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.