1323edo

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← 1322edo1323edo1324edo →
Prime factorization 33 × 72
Step size 0.907029¢
Fifth 774\1323 (702.041¢) (→86\147)
Semitones (A1:m2) 126:99 (114.3¢ : 89.8¢)
Consistency limit 29
Distinct consistency limit 29

1323 equal divisions of the octave (1323edo), or 1323-tone equal temperament (1323tet), 1323 equal temperament (1323et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 1323 equal parts of about 0.907 ¢ each.

Theory

1323edo is the smallest uniquely consistent EDO in the 29-odd-limit.

It provides the optimal patent val for the 11-limit trinealimmal temperament, which has a period of 1\27 octave. In additoin, it tunes well 441 & 1308 temperament, which is a member of the augmented-cloudy equivalence continuum.

1323's divisors are 1, 3, 7, 9, 21, 27, 49, 63, 147, 189, 441, of which 441EDO is a member of the zeta edos. 1323edo shares the 7-limit mapping with 441edo. As such, it can be interpreted as an improvement for 441edo into the 29-limit by splitting each step of 441edo into three.

Prime harmonics

Approximation of prime harmonics in 1323edo
Harmonic 2 3 5 7 11 13 17 19 23 29
Error absolute (¢) +0.000 +0.086 +0.081 -0.118 +0.156 +0.289 +0.260 -0.007 +0.297 -0.099
relative (%) +0 +9 +9 -13 +17 +32 +29 -1 +33 -11
Steps
(reduced)
1323
(0)
2097
(774)
3072
(426)
3714
(1068)
4577
(608)
4896
(927)
5408
(116)
5620
(328)
5985
(693)
6427
(1135)

Regular temperament properties

Rank-2 temperaments

Periods

per octave

Generator

(reduced)

Cents

(reduced)

Associated

ratio

Temperaments
3 177\1323 160.544 154478651796875/140737488355328 441 & 1308
27 299\1323
(5\1323)
271.201
(4.535)
1375/1176
(?)
Trinealimmal