Marvel temperaments: Difference between revisions

Revision as of 20:07, 27 December 2010

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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, escapade and marvo. Considered elsewhere are meantone, miracle, magic, pajara, orwell, catakleismic, garibaldi, august, compton, sharp 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 temperament]]: 126.431

Map: [<1 2 2 3 4 4|, <0 -4 3 -2 -5 -3|]
EDOs: 9, 10, 19

==Wizard==
Commas: 225/224, 118098/117649

==Tritonic==
Commas: 225/224, 50421/50000

==Septimin==
Commas: 225/224, 84035/82944

==Slender==
Commas: 225/225, 589824/588245

==Triton==
Commas: 225/224, 1029/1000

==Escapade==
Commas: 225/224, 12288/12005

==Marvo==
Commas: 225/224, 78125000/78121827

Original HTML content:

<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, escapade and marvo. Considered elsewhere are meantone, miracle, magic, pajara, orwell, catakleismic, garibaldi, august, compton, sharp 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:&lt;h2&gt; --><h2 id="toc0"><a name="x-Negri"></a><!-- ws:end:WikiTextHeadingRule:0 -->Negri</h2>
Commas: 49/48, 225/224<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 125.608<br />
<br />
Map: [&lt;1 2 2 3|, &lt;0 -4 3 -2|]<br />
Wedgie: &lt;&lt;4 -3 2 -14 -8 13||<br />
EDOs: 9, 10, 19, 86<br />
<br />
11-limit<br />
Commas: 45/44, 49/48, 56/55<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 126.474<br />
<br />
Map: [&lt;1 2 2 3 4|, &lt;0 -4 3 -2 -5|]<br />
EDOs: 9, 10, 19<br />
<br />
13-limit<br />
Commas: 45/44, 49/48, 56/55, 78/77<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 126.431<br />
<br />
Map: [&lt;1 2 2 3 4 4|, &lt;0 -4 3 -2 -5 -3|]<br />
EDOs: 9, 10, 19<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-Wizard"></a><!-- ws:end:WikiTextHeadingRule:2 -->Wizard</h2>
Commas: 225/224, 118098/117649<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="x-Tritonic"></a><!-- ws:end:WikiTextHeadingRule:4 -->Tritonic</h2>
Commas: 225/224, 50421/50000<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="x-Septimin"></a><!-- ws:end:WikiTextHeadingRule:6 -->Septimin</h2>
Commas: 225/224, 84035/82944<br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="x-Slender"></a><!-- ws:end:WikiTextHeadingRule:8 -->Slender</h2>
Commas: 225/225, 589824/588245<br />
<br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="x-Triton"></a><!-- ws:end:WikiTextHeadingRule:10 -->Triton</h2>
Commas: 225/224, 1029/1000<br />
<br />
<!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="x-Escapade"></a><!-- ws:end:WikiTextHeadingRule:12 -->Escapade</h2>
Commas: 225/224, 12288/12005<br />
<br />
<!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="x-Marvo"></a><!-- ws:end:WikiTextHeadingRule:14 -->Marvo</h2>
Commas: 225/224, 78125000/78121827</body></html>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 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>2010-12-27 15:55:18 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-12-27 20:07:43 UTC</tt>.<br>
-: The original revision id was <tt>190064932</tt>.<br>
+: The original revision id was <tt>190079766</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>
@@ Line 12: / Line 12: @@
 ==Negri==
 Commas: 49/48, 225/224
+[[POTE tuning|POTE temperament]]: 125.608
+Map: [&lt;1 2 2 3|, &lt;0 -4 3 -2|]
+Wedgie: &lt;&lt;4 -3 2 -14 -8 13||
+EDOs: 9, 10, 19, 86
+-limit
+Commas: 45/44, 49/48, 56/55
+[[POTE tuning|POTE temperament]]: 126.474
+Map: [&lt;1 2 2 3 4|, &lt;0 -4 3 -2 -5|]
+EDOs: 9, 10, 19
+-limit
+Commas: 45/44, 49/48, 56/55, 78/77
+[[POTE tuning|POTE temperament]]: 126.431
+Map: [&lt;1 2 2 3 4 4|, &lt;0 -4 3 -2 -5 -3|]
+EDOs: 9, 10, 19
 ==Wizard==
@@ Line 44: / Line 66: @@
 &lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Negri"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Negri&lt;/h2&gt;
 Commas: 49/48, 225/224&lt;br /&gt;
+&lt;br /&gt;
+&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: 125.608&lt;br /&gt;
+&lt;br /&gt;
+Map: [&amp;lt;1 2 2 3|, &amp;lt;0 -4 3 -2|]&lt;br /&gt;
+Wedgie: &amp;lt;&amp;lt;4 -3 2 -14 -8 13||&lt;br /&gt;
+EDOs: 9, 10, 19, 86&lt;br /&gt;
+&lt;br /&gt;
+-limit&lt;br /&gt;
+Commas: 45/44, 49/48, 56/55&lt;br /&gt;
+&lt;br /&gt;
+&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: 126.474&lt;br /&gt;
+&lt;br /&gt;
+Map: [&amp;lt;1 2 2 3 4|, &amp;lt;0 -4 3 -2 -5|]&lt;br /&gt;
+EDOs: 9, 10, 19&lt;br /&gt;
+&lt;br /&gt;
+-limit&lt;br /&gt;
+Commas: 45/44, 49/48, 56/55, 78/77&lt;br /&gt;
+&lt;br /&gt;
+&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: 126.431&lt;br /&gt;
+&lt;br /&gt;
+Map: [&amp;lt;1 2 2 3 4 4|, &amp;lt;0 -4 3 -2 -5 -3|]&lt;br /&gt;
+EDOs: 9, 10, 19&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x-Wizard"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Wizard&lt;/h2&gt;

Marvel temperaments: Difference between revisions

Revision as of 20:07, 27 December 2010

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