1517edo: Difference between revisions

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1517edo, despite its size, is a dual fifths system with a consistency limit of only 5.
1517edo, despite its size, is a dual fifths system with a consistency limit of only 5.


[[Category:Equal divisions of the octave|####]]
{{Harmonics in equal|1517}}
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[[Category:Equal divisions of the octave|####]] <!-- 4-digit number -->

Revision as of 14:26, 8 December 2022

← 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

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, despite its size, is a dual fifths system with a consistency limit of only 5.


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)