120edo: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
120edo means division of the octave into equal parts of 10 cents each. 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). Being the simplest division of the octave by the Germanic [https://en.wikipedia.org/wiki/Long_hundred long hundred], it has a unit step which is the fine relative cent of [[1edo|1edo]].
{{EDO intro|120}}
 
== 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.
 
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 the 5th factorial EDO (120 = 1*2*3*4*5), and the 10th highly composite EDO.
 
=== Prime harmonics ===
{{Harmonics in equal|120}}
 
=== Miscellaneous properties ===
Being the simplest division of the octave by the Germanic [[wikipedia:Long_hundred|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.
120edo also has a concoctic generator that resembles the leap day excess of earth, 29\120 corresponding to 5 hours and 48 minutes.
120edo is the 5th factorial EDO, and the 10th highly melodic EDO.


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

Revision as of 17:35, 12 October 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 approximates with less than 25% error harmoincs: 2, 3, 7, 11, 13, 23, 29. Therefore, it's well suited for no-5s 13-limit.

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

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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