# 122edo

 ← 121edo 122edo 123edo →
Prime factorization 2 × 61
Step size 9.83607¢
Fifth 71\122 (698.361¢)
Semitones (A1:m2) 9:11 (88.52¢ : 108.2¢)
Dual sharp fifth 72\122 (708.197¢) (→36\61)
Dual flat fifth 71\122 (698.361¢)
Dual major 2nd 21\122 (206.557¢)
Consistency limit 7
Distinct consistency limit 7

122 equal divisions of the octave (abbreviated 122edo or 122ed2), also called 122-tone equal temperament (122tet) or 122 equal temperament (122et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 122 equal parts of about 9.84 ¢ each. Each step represents a frequency ratio of 21/122, or the 122nd root of 2.

122 is flat in tendency, with the prime harmonics from 3 to 13 tuned flat. The equal temperament tempers out 78732/78125 in the 5-limit; 225/224 in the 7-limit; 385/384 and 4000/3993 in the 11-limit; and 351/350 and 364/363 in the 13-limit. It provides the optimal patent val for the 7-limit tritonic temperament and the 11-limit tritoni temperament, and the planar squalentine temperament.

122 = 55 + 67, and so using the 122c val it is the convergent towards 1/6-comma meantone, with a fifth just a hundredth of a cent flatter.

### Odd harmonics

Approximation of odd harmonics in 122edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -3.59 -2.71 -4.89 +2.65 -0.50 -4.46 +3.53 +3.24 -2.43 +1.35 +1.23
Relative (%) -36.5 -27.5 -49.7 +26.9 -5.1 -45.4 +35.9 +33.0 -24.7 +13.7 +12.5
Steps
(reduced)
193
(71)
283
(39)
342
(98)
387
(21)
422
(56)
451
(85)
477
(111)
499
(11)
518
(30)
536
(48)
552
(64)

### Subsets and supersets

Since 122 factors into 2 × 61, 122edo contains 2edo and 61edo as its subsets.