16625edo

From Xenharmonic Wiki
Jump to navigation Jump to search
← 16624edo16625edo16626edo →
Prime factorization 53 × 7 × 19
Step size 0.0721805¢
Fifth 9725\16625 (701.955¢) (→389\665)
Semitones (A1:m2) 1575:1250 (113.7¢ : 90.23¢)
Consistency limit 29
Distinct consistency limit 29

16625 equal divisions of the octave (abbreviated 16625edo), or 16625-tone equal temperament (16625tet), 16625 equal temperament (16625et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 16625 equal parts of about 0.0722 ¢ each. Each step of 16625edo represents a frequency ratio of 21/16625, or the 16625th root of 2.

16625edo is consistent in the 29-odd-limit. It tempers out the comma [802 -799 200 which equates a stack of two hundred syntonic commas with 12/1, and supports the rank-2 temperament 6862 & 9763 tempering out this comma.

Prime harmonics

Approximation of prime harmonics in 16625edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error absolute (¢) +0.0000 -0.0001 -0.0039 -0.0199 -0.0037 +0.0137 -0.0050 +0.0148 -0.0157 +0.0048 +0.0351
relative (%) +0 -0 -5 -28 -5 +19 -7 +21 -22 +7 +49
Steps
(reduced)
16625
(0)
26350
(9725)
38602
(5352)
46672
(13422)
57513
(7638)
61520
(11645)
67954
(1454)
70622
(4122)
75204
(8704)
80764
(14264)
82364
(15864)

Subsets and supersets

16625edo has subset edos 5, 7, 19, 25, 35, 95, 125, 133, 175, 475, 665, 875, 2375, and 3325, of which 665 is a continued fraction approximant to the perfect fifth 3/2.