Marvel family: Difference between revisions

Revision as of 03:50, 20 September 2010

IMPORTED REVISION FROM WIKISPACES

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This revision was by author genewardsmith and made on 2010-09-20 03:50:51 UTC.

The original revision id was 163864553.

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Original Wikitext content:

The head of the marvel family is marvel, which tempers out 225/224, the septimal kleisma or marvel comma. Marvel has a [[Normal lists|normal list basis]] of [2, 3, 5]; hence a [[Harmonic Limit|5-limit]] scale can be converted to marvel simply by tempering it. One way to do that, and an excellent marvel tuning, is given by [[197edo]]. 

Little is gained in tuning accuracy by not tempering out 4375/4374 as well as 225/224, leading to [[Kleismic family|catakleismic temperament]]. Another temperament which does little damage to tuning accuracy is [[Pythagorean family|compton temperament]], for which [[240edo]] may be used.

===Vital statistics===
Comma c = 225/224

7-limit minmax: 3 and 5 1/4c flat, 7 just
[|1 0 0 0>, |5/4 1/2 -1/2 1/4>, |5/4 -1/2 1/2 1/4>, |0 0 0 1>]
Eigenmonzos: 2, 5/4, 6/5

9-limit minimx: 3 1/6c flat, 5 1/3c flat, 7 just
[|1 0 0 0>, |5/6 2/3 -1/3 1/6>, |5/3 -2/3 1/3 1/3>, |0 0 0 1>]
Eigenmonzos: 2, 8/7, 10/9

Minkowski lattice basis: secor length 1.256, 3/2 length 1.369
Angle(secor, 3/2) = 106.958 cents 
Map to lattice: [<0 0 -1 -2|, <0 1 -1 0|]
EDOs 197

==Eleven limit children==
The second comma of the [[Normal lists|normal comma list]] defines which 11-limit family member we are looking at. Adding 4125/4096 gives unidecimal marvel, 91125/90112 gives prodigy, 5632/5625 minerva and 243/242 spectacle.

===Unidecimal marvel===
Commas: 225/224, 385/384

Minimax: 
[|1 0 0 0 0>, |4/3 8/9 -1/3 0 -1/9>, |8/3 -2/9 1/3 0 -2/9>,
|3 4/3 0 0 -2/3>, |8/3 -2/9 -2/3 0 7/9>]
Eigenmonzos: 2, 10/9, 11/9

Lattice basis: secor length 1.0364 5/4 length 1.0759
Angle(secor, 5/4) = 104.028 degrees
Map to lattice: [<0 -1 0 -2 1|, <0 -1 1 0 -2|]

===Prodigy===
Commas: 225/224, 441/440
Minimax: 
[|1 0 0 0 0>, |13/12 1/2 -1/4 0 1/12>, 
|13/6 -1 1/2 0 1/6>,
|3/2 -1 1/2 0 1/2>, |0 0 0 0 1>]
Eigenmonzos: 2, 10/9, 11/8

Lattice basis: secor length 0.9111, 3/2 length 0.9477
Angle(secor, 3/2) = 65.933
Map to lattice: [<0 0 -1 -2 -3|, <0 1 -1 0 3|]

Original HTML content:

