:WikiTextTocRule:48: --><!-- ws:end:WikiTextTocRule:48 --><!-- ws:start:WikiTextTocRule:49: --><!-- ws:end:WikiTextTocRule:49 --><!-- ws:start:WikiTextTocRule:50: --><!-- ws:end:WikiTextTocRule:50 --><!-- ws:start:WikiTextTocRule:51: --> | <a href="#Tritonic">Tritonic</a><!-- ws:end:WikiTextTocRule:51 --><!-- ws:start:WikiTextTocRule:52: --><!-- ws:end:WikiTextTocRule:52 --><!-- ws:start:WikiTextTocRule:53: --> | <a href="#Septimin">Septimin</a><!-- ws:end:WikiTextTocRule:53 --><!-- ws:start:WikiTextTocRule:54: --><!-- ws:end:WikiTextTocRule:54 --><!-- ws:start:WikiTextTocRule:55: --><!-- ws:end:WikiTextTocRule:55 --><!-- ws:start:WikiTextTocRule:56: --> | <a href="#Slender">Slender</a><!-- ws:end:WikiTextTocRule:56 --><!-- ws:start:WikiTextTocRule:57: --><!-- ws:end:WikiTextTocRule:57 --><!-- ws:start:WikiTextTocRule:58: --> | <a href="#Triton">Triton</a><!-- ws:end:WikiTextTocRule:58 --><!-- ws:start:WikiTextTocRule:59: --> | <a href="#Marvo">Marvo</a><!-- ws:end:WikiTextTocRule:59 --><!-- ws:start:WikiTextTocRule:60: --><!-- ws:end:WikiTextTocRule:60 --><!-- ws:start:WikiTextTocRule:61: --> | ||
<!-- ws:end:WikiTextTocRule:61 --><br /> | |||
This page discusses some of the temperaments tempering out 225/224, the marvel comma or septimal kleisma. These include negri, wizard, tritonic, septimin, slender, triton and marvo. Considered elsewhere are meantone, miracle, magic, pajara, orwell, catakleismic, garibaldi, august, compton, sharp, escapade and mavila.<br /> | |||
<br /> | <br /> | ||
Since (5/4)^3 = 225/224 * 14/9, these temperaments tend to have a relatively small complexity for 5/4. They also possess 5/4-5/4-9/7 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)^3 = 225/224 * 14/9, these temperaments tend to have a relatively small complexity for 5/4. They also possess 5/4-5/4-9/7 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 /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt; | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Negri"></a><!-- ws:end:WikiTextHeadingRule:0 -->Negri</h1> | ||
Commas: 49/48, 225/224<br /> | Commas: 49/48, 225/224<br /> | ||
<br /> | <br /> | ||
| Line 193: | Line 196: | ||
EDOs: 9, 10, 19, 86<br /> | EDOs: 9, 10, 19, 86<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt; | <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="Negri-11-limit"></a><!-- ws:end:WikiTextHeadingRule:2 -->11-limit</h2> | ||
Commas: 45/44, 49/48, 56/55<br /> | Commas: 45/44, 49/48, 56/55<br /> | ||
<br /> | <br /> | ||
| Line 201: | Line 204: | ||
EDOs: 9, 10, 19<br /> | EDOs: 9, 10, 19<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt; | <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Negri-13-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->13-limit</h2> | ||
Commas: 45/44, 49/48, 56/55, 78/77<br /> | Commas: 45/44, 49/48, 56/55, 78/77<br /> | ||
<br /> | <br /> | ||
| Line 209: | Line 212: | ||
