1171edo: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
The '''1171 equal divisions of the octave''' ('''1171edo''') divides the [[octave]] into 1171 parts of size 1.0248 [[cent]]s each. It is a very strong 5-limit division, being the first one past [[612edo|612]] with a lower 5-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]]. It has a 5-limit [[comma basis]] consisting of the [[monzisma]], {{monzo| 54 -37 2 }} and whoosh, {{monzo| 37 25 -33 }}. While not a strong higher-limit system, it is uniquely consistent through the [[27-odd-limit]], and is very strong on the 2.3.5.11 subgroup. We might also note that 1171 is a [[prime number]].
{{EDO intro|1171}}
 
1171edo is a very strong 5-limit division, being the first one past [[612edo|612]] with a lower 5-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]]. It has a 5-limit [[comma basis]] consisting of the [[monzisma]], {{monzo| 54 -37 2 }} and whoosh, {{monzo| 37 25 -33 }}. While not a strong higher-limit system, it is uniquely consistent through the [[27-odd-limit]], and is very strong on the 2.3.5.11 subgroup.
 
=== Subsets and supersets ===
1171edo is the 193rd [[prime edo]].


=== Prime harmonics ===
=== Prime harmonics ===

Revision as of 21:22, 27 September 2023

← 1170edo 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

Template:EDO intro

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 uniquely consistent through the 27-odd-limit, and is very strong on the 2.3.5.11 subgroup.

Subsets and supersets

1171edo is the 193rd prime edo.

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)