256ed5

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← 255ed5256ed5257ed5 →
Prime factorization 28
Step size 10.884¢ 
Octave 110\256ed5 (1197.24¢) (→55\128ed5)
Twelfth 175\256ed5 (1904.71¢)
Consistency limit 2
Distinct consistency limit 2

256 equal divisions of the 5th harmonic is an equal-step tuning where each step represents a frequency ratio of 256th root of 5, which amounts to 3.90625 millipentaves or about 10.884 cents. It is equivalent to 110.2532 EDO.

256ed5 combines dual-fifth systems 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.

Table of intervals

Step Name Size (cents) Size (millipentaves) Associated ratio
0 prime, unison 0 0 exact 1/1
29 classical minor third 315.63710 113.28125 6/5
64 minor fifth 696.57843 250 3/2 I, exact 4th root of(5)
65 major fifth 253.90625
128 octitone, symmetric ninth 1393.15686 500
256 pentave, fifth harmonic 2786.31371 1000 exact 5/1

See also