1171edo

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1171edo

1172edo →

Prime factorization	1171 (prime)
Step size	1.02477 ¢
Fifth	685\1171 (701.964 ¢)
Semitones (A1:m2)	111:88 (113.7 ¢ : 90.18 ¢)
Consistency limit	27
Distinct consistency limit	27

Theory

1171edo is a very strong 5-limit division, being the first one past 612 with a lower 5-limit relative error. It has a 5-limit comma basis consisting of the monzisma, [54 -37 2⟩ and whoosh, [37 25 -33⟩. While not a strong higher-limit system, it is distinctly consistent through the 27-odd-limit, and is very strong on the 2.3.5.11 subgroup.

Prime harmonics

Approximation of prime harmonics in 1171edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	+0.009	+0.023	-0.423	+0.006	-0.220	-0.429	-0.331	-0.093	+0.312	-0.373
	Relative (%)	+0.0	+0.9	+2.2	-41.3	+0.6	-21.5	-41.9	-32.3	-9.1	+30.4	-36.4
Steps (reduced)		1171 (0)	1856 (685)	2719 (377)	3287 (945)	4051 (538)	4333 (820)	4786 (102)	4974 (290)	5297 (613)	5689 (1005)	5801 (1117)

Subsets and supersets

1171edo is the 193rd prime edo. 2342edo which doubles it, corrects its harmonic 7 to a near-just quality.

Regular temperament properties

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator*	Cents*	Associated ratio*	Temperaments
1	129\1171	132.195	[-38 5 13⟩	Astro
1	243\1171	249.018	[-26 18 -1⟩	Monzismic
1	315\1171	322.801	[-6 23 -13⟩	Senior
1	335\1171	343.296	8000/6561	Raider
1	547\1171	560.547	864/625	Whoosh

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

Music

Francium

• "Right On Friendly Lovers" from Naughty Girl Era (2024) – Spotify | Bandcamp | YouTube − friesachic in 1171edo