2024edo: Difference between revisions
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2024edo is [[Enfactoring|enfactored]] in the 13-limit, with the same tuning as [[1012edo]], which is also a [[zeta]] edo. Beyond that, it does make for a reasonable 17- an 19-limit system. | 2024edo is [[Enfactoring|enfactored]] in the 13-limit, with the same tuning as [[1012edo]], which is also a [[zeta]] edo. Beyond that, it does make for a reasonable 17- an 19-limit system. | ||
It has two suitable mappings for [[5/1|5th harmonic]], one which derives from 1012edo, and other in the 2024c val. In the 2024c val, it tempers out the [[wizma]], 420175/419904 in the 7-limit, as well as [[3025/3024]], [[4225/4224]] and [[10648/10647]] in the 13-limit. | It has two suitable mappings for [[5/1|5th harmonic]], one which derives from 1012edo, and other in the 2024c val. In the 2024c val, it [[tempering out|tempers out]] the [[wizma]], 420175/419904 in the 7-limit, as well as [[3025/3024]], [[4225/4224]] and [[10648/10647]] in the 13-limit. | ||
If the sharp and flat mappings of 5/4 are combined, then 2024edo is a good 2.3.25 [[subgroup]] tuning. In the 2.3.25.7.11 subgroup, it tempers out [[4375/4374]] and [[117649/117612]] and tunes a messed-up version of the [[heimdall]] temperament, which reaches 7th harmonic in 2 second generators instead of 4, and 11th harmonic in 6 second generators instead of 12, taking half as much. | If the sharp and flat mappings of 5/4 are combined, then 2024edo is a good 2.3.25 [[subgroup]] tuning. In the 2.3.25.7.11 subgroup, it tempers out [[4375/4374]] and [[117649/117612]] and tunes a messed-up version of the [[heimdall]] temperament, which reaches 7th harmonic in 2 second generators instead of 4, and 11th harmonic in 6 second generators instead of 12, taking half as much. | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
Since 2024 factors into | Since 2024 factors into {{factorization|2024}}, 2024edo has subset edos {{EDOs| 2, 4, 8, 11, 22, 23, 44, 46, 88, 92, 184, 253, 506, and 1012 }}. | ||
Revision as of 11:35, 30 October 2023
| ← 2023edo | 2024edo | 2025edo → |
2024edo is enfactored in the 13-limit, with the same tuning as 1012edo, which is also a zeta edo. Beyond that, it does make for a reasonable 17- an 19-limit system.
It has two suitable mappings for 5th harmonic, one which derives from 1012edo, and other in the 2024c val. In the 2024c val, it tempers out the wizma, 420175/419904 in the 7-limit, as well as 3025/3024, 4225/4224 and 10648/10647 in the 13-limit.
If the sharp and flat mappings of 5/4 are combined, then 2024edo is a good 2.3.25 subgroup tuning. In the 2.3.25.7.11 subgroup, it tempers out 4375/4374 and 117649/117612 and tunes a messed-up version of the heimdall temperament, which reaches 7th harmonic in 2 second generators instead of 4, and 11th harmonic in 6 second generators instead of 12, taking half as much.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.021 | +0.248 | -0.051 | +0.065 | +0.184 | -0.015 | +0.115 | +0.184 | +0.265 | -0.174 |
| Relative (%) | +0.0 | +3.6 | +41.8 | -8.6 | +11.0 | +31.0 | -2.5 | +19.5 | +31.1 | +44.6 | -29.3 | |
| Steps (reduced) |
2024 (0) |
3208 (1184) |
4700 (652) |
5682 (1634) |
7002 (930) |
7490 (1418) |
8273 (177) |
8598 (502) |
9156 (1060) |
9833 (1737) |
10027 (1931) | |
Subsets and supersets
Since 2024 factors into 23 × 11 × 23, 2024edo has subset edos 2, 4, 8, 11, 22, 23, 44, 46, 88, 92, 184, 253, 506, and 1012.