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

The 1517 equal divisions of the octave, or the 1517-tone equal temperament (1517tet), 1517 equal temperament (1517et) when viewed from a regular temperament perspective, divides the octave into 1517 equal parts of about 0.791 cents each.

Theory

1517edo is a dual fifths system with a consistency limit of only 5.

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⟩}.

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)