# 3696edo

 ← 3695edo 3696edo 3697edo →
Prime factorization 24 × 3 × 7 × 11
Step size 0.324675¢
Fifth 2162\3696 (701.948¢) (→1081\1848)
Semitones (A1:m2) 350:278 (113.6¢ : 90.26¢)
Consistency limit 17
Distinct consistency limit 17

3696 equal divisions of the octave (abbreviated 3696edo or 3696ed2), also called 3696-tone equal temperament (3696tet) or 3696 equal temperament (3696et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 3696 equal parts of about 0.325 ¢ each. Each step represents a frequency ratio of 21/3696, or the 3696th root of 2.

## Theory

3696edo is consistent in the 17-odd-limit. It is contorted in the 11-limit, sharing the mapping with 1848edo, and provides a satisfactory correction to 1848edo's representation for 13 and 17. Besides that, it is a strong tuning in 2.3.5.7.11.23.29.

### Harmonics

Approximation of prime harmonics in 3696edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 -0.007 +0.050 +0.005 -0.019 +0.057 -0.085 -0.110 -0.028 -0.032 +0.094
Relative (%) +0.0 -2.1 +15.4 +1.6 -5.9 +17.5 -26.3 -34.0 -8.5 -9.8 +29.0
Steps
(reduced)
3696
(0)
5858
(2162)
8582
(1190)
10376
(2984)
12786
(1698)
13677
(2589)
15107
(323)
15700
(916)
16719
(1935)
17955
(3171)
18311
(3527)