122edo: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
'''122edo''' is the [[Equal_division_of_the_octave|equal division of the octave]] into 122 parts of 9.836 [[cent|cent]]s each. It is the [[Optimal_patent_val|optimal patent val]] for 7-limit [[Marvel_temperaments|tritonic temperament]] and 11-limit [[Marvel_temperaments|tritoni temperament]], and the planar [[Squalentine_temperament|squalentine temperament]]. It [[tempering_out|tempers out]] 78732/78125 in the [[5-limit|5-limit]], 225/224 in the [[7-limit|7-limit]], 385/384 and 4000/3993 in the [[11-limit|11-limit]], and 351/350 and 364/363 in the [[13-limit|13-limit]].
{{EDO intro}}


122 is flat in tendency, with the odd primes from 3 to 13 tuned flat. 122 = 2 * [[61edo|61]]. 122=[[55edo|55]]+[[67edo|67]], and so using the c val it is the convergent towards [[1/6-comma meantone]], with a fifth just a hundredth of a cent flatter.
It is the [[optimal patent val]] for the 7-limit [[tritonic]] temperament and the 11-limit [[Marvel temperaments #Tritoni|tritoni]] temperament, and the planar [[squalentine]] temperament. It [[tempering out|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]].
{{harmonics in equal|122}}
 
122 is flat in tendency, with the odd primes from 3 to 13 tuned flat. 122 = 2 × [[61edo|61]]. 122 = [[55edo|55]] + [[67edo|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 ===
{{Harmonics in equal|122}}


[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
[[Category:Meantone]]
[[Category:Meantone]]

Revision as of 08:29, 29 May 2024

← 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

Template:EDO intro

It is the optimal patent val for the 7-limit tritonic temperament and the 11-limit tritoni temperament, and the planar squalentine temperament. It 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.

122 is flat in tendency, with the odd primes from 3 to 13 tuned flat. 122 = 2 × 61. 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)