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Yet another arrgangement of 7-limit linear temperaments

🔗Gene W Smith <genewardsmith@juno.com>

7/15/2002 4:46:41 PM

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