Catalog of rank-4 temperaments
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 2010-10-06 18:25:35 UTC.
- The original revision id was 168437071.
- 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:
==441/440== ===Commas 441/440, 364/363=== 13-limit minimax [|1 0 0 0 0 0>, |5/3 0 1/3 -1/3 -1/3 1/3>, |1/6 0 5/6 2/3 -5/6 1/3>, |0 0 0 1 0 0>, |1/6 0 -1/6 2/3 1/6 1/3>, |0 0 0 0 0 1>] Eigenmonzos: 2, 11/10, 8/7, 16/13 15-limit minimax [|1 0 0 0 0 0>, |5/4 1/4 1/4 -1/4 -1/4 1/4>, |5/4 -3/4 5/4 -1/4 -1/4 1/4>, |17/8 -11/8 5/8 -1/8 3/8 1/8>, |5/2 -3/2 1/2 -1/2 1/2 1/2>, |17/8 -11/8 5/8 -9/8 3/8 9/8>] Eigenmonzos: 2, 14/13, 6/5, 11/9 Lattice basis: 3/2 1.2263 14/11 1.4629 21/16 1.4657 Map to lattice: [<0 1 1 -1 -1 0|, <0 0 1 0 -1 -2|, <0 0 1 1 1 1|] Map: [<1 0 0 0 -3 -8|, <0 1 0 0 2 5|, <0 0 1 0 -1 -2|, <0 0 0 1 2 3|] Generators: 2, 3, 5 Edos: 15, 23, 26, 29, 41, 43, 46, 58, 113, 130, 159, 217, 289, 393 ==9801/9800== ===Commas 2080/2079, 1716/1715=== 13 and 15 limit minimax [|1 0 0 0 0 0>, |7/10 4/5 0 -2/5 0 1/5>, |7/10 -1/5 1 -2/5 0 1/5>, |7/5 -2/5 0 1/5 0 2/5>, |11/5 -11/5 1 3/5 0 1/5>, |0 0 0 0 0 1>] Eigenmonzos: 2, 6/5, 16/13, 9/7 Lattice basis: 3/2 length 1.1956 7/4 length 1.4506 14/13 1.8299 Map: [<2 0 0 0 3 -7|, <0 1 0 0 -2 1|, <0 0 1 0 1 0|, <0 0 0 1 1 2|] Generators: 99/70, 3, 5, 7 Edos: 26, 36, 46, 58, 68, 72, 84, 94, 130, 140, 166, 198, 224, 270, 494, 764, 1186, 1892
Original HTML content:
<html><head><title>Rank four temperaments</title></head><body><!-- ws:start:WikiTextHeadingRule:0:<h2> --><h2 id="toc0"><a name="x-441/440"></a><!-- ws:end:WikiTextHeadingRule:0 -->441/440</h2> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h3> --><h3 id="toc1"><a name="x-441/440-Commas 441/440, 364/363"></a><!-- ws:end:WikiTextHeadingRule:2 -->Commas 441/440, 364/363</h3> <br /> 13-limit minimax<br /> [|1 0 0 0 0 0>, |5/3 0 1/3 -1/3 -1/3 1/3>, <br /> |1/6 0 5/6 2/3 -5/6 1/3>, |0 0 0 1 0 0>, <br /> |1/6 0 -1/6 2/3 1/6 1/3>, |0 0 0 0 0 1>]<br /> Eigenmonzos: 2, 11/10, 8/7, 16/13<br /> <br /> 15-limit minimax<br /> [|1 0 0 0 0 0>, |5/4 1/4 1/4 -1/4 -1/4 1/4>, <br /> |5/4 -3/4 5/4 -1/4 -1/4 1/4>, <br /> |17/8 -11/8 5/8 -1/8 3/8 1/8>, <br /> |5/2 -3/2 1/2 -1/2 1/2 1/2>, <br /> |17/8 -11/8 5/8 -9/8 3/8 9/8>]<br /> Eigenmonzos: 2, 14/13, 6/5, 11/9<br /> <br /> Lattice basis: 3/2 1.2263 14/11 1.4629 21/16 1.4657<br /> Map to lattice: [<0 1 1 -1 -1 0|, <br /> <0 0 1 0 -1 -2|, <0 0 1 1 1 1|]<br /> <br /> Map: [<1 0 0 0 -3 -8|, <0 1 0 0 2 5|, <br /> <0 0 1 0 -1 -2|, <0 0 0 1 2 3|]<br /> Generators: 2, 3, 5<br /> Edos: 15, 23, 26, 29, 41, 43, 46, 58, 113, 130, 159, 217, 289, 393<br /> <br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="x-9801/9800"></a><!-- ws:end:WikiTextHeadingRule:4 -->9801/9800</h2> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h3> --><h3 id="toc3"><a name="x-9801/9800-Commas 2080/2079, 1716/1715"></a><!-- ws:end:WikiTextHeadingRule:6 -->Commas 2080/2079, 1716/1715</h3> <br /> 13 and 15 limit minimax<br /> [|1 0 0 0 0 0>, |7/10 4/5 0 -2/5 0 1/5>, <br /> |7/10 -1/5 1 -2/5 0 1/5>, |7/5 -2/5 0 1/5 0 2/5>, <br /> |11/5 -11/5 1 3/5 0 1/5>, |0 0 0 0 0 1>]<br /> Eigenmonzos: 2, 6/5, 16/13, 9/7<br /> <br /> Lattice basis: 3/2 length 1.1956 7/4 length 1.4506 14/13 1.8299<br /> <br /> Map: [<2 0 0 0 3 -7|, <0 1 0 0 -2 1|, <br /> <0 0 1 0 1 0|, <0 0 0 1 1 2|]<br /> Generators: 99/70, 3, 5, 7<br /> Edos: 26, 36, 46, 58, 68, 72, 84, 94, 130, 140, 166, 198, 224, 270, 494, 764, 1186, 1892</body></html>