<html><head><title>Marvel family</title></head><body>The head of the marvel family is marvel, which tempers out 225/224, the septimal kleisma or marvel comma. Marvel has a <a class="wiki_link" href="/Normal%20lists">normal list basis</a> of [2, 3, 5]; hence a <a class="wiki_link" href="/Harmonic%20Limit">5-limit</a> scale can be converted to marvel simply by tempering it. One way to do that, and an excellent marvel tuning, is given by <a class="wiki_link" href="/197edo">197edo</a>. <br />
<br />
Little is gained in tuning accuracy by not tempering out 4375/4374 as well as 225/224, leading to <a class="wiki_link" href="/Kleismic%20family">catakleismic temperament</a>. Another temperament which does little damage to tuning accuracy is <a class="wiki_link" href="/Pythagorean%20family">compton temperament</a>, for which <a class="wiki_link" href="/240edo">240edo</a> may be used.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h3&gt; --><h3 id="toc0"><a name="x--Vital statistics"></a><!-- ws:end:WikiTextHeadingRule:0 -->Vital statistics</h3>
Comma c = 225/224<br />
<br />
7-limit minmax: 3 and 5 1/4c flat, 7 just<br />
[|1 0 0 0&gt;, |5/4 1/2 -1/2 1/4&gt;, |5/4 -1/2 1/2 1/4&gt;, |0 0 0 1&gt;]<br />
Eigenmonzos: 2, 5/4, 6/5<br />
<br />
9-limit minimx: 3 1/6c flat, 5 1/3c flat, 7 just<br />
[|1 0 0 0&gt;, |5/6 2/3 -1/3 1/6&gt;, |5/3 -2/3 1/3 1/3&gt;, |0 0 0 1&gt;]<br />
Eigenmonzos: 2, 8/7, 10/9<br />
<br />
Minkowski lattice basis: secor length 1.256, 3/2 length 1.369<br />
Angle(secor, 3/2) = 106.958 cents <br />
Map to lattice: [&lt;0 0 -1 -2|, &lt;0 1 -1 0|]<br />
EDOs 197<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-Eleven limit children"></a><!-- ws:end:WikiTextHeadingRule:2 -->Eleven limit children</h2>
The second comma of the <a class="wiki_link" href="/Normal%20lists">normal comma list</a> defines which 11-limit family member we are looking at. Adding 4125/4096 gives unidecimal marvel, 91125/90112 gives prodigy, 5632/5625 minerva and 243/242 spectacle.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc2"><a name="x-Eleven limit children-Unidecimal marvel"></a><!-- ws:end:WikiTextHeadingRule:4 -->Unidecimal marvel</h3>
Commas: 225/224, 385/384<br />
<br />
Minimax: <br />
[|1 0 0 0 0&gt;, |4/3 8/9 -1/3 0 -1/9&gt;, |8/3 -2/9 1/3 0 -2/9&gt;,<br />
|3 4/3 0 0 -2/3&gt;, |8/3 -2/9 -2/3 0 7/9&gt;]<br />
Eigenmonzos: 2, 10/9, 11/9<br />
<br />
Lattice basis: secor length 1.0364 5/4 length 1.0759<br />
Angle(secor, 5/4) = 104.028 degrees<br />
Map to lattice: [&lt;0 -1 0 -2 1|, &lt;0 -1 1 0 -2|]<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h3&gt; --><h3 id="toc3"><a name="x-Eleven limit children-Prodigy"></a><!-- ws:end:WikiTextHeadingRule:6 -->Prodigy</h3>
Commas: 225/224, 441/440<br />
Minimax: <br />
[|1 0 0 0 0&gt;, |13/12 1/2 -1/4 0 1/12&gt;, <br />
|13/6 -1 1/2 0 1/6&gt;,<br />
|3/2 -1 1/2 0 1/2&gt;, |0 0 0 0 1&gt;]<br />
Eigenmonzos: 2, 10/9, 11/8<br />
<br />
Lattice basis: secor length 0.9111, 3/2 length 0.9477<br />
Angle(secor, 3/2) = 65.933<br />
Map to lattice: [&lt;0 0 -1 -2 -3|, &lt;0 1 -1 0 3|]</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>2010-09-20 02:20:13 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-09-20 03:50:51 UTC</tt>.<br>
-: The original revision id was <tt>163856927</tt>.<br>
+: The original revision id was <tt>163864553</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 30: / Line 30: @@
 ===Unidecimal marvel===
-Commas c = 225/224, e = 4125/4096
+Commas: 225/224, 385/384
 Minimax:
@@ Line 42: / Line 42: @@
 ===Prodigy===
-Commas c = 225/224, e = 91125/90112
+Commas: 225/224, 441/440
-Minimax: 3 1/12e flat, 5 1/6e flat, 7 1/2e-c flat, 11 just
+Minimax:
+[|1 0 0 0 0&gt;, |13/12 1/2 -1/4 0 1/12&gt;,
+|13/6 -1 1/2 0 1/6&gt;,
+|3/2 -1 1/2 0 1/2&gt;, |0 0 0 0 1&gt;]
+Eigenmonzos: 2, 10/9, 11/8
 Lattice basis: secor length 0.9111, 3/2 length 0.9477
 Angle(secor, 3/2) = 65.933
@@ Line 75: / Line 80: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="x-Eleven limit children-Unidecimal marvel"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Unidecimal marvel&lt;/h3&gt;
-Commas c = 225/224, e = 4125/4096&lt;br /&gt;
+Commas: 225/224, 385/384&lt;br /&gt;
 &lt;br /&gt;
 Minimax: &lt;br /&gt;
@@ Line 87: / Line 92: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc3"&gt;&lt;a name="x-Eleven limit children-Prodigy"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Prodigy&lt;/h3&gt;
-Commas c = 225/224, e = 91125/90112&lt;br /&gt;
+Commas: 225/224, 441/440&lt;br /&gt;
-Minimax: 3 1/12e flat, 5 1/6e flat, 7 1/2e-c flat, 11 just&lt;br /&gt;
+Minimax: &lt;br /&gt;
+[|1 0 0 0 0&amp;gt;, |13/12 1/2 -1/4 0 1/12&amp;gt;, &lt;br /&gt;
+|13/6 -1 1/2 0 1/6&amp;gt;,&lt;br /&gt;
+|3/2 -1 1/2 0 1/2&amp;gt;, |0 0 0 0 1&amp;gt;]&lt;br /&gt;
+Eigenmonzos: 2, 10/9, 11/8&lt;br /&gt;
+&lt;br /&gt;
 Lattice basis: secor length 0.9111, 3/2 length 0.9477&lt;br /&gt;
 Angle(secor, 3/2) = 65.933&lt;br /&gt;
 Map to lattice: [&amp;lt;0 0 -1 -2 -3|, &amp;lt;0 1 -1 0 3|]&lt;/body&gt;&lt;/html&gt;</pre></div>

Marvel family: Difference between revisions

Revision as of 03:50, 20 September 2010

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