4172edo

← 4171edo

4172edo

4173edo →

Prime factorization	22 × 7 × 149
Step size	0.287632 ¢
Fifth	2440\4172 (701.822 ¢) (→ 610\1043)
Semitones (A1:m2)	392:316 (112.8 ¢ : 90.89 ¢)
Dual sharp fifth	2441\4172 (702.109 ¢)
Dual flat fifth	2440\4172 (701.822 ¢) (→ 610\1043)
Dual major 2nd	709\4172 (203.931 ¢)
Consistency limit	7
Distinct consistency limit	7

Theory

The first 8 prime harmonics below 25% in 4172edo are 2, 5, 13, 17, 31, 37, 53, 61. Therefore, 4172edo can be thought of as a 2.5.13.17.31.37.53.61 subgroup temperament, on which it is consistent. Other than that, it offers satisfactory representation of the 13-odd-limit (<28% error).

4172's divisors are 1, 2, 4, 7, 14, 28, 149, 298, 596, 1043, 2086. Notable member of the group is 149edo, which is the smallest edo uniquely consistent in the 17-odd limit. Therefore from a logarithmic pitch or highly composite EDO theory perspective, 4172edo can be thought of as a compound of 28 149edos interlocked together.

Odd harmonics

Approximation of odd harmonics in 4172edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-0.133	-0.024	-0.082	+0.021	+0.072	-0.067	+0.130	+0.030	-0.102	+0.072	-0.086
	Relative (%)	-46.4	-8.4	-28.5	+7.3	+25.1	-23.5	+45.2	+10.5	-35.4	+25.2	-30.0
Steps (reduced)		6612 (2440)	9687 (1343)	11712 (3368)	13225 (709)	14433 (1917)	15438 (2922)	16300 (3784)	17053 (365)	17722 (1034)	18325 (1637)	18872 (2184)