EDOs: 9, 10, 19<br /> | EDOs: 9, 10, 19<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:6:&lt; | <!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Negric"></a><!-- ws:end:WikiTextHeadingRule:6 -->Negric</h1> | ||
Commas: 33/32, 49/48, 77/75<br /> | Commas: 33/32, 49/48, 77/75<br /> | ||
<br /> | <br /> | ||
| Line 219: | Line 221: | ||
Badness: 0.0306<br /> | Badness: 0.0306<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Negric-13-limit"></a><!-- ws:end:WikiTextHeadingRule:8 -->13-limit</h2> | ||
Commas: 33/32, 49/48, 65/64, 91/90<br /> | Commas: 33/32, 49/48, 65/64, 91/90<br /> | ||
<br /> | <br /> | ||
| Line 228: | Line 230: | ||
Badness: 0.0202<br /> | Badness: 0.0202<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="Wizard"></a><!-- ws:end:WikiTextHeadingRule:10 -->Wizard</h1> | ||
Commas: 225/224, 118098/117649<br /> | Commas: 225/224, 118098/117649<br /> | ||
<br /> | <br /> | ||
| Line 237: | Line 239: | ||
EDOs: 22, 50, 72, 382, 454<br /> | EDOs: 22, 50, 72, 382, 454<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Wizard-11-limit"></a><!-- ws:end:WikiTextHeadingRule:12 -->11-limit</h2> | ||
Commas: 225/224, 385/384, 4000/3993<br /> | Commas: 225/224, 385/384, 4000/3993<br /> | ||
<br /> | <br /> | ||
| Line 245: | Line 247: | ||
EDOs: 22, 50, 72, 166, 310<br /> | EDOs: 22, 50, 72, 166, 310<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="Wizard-13-limit"></a><!-- ws:end:WikiTextHeadingRule:14 -->13-limit</h2> | ||
Commas: 225/224, 351/350, 364/363, 385/384<br /> | Commas: 225/224, 351/350, 364/363, 385/384<br /> | ||
<br /> | <br /> | ||
| Line 253: | Line 255: | ||
EDOs: 22, 50, 72<br /> | EDOs: 22, 50, 72<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="Wizard-17-limit"></a><!-- ws:end:WikiTextHeadingRule:16 -->17-limit</h2> | ||
Commas: 221/220, 273/272, 289/288, 351/350, 375/374<br /> | Commas: 221/220, 273/272, 289/288, 351/350, 375/374<br /> | ||
<br /> | <br /> | ||
| Line 261: | Line 263: | ||
EDOs: 22, 50, 72<br /> | EDOs: 22, 50, 72<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="Wizard-19-limit"></a><!-- ws:end:WikiTextHeadingRule:18 -->19-limit</h2> | ||
Commas: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342<br /> | Commas: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342<br /> | ||
<br /> | <br /> | ||
| Line 269: | Line 271: | ||
EDOs: 22, 50, 72, 194, 460<br /> | EDOs: 22, 50, 72, 194, 460<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc10"><a name="Tritonic"></a><!-- ws:end:WikiTextHeadingRule:20 -->Tritonic</h1> | ||
Commas: 225/224, 50421/50000<br /> | Commas: 225/224, 50421/50000<br /> | ||
<br /> | <br /> | ||
| Line 278: | Line 280: | ||
EDOs: 29, 31, 60, 91, 122, 213<br /> | EDOs: 29, 31, 60, 91, 122, 213<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:22:&lt;h2&gt; --><h2 id="toc11"><a name="Tritonic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:22 -->11-limit</h2> | ||
Commas: 225/224, 385/384, 27783/27500<br /> | Commas: 225/224, 385/384, 27783/27500<br /> | ||
<br /> | <br /> | ||
| Line 286: | Line 288: | ||
