350edo: Difference between revisions
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{{ | {{ED intro}} | ||
The equal temperament [[tempering out|tempers out]] 1600000/1594323, the [[amity comma]], in the 5-limit, and [[4375/4374]], [[5120/5103]] and [[6144/6125]] in the 7-limit, and it provides the [[optimal patent val]] for the 7-limit [[amity]] temperament. In the 11-limit it tempers out [[3025/3024]] and [[9801/9800]], and provides the optimal patent val for 11-limit [[hemiamity]]. | 350edo has a sharp tendency, with [[harmonic]]s 3 to 11 all tuned sharp. The equal temperament [[tempering out|tempers out]] 1600000/1594323, the [[amity comma]], in the 5-limit, and [[4375/4374]], [[5120/5103]] and [[6144/6125]] in the 7-limit, and it provides the [[optimal patent val]] for the 7-limit [[amity]] temperament. In the 11-limit it tempers out [[3025/3024]] and [[9801/9800]], and provides the optimal patent val for 11-limit [[hemiamity]], whereas the 350f [[val]] is an excellent tuning for 13-limit hemiamity. | ||
=== Odd harmonics === | === Odd harmonics === | ||
Latest revision as of 14:45, 20 February 2025
| ← 349edo | 350edo | 351edo → |
350 equal divisions of the octave (abbreviated 350edo or 350ed2), also called 350-tone equal temperament (350tet) or 350 equal temperament (350et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 350 equal parts of about 3.43 ¢ each. Each step represents a frequency ratio of 21/350, or the 350th root of 2.
350edo has a sharp tendency, with harmonics 3 to 11 all tuned sharp. The equal temperament tempers out 1600000/1594323, the amity comma, in the 5-limit, and 4375/4374, 5120/5103 and 6144/6125 in the 7-limit, and it provides the optimal patent val for the 7-limit amity temperament. In the 11-limit it tempers out 3025/3024 and 9801/9800, and provides the optimal patent val for 11-limit hemiamity, whereas the 350f val is an excellent tuning for 13-limit hemiamity.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.90 | +1.11 | +1.46 | -1.62 | +0.68 | -0.53 | -1.41 | +1.33 | +0.77 | -1.07 | -0.85 |
| Relative (%) | +26.3 | +32.5 | +42.6 | -47.4 | +19.9 | -15.4 | -41.2 | +38.8 | +22.5 | -31.1 | -24.7 | |
| Steps (reduced) |
555 (205) |
813 (113) |
983 (283) |
1109 (59) |
1211 (161) |
1295 (245) |
1367 (317) |
1431 (31) |
1487 (87) |
1537 (137) |
1583 (183) | |
Subsets and supersets
Since 350 factors into 2 × 52 × 7, 350edo has subset edos 2, 5, 7, 10, 14, 25, 35, 50, 70 and 175.