User:Aura/4191814edo: Difference between revisions
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Prime factorization
2 × 11 × 190537
Step size
0.000286272 ¢
Fifth
2452054\4191814 (701.955 ¢) (→ 111457\190537)
Semitones (A1:m2)
397122:315172 (113.7 ¢ : 90.22 ¢)
Consistency limit
21
Distinct consistency limit
21
Created page with "{{Infobox ET}} {{EDO intro|4191814}} == Theory == This EDO has a consistency limit of 21, which is the most impressive out of all of the 3-2 telic multiples of [..." |
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== Theory == | == Theory == | ||
This EDO has a consistency limit of 21, which is the most impressive out of all of the 3-2 [[telicity|telic]] multiples of [[190537edo]], though this EDO seems to be at its best in the 2.3.11.13.17.19 subgroup. It tempers out the [[Archangelic comma]] in the 3-limit. | This EDO has a consistency limit of 21, which is the most impressive out of all of the 3-2 [[telicity|telic]] multiples of [[190537edo]], though this EDO seems to be at its best in the 2.3.11.13.17.19 subgroup. Thus, it is worthy of a great deal of further exploration in the [[19-limit]]. It tempers out the [[Archangelic comma]] in the 3-limit. | ||
{{Harmonics in equal|4191814}} | {{Harmonics in equal|4191814}} | ||
[[Category:Equal divisions of the octave|#####]] <!-- 7-digit number --> | [[Category:Equal divisions of the octave|#####]] <!-- 7-digit number --> | ||
Revision as of 17:02, 22 December 2022
| ← 4191813edo | 4191814edo | 4191815edo → |
Theory
This EDO has a consistency limit of 21, which is the most impressive out of all of the 3-2 telic multiples of 190537edo, though this EDO seems to be at its best in the 2.3.11.13.17.19 subgroup. Thus, it is worthy of a great deal of further exploration in the 19-limit. It tempers out the Archangelic comma in the 3-limit.
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000000 | +0.000000 | +0.000087 | +0.000096 | +0.000031 | -0.000005 | +0.000011 | -0.000006 | -0.000097 | +0.000072 | -0.000130 |
| Relative (%) | +0.0 | +0.0 | +30.5 | +33.5 | +10.9 | -1.7 | +3.8 | -2.2 | -33.7 | +25.3 | -45.3 | |
| Steps (reduced) |
4191814 (0) |
6643868 (2452054) |
9733091 (1349463) |
11767910 (3384282) |
14501294 (1925852) |
15511555 (2936113) |
17133884 (366628) |
17806522 (1039266) |
18961930 (2194674) |
20363753 (3596497) |
20767069 (3999813) | |