Octagar family: Difference between revisions
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Wikispaces>genewardsmith **Imported revision 160953089 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 165363865 - 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>2010-09-25 14:17:30 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>165363865</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 = 4000/3969 | Comma c = 4000/3969 | ||
7-limit minimax: 3 and 7 1/6c sharp, 5 just | 7-limit minimax: 3 and 7 1/6c sharp, 5 just | ||
[|1 0 0 0>, |5/6 1/3 1/2 -1/3>, | |||
|0 0 1 0>, |5/6 -2/3 1/2 2/3>] | |||
Eigenmonzos: 2, 7/6, 5/4 | |||
9-limit minimax: 3 1/8c sharp, 5 just, 7 1/4c sharp | 9-limit minimax: 3 1/8c sharp, 5 just, 7 1/4c sharp | ||
[|1 0 0 0>, |5/8 1/2 3/8 -1/4>, | |||
|0 0 1 0>, |5/4 -1 3/4 1/2>] | |||
Eigenmonzos: 2, 5/4, 9/7 | |||
Lattice basis: 63/50 length 0.8966, 21/20 length 1.0605 | Lattice basis: 63/50 length 0.8966, 21/20 length 1.0605 | ||
Angle(63/50, 21/20) = 97.743 cents | Angle(63/50, 21/20) = 97.743 cents | ||
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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 = 4000/3969<br /> | Comma c = 4000/3969<br /> | ||
<br /> | |||
7-limit minimax: 3 and 7 1/6c sharp, 5 just<br /> | 7-limit minimax: 3 and 7 1/6c sharp, 5 just<br /> | ||
[|1 0 0 0&gt;, |5/6 1/3 1/2 -1/3&gt;, <br /> | |||
|0 0 1 0&gt;, |5/6 -2/3 1/2 2/3&gt;]<br /> | |||
Eigenmonzos: 2, 7/6, 5/4<br /> | |||
<br /> | |||
9-limit minimax: 3 1/8c sharp, 5 just, 7 1/4c sharp<br /> | 9-limit minimax: 3 1/8c sharp, 5 just, 7 1/4c sharp<br /> | ||
[|1 0 0 0&gt;, |5/8 1/2 3/8 -1/4&gt;, <br /> | |||
|0 0 1 0&gt;, |5/4 -1 3/4 1/2&gt;]<br /> | |||
Eigenmonzos: 2, 5/4, 9/7<br /> | |||
<br /> | |||
Lattice basis: 63/50 length 0.8966, 21/20 length 1.0605<br /> | Lattice basis: 63/50 length 0.8966, 21/20 length 1.0605<br /> | ||
Angle(63/50, 21/20) = 97.743 cents<br /> | Angle(63/50, 21/20) = 97.743 cents<br /> | ||
Map to lattice: [&lt;0 -1 -2 -1|, &lt;0 -1 0 2|]<br /> | Map to lattice: [&lt;0 -1 -2 -1|, &lt;0 -1 0 2|]<br /> | ||
EDOs: 162, 189, 215, 230</body></html></pre></div> | EDOs: 162, 189, 215, 230</body></html></pre></div> | ||
Revision as of 14:17, 25 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 2010-09-25 14:17:30 UTC.
- The original revision id was 165363865.
- 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:
Octagar temperament is the 7-limit planar temperament tempering out 4000/3969. While most 7-limit planar temperaments exhibit a tendency towards tuning flat, many people seem to prefer a slight sharp tendency instead. Octagar provides this; for instance the 7 odd limit minimax tuning has fifths and 7s 2.245 cents sharp, with just major thirds. ===Vital statistics=== Comma c = 4000/3969 7-limit minimax: 3 and 7 1/6c sharp, 5 just [|1 0 0 0>, |5/6 1/3 1/2 -1/3>, |0 0 1 0>, |5/6 -2/3 1/2 2/3>] Eigenmonzos: 2, 7/6, 5/4 9-limit minimax: 3 1/8c sharp, 5 just, 7 1/4c sharp [|1 0 0 0>, |5/8 1/2 3/8 -1/4>, |0 0 1 0>, |5/4 -1 3/4 1/2>] Eigenmonzos: 2, 5/4, 9/7 Lattice basis: 63/50 length 0.8966, 21/20 length 1.0605 Angle(63/50, 21/20) = 97.743 cents Map to lattice: [<0 -1 -2 -1|, <0 -1 0 2|] EDOs: 162, 189, 215, 230
Original HTML content:
<html><head><title>Octagar family</title></head><body>Octagar temperament is the 7-limit planar temperament tempering out 4000/3969. While most 7-limit planar temperaments exhibit a tendency towards tuning flat, many people seem to prefer a slight sharp tendency instead. Octagar provides this; for instance the 7 odd limit minimax tuning has fifths and 7s 2.245 cents sharp, with just major thirds.<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 = 4000/3969<br /> <br /> 7-limit minimax: 3 and 7 1/6c sharp, 5 just<br /> [|1 0 0 0>, |5/6 1/3 1/2 -1/3>, <br /> |0 0 1 0>, |5/6 -2/3 1/2 2/3>]<br /> Eigenmonzos: 2, 7/6, 5/4<br /> <br /> 9-limit minimax: 3 1/8c sharp, 5 just, 7 1/4c sharp<br /> [|1 0 0 0>, |5/8 1/2 3/8 -1/4>, <br /> |0 0 1 0>, |5/4 -1 3/4 1/2>]<br /> Eigenmonzos: 2, 5/4, 9/7<br /> <br /> Lattice basis: 63/50 length 0.8966, 21/20 length 1.0605<br /> Angle(63/50, 21/20) = 97.743 cents<br /> Map to lattice: [<0 -1 -2 -1|, <0 -1 0 2|]<br /> EDOs: 162, 189, 215, 230</body></html>