441edo: Difference between revisions
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| Fifth = 258\441 (702.04¢) (→ [[147edo|86\147]]) | | Fifth = 258\441 (702.04¢) (→ [[147edo|86\147]]) | ||
| Semitones = 42:33 (114.286¢ : 89.796¢) | | Semitones = 42:33 (114.286¢ : 89.796¢) | ||
| Consistency = | | Consistency = 17 | ||
}} | }} | ||
The '''441 equal divisions of the octave''' ('''441edo'''), or the '''441(-tone) equal temperament''' ('''441tet''', '''441et''') when viewed from a [[regular temperament]] perspective, is the [[EDO|equal division of the octave]] into 441 parts of about 2.721 [[cent]]s each, a size close to [[625/624]], the tunbarsma. | The '''441 equal divisions of the octave''' ('''441edo'''), or the '''441(-tone) equal temperament''' ('''441tet''', '''441et''') when viewed from a [[regular temperament]] perspective, is the [[EDO|equal division of the octave]] into 441 parts of about 2.721 [[cent]]s each, a size close to [[625/624]], the tunbarsma. | ||
Revision as of 23:43, 27 January 2022
| ← 440edo | 441edo | 442edo → |
The 441 equal divisions of the octave (441edo), or the 441(-tone) equal temperament (441tet, 441et) when viewed from a regular temperament perspective, is the equal division of the octave into 441 parts of about 2.721 cents each, a size close to 625/624, the tunbarsma.
Theory
Script error: No such module "primes_in_edo". It is a very strong 7-limit system; strong enough to qualify as a zeta peak edo. It is also very strong simply considered as a 5-limit system; it is the first division past 118 with a lower 5-limit relative error. In the 5-limit It tempers out the hemithirds comma, [38 -2 -15⟩, the ennealimma, [1 -27 18⟩, whoosh, [37 25 -33⟩, and egads, [-36 -52 51⟩. In the 7-limit it tempers out 2401/2400, 4375/4374, 420175/419904 and 250047/250000, so that it supports ennealimmal temperament. In the 11-limit it tempers out 4000/3993, and in the 13-limit, 1575/1573, 2080/2079 and 4096/4095. It provides the optimal patent val for 11- and 13-limit semiennealimmal temperament, and the 7-limit 41&359 temperament. Since it tempers out 1575/1573, the nicola, it allows the nicolic tetrad.
The steps of 441 are only 1/30 of a cent sharp of 1/8 syntonic comma. Lowering the fifth, which is only 1/12 of a cent sharp, by two steps gives a generator, 256\441, close to 1/4 comma meantone. Like 205edo but even more accurately, 441 can be used as a basis for a Vicentino style "adaptive JI" system.
441 factors into primes as 32×72, and has divisors 3, 7, 9, 21, 49, 63 and 147.
Table of intervals
| Step | Name | Asosociated ratio | Comments |
|---|---|---|---|
| 0 | Prime | 1/1 | Exact |
| 8 | Syntonic comma | 81/80 | |
| 9 | Pythagorean comma | 531441/524288 | |
| 10 | Septimal comma | 64/63 | |
| 75 | Whole tone | 9/8 | |
| 85 | Septimal supermajor second | 8/7 | |
| 98 | Septimal subminor third | 7/6 | |
| 142 | Classical major 3rd | 5/4 | |
| 150 | Pythagorean major 3rd | 81/64 | |
| 258 | Perfect 5th | 3/2 | |
| 356 | Harmonic 7th | 7/4 | |
| 441 | Octave | 2/1 | Exact |