EDOs: 29, 31, 60, 91, 122, 153<br /> | EDOs: 29, 31, 60, 91, 122, 153<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:24:&lt;h1&gt; --><h1 id="toc12"><a name="Septimin"></a><!-- ws:end:WikiTextHeadingRule:24 -->Septimin</h1> | ||
Commas: 225/224, 84035/82944<br /> | Commas: 225/224, 84035/82944<br /> | ||
<br /> | <br /> | ||
| Line 295: | Line 297: | ||
EDOs: 9, 32, 41, 91, 132<br /> | EDOs: 9, 32, 41, 91, 132<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:26:&lt;h2&gt; --><h2 id="toc13"><a name="Septimin-11-limit"></a><!-- ws:end:WikiTextHeadingRule:26 -->11-limit</h2> | ||
Commas: 225/224, 385/384, 2401/2376<br /> | Commas: 225/224, 385/384, 2401/2376<br /> | ||
<br /> | <br /> | ||
| Line 303: | Line 305: | ||
EDOs: 9, 32, 41, 91<br /> | EDOs: 9, 32, 41, 91<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:28:&lt;h2&gt; --><h2 id="toc14"><a name="Septimin-13-limit"></a><!-- ws:end:WikiTextHeadingRule:28 -->13-limit</h2> | ||
Commas: 105/104, 144/143, 196/195, 245/242<br /> | Commas: 105/104, 144/143, 196/195, 245/242<br /> | ||
<br /> | <br /> | ||
| Line 311: | Line 313: | ||
EDOs: 9, 41, 91<br /> | EDOs: 9, 41, 91<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:30:&lt;h1&gt; --><h1 id="toc15"><a name="Slender"></a><!-- ws:end:WikiTextHeadingRule:30 -->Slender</h1> | ||
Commas: 225/225, 589824/588245<br /> | Commas: 225/225, 589824/588245<br /> | ||
<br /> | <br /> | ||
| Line 320: | Line 322: | ||
EDOs: 31, 94, 125<br /> | EDOs: 31, 94, 125<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:32:&lt;h2&gt; --><h2 id="toc16"><a name="Slender-11-limit"></a><!-- ws:end:WikiTextHeadingRule:32 -->11-limit</h2> | ||
Commas: 225/224, 385/384, 1331/1323<br /> | Commas: 225/224, 385/384, 1331/1323<br /> | ||
<br /> | <br /> | ||
| Line 328: | Line 330: | ||
EDOs: 31, 63, 94, 125<br /> | EDOs: 31, 63, 94, 125<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:34:&lt;h1&gt; --><h1 id="toc17"><a name="Triton"></a><!-- ws:end:WikiTextHeadingRule:34 -->Triton</h1> | ||
Commas: 225/224, 1029/1000<br /> | Commas: 225/224, 1029/1000<br /> | ||
<br /> | <br /> | ||
| Line 337: | Line 339: | ||
EDOs: 19, 135, 289<br /> | EDOs: 19, 135, 289<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:36:&lt;h1&gt; --><h1 id="toc18"><a name="Marvo"></a><!-- ws:end:WikiTextHeadingRule:36 -->Marvo</h1> | ||
Commas: 225/224, 78125000/78121827<br /> | Commas: 225/224, 78125000/78121827<br /> | ||
<br /> | <br /> | ||
| Line 346: | Line 348: | ||
EDOs: 65, 72<br /> | EDOs: 65, 72<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:38:&lt;h2&gt; --><h2 id="toc19"><a name="Marvo-11-limit"></a><!-- ws:end:WikiTextHeadingRule:38 -->11-limit</h2> | ||
Commas: 225/224, 243/242, 4000/3993<br /> | Commas: 225/224, 243/242, 4000/3993<br /> | ||
<br /> | <br /> | ||
Revision as of 22:40, 23 March 2011
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author genewardsmith and made on 2011-03-23 22:40:03 UTC.
- The original revision id was 213446802.
