295edo: Difference between revisions
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== | 295edo is only [[consistent]] to the [[5-odd-limit]] and [[harmonic]] [[3/1|3]] is about halfway between its steps. Otherwise it does well in approximating harmonics [[5/1|5]] and [[7/1|7]], making it suitable for a 2.9.5.7 [[subgroup]] interpretation. Using the full 7-limit interpretation nonetheless, the 295d [[val]] is a tuning for the [[octagar]] temperament, and 295ccdd is a tuning for [[sensi]]. | ||
=== Odd harmonics === | |||
{{Harmonics in equal|295}} | {{Harmonics in equal|295}} | ||
[[ | === Subsets and supersets === | ||
Since 295 factors into {{factorization|295}}, 295edo contains [[5edo]] and [[59edo]] as its subsets. | |||
Latest revision as of 17:21, 20 February 2025
| ← 294edo | 295edo | 296edo → |
295 equal divisions of the octave (abbreviated 295edo or 295ed2), also called 295-tone equal temperament (295tet) or 295 equal temperament (295et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 295 equal parts of about 4.07 ¢ each. Each step represents a frequency ratio of 21/295, or the 295th root of 2.
295edo is only consistent to the 5-odd-limit and harmonic 3 is about halfway between its steps. Otherwise it does well in approximating harmonics 5 and 7, making it suitable for a 2.9.5.7 subgroup interpretation. Using the full 7-limit interpretation nonetheless, the 295d val is a tuning for the octagar temperament, and 295ccdd is a tuning for sensi.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.77 | +0.13 | -0.69 | -0.52 | +1.90 | +1.51 | +1.90 | +0.81 | -0.56 | +1.08 | -1.83 |
| Relative (%) | +43.6 | +3.1 | -17.0 | -12.8 | +46.8 | +37.0 | +46.7 | +19.8 | -13.9 | +26.6 | -45.1 | |
| Steps (reduced) |
468 (173) |
685 (95) |
828 (238) |
935 (50) |
1021 (136) |
1092 (207) |
1153 (268) |
1206 (26) |
1253 (73) |
1296 (116) |
1334 (154) | |
Subsets and supersets
Since 295 factors into 5 × 59, 295edo contains 5edo and 59edo as its subsets.