Minimal consistent EDOs
Jump to navigation
Jump to search
An edo N is consistent with respect to the q-odd-limit if the closest approximations of the odd harmonics of the q-odd-limit in that edo also give the closest approximations of all the differences between these odd harmonics. It is distinctly consistent if every one of those closest approximations is a distinct value. Below is a table of the smallest consistent, and the smallest distinctly consistent, edo for every odd number up to 135.
Odd Limit |
Smallest Consistent Edo* |
Smallest Distinctly Consistent Edo |
---|---|---|
1 | 1 | 1 |
3 | 1 | 3 |
5 | 3 | 9 |
7 | 4 | 27 |
9 | 5 | 41 |
11 | 22 | 58 |
13 | 26 | 87 |
15 | 29 | 111 |
17 | 58 | 149 |
19 | 80 | 217 |
21 | 94 | 282 |
23 | 94 | 282 |
25 | 282 | 388 |
27 | 282 | 388 |
29 | 282 | 1323 |
31 | 311 | 1600 |
33 | 311 | 1600 |
35 | 311 | 1600 |
37 | 311 | 1600 |
39 | 311 | 2554 |
41 | 311 | 2554 |
43 | 17461 | 17461 |
45 | 17461 | 17461 |
47 | 20567 | 20567 |
49 | 20567 | 20567 |
51 | 20567 | 20567 |
53 | 20567 | 20567 |
55 | 20567 | 20567 |
57 | 20567 | 20567 |
59 | 253389 | 253389 |
61 | 625534 | 625534 |
63 | 625534 | 625534 |
65 | 625534 | 625534 |
67 | 625534 | 625534 |
69 | 759630 | 759630 |
71 | 759630 | 759630 |
73 | 759630 | 759630 |
75 | 2157429 | 2157429 |
77 | 2157429 | 2157429 |
79 | 2901533 | 2901533 |
81 | 2901533 | 2901533 |
83 | 2901533 | 2901533 |
85 | 2901533 | 2901533 |
87 | 2901533 | 2901533 |
89 | 2901533 | 2901533 |
91 | 2901533 | 2901533 |
93 | 2901533 | 2901533 |
95 | 2901533 | 2901533 |
97 | 2901533 | 2901533 |
99 | 2901533 | 2901533 |
101 | 2901533 | 2901533 |
103 | 2901533 | 2901533 |
105 | 2901533 | 2901533 |
107 | 2901533 | 2901533 |
109 | 2901533 | 2901533 |
111 | 2901533 | 2901533 |
113 | 2901533 | 2901533 |
115 | 2901533 | 2901533 |
117 | 2901533 | 2901533 |
119 | 2901533 | 2901533 |
121 | 2901533 | 2901533 |
123 | 2901533 | 2901533 |
125 | 2901533 | 2901533 |
127 | 2901533 | 2901533 |
129 | 2901533 | 2901533 |
131 | 2901533 | 2901533 |
133 | 70910024 | 70910024 |
135 | 70910024 | 70910024 |
*apart from 0edo
The last entry, 70910024edo, is consistent up to the 135-odd-limit. The next edo is 5407372813, reported to be consistent to the 155-odd-limit.
OEIS integer sequences links
- OEIS: Equal divisions of the octave with progressively increasing consistency levels (OEIS)
- OEIS: Equal divisions of the octave with progressively increasing consistency limits and distinct approximations for all the ratios in the tonality diamond of that limit (OEIS)
- OEIS: Equal divisions of the octave with nondecreasing consistency levels. (OEIS)
- OEIS: Equal divisions of the octave with nondecreasing consistency limits and distinct approximations for all the ratios in the tonality diamond of that limit (OEIS)