1171edo

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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

1171 equal divisions of the octave (abbreviated 1171edo or 1171ed2), also called 1171-tone equal temperament (1171tet) or 1171 equal temperament (1171et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1171 equal parts of about 1.02 ¢ each. Each step represents a frequency ratio of 21/1171, or the 1171st root of 2.

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 it is distinct

Music

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