1063edo

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Prime factorization 1063 (prime)
Step size 1.12888¢
Fifth 622\1063 (702.164¢)
Semitones (A1:m2) 102:79 (115.1¢ : 89.18¢)
Consistency limit 7
Distinct consistency limit 7

1063 equal divisions of the octave (abbreviated 1063edo), or 1063-tone equal temperament (1063tet), 1063 equal temperament (1063et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1063 equal parts of about 1.13 ¢ each. Each step of 1063edo represents a frequency ratio of 21/1063, or the 1063rd root of 2.

Theory

1063et tempers out 2401/2400 in the 7-limit; 95703125/95664294, 26214400/26198073, 78675968/78594219, 1953125/1951488, 1879453125/1879048192, 3294225/3294172, 43923/43904, 102487/102400 and 781258401/781250000 in the 11-limit.

Prime harmonics

Approximation of prime harmonics in 1063edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error absolute (¢) +0.000 +0.209 -0.237 -0.246 -0.424 +0.488 +0.030 +0.511 +0.512 -0.038 -0.351
relative (%) +0 +18 -21 -22 -38 +43 +3 +45 +45 -3 -31
Steps
(reduced)
1063
(0)
1685
(622)
2468
(342)
2984
(858)
3677
(488)
3934
(745)
4345
(93)
4516
(264)
4809
(557)
5164
(912)
5266
(1014)

Subsets and supersets

1063edo is the 179th prime EDO.

Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.3 [1685 -1063 [1063 1685]] -0.0658 0.0658 5.83
2.3.5 [-20 -24 25, [77 -31 -12 [1063 1685 2468]] -0.0099 0.0956 8.47
2.3.5.7 2401/2400, 3500000000/3486784401, 3367254360064/3363025078125 [1063 1685 2468 2984]] +0.0144 0.0930 8.24
2.3.5.7.11 2401/2400, 19712/19683, 43923/43904, 1953125/1951488 [1063 1685 2468 2984 3677]] +0.0361 0.0937 8.30

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator* Cents* Associated
Ratio*
Temperaments
1 229\1063 258.514 [-32 13 5 Lafa
1 280\1063 316.087 6/5 Counterhanson

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

Music

Francium