16625edo

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← 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 (16625edo), or 16625-tone equal temperament (16625tet), 16625 equal temperament (16625et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 16625 equal parts of about 0.0722 ¢ each.

Theory

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

16625edo is consistent in the 29-limit.

16625edo has 15 proper divisors: 1, 5, 7, 19, 25, 35, 95, 125, 133, 175, 475, 665, 875, 2375, 3325, of which 665 is a continued fraction approximant to the perfect fifth 3/2.

16625edo tempers out the comma [802 -799 200 which equates 200 syntonic commas with 12/1, and supports rank 2 temperament 9763 & 16625 tempering out this comma.