# 7315edo

 ← 7314edo 7315edo 7316edo →
Prime factorization 5 × 7 × 11 × 19
Step size 0.164046¢
Fifth 4279\7315 (701.955¢) (→389\665)
Semitones (A1:m2) 693:550 (113.7¢ : 90.23¢)
Consistency limit 27
Distinct consistency limit 27

7315 equal divisions of the octave (abbreviated 7315edo or 7315ed2), also called 7315-tone equal temperament (7315tet) or 7315 equal temperament (7315et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 7315 equal parts of about 0.164 ¢ each. Each step represents a frequency ratio of 21/7315, or the 7315th root of 2.

7315edo is consistent up to the 27-odd-limit. 7315 = 11 × 665, and 7315edo shares its excellent approximation to harmonic 3 with 665edo. It has a sharp tendency, with most lower harmonics tuned sharp. In the 13-limit it tempers out 123201/123200; in the 17-limit, 14400/14399 and 194481/194480; in the 19-limit, 14080/14079, 23409/23408, 27456/27455, 89376/89375; in the 23-limit, 23276/23275, 52326/52325 among others.

### Prime harmonics

Approximation of prime harmonics in 7315edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.0000 -0.0001 +0.0157 +0.0326 +0.0423 +0.0465 +0.0343 +0.0673 +0.0237 -0.0215 +0.0089
Relative (%) +0.0 -0.1 +9.6 +19.9 +25.8 +28.3 +20.9 +41.0 +14.4 -13.1 +5.4
Steps
(reduced)
7315
(0)
11594
(4279)
16985
(2355)
20536
(5906)
25306
(3361)
27069
(5124)
29900
(640)
31074
(1814)
33090
(3830)
35536
(6276)
36240
(6980)

### Subsets and supersets

Since 7315 factors into 5 × 7 × 11 × 19, 7315edo contains subset edos 5, 7, 11, 19, 35, 55, 77, 95, 133, 209, 385, 665, 1045, and 1463.