- The revision comment was:
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[[toc|flat]] This page discusses some of the temperaments tempering out 225/224, the marvel comma or septimal kleisma. These include negri, wizard, tritonic, septimin, slender, triton and marvo. Considered elsewhere are meantone, miracle, magic, pajara, orwell, catakleismic, garibaldi, august, compton, sharp, escapade and mavila. Since (5/4)^3 = 225/224 * 14/9, these temperaments tend to have a relatively small complexity for 5/4. They also possess 5/4-5/4-9/7 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. =Negri= Commas: 49/48, 225/224 [[POTE tuning|POTE temperament]]: 125.608 Map: [<1 2 2 3|, <0 -4 3 -2|] Wedgie: <<4 -3 2 -14 -8 13|| EDOs: 9, 10, 19, 86 ==11-limit== Commas: 45/44, 49/48, 56/55 [[POTE tuning|POTE temperament]]: 126.474 Map: [<1 2 2 3 4|, <0 -4 3 -2 -5|] EDOs: 9, 10, 19 ==13-limit== Commas: 45/44, 49/48, 56/55, 78/77 [[POTE tuning|POTE generator]]: 126.431 Map: [<1 2 2 3 4 4|, <0 -4 3 -2 -5 -3|] EDOs: 9, 10, 19 =Negric= Commas: 33/32, 49/48, 77/75 POTE generator: ~15/14 = 127.039 Map: [<1 2 2 3 3|, <0 -4 3 -2 4|] EDOs: 9, 19, 85 Badness: 0.0306 ==13-limit== Commas: 33/32, 49/48, 65/64, 91/90 POTE generator: ~15/14 = 127.039 Map: [<1 2 2 3 3 4|, <0 -4 3 -2 4 -3|] EDOs: 9, 19, 85 Badness: 0.0202 =Wizard= Commas: 225/224, 118098/117649 [[POTE tuning|POTE temperament]]: 383.256 Map: [<2 1 5 2|, <0 6 -1 10|] Wedgie: <<12 -2 20 -31 -2 52|| EDOs: 22, 50, 72, 382, 454 ==11-limit== Commas: 225/224, 385/384, 4000/3993 [[POTE tuning|POTE temperament]]: 383.232 Map: [<2 1 5 2 8|, <0 6 -1 10 -3|] EDOs: 22, 50, 72, 166, 310 ==13-limit== Commas: 225/224, 351/350, 364/363, 385/384 [[POTE tuning|POTE temperament]]: 383.389 Map: [<2 1 5 2 8 11|, <0 6 -1 10 -3 -10|] EDOs: 22, 50, 72 ==17-limit== Commas: 221/220, 273/272, 289/288, 351/350, 375/374 [[POTE tuning|POTE temperament]]: 383.381 Map: [<2 1 5 2 8 11 6|, <0 6 -1 10 -3 -10 6|] EDOs: 22, 50, 72 ==19-limit== Commas: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342 [[POTE tuning|POTE temperament]]: 383.477 Map: [<2 1 5 2 8 11 6 2|, <0 6 -1 10 -3 -10 6 18|] EDOs: 22, 50, 72, 194, 460 =Tritonic= Commas: 225/224, 50421/50000 [[POTE tuning|POTE temperament]]: 580.286 Map: [<1 4 -3 -3|, <0 -5 11 12|] Wedgie: <<5 -11 -12 -29 -33 3|| EDOs: 29, 31, 60, 91, 122, 213 ==11-limit== Commas: 225/224, 385/384, 27783/27500 [[POTE tuning|POTE temperament]]: 580.389 Map: [<1 4 -3 -3 17|, <0 -5 11 12 -28|] EDOs: 29, 31, 60, 91, 122, 153 =Septimin= Commas: 225/224, 84035/82944 [[POTE tuning|POTE temperament]]: 263.632 Map: [<1 4 1 5|, <0 -11 6 -10|] Wedgie: <<11 -6 10 -35 -15 40|| EDOs: 9, 32, 41, 91, 132 ==11-limit== Commas: 225/224, 385/384, 2401/2376 [[POTE tuning|POTE temperament]]: 263.634 Map: [<1 4 1 5 5|, <0 -11 6 -10 -7|] EDOs: 9, 32, 41, 91 ==13-limit== Commas: 105/104, 144/143, 196/195, 245/242 [[POTE tuning|POTE temperament]]: 263.700 Map: [<1 4 1 5 5 7|, <0 -11 6 -10 -7 -15|] EDOs: 9, 41, 91 =Slender= Commas: 225/225, 589824/588245 [[POTE tuning|POTE temperament]]: (~49/48) 38.413 Map: [<1 2 2 3|, <0 -13 10 -6|] Wedgie: <<13 -10 6 -46 -27 42|| EDOs: 31, 94, 125 ==11-limit== Commas: 225/224, 385/384, 1331/1323 [[POTE tuning|POTE temperament]]: 