1517edo

 ← 1516edo 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

1517 equal divisions of the octave (abbreviated 1517edo or 1517ed2), also called 1517-tone equal temperament (1517tet) or 1517 equal temperament (1517et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1517 equal parts of about 0.791 ¢ each. Each step represents a frequency ratio of 21/1517, or the 1517th root of 2.

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.