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A {2,5,7,11} linear temperament list

🔗Gene Ward Smith <genewardsmith@juno.com>

10/21/2002 3:52:34 AM

These all have Graham complexity less than 35 and badness computed using that and rms error less than 20. It is not guaranteed to be complete, but for a list like this I'm not worried about that. The theory here is exactly like the theory of 7-limit linear temperaments.

[[3, 7, 0, 2], [0, 0, 1, 1]] [0, 3, 3, -2, -7, 7]

generators [400.0000000, 3366.915067]

rms 12.83021490 comp 3 bad 115.4719341

ets [3]

[[1, 9, 10, 5], [0, 13, 14, 3]] [13, 14, 3, -40, 38, -4]

generators [1200., -616.5022610]

rms .7436768490 comp 14 bad 145.7606624

ets [2, 35, 37, 72, 109, 146, 183, 255]

[[1, 0, -3, -7], [0, 2, 5, 9]] [2, 5, 9, 8, -14, 6]

generators [1200., 1394.625830]

rms 2.941218562 comp 9 bad 238.2387035

ets [6, 25, 31, 37, 43, 68, 105]

[[1, 17, -6, 13], [0, 20, -12, 13]] [20, -12, 13, 78, 39, -84]

generators [1200., -880.6991383]

rms .2817232452 comp 32 bad 288.4846031

ets [15, 94, 109, 124, 139, 233, 342]

[[1, 22, 4, 13], [0, 33, 2, 16]] [33, 2, 16, 38, 77, -88]

generators [1200., -715.5638524]

rms .2735926046 comp 33 bad 297.9423464

ets [52, 57, 109, 161, 270, 379, 649]

[[1, 3, 2, 4], [0, 5, -6, 4]] [5, -6, 4, 32, 8, -28]

generators [1200., -161.9526191]

rms 2.548055120 comp 11 bad 308.3146695

ets [7, 8, 15, 22, 37, 52, 59]

[[1, 8, 12, 4], [0, 21, 34, 2]] [21, 34, 2, -112, 68, 20]

generators [1200., -324.4522543]

rms .2735960964 comp 34 bad 316.2770874

ets [37, 196, 233, 270, 307, 503, 773]

[[1, 6, 12, 3], [0, 8, 20, -1]] [8, 20, -1, -72, 30, 24]

generators [1200., -551.5574843]

rms .8192559146 comp 21 bad 361.2918583

ets [13, 37, 50, 87, 124, 161]

[[1, 5, 5, 2], [0, 11, 9, -6]] [11, 9, -6, -48, 52, -10]

generators [1200., -292.1250007]

rms 1.354209854 comp 17 bad 391.3666478
ets [4, 33, 37, 41, 78, 115]

[[2, 0, 1, -7], [0, 1, 1, 3]] [2, 2, 6, 10, -7, -1]

generators [600.0000000, 2784.425579]

rms 11.23571334 comp 6 bad 404.4856802

ets [6, 16, 22, 28]

[[1, 0, 4, 7], [0, 2, -1, -3]] [2, -1, -3, -5, 14, -8]

generators [1200., 1407.928958]

rms 18.69483318 comp 5 bad 467.3708295

ets [5, 6, 11]

[[1, 3, 4, 5], [0, 4, 7, 9]] [4, 7, 9, 1, -7, 5]

generators [1200., -205.2910898]

rms 5.985277878 comp 9 bad 484.8075081
ets [6, 29, 35, 41, 47]

[[1, 0, 0, 3], [0, 5, 6, 1]] [5, 6, 1, -18, 15, 0]

generators [1200., 560.6334332]

rms 13.76729468 comp 6 bad 495.6226085

ets [2, 13, 15]