132edo

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← 131edo 132edo 133edo →
Prime factorization 22 × 3 × 11
Step size 9.09091¢ 
Fifth 77\132 (700¢) (→7\12)
Semitones (A1:m2) 11:11 (100¢ : 100¢)
Consistency limit 5
Distinct consistency limit 5

132 equal divisions of the octave (abbreviated 132edo or 132ed2), also called 132-tone equal temperament (132tet) or 132 equal temperament (132et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 132 equal parts of about 9.09 ¢ each. Each step represents a frequency ratio of 21/132, or the 132nd root of 2.

132edo is only consistent to the 5-odd-limit. The equal temperament tempers out 531441/524288 (Pythagorean comma) and 48828125/47775744 (sycamore comma) in the 5-limit.

Using the patent val, it tempers out 1728/1715, 4000/3969, and 234375/229376 in the 7-limit; 625/616, 1350/1331, 2187/2156, and 2420/2401 in the 11-limit; 169/168, 325/324, 364/363, 640/637, and 1875/1859 in the 13-limit.

Odd harmonics

Approximation of odd harmonics in 132edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -1.96 -4.50 +3.90 -3.91 +3.23 -4.16 +2.64 +4.14 +2.49 +1.95 -1.00
Relative (%) -21.5 -49.5 +42.9 -43.0 +35.5 -45.8 +29.0 +45.5 +27.4 +21.4 -11.0
Steps
(reduced)
209
(77)
306
(42)
371
(107)
418
(22)
457
(61)
488
(92)
516
(120)
540
(12)
561
(33)
580
(52)
597
(69)

Subsets and supersets

Since 132 factors into 22 × 3 × 11, 132edo has subset edos 2, 3, 6, 11, 12, 22, 44, and 66.