15601edo

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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

Template:EDO intro 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.

Todo: explain its xenharmonic value