# 15601edo

 ← 15600edo 15601edo 15602edo →
Prime factorization 15601 (prime)
Step size 0.0769181¢
Fifth 9126\15601 (701.955¢)
(convergent)
Semitones (A1:m2) 1478:1173 (113.7¢ : 90.22¢)
Consistency limit 5
Distinct consistency limit 5

15601 equal divisions of the octave (abbreviated 15601edo or 15601ed2), also called 15601-tone equal temperament (15601tet) or 15601 equal temperament (15601et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 15601 equal parts of about 0.0769 ¢ each. Each step represents a frequency ratio of 21/15601, or the 15601st root of 2. It is the denominator of the next convergent for log23 past 665, before 31867, and has a fifth which is 0.000002 cents stretched.

This system is at its best behavior in the 2.3.19.23 subgroup.

### Prime harmonics

Approximation of prime harmonics in 15601edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.0000 +0.0000 -0.0308 +0.0351 +0.0313 +0.0338 +0.0379 +0.0064 -0.0069 -0.0278 -0.0320
Relative (%) +0.0 +0.0 -40.0 +45.6 +40.7 +44.0 +49.2 +8.3 -9.0 -36.2 -41.7
Steps
(reduced)
15601
(0)
24727
(9126)
36224
(5022)
43798
(12596)
53971
(7168)
57731
(10928)
63769
(1365)
66272
(3868)
70572
(8168)
75789
(13385)
77290
(14886)

### Subsets and supersets

15601edo is the 1819th prime edo.

31202edo, which doubles 15601edo, provides a good correction to harmonics 5, 7, 11, 13 and 17. 78005edo, which slices each step of 15601edo in five, is notable for an exceptional approximation quality of the 5-limit.