38.387 Map: [<1 2 2 3 4|, <0 -13 10 -6 -17|] EDOs: 31, 63, 94, 125 =Triton= Commas: 225/224, 1029/1000 [[POTE tuning|POTE temperament]]: 568.865 Map: [<1 0 6 7|, <0 3 -7 -8|] Wedgie: <<3 -7 -8 -18 -21 1|| EDOs: 19, 135, 289 =Marvo= Commas: 225/224, 78125000/78121827 [[POTE tuning|POTE temperament]]: (~27/20) 516.694 Map: [<1 5 12 29|, <0 -6 -17 -46|] Wedgie: <<6, 17, 46, 13, 56 59|| EDOs: 65, 72 ==11-limit== Commas: 225/224, 243/242, 4000/3993 [[POTE tuning|POTE temperament]]: 516.699 Map: [<1 5 12 29 12|, <0 -6 -17 -46 -15|] EDOs: 65, 72, 281, 497
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<html><head><title>Marvel temperaments</title></head><body><!-- ws:start:WikiTextTocRule:40:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextTocRule:41: --><a href="#Negri">Negri</a><!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --><!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --><!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextTocRule:44: --> | <a href="#Negric">Negric</a><!-- ws:end:WikiTextTocRule:44 --><!-- ws:start:WikiTextTocRule:45: --><!-- ws:end:WikiTextTocRule:45 --><!-- ws:start:WikiTextTocRule:46: --> | <a href="#Wizard">Wizard</a><!-- ws:end:WikiTextTocRule:46 --><!-- ws:start:WikiTextTocRule:47: --><!-- ws:end:WikiTextTocRule:47 --><!-- ws:start:WikiTextTocRule:48: --><!-- ws:end:WikiTextTocRule:48 --><!-- ws:start:WikiTextTocRule:49: --><!-- ws:end:WikiTextTocRule:49 --><!-- ws:start:WikiTextTocRule:50: --><!-- ws:end:WikiTextTocRule:50 --><!-- ws:start:WikiTextTocRule:51: --> | <a href="#Tritonic">Tritonic</a><!-- ws:end:WikiTextTocRule:51 --><!-- ws:start:WikiTextTocRule:52: --><!-- ws:end:WikiTextTocRule:52 --><!-- ws:start:WikiTextTocRule:53: --> | <a href="#Septimin">Septimin</a><!-- ws:end:WikiTextTocRule:53 --><!-- ws:start:WikiTextTocRule:54: --><!-- ws:end:WikiTextTocRule:54 --><!-- ws:start:WikiTextTocRule:55: --><!-- ws:end:WikiTextTocRule:55 --><!-- ws:start:WikiTextTocRule:56: --> | <a href="#Slender">Slender</a><!-- ws:end:WikiTextTocRule:56 --><!-- ws:start:WikiTextTocRule:57: --><!-- ws:end:WikiTextTocRule:57 --><!-- ws:start:WikiTextTocRule:58: --> | <a href="#Triton">Triton</a><!-- ws:end:WikiTextTocRule:58 --><!-- ws:start:WikiTextTocRule:59: --> | <a href="#Marvo">Marvo</a><!-- ws:end:WikiTextTocRule:59 --><!-- ws:start:WikiTextTocRule:60: --><!-- ws:end:WikiTextTocRule:60 --><!-- ws:start:WikiTextTocRule:61: --> <!-- ws:end:WikiTextTocRule:61 --><br /> This page discusses some of the temperaments tempering out 225/224, the marvel comma or septimal kleisma. These include negri, wizard, tritonic, septimin, slender, triton and marvo. Considered elsewhere are meantone, miracle, magic, pajara, orwell, catakleismic, garibaldi, august, compton, sharp, escapade and mavila.<br /> <br /> Since (5/4)^3 = 225/224 * 14/9, these temperaments tend to have a relatively small complexity for 5/4. They also possess 5/4-5/4-9/7 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 /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Negri"></a><!-- ws:end:WikiTextHeadingRule:0 -->Negri</h1> Commas: 49/48, 225/224<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 125.608<br /> <br /> Map: [<1 2 2 3|, <0 -4 3 -2|]<br /> Wedgie: <<4 -3 2 -14 -8 13||<br /> EDOs: 9, 10, 19, 86<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h2> --><h2 id="toc1"><a name="Negri-11-limit"></a><!