250edo: Difference between revisions
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superset of 125 and 50 |
"7\10" is clearer than "0.7 octaves". Harmonics -> subgroup. Add the missing 2 in 2.11.13. Resolve edo vs et |
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{{EDO intro|250}} | {{EDO intro|250}} | ||
250edo is [[enfactoring|enfactored]] in the 7-limit, with the same tuning as 125edo, but provides a closer approximation to the harmonics 11 and 13 | 250edo is [[enfactoring|enfactored]] in the 7-limit, with the same tuning as 125edo, but provides a closer approximation to the harmonics 11 and 13, where the 13/8 derives from [[10edo]] (7\10). Even so, there are a number of mappings to be considered, in particular, a less flat-tending [[patent val]] {{val| 250 396 580 '''702''' '''865''' '''925''' … }} and a more flat-tending 250deff… val {{val| 250 396 580 '''701''' '''864''' '''924''' … }}. | ||
In addition, in the patent val in the 11-limit, it is a tuning for the [[Minortonic family#Seminar|seminar]] temperament. | In addition, in the patent val in the 11-limit, it is a tuning for the [[Minortonic family#Seminar|seminar]] temperament. | ||
=== Odd harmonics === | |||
{{Harmonics in equal|250}} | |||
=== Divisors === | === Divisors === | ||
250edo has subset edos {{EDOs| | 250edo has subset edos {{EDOs| 2, 5, 10, 25, 50, 125 }}. | ||
Since the 2.3.5.7 subgroup in the patent val comes from 125et, and the 2.11.13 subgroup in the patent val comes from 50et, this system is worthy of being considered as a superset of these two temperaments. | |||
Revision as of 10:30, 24 January 2023
| ← 249edo | 250edo | 251edo → |
250edo is enfactored in the 7-limit, with the same tuning as 125edo, but provides a closer approximation to the harmonics 11 and 13, where the 13/8 derives from 10edo (7\10). Even so, there are a number of mappings to be considered, in particular, a less flat-tending patent val ⟨250 396 580 702 865 925 …] and a more flat-tending 250deff… val ⟨250 396 580 701 864 924 …].
In addition, in the patent val in the 11-limit, it is a tuning for the seminar temperament.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -1.16 | -2.31 | +0.77 | -2.31 | +0.68 | -0.53 | +1.33 | +0.64 | +0.09 | -0.38 | +0.53 |
| Relative (%) | -24.1 | -48.2 | +16.1 | -48.1 | +14.2 | -11.0 | +27.7 | +13.4 | +1.8 | -7.9 | +11.0 | |
| Steps (reduced) |
396 (146) |
580 (80) |
702 (202) |
792 (42) |
865 (115) |
925 (175) |
977 (227) |
1022 (22) |
1062 (62) |
1098 (98) |
1131 (131) | |
Divisors
250edo has subset edos 2, 5, 10, 25, 50, 125.
Since the 2.3.5.7 subgroup in the patent val comes from 125et, and the 2.11.13 subgroup in the patent val comes from 50et, this system is worthy of being considered as a superset of these two temperaments.