122edo

From Xenharmonic Wiki
Jump to navigation Jump to search
← 121edo122edo123edo →
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.