71edo

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71edo

72edo →

Prime factorization	71 (prime)
Step size	16.9014 ¢
Fifth	42\71 (709.859 ¢)
Semitones (A1:m2)	10:3 (169 ¢ : 50.7 ¢)
Dual sharp fifth	42\71 (709.859 ¢)
Dual flat fifth	41\71 (692.958 ¢)
Dual major 2nd	12\71 (202.817 ¢)
Consistency limit	5
Distinct consistency limit	5

The 71 equal temperament or 71-EDO divides the octave into 71 equal parts of 16.901 cents each.

71edo is the 20th prime EDO.

Theory

Approximation of odd harmonics in 71edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	+7.90	+2.42	-5.45	-1.09	+6.43	+4.54	-6.58	-3.55	+6.71	+2.46	-2.92
	Relative (%)	+46.8	+14.3	-32.2	-6.5	+38.0	+26.9	-38.9	-21.0	+39.7	+14.5	-17.3
Steps (reduced)		113 (42)	165 (23)	199 (57)	225 (12)	246 (33)	263 (50)	277 (64)	290 (6)	302 (18)	312 (28)	321 (37)

It tempers out 20480/19683 and 393216/390625 in the 5-limit, 875/864, 4000/3969 and 1029/1024 in the 7-limit, 245/242 and 100/99 in the 11-limit, and 91/90 in the 13-limit. In the 13-limit it supplies the optimal patent val for the 29&71 and 34&37 temperaments.