276edo: Difference between revisions
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== Theory == | == Theory == | ||
276edo's fifth is quite bad, but it corresponds to [[12edo]]'s fifth, which means | 276edo's fifth is quite bad, but it corresponds to [[12edo]]'s fifth, which means the [[patent val]] [[tempering out|tempers out]] the [[Pythagorean comma]]. It thus [[support]]s [[compton]], owing to the fact that it is a 12edo fifth. In the 7-limit, it supports [[grendel]]. | ||
276b val in the 5-limit supports [[hanson]]. In the 7-limit, it supports [[quadritikleismic]]. | Its sharp fifth comes from [[46edo]], and the 276b val in the 5-limit supports [[hanson]]. In the 7-limit, it supports [[quadritikleismic]]. | ||
=== Odd harmonics === | === Odd harmonics === | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
276edo has subset edos {{EDOs| | Since 276 factors into {{factorization|276}}, 276edo has subset edos {{EDOs| 2, 3, 4, 6, 12, 23, 46, 69, 92, 138 }}. [[552edo]], which doubles it, corrects its approximation of harmonic 3. | ||
== Intervals == | |||
See [[Table of 276edo intervals]]. | |||
== Music == | == Music == | ||
* [https://www.youtube.com/watch?v=Be6JAoqVCBY | ; [[Eliora]], [[Sevish]], and {{w|Evanescence}} | ||
* [https://www.youtube.com/watch?v=Be6JAoqVCBY ''What The Zoon (Mashup)''] (2021) – 12edo and 23edo [[polysystemic]] | |||
Latest revision as of 23:07, 20 February 2025
| ← 275edo | 276edo | 277edo → |
276 equal divisions of the octave (abbreviated 276edo or 276ed2), also called 276-tone equal temperament (276tet) or 276 equal temperament (276et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 276 equal parts of about 4.35 ¢ each. Each step represents a frequency ratio of 21/276, or the 276th root of 2.
Theory
276edo's fifth is quite bad, but it corresponds to 12edo's fifth, which means the patent val tempers out the Pythagorean comma. It thus supports compton, owing to the fact that it is a 12edo fifth. In the 7-limit, it supports grendel.
Its sharp fifth comes from 46edo, and the 276b val in the 5-limit supports hanson. In the 7-limit, it supports quadritikleismic.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -1.96 | +0.64 | +0.74 | +0.44 | +0.86 | -1.40 | -1.31 | -0.61 | -1.86 | -1.22 | +2.16 |
| Relative (%) | -45.0 | +14.8 | +17.0 | +10.1 | +19.7 | -32.1 | -30.2 | -14.0 | -42.8 | -28.0 | +49.7 | |
| Steps (reduced) |
437 (161) |
641 (89) |
775 (223) |
875 (47) |
955 (127) |
1021 (193) |
1078 (250) |
1128 (24) |
1172 (68) |
1212 (108) |
1249 (145) | |
Subsets and supersets
Since 276 factors into 22 × 3 × 23, 276edo has subset edos 2, 3, 4, 6, 12, 23, 46, 69, 92, 138. 552edo, which doubles it, corrects its approximation of harmonic 3.
Intervals
See Table of 276edo intervals.
Music
- Eliora, Sevish, and Evanescence
- What The Zoon (Mashup) (2021) – 12edo and 23edo polysystemic