415edo

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← 414edo

415edo

416edo →

Prime factorization	5 × 83
Step size	2.89157 ¢
Fifth	243\415 (702.651 ¢)
Semitones (A1:m2)	41:30 (118.6 ¢ : 86.75 ¢)
Consistency limit	7
Distinct consistency limit	7

If harmonic 5 is used, 415edo tends very sharp. In the 5-limit the equal temperament tempers out the parakleisma, [8 14 -13⟩; in the 7-limit 3136/3125 and 4375/4374, so that it supports the parakleismic temperament and provides the optimal patent val.

Odd harmonics

Approximation of odd harmonics in 415edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	+0.70	+1.16	-0.15	+1.39	+0.97	+0.92	-1.04	-0.86	+0.32	+0.54	-0.80
	Relative (%)	+24.1	+40.0	-5.2	+48.1	+33.6	+31.8	-36.0	-29.7	+11.0	+18.8	-27.8
Steps (reduced)		658 (243)	964 (134)	1165 (335)	1316 (71)	1436 (191)	1536 (291)	1621 (376)	1696 (36)	1763 (103)	1823 (163)	1877 (217)

Subsets and supersets

415edo has subset edos 5 and 83.