256ed5

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Revision as of 23:09, 17 January 2022 by Eliora (talk | contribs) (Theory)
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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

Approximation of harmonics in 256ed5
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -2.76 +2.75 +5.37 +0.00 -0.00 +5.23 +2.62 -5.38 -2.76 -4.50 -2.76
Relative (%) -25.3 +25.3 +49.4 +0.0 -0.0 +48.0 +24.0 -49.4 -25.3 -41.3 -25.4
Steps
(reduced)
110
(110)
175
(175)
221
(221)
256
(0)
285
(29)
310
(54)
331
(75)
349
(93)
366
(110)
381
(125)
395
(139)

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.

Uniquely, 6/5 is nearly perfect.

See also