From: mclaren
Subject: Wilson CPSs -- post 4 of 9
Continuing the rundown of peculiar &
interesting Wilson combination product set scales,
a Wilson 4 out of 9 CPS. 4, 9 [1,3,5,7,9,11,13,15,17]
This set contains a number of generators which
are powers of other generators, and so there
are nowhere near the full set of 252 pitches.
1: 16575/16384 20.06550
2: 2079/2048 26.00886
3: 525/512 43.40835
4: 8415/8192 46.49708
5: 17017/16384 65.62695
6: 1071/1024 77.69135
7: 2145/2048 80.11435
8: 135/128 92.17876
9: 273/256 111.3086
10: 8775/8192 119.0201
11: 1105/1024 131.7968
12: 4455/4096 145.4517
13: 8925/8192 148.3638
14: 561/512 158.2284
15: 9009/8192 164.5815
16: 36465/32768 185.0698
17: 2295/2048 197.1342
18: 1155/1024 208.4126
19: 4641/4096 216.2640
20: 585/512 230.7514
21: 4725/4096 247.3184
22: 297/256 257.1830
23: 595/512 260.0951
24: 19305/16384 284.0244
25: 2431/2048 296.8011
26: 19635/16384 313.3681
27: 2457/2048 315.2187
28: 2475/2048 327.8555
29: 9945/8192 335.7069
30: 5005/4096 346.9853
31: 315/256 359.0498
32: 5049/4096 362.1385
33: 1275/1024 379.5380
34: 1287/1024 395.7557
35: 10395/8192 412.3227
36: 1309/1024 425.0994
37: 5265/4096 434.6615
38: 165/128 439.5868
39: 663/512 447.4382
40: 5355/4096 464.0052
41: 10725/8192 466.4282
42: 675/512 478.4926
43: 1365/1024 497.6225
44: 21879/16384 500.7112
45: 693/512 524.0540
46: 2805/2048 544.5422
47: 351/256 546.3928
48: 2835/2048 562.9598
49: 357/256 575.7365
50: 715/512 578.1596
51: 11475/8192 583.4481
52: 5775/4096 594.7265
53: 23205/16384 602.5780
54: 2925/2048 617.0653
55: 11781/8192 629.0095
56: 1485/1024 643.4969
57: 5967/4096 651.3483
58: 3003/2048 662.6268
59: 189/128 674.6912
60: 12155/8192 683.1150
61: 765/512 695.1794
62: 12285/8192 701.5325
63: 385/256 706.4579
64: 1547/1024 714.3093
65: 195/128 728.7967
66: 1575/1024 745.3637
67: 25245/16384 748.4524
68: 3213/2048 779.6466
69: 6435/4096 782.0697
70: 405/256 794.1340
71: 6545/4096 811.4133
72: 819/512 813.2639
73: 825/512 825.9007
74: 3315/2048 833.7521
75: 105/64 857.0950
76: 1683/1024 860.1837
77: 6825/4096 883.9364
78: 429/256 893.8010
79: 6885/4096 899.0895
80: 3465/2048 910.3679
81: 13923/8192 918.2194
82: 14025/8192 930.8562
83: 1755/1024 932.7067
84: 1785/1024 962.0505
85: 225/128 976.5379
86: 455/256 995.6677
87: 7293/4096 998.7565
88: 459/256 1010.820
89: 231/128 1022.099
90: 7425/4096 1029.810
91: 29835/16384 1037.662
92: 935/512 1042.587
93: 15015/8192 1048.940
94: 945/512 1061.005
95: 3825/2048 1081.493
96: 3861/2048 1097.711
97: 7735/4096 1100.623
98: 975/512 1115.110
99: 3927/2048 1127.054
100: 495/256 1141.542
101: 1989/1024 1149.393
102: 1001/512 1160.672
103: 16065/8192 1165.960
104: 2025/1024 1180.447
105: 255/128 1193.224
106: 4095/2048 1199.577
49-tone combination product set produced by
Wilson CPS 3, 13 [1,2,3,4,5,6,7,8,9,10,11,12,13]:
0: 1/1 00.00000
1: 65/64 26.84138
2: 33/32 53.27296
3: 135/128 92.17876
4: 273/256 111.3086
5: 275/256 123.9454
6: 35/32 155.1396
