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Relative complexity for 225/224 planar

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

12/11/2002 6:07:32 PM

Here is the ordered listing of class representatives:

4/3, 15/14, 5/4, 7/5, 6/5, 9/8, 7/6, 8/7, 9/7, 21/20, 10/9, 21/16, 25/21, 25/24, 35/32, 48/35, 60/49, 80/63, 50/49, 27/20, 36/35, 25/18, 63/50, 49/40, 35/27 ...

Here is a basis for the lattice:

3/2 ~ [2.973037720, 1.272695617]
15/14 ~ [-2.808540818, 2.730573683]

Here are lattice points. Plotting the middle column and labeling the points using the first column is what I have done before, in a rough and ready way. Plotting the third column and lableing by the first column, and -1 times the third column and lableing by 2 / first column, gives something which does not depend on the particular choice of coordinates, but is intrinsic to the temperament, and which seems to be a good way to look at it.

4/3 [-1, 0] [-2.973037720, -1.272695617]
15/14 [0, 1] [-2.808540818, 2.730573683]
5/4 [-1, -1] [-.164496902, -4.003269300]
7/5 [1, -1] [5.781578538, -1.457878066]
6/5 [2, 1] [3.137534622, 5.275964917]
9/8 [2, 0] [5.946075440, 2.545391234]
7/6 [-1, -2] [2.644043916, -6.733842983]
8/7 [0, 2] [-5.617081636, 5.461147366]
9/7 [2, 2] [.328993804, 8.006538600]
21/20 [2, -1] [8.754616258, -.185182449]
10/9 [-3, -1] [-6.110572342, -6.548660534]
21/16 [1, -2] [8.590119356, -4.188451749]
25/21 [-3, 0] [-8.919113160, -3.818086851]
25/24 [-3, -2] [-3.302031524, -9.279234217]
35/32 [-1, -3] [5.452584734, -9.464416666]
48/35 [2, 3] [-2.479547014, 10.73711228]
60/49 [0, 3] [-8.425622454, 8.191721049]
80/63 [-3, 1] [-11.72765398, -1.087513168]
50/49 [-2, 2] [-11.56315708, 2.915756132]
27/20 [4, 1] [9.083610062, 7.821356151]
36/35 [3, 3] [.493490706, 12.00980790]
25/18 [-4, -2] [-6.275069244, -10.55192983]
63/50 [4, 0] [11.89215088, 5.090782468]
49/40 [1, -3] [11.39866017, -6.919025432]
35/27 [-4, -3] [-3.466528426, -13.28250352]