757edo

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757edo

758edo →

Prime factorization	757 (prime)
Step size	1.5852¢
Fifth	443\757 (702.246¢)
Semitones (A1:m2)	73:56 (115.7¢ : 88.77¢)
Consistency limit	7
Distinct consistency limit	7

757 equal divisions of the octave (abbreviated 757edo or 757ed2), also called 757-tone equal temperament (757tet) or 757 equal temperament (757et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 757 equal parts of about 1.59 ¢ each. Each step represents a frequency ratio of 2^1/757, or the 757th root of 2.

Theory

757edo is consistent to the 7-odd-limit. As an equal temperament, it tempers out 4375/4374, 67108864/66976875 and 282475249/281250000. Using the patent val, it tempers out 5632/5625, 160083/160000 and 5764801/5749920 in the 11-limit.

Prime harmonics

Approximation of prime harmonics in 757edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	+0.291	+0.476	-0.266	+0.333	-0.369	-0.332	+0.505	-0.533	-0.779	-0.518
	Relative (%)	+0.0	+18.3	+30.0	-16.8	+21.0	-23.3	-20.9	+31.9	-33.6	-49.2	-32.7
Steps (reduced)		757 (0)	1200 (443)	1758 (244)	2125 (611)	2619 (348)	2801 (530)	3094 (66)	3216 (188)	3424 (396)	3677 (649)	3750 (722)

Subsets and supersets

757edo is the 134th prime edo.

Regular temperament properties

Subgroup	Comma list	Mapping	Optimal 8ve stretch (¢)	Tuning error
				Absolute (¢)	Relative (%)
2.3	[1200 -757⟩	[⟨757 1200]]	-0.0917	0.0917	5.78
2.3.5	[24 -21 4⟩, [78 5 -37⟩	[⟨757 1200 1758]]	-0.1295	0.0920	5.80
2.3.5.7	4375/4374, 67108864/66976875, 282475249/281250000	[⟨757 1200 1758 2125]]	-0.0735	0.1256	7.92
2.3.5.7.11	4375/4374, 5632/5625, 160083/160000, 5764801/5749920	[⟨757 1200 1758 2125 2619]]	-0.0780	0.1127	7.11

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator*	Cents*	Associated ratio*	Temperaments
1	300\757	475.561	320/243	Vulture

* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct