346edo: Difference between revisions
Wikispaces>genewardsmith **Imported revision 155492901 - Original comment: ** |
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346edo is [[consistent]] to the [[7-odd-limit]], but the errors of [[harmonic]]s [[3/1|3]], [[5/1|5]], and [[7/1|7]] are all quite large, commending itself as a 2.9.15.21.11 [[subgroup]] temperament, in which it tempers out [[3025/3024]], [[4375/4374]] and [[5632/5625]], [[support]]ing the 76 & 270 temperament i.e. every other step of [[vishnu]]. | |||
Using the [[patent val]] nonetheless, the equal temperament [[tempering out|tempers out]] [[243/242]], [[441/440]], [[540/539]], [[2401/2400]], [[4000/3993]], [[9801/9800]] and [[19683/19600]]. It is a possible tuning for the 11-limit version of [[harry]], the 72 & 274 temperament, as well as the rank-3 temperament [[jove]], which tempers out 243/242 and 441/440. The 346e val tempers out [[385/384]] and [[1375/1372]], and provides a possible tuning for [[fibo]], the 103 & 243 temperament. | |||
=== Odd harmonics === | |||
{{Harmonics in equal|346}} | |||
=== Subsets and supersets === | |||
Since 346 factors into primes as {{nowrap| 2 × 173 }}, 346edo contains [[2edo]] and [[173edo]] as subsets. | |||
Latest revision as of 12:47, 14 June 2026
| ← 345edo | 346edo | 347edo → |
346 equal divisions of the octave (abbreviated 346edo or 346ed2), also called 346-tone equal temperament (346tet) or 346 equal temperament (346et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 346 equal parts of about 3.47 ¢ each. Each step represents a frequency ratio of 21/346, or the 346th root of 2.
346edo is consistent to the 7-odd-limit, but the errors of harmonics 3, 5, and 7 are all quite large, commending itself as a 2.9.15.21.11 subgroup temperament, in which it tempers out 3025/3024, 4375/4374 and 5632/5625, supporting the 76 & 270 temperament i.e. every other step of vishnu.
Using the patent val nonetheless, the equal temperament tempers out 243/242, 441/440, 540/539, 2401/2400, 4000/3993, 9801/9800 and 19683/19600. It is a possible tuning for the 11-limit version of harry, the 72 & 274 temperament, as well as the rank-3 temperament jove, which tempers out 243/242 and 441/440. The 346e val tempers out 385/384 and 1375/1372, and provides a possible tuning for fibo, the 103 & 243 temperament.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -1.38 | -1.34 | -1.20 | +0.71 | +0.13 | -1.22 | +0.75 | -0.91 | +0.75 | +0.90 | -0.53 |
| Relative (%) | -39.7 | -38.7 | -34.5 | +20.6 | +3.7 | -35.2 | +21.6 | -26.2 | +21.7 | +25.8 | -15.2 | |
| Steps (reduced) |
548 (202) |
803 (111) |
971 (279) |
1097 (59) |
1197 (159) |
1280 (242) |
1352 (314) |
1414 (30) |
1470 (86) |
1520 (136) |
1565 (181) | |
Subsets and supersets
Since 346 factors into primes as 2 × 173, 346edo contains 2edo and 173edo as subsets.