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== Theory ==
== Theory ==
120edo approximates with less than 25% error harmoincs: 2, 3, 7, 11, 13, 23, 29. Therefore, it's well suited for no-5s 13-limit.
120edo is the 10th highly composite EDO and the 5th factorial EDO (120 = 1*2*3*4*5 = 5!).


Its [[patent val]] is [[contorted]] only through the 3-limit and does not temper out 81/80 in the 5-limit or 64/63 and 5120/5103 in the 7-limit. However, 5120/5103 is done about as badly as this interval can be done relative to an equal division, falling close to exactly in the middle of a step (1\120 is ~42.42 relative cents sharp of it).  
120edo is an excellent tuning in the 2.3.7.11.13.23.29 subgroup. In the no-5s 11-limit, it tempers out [[243/242]].


120edo is the 5th factorial EDO (120 = 1*2*3*4*5), and the 10th highly composite EDO.
120edo shares the perfect fifth with 12edo, tempering out the [[Pythagorean comma]]. The sharp fifth of 710 cents also has regular temperament interpretations. It is used in the 120b val for tuning the 5-limit [[superpyth]] temperament where it represents 3/2, and in the 120g val as a tuning for the 19-limit [[surmarvelpyth]] temperament where it represents 675/448, which is [[marvel comma]] sharp of 3/2.


=== Prime harmonics ===
=== Prime harmonics ===

Revision as of 23:12, 25 December 2022

← 119edo 120edo 121edo →
Prime factorization 23 × 3 × 5 (highly composite)
Step size 10 ¢ 
Fifth 70\120 (700 ¢) (→ 7\12)
Semitones (A1:m2) 10:10 (100 ¢ : 100 ¢)
Consistency limit 3
Distinct consistency limit 3

Template:EDO intro

Theory

120edo is the 10th highly composite EDO and the 5th factorial EDO (120 = 1*2*3*4*5 = 5!).

120edo is an excellent tuning in the 2.3.7.11.13.23.29 subgroup. In the no-5s 11-limit, it tempers out 243/242.

120edo shares the perfect fifth with 12edo, tempering out the Pythagorean comma. The sharp fifth of 710 cents also has regular temperament interpretations. It is used in the 120b val for tuning the 5-limit superpyth temperament where it represents 3/2, and in the 120g val as a tuning for the 19-limit surmarvelpyth temperament where it represents 675/448, which is marvel comma sharp of 3/2.

Prime harmonics

Approximation of prime harmonics in 120edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 -1.96 +3.69 +1.17 -1.32 -0.53 -4.96 +2.49 +1.73 +0.42 +4.96
Relative (%) +0.0 -19.6 +36.9 +11.7 -13.2 -5.3 -49.6 +24.9 +17.3 +4.2 +49.6
Steps
(reduced) 		120
(0) 		190
(70) 		279
(39) 		337
(97) 		415
(55) 		444
(84) 		490
(10) 		510
(30) 		543
(63) 		583
(103) 		595
(115)

Miscellaneous properties

Being the simplest division of the octave by the Germanic long hundred, it has a unit step which is the fine relative cent of 1edo.

120edo also has a concoctic generator that resembles the leap day excess of earth, 29\120 corresponding to 5 hours and 48 minutes.

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