255edo: Difference between revisions
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The ''255 equal division'' divides the octave into 255 equal parts of 4.706 cents each. It tempers out the parakleisma, |8 14 -13 | The '''255 equal division''' divides the octave into 255 equal parts of 4.706 cents each. It tempers out the [[parakleisma]], {{monzo| 8 14 -13 }}, and the septendecima, {{monzo| -52 -17 34 }}, in the 5-limit. In the 7-limit it tempers out [[cataharry]], 19683/19600, [[mirkwai]], 16875/16807 and [[horwell]], 65625/65536, so that it [[support]]s the [[mirkat]] temperament, and in fact provides the [[optimal patent val]]. It also gives the optimal patent val for mirkat in the 11-limit, tempering out [[540/539]], 1375/1372, [[3025/3024]] and [[8019/8000]]. In the 13-limit it tempers out [[847/845]], [[625/624]], [[1575/1573]] and [[1716/1715]]. | ||
=== Prime harmonics === | |||
{{Harmonics in equal|255}} | |||
[[Category:Equal divisions of the octave]] | |||
[[Category:Mirkat]] | |||
Revision as of 09:40, 3 March 2022
The 255 equal division divides the octave into 255 equal parts of 4.706 cents each. It tempers out the parakleisma, [8 14 -13⟩, and the septendecima, [-52 -17 34⟩, in the 5-limit. In the 7-limit it tempers out cataharry, 19683/19600, mirkwai, 16875/16807 and horwell, 65625/65536, so that it supports the mirkat temperament, and in fact provides the optimal patent val. It also gives the optimal patent val for mirkat in the 11-limit, tempering out 540/539, 1375/1372, 3025/3024 and 8019/8000. In the 13-limit it tempers out 847/845, 625/624, 1575/1573 and 1716/1715.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | -0.78 | -0.43 | +0.59 | -0.73 | +1.83 | -1.43 | -1.04 | +2.31 | +1.01 | -1.51 |
| Relative (%) | +0.0 | -16.5 | -9.2 | +12.4 | -15.5 | +38.8 | -30.3 | -22.2 | +49.2 | +21.5 | -32.0 | |
| Steps (reduced) |
255 (0) |
404 (149) |
592 (82) |
716 (206) |
882 (117) |
944 (179) |
1042 (22) |
1083 (63) |
1154 (134) |
1239 (219) |
1263 (243) | |