297edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
[[ | Since {{nowrap|297 {{=}} 3 × 99}}, 297edo is [[enfactoring|enfactored]] in the [[7-limit]] with the same tuning as [[99edo]]. It is only [[consistent]] in the [[7-odd-limit]], unlike 99edo. In the 11-limit, the 297e [[val]] is the most reasonable, and it corrects [[99edo]]'s [[harmonic]] [[11/1|11]] somewhat closer to just, tempering out [[4000/3993]]. | ||
The 297cddee val is a tuning for the [[musneb]] temperament. | |||
=== Odd harmonics === | |||
{{Harmonics in equal|297}} | |||
=== Subsets and supersets === | |||
Since 297 factors into {{factorization|297}}, 297edo has subset edos {{EDOs| 3, 9, 11, 27, 33, and 99 }}. | |||
Latest revision as of 23:13, 20 February 2025
| ← 296edo | 297edo | 298edo → |
297 equal divisions of the octave (abbreviated 297edo or 297ed2), also called 297-tone equal temperament (297tet) or 297 equal temperament (297et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 297 equal parts of about 4.04 ¢ each. Each step represents a frequency ratio of 21/297, or the 297th root of 2.
Since 297 = 3 × 99, 297edo is enfactored in the 7-limit with the same tuning as 99edo. It is only consistent in the 7-odd-limit, unlike 99edo. In the 11-limit, the 297e val is the most reasonable, and it corrects 99edo's harmonic 11 somewhat closer to just, tempering out 4000/3993.
The 297cddee val is a tuning for the musneb temperament.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.08 | +1.57 | +0.87 | -1.89 | -1.82 | -0.12 | -1.40 | +0.10 | +1.48 | +1.95 | -2.01 |
| Relative (%) | +26.6 | +38.7 | +21.6 | -46.8 | -45.1 | -3.1 | -34.7 | +2.4 | +36.6 | +48.2 | -49.8 | |
| Steps (reduced) |
471 (174) |
690 (96) |
834 (240) |
941 (50) |
1027 (136) |
1099 (208) |
1160 (269) |
1214 (26) |
1262 (74) |
1305 (117) |
1343 (155) | |
Subsets and supersets
Since 297 factors into 33 × 11, 297edo has subset edos 3, 9, 11, 27, 33, and 99.