190edo: Difference between revisions
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The '''190 equal divisions of the octave''' ('''190edo''') or '''190(-tone) equal temperament''' ('''190tet''', '''190et''') when view from a [[regular temperament]] perspective, divides the [[octave]] into 190 equal parts of | {{Infobox ET | ||
| Prime factorization = 2 × 5 × 19 | |||
| Step size = 6.31579¢ | |||
| Fifth = 111\190 (701.05¢) | |||
| Semitones = 17:15 (107.37¢ : 94.74¢) | |||
| Consistency = 15 | |||
}} | |||
The '''190 equal divisions of the octave''' ('''190edo''') or '''190(-tone) equal temperament''' ('''190tet''', '''190et''') when view from a [[regular temperament]] perspective, divides the [[octave]] into 190 equal parts of about 6.32 [[cent]]s each. | |||
== Theory == | == Theory == | ||
Revision as of 12:48, 11 November 2021
| ← 189edo | 190edo | 191edo → |
The 190 equal divisions of the octave (190edo) or 190(-tone) equal temperament (190tet, 190et) when view from a regular temperament perspective, divides the octave into 190 equal parts of about 6.32 cents each.
Theory
190edo is interesting because of the utility of its approximations; it tempers out 1029/1024, 4375/4374, 385/384, 441/440, 3025/3024 and 9801/9800. It provides the optimal patent val for both the 7- and 11-limit versions of unidec, the 72 & 118 temperament, which tempers out 1029/1024, 4375/4374, and in the 11-limit, 385/384 and 441/440. It also provides the optimal patent val for the rank-3 11-limit temperament portent, which tempers out 385/384 and 441/440, and gamelan, the rank-3 7-limit temperament which tempers out 1029/1024, as well as slendric, the 2.3.7 subgroup temperament featured in the #Music section. In the 13-limit, 190et tempers out 847/845, 625/624, 729/728, 1575/1573 and 1001/1000, and provides the optimal patent val for the ekadash temperament and the rank-3 portentous temperament.
Prime harmonics
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