759edo

← 758edo

759edo

760edo →

Prime factorization	3 × 11 × 23
Step size	1.58103¢
Fifth	444\759 (701.976¢) (→148\253)
Semitones (A1:m2)	72:57 (113.8¢ : 90.12¢)
Consistency limit	5
Distinct consistency limit	5

759 equal divisions of the octave (abbreviated 759edo or 759ed2), also called 759-tone equal temperament (759tet) or 759 equal temperament (759et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 759 equal parts of about 1.58 ¢ each. Each step represents a frequency ratio of 2^1/759, or the 759th root of 2.

Since 759 = 3 × 253, and 759edo shares its excellent perfect fifth with 253edo. However, the primes 5, 7, 11, and 13 are mapped differently. With octave stretching, one may use 2.7.11.13 subgroup, all sharp, or 2.5.17.19.23.29.31 subgroup, all tuned flat. The 759def val supports noletaland, the 282 & 759def temperament, in the 23-limit. 759edo is an amazingly accurate 2.3.37.103.229 system.

Prime harmonics

Approximation of prime harmonics in 759edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	+0.021	-0.543	+0.344	+0.461	+0.579	-0.608	-0.280	-0.606	-0.328	-0.372
	Relative (%)	+0.0	+1.3	-34.3	+21.8	+29.1	+36.6	-38.4	-17.7	-38.4	-20.8	-23.5
Steps (reduced)		759 (0)	1203 (444)	1762 (244)	2131 (613)	2626 (349)	2809 (532)	3102 (66)	3224 (188)	3433 (397)	3687 (651)	3760 (724)

Subsets and supersets

759edo notably contains 253edo.