256ed5: Difference between revisions
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== Theory == | == Theory == | ||
{| class="wikitable" | {| class="wikitable center-all" | ||
|- | |||
|+Approximation of prime harmonics in 256 e.d. 5 | |+Approximation of prime harmonics in 256 e.d. 5 | ||
|- | |- | ||
| | ! style="text-align:right" | Prime | ||
|25 | ! 2 | ||
! 3 | |||
! 5 | |||
! 7 | |||
! 11 | |||
! 13 | |||
! 17 | |||
! 19 | |||
! 23 | |||
|- | |||
! style="text-align:right" | Error (rc) | |||
| +25 | |||
| -26 | | -26 | ||
|0 | | 0 | ||
| -48 | | -48 | ||
|41 | | +41 | ||
| -1 | | -1 | ||
| -34 | | -34 | ||
|35 | | +35 | ||
| -26 | | -26 | ||
|- | |- | ||
| | ! style="text-align:right" | Steps (reduced) | ||
|110 (110) | | 110 (110) | ||
|175 (175) | | 175 (175) | ||
|256 (0) | | 256 (0) | ||
|310 (54) | | 310 (54) | ||
|381 (125) | | 381 (125) | ||
|408 (152) | | 408 (152) | ||
|451 (195) | | 451 (195) | ||
|468 (212) | | 468 (212) | ||
|499 (243) | | 499 (243) | ||
|} | |} | ||
In 256ed5, the just perfect fifth of [[3/2]], corresponds to approximately 64.5 steps, thus occurring almost halfway between the [[quarter-comma meantone]] fifth and it's next step. | In 256ed5, the just perfect fifth of [[3/2]], corresponds to approximately 64.5 steps, thus occurring almost halfway between the [[quarter-comma meantone]] fifth and it's next step. | ||
[[Category:Ed5]] | |||
Revision as of 15:07, 28 November 2021
256 equal divisions of the 5th harmonic is an equal-step tuning of 10.884 cents per each step. It is equivalent to 110.2532 EDO.
256ed5 combines dual-fifth temperaments with quarter-comma meantone.
Theory
| Prime | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 |
|---|---|---|---|---|---|---|---|---|---|
| Error (rc) | +25 | -26 | 0 | -48 | +41 | -1 | -34 | +35 | -26 |
| Steps (reduced) | 110 (110) | 175 (175) | 256 (0) | 310 (54) | 381 (125) | 408 (152) | 451 (195) | 468 (212) | 499 (243) |
In 256ed5, the just perfect fifth of 3/2, corresponds to approximately 64.5 steps, thus occurring almost halfway between the quarter-comma meantone fifth and it's next step.