32768edo

From Xenharmonic Wiki
Jump to navigation Jump to search
← 32767edo32768edo32769edo →
Prime factorization 215
Step size 0.0366211¢ 
Fifth 19168\32768 (701.953¢) (→599\1024)
Semitones (A1:m2) 3104:2464 (113.7¢ : 90.23¢)
Consistency limit 9
Distinct consistency limit 9

32768 equal divisions of the octave (abbreviated 32768edo or 32768ed2), also called 32768-tone equal temperament (32768tet) or 32768 equal temperament (32768et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 32768 equal parts of about 0.0366 ¢ each. Each step represents a frequency ratio of 21/32768, or the 32768th root of 2.

Theory

Approximation of prime harmonics in 32768edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.0000 -0.0019 +0.0022 -0.0149 +0.0126 -0.0003 +0.0006 -0.0033 -0.0029 -0.0118 -0.0038
Relative (%) +0.0 -5.1 +6.0 -40.6 +34.5 -0.9 +1.8 -8.9 -7.8 -32.1 -10.5
Steps
(reduced)
32768
(0)
51936
(19168)
76085
(10549)
91991
(26455)
113359
(15055)
121256
(22952)
133938
(2866)
139196
(8124)
148228
(17156)
159186
(28114)
162339
(31267)

This is the 15th power of two EDO. It has a consistency limit of only 9.