# 129edo

 ← 128edo 129edo 130edo →
Prime factorization 3 × 43
Step size 9.30233¢
Fifth 75\129 (697.674¢) (→25\43)
Semitones (A1:m2) 9:12 (83.72¢ : 111.6¢)
Dual sharp fifth 76\129 (706.977¢)
Dual flat fifth 75\129 (697.674¢) (→25\43)
Dual major 2nd 22\129 (204.651¢)
Consistency limit 3
Distinct consistency limit 3

129 equal divisions of the octave (abbreviated 129edo or 129ed2), also called 129-tone equal temperament (129tet) or 129 equal temperament (129et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 129 equal parts of about 9.3 ¢ each. Each step represents a frequency ratio of 21/129, or the 129th root of 2.

129edo is inconsistent to the 5-odd-limit and both harmonics 3 and 5 are about halfway between its steps. The patent val is enfactored in the 5-limit, with the same tuning as 43edo. It is the last patent val that tempers out 81/80 so as to support meantone and its higher-limit expansions. It also tempers out 1029/1024 and 1728/1715 in the 7-limit; 176/175 and 540/539 in the 11-limit; 507/500, 676/675 and 847/845 in the 13-limit; 221/220 in the 17-limit; 171/170 and 286/285 in the 19-limit. It provides the optimal patent val for the 11-limit rank-3 clio temperament.

### Odd harmonics

Approximation of odd harmonics in 129edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -4.28 +4.38 -1.38 +0.74 -2.48 -3.32 +0.10 -2.63 +0.16 +3.64 +4.28
Relative (%) -46.0 +47.1 -14.9 +8.0 -26.7 -35.7 +1.1 -28.3 +1.7 +39.1 +46.1
Steps
(reduced)
204
(75)
300
(42)
362
(104)
409
(22)
446
(59)
477
(90)
504
(117)
527
(11)
548
(32)
567
(51)
584
(68)

### Subsets and supersets

Since 129 factors into 3 × 43, 129edo contains 3edo and 43edo as its subsets.