1166edo

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← 1165edo1166edo1167edo →
Prime factorization 2 × 11 × 53
Step size 1.02916¢ 
Fifth 682\1166 (701.887¢) (→31\53)
Semitones (A1:m2) 110:88 (113.2¢ : 90.57¢)
Consistency limit 9
Distinct consistency limit 9

1166 equal divisions of the octave (abbreviated 1166edo or 1166ed2), also called 1166-tone equal temperament (1166tet) or 1166 equal temperament (1166et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1166 equal parts of about 1.03 ¢ each. Each step represents a frequency ratio of 21/1166, or the 1166th root of 2.

1166edo is consistent in the 9-odd-limit.

In the 5-limit, 1166edo naturally lends itself to interpretation as a superset of 22edo and 53edo. It inherits the mapping for 3/2 from 53edo, tempering out the 53rd-octave Mercator's comma, [-84 53, as well as the 22nd-octave major arcana comma, [-193 154 -22. In the 7-limit, it tempers out 2401/2400, 65625/65536, and [36 -50 15 3, providing a tuning for the tertiaseptal temperament.

In higher limits, it is a strong 2.3.17.19.41.43 subgroup tuning. Alternatively, 2.3.7/5.13/11.17.19 is also a strong subgroup choice.

Prime harmonics

Approximation of prime harmonics in 1166edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 -0.068 -0.379 -0.387 +0.312 +0.296 +0.019 -0.086 -0.487 -0.418 +0.419
Relative (%) +0.0 -6.6 -36.8 -37.6 +30.3 +28.7 +1.8 -8.3 -47.3 -40.6 +40.7
Steps
(reduced)
1166
(0)
1848
(682)
2707
(375)
3273
(941)
4034
(536)
4315
(817)
4766
(102)
4953
(289)
5274
(610)
5664
(1000)
5777
(1113)

Subsets and supersets

1166edo factors as 2 × 11 × 53, with subset edos 1, 2, 11, 22, 53, 106, 583, of which 22edo and 53edo are particularly notable. See above.