294edo: Difference between revisions
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294edo has a very accurate fifth inherited from [[147edo]], only 0.086{{c}} sharp, but it has a [[5/4]] which is 1.441{{c}} sharp and a [[7/4]] which is 1.479{{c}} flat, so that 7/5 is 2.920{{c}} flat, rendering it in[[consistent]] in the [[7-odd-limit]]. | |||
[[ | In the 5-limit 294edo [[tempering out|tempers out]] 393216/390625, the [[würschmidt comma]], and {{monzo| 54 -37 2 }}, the [[monzisma]]. The [[patent val]] tempers out 10976/10935, the [[hemimage comma]], and 50421/50000, the [[trimyna comma]], and supplies the [[optimal patent val]] for [[trimyna]] temperament, as well as its 11-limit [[extension]], and also supplies the optimal patent val for the rank-4 temperament tempering out [[3773/3750]]. The 294d val tempers out [[16875/16807]] and [[19683/19600]] instead, supporting [[mirkat]], whereas 294c tempers out [[126/125]] and [[1029/1024]], supporting [[valentine]]. | ||
=== Prime harmonics === | |||
{{Harmonics in equal|294}} | |||
=== Subsets and supersets === | |||
Since 294 factors into 2 × 3 × 49, 294edo has {{EDOs| 2, 3, 6, 7, 14, 21, 42, 49, 98, and 147 }} as its subsets. | |||
[[Category:Trimyna]] | |||
Latest revision as of 14:30, 20 February 2025
| ← 293edo | 294edo | 295edo → |
294 equal divisions of the octave (abbreviated 294edo or 294ed2), also called 294-tone equal temperament (294tet) or 294 equal temperament (294et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 294 equal parts of about 4.08 ¢ each. Each step represents a frequency ratio of 21/294, or the 294th root of 2.
294edo has a very accurate fifth inherited from 147edo, only 0.086 ¢ sharp, but it has a 5/4 which is 1.441 ¢ sharp and a 7/4 which is 1.479 ¢ flat, so that 7/5 is 2.920 ¢ flat, rendering it inconsistent in the 7-odd-limit.
In the 5-limit 294edo tempers out 393216/390625, the würschmidt comma, and [54 -37 2⟩, the monzisma. The patent val tempers out 10976/10935, the hemimage comma, and 50421/50000, the trimyna comma, and supplies the optimal patent val for trimyna temperament, as well as its 11-limit extension, and also supplies the optimal patent val for the rank-4 temperament tempering out 3773/3750. The 294d val tempers out 16875/16807 and 19683/19600 instead, supporting mirkat, whereas 294c tempers out 126/125 and 1029/1024, supporting valentine.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | +0.09 | +1.44 | -1.48 | -0.30 | +0.29 | +1.17 | +0.45 | +0.30 | -1.01 | +1.90 |
| Relative (%) | +0.0 | +2.1 | +35.3 | -36.2 | -7.3 | +7.1 | +28.6 | +10.9 | +7.3 | -24.6 | +46.6 | |
| Steps (reduced) |
294 (0) |
466 (172) |
683 (95) |
825 (237) |
1017 (135) |
1088 (206) |
1202 (26) |
1249 (73) |
1330 (154) |
1428 (252) |
1457 (281) | |
Subsets and supersets
Since 294 factors into 2 × 3 × 49, 294edo has 2, 3, 6, 7, 14, 21, 42, 49, 98, and 147 as its subsets.