[tuning-math] Yet another arrgangement of 7-limit linear temperaments
- From: Gene W Smith <genewardsmith@xxxxxxxx>
- To: tuning-math@xxxxxxxxxxxxxxx
- Date: Mon, 15 Jul 2002 16:46:41 -0700
This time I used symmetrical geometric complexity; the result probably
seems less plausible, but in fact there is a good reason to look at this
if our interest is strictly 7 (not 9) limit and we are allowing ourselves
the freedom to construct scales along non-MOS lines.
[18, 27, 18, -34, 22, 1] Ennealimmal
bad 200.7612789 comp 39.23009049 rms .1304491741
[16, 2, 5, 6, 37, -34] Hemiwuerschmidt
bad 534.8468679 comp 24.71841419 rms .8753631224
[6, -7, -2, 15, 20, -25] Miracle
bad 568.1796030 comp 18.62793601 rms 1.637405196
[4, 2, 2, -1, 8, -6] Decimal
bad 766.2480478 comp 5.656854249 rms 23.94525150
[10, 9, 7, -9, 17, -9] Small diesic
bad 810.1208287 comp 15.62049935 rms 3.320167332
[1, 4, 10, 12, -13, 4] Meantone
bad 890.6035608 comp 15.58845727 rms 3.665035228
[7, -3, 8, 27, 7, -21] Orwell
bad 890.6976986 comp 18.54723699 rms 2.589237496
[4, 4, 4, -2, 5, -3] Diminished
bad 918.5756443 comp 6.928203230 rms 19.13699259
[2, 25, 13, -40, -15, 35] Hemififth
bad 931.5691063 comp 39.89987469 rms .5851564738
[6, 5, 3, -7, 12, -6] Kleismic
bad 1031.000003 comp 9.165151390 rms 12.27380956
[9, 5, -3, -21, 30, -13] Quartaminorthirds
bad 1039.361025 comp 18.41195264 rms 3.065961726
[2, -4, -4, 2, 12, -11] Pajara
bad 1177.543176 comp 10.39230485 rms 10.90317755
[0, 5, 0, -14, 0, 8] Quintal
bad 1186.151431 comp 8.660254038 rms 15.81535241
[4, -3, 2, 13, 8, -14] Tertiathirds
bad 1304.177048 comp 10.34408043 rms 12.18857055
[8, 18, 11, -25, 5, 10] Octafifths
bad 1376.914655 comp 25.82634314 rms 2.064339812
[3, 0, -6, -14, 18, -7] Tripletone
bad 1385.216081 comp 13.07669683 rms 8.100678834
[8, 6, 6, -3, 13, -9] Double wide
bad 1459.046339 comp 12.00000000 rms 10.13226624
[5, 1, 12, 25, -5, -10] Magic
bad 1473.502081 comp 18.86796226 rms 4.139050792
[3, 12, -1, -36, 10, 12] Supermajor seconds
bad 1503.290103 comp 20.49390153 rms 3.579262150
[1, 4, -2, -16, 6, 4] Dominant seventh
bad 1512.246113 comp 8.660254038 rms 20.16328150
[5, 13, -17, -76, 41, 9] Amt
bad 1633.393513 comp 43.94314509 rms .8458796028
[3, 0, 6, 14, -1, -7] Augmented
bad 1643.269165 comp 9.949874371 rms 16.59867843
[15, -2, -5, -6, 50, -38] Hemithird
bad 1648.130712 comp 30.85449724 rms 1.731229740
[1, -8, -14, -10, 25, -15] Schismic
bad 1724.179823 comp 24.55605832 rms 2.859336356
[6, 5, 22, 37, -18, -6] Catakleismic
bad 1757.115994 comp 33.03028913 rms 1.610555448
[2, -9, -4, 16, 12, -19] Neutral thirds
bad 1767.424388 comp 16.82260384 rms 6.245315858
[7, 9, 13, 5, -1, -2] Semisixths (tiny diesic)
bad 1793.790515 comp 18.84144368 rms 5.052931030
[1, 9, -2, -30, 6, 12] Superpythagorean
bad 1794.928339 comp 16.73320053 rms 6.410458352
[3, 5, -6, -28, 18, 1] Porcupine
bad 1879.273475 comp 16.61324773 rms 6.808961862
[13, -10, 6, 42, 27, -46]
bad 1911.832046 comp 33.74907406 rms 1.678518039
[2, 8, 1, -20, 4, 8]
bad 1966.962149 comp 12.44989960 rms 12.69007837
[2, 6, 6, -3, -4, 5] Supersharp
bad 2037.299988 comp 10.39230485 rms 18.86388876
[9, 10, -3, -35, 30, -5]
bad 2042.562846 comp 22.44994432 rms 4.052704060
[12, 10, -9, -49, 48, -12] Hemikleismic
bad 2144.955624 comp 33.63034344 rms 1.896512488
[5, -11, -12, 3, 33, -29]
bad 2255.013430 comp 28.91366459 rms 2.697384486
[4, -8, 14, 55, -11, -22] Shrutar
bad 2259.485358 comp 31.68595904 rms 2.250483424
[12, -2, 20, 52, 2, -31]
bad 2265.152215 comp 35.94440151 rms 1.753213789
[3, 17, -1, -50, 10, 20]
bad 2278.812132 comp 28.89636655 rms 2.729116326
[2, 8, 8, -4, -7, 8] Injera
bad 2288.664030 comp 14.28285686 rms 11.21894132
[0, 12, 24, 22, -38, 19]
bad 2371.077791 comp 39.79949748 rms 1.496892545
[1, -3, 5, 20, -5, -7] Hexadecimal
bad 2434.569514 comp 11.44552314 rms 18.58450012
[5, 1, -7, -19, 25, -10]
bad 2609.423437 comp 17.29161647 rms 8.727168682
[2, 8, -11, -48, 23, 8]
bad 2817.934201 comp 27.47726333 rms 3.732363180
[1, 4, -9, -32, 17, 4] Flattone
bad 2877.300282 comp 19.39071943 rms 7.652394368
[2, -4, -16, -26, 31, -11] Diaschismic
bad 2980.871818 comp 27.92848009 rms 3.821630536
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