-- ws:end:WikiTextHeadingRule:2 -->11-limit</h2> Commas: 45/44, 49/48, 56/55<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 126.474<br /> <br /> Map: [<1 2 2 3 4|, <0 -4 3 -2 -5|]<br /> EDOs: 9, 10, 19<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="Negri-13-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->13-limit</h2> Commas: 45/44, 49/48, 56/55, 78/77<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 126.431<br /> <br /> Map: [<1 2 2 3 4 4|, <0 -4 3 -2 -5 -3|]<br /> EDOs: 9, 10, 19<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h1> --><h1 id="toc3"><a name="Negric"></a><!-- ws:end:WikiTextHeadingRule:6 -->Negric</h1> Commas: 33/32, 49/48, 77/75<br /> <br /> POTE generator: ~15/14 = 127.039<br /> <br /> Map: [<1 2 2 3 3|, <0 -4 3 -2 4|]<br /> EDOs: 9, 19, 85<br /> Badness: 0.0306<br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h2> --><h2 id="toc4"><a name="Negric-13-limit"></a><!-- ws:end:WikiTextHeadingRule:8 -->13-limit</h2> Commas: 33/32, 49/48, 65/64, 91/90<br /> <br /> POTE generator: ~15/14 = 127.039<br /> <br /> Map: [<1 2 2 3 3 4|, <0 -4 3 -2 4 -3|]<br /> EDOs: 9, 19, 85<br /> Badness: 0.0202<br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h1> --><h1 id="toc5"><a name="Wizard"></a><!-- ws:end:WikiTextHeadingRule:10 -->Wizard</h1> Commas: 225/224, 118098/117649<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 383.256<br /> <br /> Map: [<2 1 5 2|, <0 6 -1 10|]<br /> Wedgie: <<12 -2 20 -31 -2 52||<br /> EDOs: 22, 50, 72, 382, 454<br /> <br /> <!-- ws:start:WikiTextHeadingRule:12:<h2> --><h2 id="toc6"><a name="Wizard-11-limit"></a><!-- ws:end:WikiTextHeadingRule:12 -->11-limit</h2> Commas: 225/224, 385/384, 4000/3993<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 383.232<br /> <br /> Map: [<2 1 5 2 8|, <0 6 -1 10 -3|]<br /> EDOs: 22, 50, 72, 166, 310<br /> <br /> <!-- ws:start:WikiTextHeadingRule:14:<h2> --><h2 id="toc7"><a name="Wizard-13-limit"></a><!-- ws:end:WikiTextHeadingRule:14 -->13-limit</h2> Commas: 225/224, 351/350, 364/363, 385/384<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 383.389<br /> <br /> Map: [<2 1 5 2 8 11|, <0 6 -1 10 -3 -10|]<br /> EDOs: 22, 50, 72<br /> <br /> <!-- ws:start:WikiTextHeadingRule:16:<h2> --><h2 id="toc8"><a name="Wizard-17-limit"></a><!-- ws:end:WikiTextHeadingRule:16 -->17-limit</h2> Commas: 221/220, 273/272, 289/288, 351/350, 375/374<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 383.381<br /> <br /> Map: [<2 1 5 2 8 11 6|, <0 6 -1 10 -3 -10 6|]<br /> EDOs: 22, 50, 72<br /> <br /> <!-- ws:start:WikiTextHeadingRule:18:<h2> --><h2 id="toc9"><a name="Wizard-19-limit"></a><!-- ws:end:WikiTextHeadingRule:18 -->19-limit</h2> Commas: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 383.477<br /> <br /> Map: [<2 1 5 2 8 11 6 2|, <0 6 -1 10 -3 -10 6 18|]<br /> EDOs: 22, 50, 72, 194, 460<br /> <br /> <!-- ws:start:WikiTextHeadingRule:20:<h1> --><h1 id="toc10"><a name="Tritonic"></a><!