Marvel family: Difference between revisions
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Wikispaces>genewardsmith **Imported revision 160328937 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 160358531 - 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>2010-09- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-09-04 02:42:27 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>160358531</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> | ||
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==Eleven limit children== | ==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.</pre></div> | 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|] | |||
</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 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 /> | <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 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 /> | ||
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<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> | <!-- 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.</body></html></pre></div> | 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|]</body></html></pre></div> | |||
Revision as of 02:42, 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 02:42:27 UTC.
- The original revision id was 160358531.
- 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|]
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:<h3> --><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: [<0 0 -1 -2|, <0 1 -1 0|]<br /> EDOs 197<br /> <br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h2> --><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:<h3> --><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: [<0 -1 0 -2 1|, <0 -1 1 0 -2|]</body></html>