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A closer look at bridgables

🔗Gene Ward Smith <gwsmith@svpal.org>

7/20/2004 12:48:08 AM

I zoomed in to +-3 cents of a fifth, but set a badness bound of 100
for TOP badness, while letting the denominators get as high as 300.
Nothing new emerges; we seem to have a pretty good grasp of the fifth
as a generator. Below I give the generator, the two ets on either
side, the wedgie, and the TOP badness. We get dominant, a range of
grackle from 66/113 to 83/142, a range of pontiac (with the lowest
badness figure, please note) from 107/183 to 162/277, a range of
garibaldi from 31/53 to 24/41 with a sporadic 38/65 serving as boundry
between grackle and pontiac. Then we have a range of kwai from 161/175
to 106/181, with garibaldi again serving as a boundry, this time 41/70
between kwai and the 29&70 temperament, which ranges from 99/169 to
92/157. Then schism, and on to sharper temperaments.

7/12 [7, 5] [1, 4, -2, 4, -6, -16] 28.744954
66/113 [12, 101] [1, -8, -26, -15, -44, -38] 99.875370
59/101 [12, 89] [1, -8, -26, -15, -44, -38] 99.875370
111/190 [101, 89] [1, -8, -26, -15, -44, -38] 99.875370157
52/89 [12, 77] [1, -8, -26, -15, -44, -38] 99.875370
97/166 [89, 77] [1, -8, -26, -15, -44, -38] 99.875370
45/77 [12, 65] [1, -8, -26, -15, -44, -38] 99.875370
83/142 [77, 65] [1, -8, -26, -15, -44, -38] 99.875370
38/65 [12, 53] [1, -8, -14, -15, -25, -10] 28.818557
107/183 [65, 118] [1, -8, 39, -15, 59, 113] 22.393674
69/118 [65, 53] [1, -8, 39, -15, 59, 113] 22.393674
169/289 [118, 171] [1, -8, 39, -15, 59, 113] 22.393674
100/171 [118, 53] [1, -8, 39, -15, 59, 113] 22.393674
131/224 [171, 53] [1, -8, 39, -15, 59, 113] 22.393674
162/277 [224, 53] [1, -8, 39, -15, 59, 113] 22.393674
31/53 [12, 41] [1, -8, -14, -15, -25, -10] 28.818557
117/200 [53, 147] [1, -8, -14, -15, -25, -10] 28.818557
86/147 [53, 94] [1, -8, -14, -15, -25, -10] 28.818557
141/241 [147, 94] [1, -8, -14, -15, -25, -10] 28.818557
55/94 [53, 41] [1, -8, -14, -15, -25, -10] 28.818557
134/229 [94, 135] [1, -8, -14, -15, -25, -10] 28.818557
79/135 [94, 41] [1, -8, -14, -15, -25, -10] 28.818557
103/176 [135, 41] [1, -8, -14, -15, -25, -10] 28.818557
24/41 [12, 29] [1, -8, -14, -15, -25, -10] 28.818557
161/275 [41, 234] [1, 33, 27, 50, 40, -30] 64.536859
137/234 [41, 193] [1, 33, 27, 50, 40, -30] 64.536859
113/193 [41, 152] [1, 33, 27, 50, 40, -30] 64.536859
89/152 [41, 111] [1, 33, 27, 50, 40, -30] 64.536859
154/263 [152, 111] [1, 33, 27, 50, 40, -30] 64.536859
65/111 [41, 70] [1, 33, 27, 50, 40, -30] 64.536859
106/181 [111, 70] [1, 33, 27, 50, 40, -30] 64.536859
41/70 [41, 29] [1, -8, -14, -15, -25, -10] 28.818557
99/169 [70, 99] [1, -37, -43, -61, -71, 4] 93.148463
58/99 [70, 29] [1, -37, -43, -61, -71, 4] 93.148463
133/227 [99, 128] [1, -37, -43, -61, -71, 4] 93.148463
75/128 [99, 29] [1, -37, -43, -61, -71, 4] 93.148463
92/157 [128, 29] [1, -37, -43, -61, -71, 4] 93.148463
17/29 [12, 17] [1, -8, -2, -15, -6, 18] 82.638059