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Stepping through generators of a fifth

🔗Gene Ward Smith <gwsmith@svpal.org>

7/18/2004 3:57:29 AM

In the table below, the fractions are from a portion of the 99th row
of the Farey sequence; then we have the corresponding range of ets,
flat to sharp, and the 7-limit wedgie obtained from the standard vals.
It is interesting to see what lurks in regions which have recieved
less attention in the vicinity of a fifth as generator; of course
occasionally near the endpoints the fifth does not turn out to even be
the generator, due to the use of standard vals. One could take the
same list and work it up for other periods, other prime limits, or
even other ways of deciding on the vals.

53/92 [33, 59] [34, -22, -9, -114, -110, 41]
34/59 [33, 26] [1, -22, -9, -37, -17, 41]
49/85 [59, 26] [25, 22, 9, -23, -56, -41]
15/26 [7, 19] [1, 4, -9, 4, -17, -32]
56/97 [26, 71] [9, 10, -3, -5, -30, -35]
41/71 [26, 45] [1, 4, -9, 4, -17, -32]
26/45 [26, 19] [1, 4, -9, 4, -17, -32]
37/64 [45, 19] [1, 4, -9, 4, -17, -32]
48/83 [64, 19] [1, -15, -28, -26, -47, -23]
11/19 [7, 12] [1, 4, -2, 4, -6, -16]
51/88 [19, 69] [1, 4, 29, 4, 43, 56]
40/69 [19, 50] [1, 4, 10, 4, 13, 12]
29/50 [19, 31] [1, 4, 10, 4, 13, 12]
47/81 [50, 31] [1, 4, 10, 4, 13, 12]
18/31 [19, 12] [1, 4, 10, 4, 13, 12]
43/74 [31, 43] [1, 4, 10, 4, 13, 12]
25/43 [31, 12] [1, 4, 10, 4, 13, 12]
57/98 [43, 55] [1, 4, -33, 4, -55, -88]
32/55 [43, 12] [1, 4, 10, 4, 13, 12]
39/67 [55, 12] [1, 4, 22, 4, 32, 40]
46/79 [67, 12] [1, 4, 22, 4, 32, 40]
53/91 [79, 12] [1, 16, 22, 23, 32, 6]
7/12 [7, 5] [1, 4, -2, 4, -6, -16]
52/89 [12, 77] [1, -8, -26, -15, -44, -38]
45/77 [12, 65] [1, -8, -26, -15, -44, -38]
38/65 [12, 53] [1, -8, -14, -15, -25, -10]
31/53 [12, 41] [1, -8, -14, -15, -25, -10]
55/94 [53, 41] [1, -8, -14, -15, -25, -10]
24/41 [12, 29] [1, -8, -14, -15, -25, -10]
41/70 [41, 29] [1, -8, -14, -15, -25, -10]
58/99 [70, 29] [1, -37, -43, -61, -71, 4]
17/29 [12, 17] [1, -8, -2, -15, -6, 18]
44/75 [29, 46] [1, 21, 15, 31, 21, -24]
27/46 [29, 17] [1, -8, 15, -15, 21, 57]
37/63 [46, 17] [1, -25, 15, -42, 21, 105]
47/80 [63, 17] [1, -25, 15, -42, 21, 105]
57/97 [80, 17] [1, -42, 15, -69, 21, 153]
10/17 [12, 5] [1, 4, -2, 4, -6, -16]
53/90 [17, 73] [1, 43, -19, 66, -33, -165]
43/73 [17, 56] [1, 26, -19, 39, -33, -117]
33/56 [17, 39] [1, 26, -19, 39, -33, -117]
56/95 [56, 39] [1, 26, -19, 39, -33, -117]
23/39 [17, 22] [1, 9, -2, 12, -6, -30]
36/61 [39, 22] [1, -13, 20, -23, 29, 83]
49/83 [61, 22] [1, -13, 20, -23, 29, 83]
13/22 [17, 5] [1, 9, -2, 12, -6, -30]
55/93 [22, 71] [1, 9, -24, 12, -41, -81]
42/71 [22, 49] [1, 9, -2, 12, -6, -30]
29/49 [22, 27] [1, 9, -2, 12, -6, -30]
45/76 [49, 27] [1, 9, -2, 12, -6, -30]
16/27 [22, 5] [1, 9, -2, 12, -6, -30]
51/86 [27, 59] [1, -18, -2, -31, -6, 46]