992edo: Difference between revisions
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992edo is a decent 7-limit system, although it is in[[consistent]] in the [[9-odd-limit]]. In the 13-limit the 992def [[val]] {{val| 992 1572 2303 '''2784''' '''3431''' '''3670''' }}, the 992ef val {{val| 992 1572 2303 2785 '''3431''' '''3670''' }} as well as the [[patent val]] {{val| 992 1572 2303 2785 3432 3671 }} are worth considering. | |||
992edo | |||
It | It supports [[windrose]] in the 7-limit. | ||
=== Odd harmonics === | === Odd harmonics === | ||
{{Harmonics in equal|992}} | {{Harmonics in equal|992}} | ||
=== Subsets and supersets === | |||
Since 992 factors into {{factorization|992}}, 992edo has subset edos {{EDOs| 2, 4, 8, 16, 31, 32, 62, 124, 248, and 496 }}. | |||
Latest revision as of 23:16, 20 February 2025
| ← 991edo | 992edo | 993edo → |
992 equal divisions of the octave (abbreviated 992edo or 992ed2), also called 992-tone equal temperament (992tet) or 992 equal temperament (992et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 992 equal parts of about 1.21 ¢ each. Each step represents a frequency ratio of 21/992, or the 992nd root of 2.
992edo is a decent 7-limit system, although it is inconsistent in the 9-odd-limit. In the 13-limit the 992def val ⟨992 1572 2303 2784 3431 3670], the 992ef val ⟨992 1572 2303 2785 3431 3670] as well as the patent val ⟨992 1572 2303 2785 3432 3671] are worth considering.
It supports windrose in the 7-limit.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.342 | -0.427 | +0.126 | +0.525 | +0.295 | +0.198 | +0.441 | +0.287 | +0.068 | -0.216 | -0.452 |
| Relative (%) | -28.3 | -35.3 | +10.4 | +43.4 | +24.4 | +16.4 | +36.5 | +23.7 | +5.6 | -17.9 | -37.3 | |
| Steps (reduced) |
1572 (580) |
2303 (319) |
2785 (801) |
3145 (169) |
3432 (456) |
3671 (695) |
3876 (900) |
4055 (87) |
4214 (246) |
4357 (389) |
4487 (519) | |
Subsets and supersets
Since 992 factors into 25 × 31, 992edo has subset edos 2, 4, 8, 16, 31, 32, 62, 124, 248, and 496.