773edo

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773edo

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Prime factorization	773 (prime)
Step size	1.55239 ¢
Fifth	452\773 (701.682 ¢)
Semitones (A1:m2)	72:59 (111.8 ¢ : 91.59 ¢)
Consistency limit	7
Distinct consistency limit	7

773 equal divisions of the octave (abbreviated 773edo or 773ed2), also called 773-tone equal temperament (773tet) or 773 equal temperament (773et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 773 equal parts of about 1.55 ¢ each. Each step represents a frequency ratio of 2^1/773, or the 773rd root of 2.

Theory

773edo is consistent to the 7-odd-limit. Using the patent val, it tempers out 2401/2400, 32805/32768, 137781/137500 and 766656/765625 in the 11-limit. It supports counterultrakleismic.

Prime harmonics

Approximation of prime harmonics in 773edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	-0.273	+0.232	-0.133	-0.218	-0.683	+0.607	+0.546	+0.445	-0.340	+0.631
	Relative (%)	+0.0	-17.6	+15.0	-8.5	-14.1	-44.0	+39.1	+35.2	+28.7	-21.9	+40.6
Steps (reduced)		773 (0)	1225 (452)	1795 (249)	2170 (624)	2674 (355)	2860 (541)	3160 (68)	3284 (192)	3497 (405)	3755 (663)	3830 (738)

Subsets and supersets

773edo is the 137th prime edo.

Regular temperament properties

Subgroup	Comma list	Mapping	Optimal 8ve stretch (¢)	Tuning error
				Absolute (¢)	Relative (%)
2.3	[-1225 773⟩	[⟨773 1225]]	+0.0862	0.0862	5.55
2.3.5	32805/32768, [65 85 -86⟩	[⟨773 1225 1795]]	+0.0241	0.1125	7.25
2.3.5.7	2401/2400, 32805/32768, [20 22 -20 -3⟩	[⟨773 1225 1795 2170]]	+0.0299	0.0979	6.31
2.3.5.7.11	2401/2400, 32805/32768, 137781/137500, 766656/765625	[⟨773 1225 1795 2170 2674]]	+0.0365	0.0886	5.71

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator*	Cents*	Associated ratio*	Temperaments
1	113\773	175.420	448/405	Sesquiquartififths
1	321\773	498.318	4/3	Helmholtz

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