Marvel family: Difference between revisions
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Wikispaces>genewardsmith **Imported revision 160363683 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 163856927 - 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>2010-09-20 02:20:13 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>163856927</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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===Vital statistics=== | ===Vital statistics=== | ||
Comma c = 225/224 | Comma c = 225/224 | ||
7-limit minmax: 3 and 5 1/4c flat, 7 just | 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 | 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 | Minkowski lattice basis: secor length 1.256, 3/2 length 1.369 | ||
Angle(secor, 3/2) = 106.958 cents | Angle(secor, 3/2) = 106.958 cents | ||
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===Unidecimal marvel=== | ===Unidecimal marvel=== | ||
Commas c = 225/224, e = 4125/4096 | Commas c = 225/224, e = 4125/4096 | ||
Minimax: 3 1/ | |||
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 | Lattice basis: secor length 1.0364 5/4 length 1.0759 | ||
Angle(secor, 5/4) = 104.028 degrees | Angle(secor, 5/4) = 104.028 degrees | ||
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<!-- ws:start:WikiTextHeadingRule:0:&lt;h3&gt; --><h3 id="toc0"><a name="x--Vital statistics"></a><!-- ws:end:WikiTextHeadingRule:0 -->Vital statistics</h3> | <!-- 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 /> | Comma c = 225/224<br /> | ||
<br /> | |||
7-limit minmax: 3 and 5 1/4c flat, 7 just<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 /> | 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 /> | Minkowski lattice basis: secor length 1.256, 3/2 length 1.369<br /> | ||
Angle(secor, 3/2) = 106.958 cents <br /> | Angle(secor, 3/2) = 106.958 cents <br /> | ||
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<!-- 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> | <!-- 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 /> | Commas c = 225/224, e = 4125/4096<br /> | ||
Minimax: 3 1/ | <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 /> | Lattice basis: secor length 1.0364 5/4 length 1.0759<br /> | ||
Angle(secor, 5/4) = 104.028 degrees<br /> | Angle(secor, 5/4) = 104.028 degrees<br /> | ||
Revision as of 02:20, 20 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 2010-09-20 02:20:13 UTC.
- The original revision id was 163856927.
- 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 [|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 c = 225/224, e = 4125/4096 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 c = 225/224, e = 91125/90112 Minimax: 3 1/12e flat, 5 1/6e flat, 7 1/2e-c flat, 11 just 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:<h3> --><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>, |5/4 1/2 -1/2 1/4>, |5/4 -1/2 1/2 1/4>, |0 0 0 1>]<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>, |5/6 2/3 -1/3 1/6>, |5/3 -2/3 1/3 1/3>, |0 0 0 1>]<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: [<0 0 -1 -2|, <0 1 -1 0|]<br /> EDOs 197<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 /> <br /> Minimax: <br /> [|1 0 0 0 0>, |4/3 8/9 -1/3 0 -1/9>, |8/3 -2/9 1/3 0 -2/9>,<br /> |3 4/3 0 0 -2/3>, |8/3 -2/9 -2/3 0 7/9>]<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: [<0 -1 0 -2 1|, <0 -1 1 0 -2|]<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h3> --><h3 id="toc3"><a name="x-Eleven limit children-Prodigy"></a><!-- ws:end:WikiTextHeadingRule:6 -->Prodigy</h3> Commas c = 225/224, e = 91125/90112<br /> Minimax: 3 1/12e flat, 5 1/6e flat, 7 1/2e-c flat, 11 just<br /> Lattice basis: secor length 0.9111, 3/2 length 0.9477<br /> Angle(secor, 3/2) = 65.933<br /> Map to lattice: [<0 0 -1 -2 -3|, <0 1 -1 0 3|]</body></html>