1517edo

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1517edo

1518edo →

Prime factorization	37 × 41
Step size	0.791035 ¢
Fifth	887\1517 (701.648 ¢)
Semitones (A1:m2)	141:116 (111.5 ¢ : 91.76 ¢)
Dual sharp fifth	888\1517 (702.439 ¢) (→ 24\41)
Dual flat fifth	887\1517 (701.648 ¢)
Dual major 2nd	258\1517 (204.087 ¢)
Consistency limit	5
Distinct consistency limit	5

1517edo is only consistent to the 5-odd-limit and the errors of both harmonics 3 and 5 are quite large. To start with, we may consider the patent val and 1517d val up to the 11-limit. Otherwise, it has a reasonable approximation to the 2.9.15.7.11.17 subgroup with optional additions of either 13 or 19.

For higher harmonics, the first 5 prime harmonics which are approximated below 25% are: 7, 11, 19, 23, 59. In the 2.7.11.19.23.59 subgroup, 1517edo has a comma basis {52877/52864, 157757/157696, 194672/194579, [18 -12  2  1 1  0⟩, [44  -4 -9  1 0 -1⟩}.

Odd harmonics

Approximation of odd harmonics in 1517edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-0.307	-0.289	+0.192	+0.177	+0.033	+0.342	+0.195	+0.252	-0.084	-0.115	-0.193
	Relative (%)	-38.8	-36.5	+24.3	+22.4	+4.2	+43.3	+24.7	+31.9	-10.6	-14.6	-24.3
Steps (reduced)		2404 (887)	3522 (488)	4259 (1225)	4809 (258)	5248 (697)	5614 (1063)	5927 (1376)	6201 (133)	6444 (376)	6663 (595)	6862 (794)

Subsets and supersets

Since 1517 factors into 37 × 41, 1517edo contains 37edo and 41edo as subsets.