15601edo

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← 15600edo15601edo15602edo →
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.