8745edo

From Xenharmonic Wiki
Jump to navigation Jump to search
← 8744edo8745edo8746edo →
Prime factorization 3 × 5 × 11 × 53
Step size 0.137221¢
Fifth 5115\8745 (701.887¢) (→31\53)
Semitones (A1:m2) 825:660 (113.2¢ : 90.57¢)
Dual sharp fifth 5116\8745 (702.024¢)
Dual flat fifth 5115\8745 (701.887¢) (→31\53)
Dual major 2nd 1486\8745 (203.911¢)
Consistency limit 7
Distinct consistency limit 7

8745 equal divisions of the octave (abbreviated 8745edo), or 8745-tone equal temperament (8745tet), 8745 equal temperament (8745et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 8745 equal parts of about 0.137 ¢ each. Each step of 8745edo represents a frequency ratio of 21/8745, or the 8745th root of 2. This dual-fifths system is the largest number EDO which tempers out Mercator's comma.

Prime harmonics

Approximation of odd harmonics in 8745edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error absolute (¢) -0.0682 -0.0358 -0.0437 +0.0008 +0.0371 -0.0474 +0.0332 +0.0189 -0.0173 +0.0253 +0.0618
relative (%) -50 -26 -32 +1 +27 -35 +24 +14 -13 +18 +45
Steps
(reduced)
13860
(5115)
20305
(2815)
24550
(7060)
27721
(1486)
30253
(4018)
32360
(6125)
34166
(7931)
35745
(765)
37148
(2168)
38411
(3431)
39559
(4579)