# 133edo

 ← 132edo 133edo 134edo →
Prime factorization 7 × 19
Step size 9.02256¢
Fifth 78\133 (703.759¢)
Semitones (A1:m2) 14:9 (126.3¢ : 81.2¢)
Consistency limit 5
Distinct consistency limit 5

133 equal divisions of the octave (abbreviated 133edo or 133ed2), also called 133-tone equal temperament (133tet) or 133 equal temperament (133et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 133 equal parts of about 9.02 ¢ each. Each step represents a frequency ratio of 21/133, or the 133rd root of 2.

133edo is only consistent to the 5-odd-limit. The equal temperament tempers out 393216/390625 (würschmidt comma) and 131072000/129140163 (rodan comma) in the 5-limit.

Using the patent val, it tempers out 245/243, 1029/1024 and 395136/390625 in the 7-limit; 385/384, 441/440, 896/891 and 43923/43750 in the 11-limit; 196/195, 325/324, 352/351, 364/363 and 3146/3125 in the 13-limit. It supports rodan and superenneadecal.

Using the 133d val, it tempers out 1728/1715, 4000/3969 and 4375/4374. It supports enneadecal.

### Prime harmonics

Approximation of prime harmonics in 133edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 +1.80 +1.66 -3.41 -0.94 -1.43 +3.32 +0.23 +3.30 -1.01 +0.83
Relative (%) +0.0 +20.0 +18.4 -37.8 -10.4 -15.8 +36.7 +2.6 +36.6 -11.1 +9.2
Steps
(reduced)
133
(0)
211
(78)
309
(43)
373
(107)
460
(61)
492
(93)
544
(12)
565
(33)
602
(70)
646
(114)
659
(127)

### Subsets and supersets

Since 133 factors into 7 × 19, 133edo contains 7edo and 19edo as its subsets.