350edo

Revision as of 06:51, 15 November 2023 by FloraC (talk | contribs) (Expand on theory)

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← 349edo 350edo 351edo →
Prime factorization 2 × 52 × 7
Step size 3.42857 ¢ 
Fifth 205\350 (702.857 ¢) (→ 41\70)
Semitones (A1:m2) 35:25 (120 ¢ : 85.71 ¢)
Consistency limit 7
Distinct consistency limit 7

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

Approximation of odd harmonics in 350edo
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.