4172edo: Difference between revisions

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← 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

Template:EDO intro

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.

Subsets and supersets

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, although its approximations have long been diluted by edo of this size.

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
Error	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)

Todo: explain its xenharmonic value

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