1277edo

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1277edo

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Prime factorization	1277 (prime)
Step size	0.939702 ¢
Fifth	747\1277 (701.958 ¢)
Semitones (A1:m2)	121:96 (113.7 ¢ : 90.21 ¢)
Consistency limit	11
Distinct consistency limit	11

Theory

1277edo is consistent to the 11-odd-limit. The equal temperament tempers out 4375/4374, 52734375/52706752 and [51 -13 -1 -10⟩ in the 7-limit; 4375/4374, 759375/758912, 151263/151250 and 2097152/2096325 in the 11-limit. It supports nanismic, nanic, ragismic, bragi, revopentic, revopent, sasaquinbizo-atriyo, starscape, nommismic, technologismic, supermajor and monzismic.

Prime harmonics

Approximation of prime harmonics in 1277edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	+0.003	-0.096	+0.007	+0.287	-0.434	+0.291	+0.373	+0.387	+0.337	+0.462
	Relative (%)	+0.0	+0.3	-10.2	+0.8	+30.6	-46.2	+31.0	+39.7	+41.1	+35.8	+49.1
Steps (reduced)		1277 (0)	2024 (747)	2965 (411)	3585 (1031)	4418 (587)	4725 (894)	5220 (112)	5425 (317)	5777 (669)	6204 (1096)	6327 (1219)

Subsets and supersets

1277edo is the 206th prime EDO.

2554edo, which divides the edostep in two, is the smallest EDO distinctly consistent through the 41-odd-limit, hence provides correction for harmonics 11 through 41.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[2024 -1277⟩	[⟨1277 2024]]	-0.0009	0.0009	0.10
2.3.5	[54 -37 2⟩, [-67 -9 35⟩	[⟨1277 2024 2965]]	+0.0132	0.0199	2.12
2.3.5.7	4375/4374, 52734375/52706752, [51 -13 -1 -10⟩	[⟨1277 2024 2965 3585]]	+0.0093	0.0186	1.98
2.3.5.7.11	4375/4374, 759375/758912, 151263/151250, 2097152/2096325	[⟨1277 2024 2965 3585 4418]]	-0.0092	0.0405	4.31

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator*	Cents*	Associated Ratio*	Temperaments
1	265\1277	249.021	[-27 11 3 1⟩	Monzismic
1	380\1277	357.087	768/625	Dodifo
1	463\1277	435.082	9/7	Supermajor

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