954edo

← 953edo

954edo

955edo →

Prime factorization	2 × 32 × 53
Step size	1.25786¢
Fifth	558\954 (701.887¢) (→31\53)
Semitones (A1:m2)	90:72 (113.2¢ : 90.57¢)
Consistency limit	17
Distinct consistency limit	17
Special properties	zeta peak zeta integral zeta gap

954 equal divisions of the octave (abbreviated 954edo or 954ed2), also called 954-tone equal temperament (954tet) or 954 equal temperament (954et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 954 equal parts of about 1.26 ¢ each. Each step represents a frequency ratio of 2^1/954, or the 954th root of 2.

954edo is a very strong 17-limit system, distinctly consistent in the 17-limit, and is a zeta peak, integral and gap edo. The tuning of the primes to 17 are all flat, and the equal temperament tempers out the ennealimma, [1 -27 18⟩, in the 5-limit and 2401/2400 and 4375/4374 in the 7-limit, so that it supports the ennealimmal temperament. In the 11-limit it tempers out 3025/3024, 9801/9800, 43923/43904, and 151263/151250 so that it supports hemiennealimmal. In the 13-limit it tempers out 4225/4224 and 10648/10647 and in the 17-limit 2431/2430 and 2601/2600. It supports and gives the optimal patent val for the semihemiennealimmal temperament.

Prime harmonics

Approximation of prime harmonics in 954edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	absolute (¢)	+0.000	-0.068	-0.150	-0.272	-0.375	-0.276	-0.553	+0.600	-0.601	+0.611	-0.381
	relative (%)	+0	-5	-12	-22	-30	-22	-44	+48	-48	+49	-30
Steps (reduced)		954 (0)	1512 (558)	2215 (307)	2678 (770)	3300 (438)	3530 (668)	3899 (83)	4053 (237)	4315 (499)	4635 (819)	4726 (910)

Subsets and supersets

Since 954 = 2 × 3² × 53, 954edo has subset edos 2, 3, 6, 9, 18, 53, 106, 159, 318, 477.