42ed11

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Division of the 11th harmonic into 42 equal parts (42ED11) is related to 12 EDO, but with the 11/1 rather than the 2/1 being just. The octave is about 13.9092 cents compressed and the step size is about 98.8409 cents. It is consistent to the 11-integer-limit, but not to the 12-integer-limit. In comparison, 12EDO is only consistent up to the 10-integer-limit.

degree cents value corresponding
JI intervals
comments
0 0.0000 exact 1/1
1 98.8409 18/17
2 197.6818
3 296.5227 19/16
4 395.3636
5 494.2045 4/3
6 593.0454 45/32
7 691.8863
8 790.7272 30/19
9 889.5681
10 988.4090 16/9
11 1087.2499 15/8
12 1186.0908
13 1284.9317 21/10
14 1383.7726
15 1482.6136 33/14
16 1581.4545 5/2
17 1680.2954
18 1779.1363
19 1877.9772
20 1976.8181 22/7
21 2075.6590
22 2174.4999 7/2
23 2273.3408
24 2372.1817
25 2471.0226
26 2569.8635 22/5
27 2668.7044 14/3
28 2767.5453
29 2866.3862 110/21
30 2965.2271
31 3064.0680
32 3162.9089
33 3261.7498
34 3360.5907
35 3459.4316
36 3558.2725
37 3657.1134 33/4
38 3755.9543
39 3854.7952
40 3953.6361
41 4052.4770
42 4151.3179 exact 11/1 paramajor fourth plus three octaves

Regular temperaments

See also: Quintaleap family

42ED11 can also be thought of as a generator of the 11-limit temperament which tempers out 100/99, 225/224, and 85184/84035, which is a cluster temperament with 12 clusters of notes in an octave (quintapole temperament, 12&85). Alternative 12&97 temperament can also be used, which tempers out 100/99, 245/242, and 458752/455625 in the 11-limit.

See also