1778edo: Difference between revisions
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recalculated the consistency limit |
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{{Infobox ET| | |||
|Prime factorization = 2 × 7 × 127 | |||
|Step size = 0.6749¢ | |||
|Fifth=1040\1778 (520\889) | |||
|Consistency limit=7 | |||
}} | |||
{{EDO intro|1778}} | {{EDO intro|1778}} | ||
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Prime harmonics with less than 1 standard deviation in 1778edo are: 2, 3, 11, 23, 43, 47, 61. As such, it is best for use with the 2.3.11.23.43.47.61 subgroup. | Prime harmonics with less than 1 standard deviation in 1778edo are: 2, 3, 11, 23, 43, 47, 61. As such, it is best for use with the 2.3.11.23.43.47.61 subgroup. | ||
In the 7-limit, it provides the optimal patent val for the [[neptune]] temperament. | In the 7-limit, in which it is consistent, it provides the optimal patent val for the [[neptune]] temperament. | ||
Revision as of 11:17, 4 May 2022
| ← 11edo | [[edo|]] | 13edo → |
(convergent)
Theory
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.043 | -0.262 | -0.322 | -0.085 | +0.088 | -0.258 | -0.305 | +0.331 | +0.125 | +0.310 | +0.072 |
| Relative (%) | -6.3 | -38.8 | -47.7 | -12.7 | +13.1 | -38.2 | -45.1 | +49.1 | +18.5 | +46.0 | +10.7 | |
| Steps (reduced) |
2818 (1040) |
4128 (572) |
4991 (1435) |
5636 (302) |
6151 (817) |
6579 (1245) |
6946 (1612) |
7268 (156) |
7553 (441) |
7810 (698) |
8043 (931) | |
Prime harmonics with less than 1 standard deviation in 1778edo are: 2, 3, 11, 23, 43, 47, 61. As such, it is best for use with the 2.3.11.23.43.47.61 subgroup.
In the 7-limit, in which it is consistent, it provides the optimal patent val for the neptune temperament.