58973edo

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Prime factorization 17 × 3469
Step size 0.0203483¢
Fifth 34497\58973 (701.955¢)
Semitones (A1:m2) 5587:4434 (113.7¢ : 90.22¢)
Consistency limit 47
Distinct consistency limit 47
Special properties

58973 equal divisions of the octave (abbreviated 58973edo), or 58973-tone equal temperament (58973tet), 58973 equal temperament (58973et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 58973 equal parts of about 0.0203 ¢ each. Each step of 58973edo represents a frequency ratio of 21/58973, or the 58973rd root of 2.

58973edo is a zeta peak, integral, and gap edo. It is distinctly consistent in the 47-odd-limit, and has lower relative errors than any smaller equal temperaments in the 37-limit and way beyond.

Prime harmonics

Approximation of prime harmonics in 58973edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47
Error absolute (¢) +0.00000 +0.00013 -0.00133 -0.00289 -0.00124 -0.00064 +0.00110 -0.00060 -0.00039 +0.00584 +0.00368 -0.00190 +0.00174 -0.00227 +0.00471
relative (%) +0 +1 -7 -14 -6 -3 +5 -3 -2 +29 +18 -9 +9 -11 +23
Steps
(reduced)
58973
(0)
93470
(34497)
136931
(18985)
165558
(47612)
204013
(27094)
218226
(41307)
241050
(5158)
250513
(14621)
266768
(30876)
286490
(50598)
292164
(56272)
307217
(12352)
315951
(21086)
320003
(25138)
327571
(32706)