-- ws:end:WikiTextHeadingRule:20 -->Tritonic</h1> Commas: 225/224, 50421/50000<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 580.286<br /> <br /> Map: [<1 4 -3 -3|, <0 -5 11 12|]<br /> Wedgie: <<5 -11 -12 -29 -33 3||<br /> EDOs: 29, 31, 60, 91, 122, 213<br /> <br /> <!-- ws:start:WikiTextHeadingRule:22:<h2> --><h2 id="toc11"><a name="Tritonic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:22 -->11-limit</h2> Commas: 225/224, 385/384, 27783/27500<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 580.389<br /> <br /> Map: [<1 4 -3 -3 17|, <0 -5 11 12 -28|]<br /> EDOs: 29, 31, 60, 91, 122, 153<br /> <br /> <!-- ws:start:WikiTextHeadingRule:24:<h1> --><h1 id="toc12"><a name="Septimin"></a><!-- ws:end:WikiTextHeadingRule:24 -->Septimin</h1> Commas: 225/224, 84035/82944<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 263.632<br /> <br /> Map: [<1 4 1 5|, <0 -11 6 -10|]<br /> Wedgie: <<11 -6 10 -35 -15 40||<br /> EDOs: 9, 32, 41, 91, 132<br /> <br /> <!-- ws:start:WikiTextHeadingRule:26:<h2> --><h2 id="toc13"><a name="Septimin-11-limit"></a><!-- ws:end:WikiTextHeadingRule:26 -->11-limit</h2> Commas: 225/224, 385/384, 2401/2376<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 263.634<br /> <br /> Map: [<1 4 1 5 5|, <0 -11 6 -10 -7|]<br /> EDOs: 9, 32, 41, 91<br /> <br /> <!-- ws:start:WikiTextHeadingRule:28:<h2> --><h2 id="toc14"><a name="Septimin-13-limit"></a><!-- ws:end:WikiTextHeadingRule:28 -->13-limit</h2> Commas: 105/104, 144/143, 196/195, 245/242<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 263.700<br /> <br /> Map: [<1 4 1 5 5 7|, <0 -11 6 -10 -7 -15|]<br /> EDOs: 9, 41, 91<br /> <br /> <!-- ws:start:WikiTextHeadingRule:30:<h1> --><h1 id="toc15"><a name="Slender"></a><!-- ws:end:WikiTextHeadingRule:30 -->Slender</h1> Commas: 225/225, 589824/588245<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: (~49/48) 38.413<br /> <br /> Map: [<1 2 2 3|, <0 -13 10 -6|]<br /> Wedgie: <<13 -10 6 -46 -27 42||<br /> EDOs: 31, 94, 125<br /> <br /> <!-- ws:start:WikiTextHeadingRule:32:<h2> --><h2 id="toc16"><a name="Slender-11-limit"></a><!-- ws:end:WikiTextHeadingRule:32 -->11-limit</h2> Commas: 225/224, 385/384, 1331/1323<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 38.387<br /> <br /> Map: [<1 2 2 3 4|, <0 -13 10 -6 -17|]<br /> EDOs: 31, 63, 94, 125<br /> <br /> <!-- ws:start:WikiTextHeadingRule:34:<h1> --><h1 id="toc17"><a name="Triton"></a><!-- ws:end:WikiTextHeadingRule:34 -->Triton</h1> Commas: 225/224, 1029/1000<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 568.865<br /> <br /> Map: [<1 0 6 7|, <0 3 -7 -8|]<br /> Wedgie: <<3 -7 -8 -18 -21 1||<br /> EDOs: 19, 135, 289<br /> <br /> <!-- ws:start:WikiTextHeadingRule:36:<h1> --><h1 id="toc18"><a name="Marvo"></a><!-- ws:end:WikiTextHeadingRule:36 -->Marvo</h1> Commas: 225/224, 78125000/78121827<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: (~27/20) 516.694<br /> <br /> Map: [<1 5 12 29|, <0 -6 -17 -46|]<br /> Wedgie: <<6, 17, 46, 13, 56 59||<br /> EDOs: 65, 72<br /> <br /> <!-- ws:start:WikiTextHeadingRule:38:<h2> --><h2 id="toc19"><a name="Marvo-11-limit"></a><!-- ws:end:WikiTextHeadingRule:38 -->11-limit</h2> Commas: 225/224, 243/242, 4000/3993<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 516.699<br /> <br /> Map: [<1 5 12 29 12|, <0 -6 -17 -46 -15|]<br /> EDOs: 65, 72, 281, 497</body></html>