Octagar family
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- This revision was by author genewardsmith and made on 2010-09-25 14:17:30 UTC.
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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>