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Justin case

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

11/9/2000 12:48:26 PM

you're interested in those superparticulars, I made a few minor changes to
the scale (11/6 -> 64/35 and 5/3 -> 33/20) to reduce their multiplicity:

note # ratio step size
0 1/1 65/64
1 65/64 66/65
2 33/32 56/55
3 21/20 50/49
4 15/14 49/48
5 35/32 64/63
6 10/9 81/80
7 9/8 64/63
8 8/7 65/64
9 65/56 66/65
10 33/28 56/55
11 6/5 49/48
12 49/40 50/49
13 5/4 81/80
14 81/64 64/63
15 9/7 49/48
16 21/16 64/63
17 4/3 65/64
18 65/48 66/65
19 11/8 56/55
20 7/5 50/49
21 10/7 49/48
22 35/24 64/63
23 40/27 81/80
24 3/2 49/48
25 49/32 64/63
26 14/9 81/80
27 63/40 64/63
28 8/5 65/64
29 13/8 66/65
30 33/20 45/44
31 27/16 64/63
32 12/7 49/48
33 7/4 64/63
34 16/9 81/80
35 9/5 64/63
36 64/35 65/64
37 13/7 49/48
38 91/48 66/65
39 77/40 50/49
40 55/28 56/55

The list of otonalities is now:

1/1: 1-3-5-7-9-11-13
21/20: 1-3-5
9/8: 1-3-9
8/7: 1-3-5-7-9-13
6/5: 1-3-5-7-11
5/4: 1-7-13
4/3: 1-3-9
7/5: 1-3-5-7-9-11
10/7: 1-3-7-11-13
3/2: 1-3-7-9-11
8/5: 1-3-5-7-9
12/7: 1-3-5-7-11
7/4: 1-3-5-7
16/9: 1-3-5-7-9
9/5: 1-5-7
64/35: 1-5-7
13/7: 1-5-7

In cents, the scale is

0 0 26.841
1 26.841 26.432
2 53.273 31.194
3 84.467 34.976
4 119.44 35.697
5 155.14 27.264
6 182.4 21.506
7 203.91 27.264
8 231.17 26.841
9 258.02 26.432
10 284.45 31.194
11 315.64 35.697
12 351.34 34.976
13 386.31 21.506
14 407.82 27.264
15 435.08 35.697
16 470.78 27.264
17 498.04 26.841
18 524.89 26.432
19 551.32 31.194
20 582.51 34.976
21 617.49 35.697
22 653.18 27.264
23 680.45 21.506
24 701.96 35.697
25 737.65 27.264
26 764.92 21.506
27 786.42 27.264
28 813.69 26.841
29 840.53 26.432
30 866.96 38.906
31 905.87 27.264
32 933.13 35.697
33 968.83 27.264
34 996.09 21.506
35 1017.6 27.264
36 1044.9 26.841
37 1071.7 35.697
38 1107.4 26.432
39 1133.8 34.976
40 1168.8 31.194

I've asked Kraig Grady to see if Wilson ever made a scale like this -- I'll
bet he has.