58973edo: Difference between revisions

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{{Infobox ET|Consistency=47}}
{{Infobox ET|Consistency=47|Distinct consistency=47}}
'''58973edo''' divides the octave into equal steps of about 0.0203483¢ each. It is [[consistent]] in the 47-odd limit and is a [[zeta peak integer edo]] and a [[zeta integral edo]].
{{EDO intro|58973}} It is [[consistent]] in the 47-odd-limit and is a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak, integral, and gap edo]].


{{Primes in edo|58973|prec=5|columns=15}}
=== Prime harmonics ===
 
{{Harmonics in equal|58973|prec=5|columns=15}}
[[Category:Equal divisions of the octave|#####]] <!-- 5-digit number -->
[[Category:Zeta]]

Revision as of 08:05, 14 February 2023

← 58972edo 58973edo 58974edo →
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

Template:EDO intro It is consistent in the 47-odd-limit and is a zeta peak, integral, and gap edo.

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 (%) +0.0 +0.6 -6.6 -14.2 -6.1 -3.1 +5.4 -2.9 -1.9 +28.7 +18.1 -9.3 +8.6 -11.1 +23.2
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)