Marvel family: Difference between revisions

Revision as of 04:46, 4 September 2010

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 2010-09-04 04:46:30 UTC.

The original revision id was 160362321.

The revision comment was:

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

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
9-limit minimx: 3 1/6c flat, 5 1/3c flat, 7 just
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 c = 225/224, e = 4125/4096
Minimax: 3 1/9e flat, 5 and 11 2/9e flat, 7 2/3e - c flat
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 c = 225/224, t = 91125/90112
Minimax: 3 1/12t flat, 5 1/6t flat, 7 1/2t-c flat, 11 just
Lattice basis: secor length 0.9111, 3/2 length 0.9477
Angle(15/14, 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 />
7-limit minmax: 3 and 5 1/4c flat, 7 just<br />
9-limit minimx: 3 1/6c flat, 5 1/3c flat, 7 just<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 c = 225/224, e = 4125/4096<br />
Minimax: 3 1/9e flat, 5 and 11 2/9e flat, 7 2/3e - c flat<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 c = 225/224, t = 91125/90112<br />
Minimax: 3 1/12t flat, 5 1/6t flat, 7 1/2t-c flat, 11 just<br />
Lattice basis: secor length 0.9111, 3/2 length 0.9477<br />
Angle(15/14, 3/2) = 65.933<br />
Map to lattice: [&lt;0 0 -1 -2 -3|, [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>2010-09-04 02:42:27 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-09-04 04:46:30 UTC</tt>.<br>
-: The original revision id was <tt>160358531</tt>.<br>
+: The original revision id was <tt>160362321</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 18: / Line 18: @@
 Map to lattice: [&lt;0 0 -1 -2|, &lt;0 1 -1 0|]
 EDOs 197
 ==Eleven limit children==
@@ Line 29: / Line 28: @@
 Angle(secor, 5/4) = 104.028 degrees
 Map to lattice: [&lt;0 -1 0 -2 1|, &lt;0 -1 1 0 -2|]
+===Prodigy===
+Commas c = 225/224, t = 91125/90112
+Minimax: 3 1/12t flat, 5 1/6t flat, 7 1/2t-c flat, 11 just
+Lattice basis: secor length 0.9111, 3/2 length 0.9477
+Angle(15/14, 3/2) = 65.933
+Map to lattice: [&lt;0 0 -1 -2 -3|, [0 1 -1 0 3|]
 </pre></div>
 <h4>Original HTML content:</h4>
@@ Line 43: / Line 51: @@
 Map to lattice: [&amp;lt;0 0 -1 -2|, &amp;lt;0 1 -1 0|]&lt;br /&gt;
 EDOs 197&lt;br /&gt;
-&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-Eleven limit children"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Eleven limit children&lt;/h2&gt;
@@ Line 53: / Line 60: @@
 Lattice basis: secor length 1.0364 5/4 length 1.0759&lt;br /&gt;
 Angle(secor, 5/4) = 104.028 degrees&lt;br /&gt;
-Map to lattice: [&amp;lt;0 -1 0 -2 1|, &amp;lt;0 -1 1 0 -2|]&lt;/body&gt;&lt;/html&gt;</pre></div>
+Map to lattice: [&amp;lt;0 -1 0 -2 1|, &amp;lt;0 -1 1 0 -2|]&lt;br /&gt;
+&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, t = 91125/90112&lt;br /&gt;
+Minimax: 3 1/12t flat, 5 1/6t flat, 7 1/2t-c flat, 11 just&lt;br /&gt;
+Lattice basis: secor length 0.9111, 3/2 length 0.9477&lt;br /&gt;
+Angle(15/14, 3/2) = 65.933&lt;br /&gt;
+Map to lattice: [&amp;lt;0 0 -1 -2 -3|, [0 1 -1 0 3|]&lt;/body&gt;&lt;/html&gt;</pre></div>

Marvel family: Difference between revisions

Revision as of 04:46, 4 September 2010

IMPORTED REVISION FROM WIKISPACES

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Original HTML content:

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