2513edo

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← 2512edo2513edo2514edo →
Prime factorization 7 × 359
Step size 0.477517¢ 
Fifth 1470\2513 (701.95¢) (→210\359)
Semitones (A1:m2) 238:189 (113.6¢ : 90.25¢)
Consistency limit 11
Distinct consistency limit 11

2513 equal divisions of the octave (abbreviated 2513edo or 2513ed2), also called 2513-tone equal temperament (2513tet) or 2513 equal temperament (2513et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2513 equal parts of about 0.478 ¢ each. Each step represents a frequency ratio of 21/2513, or the 2513th root of 2.

2513edo is a very strong 5-limit system, with a lower 5-limit relative error than any edo until we reach the cosmically excellent 4296edo. 2513 = 7 × 359, and it shares its harmonic 3 with 359edo. A basis for its 5-limit commas consists of senior, [-17 62 -35, and fortune, [-107 47 14; it also tempers out pirate, [-90 -15 49. It is uniquely consistent through to the 11-odd-limit, and tempers out 420175/419904 in the 7-limit and 151263/151250 and 234375/234256 in the 11-limit.

Prime harmonics

Approximation of prime harmonics in 2513edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.0000 -0.0051 -0.0025 +0.0559 +0.2141 -0.0979 +0.0983 -0.0200 +0.1379 -0.0507 +0.0500
Relative (%) +0.0 -1.1 -0.5 +11.7 +44.8 -20.5 +20.6 -4.2 +28.9 -10.6 +10.5
Steps
(reduced)
2513
(0)
3983
(1470)
5835
(809)
7055
(2029)
8694
(1155)
9299
(1760)
10272
(220)
10675
(623)
11368
(1316)
12208
(2156)
12450
(2398)