7: 143/128 191.8457
8: 9/8 203.9100
9: 585/512 230.7514
10: 297/256 257.1830
11: 75/64 274.5825
12: 77/64 320.1440
13: 39/32 342.4828
14: 315/256 359.0498
15: 5/4 386.3139
16: 1287/1024 395.7557
17: 81/64 407.8201
18: 325/256 413.1552
19: 165/128 439.5868
20: 21/16 470.7811
21: 693/512 524.0540
22: 175/128 541.4535
23: 351/256 546.3928
24: 11/8 551.3181
25: 715/512 578.1596
26: 45/32 590.2239
27: 91/64 609.3538
28: 189/128 674.6912
29: 3/2 701.9553
30: 385/256 706.4579
31: 195/128 728.7967
32: 99/64 755.2283
33: 25/16 772.6278
34: 819/512 813.2639
35: 13/8 840.5280
36: 105/64 857.0950
37: 429/256 893.8010
38: 27/16 905.8654
39: 55/32 937.6320
40: 7/4 968.8264
41: 225/128 976.5379
42: 455/256 995.6677
43: 231/128 1022.099
44: 117/64 1044.438
45: 15/8 1088.269
46: 495/256 1141.542
47: 1001/512 1160.672
48: 63/32 1172.736
Wilson CPS 3,13 [1,2,3,4,5,6,8,9,10,12,14,15,16];
1: 525/512 43.40835
2: 135/128 92.17876
3: 35/32 155.1396
4: 9/8 203.9100
5: 75/64 274.5825
6: 315/256 359.0498
7: 5/4 386.3139
8: 81/64 407.8201
9: 21/16 470.7811
10: 675/512 478.4926
11: 175/128 541.4535
12: 45/32 590.2239
13: 375/256 660.8964
14: 189/128 674.6912
15: 3/2 701.9553
16: 25/16 772.6278
17: 405/256 794.1340
18: 105/64 857.0950
19: 27/16 905.8654
20: 7/4 968.8264
21: 225/128 976.5379
22: 945/512 1061.005
23: 15/8 1088.269
24: 63/32 1172.736
25: 2/1 1200.000
Another collapsed Wilson CPS formed by
a set of generators most of which are
multiples of one another--in this case,
4 out of 8 from [1,2,3,4,5,6,7,8]:
0: 1/1 000.0000
1: 35/32 155.1396
2: 9/8 203.9100
3: 315/256 359.0498
4: 5/4 386.3139
5: 21/16 470.7811
6: 45/32 590.2239
7: 3/2 701.9553
8: 105/64 857.0950
9: 7/4 968.8264
10: 15/8 1088.269
11: 63/32 1172.736
For a change of pace, here's an oddball
Wilson 4 out of 8--but NOT a hebdomekontany.
Because the first 8 integers are chosen as
generators, most of the generators are
factors of other generators. As a result
there are only 12 unique pitches rather
than the usual 70.
Wilson CPS 4,8 [1,2,3,4,5,6,7,8]:
1: 35/32 155.1396
2: 9/8 203.9100
3: 315/256 359.0498
4: 5/4 386.3139
5: 21/16 470.7811
6: 45/32 590.2239
7: 3/2 701.9553
8: 105/64 857.0950
9: 7/4 968.8264
10: 15/8 1088.269
11: 63/32 1172.736
12: 2/1 1200.000
Wilson 2 out of 13 CPS. This is the CPS formed by
2, 13 [1,2,3,4,5,6,7,8,9,10,11,12,13]:
The result is an interesting 22-tone just array--
23, if we include a 1/1.
1: 65/64 26.84138
2: 33/32 53.27296
3: 35/32 155.1396
4: 143/128 191.8457
5: 9/8 203.9100
6: 77/64 320.1440
7: 39/32 342.4828
8: 5/4 386.3139
9: 21/16 470.7811
10: 11/8 551.3181
11: 45/32 590.2239
12: 91/64 609.3538
13: 3/2 701.9553
14: 99/64 755.2283
15: 25/16 772.6278
16: 13/8 840.5280
17: 27/16 905.8654
18: 55/32 937.6320
19: 7/4 968.8264
20: 117/64 1044.438
21: 15/8 1088.269
22: 63/32 1172.736
Next post, still more oddball Wilson
CPSs, and in the post after that one,
some discussion of how to
use Wilson CPSs in actual music.
--mclaren
