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Notating Unidec

🔗Gene Ward Smith <genewardsmith@juno.com> <genewardsmith@juno.com>

1/14/2003 12:13:47 AM

This is another important system, particularly interesting in the 11-limit. It is a half-octave system; in the 13-limit it has wedgie

[12, 22, -4, -6, 4, 7, -40, -51, -38, -71, -90, -72, -3, 26, 36]

and mapping

[[2, 5, 8, 5, 6, 8], [0, -6, -11, 2, 3, -2]]

The range of generators is

18/118 < 29/190 < 40/262 < 11/72

The 5-limit poptimal range is a cat's whisker above 18/118, with
281/1842 the best; it's possible 118 is 5-poptimal. In the other limits, we have 40/262 in the 7, 9, 11 and 13 limits, but 29/190 is an
improvement in the 13 limit.

The corresponding vals are

l118 := [118, 187, 274, 331, 408, 436]
l1842 := [1842, 2919, 4277, 5167, 6369, 6806]
l190 := [190, 301, 441, 533, 657, 702]
l262 := [262, 415, 608, 735, 906, 968]
l72 := [72, 114, 167, 202, 249, 266]

with errors

err118 := [-.2601, .1270, -2.7242, -2.1655, -6.6295]
err1842 := [-.3263, .0055, -2.7021, -2.1323, -6.6516]
err190 := [-.9024, -1.0505, -2.5101, -1.8443, -6.8436]
err262 := [-1.1916, -1.5809, -2.4137, -1.6997, -6.9400]
err72 := [-1.9550, -2.9804, -2.1592, -1.3180, -7.1945]

The choice appears to be between 72 and 118; I'd be inclined to give it to 118.