6079edo

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Prime factorization 6079 (prime)
Step size 0.197401¢ 
Fifth 3556\6079 (701.958¢)
Semitones (A1:m2) 576:457 (113.7¢ : 90.21¢)
Consistency limit 29
Distinct consistency limit 29
Special properties

6079 equal divisions of the octave (abbreviated 6079edo or 6079ed2), also called 6079-tone equal temperament (6079tet) or 6079 equal temperament (6079et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 6079 equal parts of about 0.197 ¢ each. Each step represents a frequency ratio of 21/6079, or the 6079th root of 2.

6079edo is a very strong 11- and 13-limit system, with a lower 11- and 13-limit relative error than any smaller division. It is also a zeta peak edo and distinctly consistent through the 29-odd-limit.

We may note it is a pirate, euzenius and starscape system. A basis for the 11-limit commas is {3294225/3294172, 14348907/14348180, 35156250/35153041, 100663296/100656875}, and for the 13-limit commas, {123201/123200, 1574640/1574573, 1664000/1663893, 1990656/1990625, 3294225/3294172}.

The approximation to harmonics 17 and 23 is weaker, though still quite impressive. It tempers out 14400/14399, 28561/28560, 31213/31212, 37180/37179, 194481/194480, 336141/336140 in the 17-limit; 10830/10829, 43681/43680, 89376/89375, 104976/104975, 165376/165375, 228096/228095 in the 19-limit; 12168/12167, 16929/16928, 19551/19550, 21736/21735, 25025/25024, 43264/43263 among others in the 23-limit. Its 2.3.5.7.11.13.19-subgroup is particularly strong, holding the record of relative error until 8269.

Prime harmonics

Approximation of prime harmonics in 6079edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.0000 +0.0026 -0.0002 +0.0177 +0.0227 +0.0053 +0.0619 -0.0299 +0.0527 +0.0658 +0.0870
Relative (%) +0.0 +1.3 -0.1 +8.9 +11.5 +2.7 +31.3 -15.1 +26.7 +33.4 +44.1
Steps
(reduced)
6079
(0)
9635
(3556)
14115
(1957)
17066
(4908)
21030
(2793)
22495
(4258)
24848
(532)
25823
(1507)
27499
(3183)
29532
(5216)
30117
(5801)

Subsets and supersets

6079edo is the 793rd prime edo.