333edo

 ← 332edo 333edo 334edo →
Prime factorization 32 × 37
Step size 3.6036¢
Fifth 195\333 (702.703¢) (→65\111)
Semitones (A1:m2) 33:24 (118.9¢ : 86.49¢)
Consistency limit 7
Distinct consistency limit 7

333 equal divisions of the octave (abbreviated 333edo or 333ed2), also called 333-tone equal temperament (333tet) or 333 equal temperament (333et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 333 equal parts of about 3.6 ¢ each. Each step represents a frequency ratio of 21/333, or the 333rd root of 2.

The equal temperament tempers out 15625/15552 in the 5-limit and 5120/5103 in the 7-limit, so it supports countercata. In the 11-limit it tempers out 1375/1372 and 4000/3993, and in the 13-limit 325/324, 364/363, 625/624 and 676/675, and provides the optimal patent val for the rank-2 temperament novemkleismic, for the rank-3 temperament tempering out 325/324, 625/624 and 676/675, the rank-4 temperament tempering out 325/324 and 1375/1372, and the rank-5 temperament tempering out 325/324.

Prime harmonics

Approximation of prime harmonics in 333edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 +0.75 -0.73 +0.54 +0.03 -0.89 -0.45 +1.59 -1.25 +1.05 +0.91
Relative (%) +0.0 +20.7 -20.2 +15.1 +0.9 -24.6 -12.5 +44.0 -34.6 +29.2 +25.3
Steps
(reduced)
333
(0)
528
(195)
773
(107)
935
(269)
1152
(153)
1232
(233)
1361
(29)
1415
(83)
1506
(174)
1618
(286)
1650
(318)

Subsets and supersets

Since 333 factors into 32 × 37, 333edo has subset edos 3, 9, 37, and 111.