14348edo: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
The 14348 division divides the octave into 14348 equal parts of 0.083635 cents each. It is a strong 17-limit system, with a lower 17-limit relative error than any smaller edo aside from [[7033edo|7033]]. It is also distinctly consistent in the 29 limit, and has a lower 23-limit relative error than any lower division aside from [[2460edo|2460]], [[8269edo|8269]], [[8539edo|8539]] and [[11664edo|11664]]. Besides all that it is a  [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta peak edo]]. It factors as 2^2 * 17 * 211, so [[17edo|17]], [[34edo|34]], [[68edo|68]] and [[422edo|422]] are all divisors.
{{EDO intro|14348}}


[[Category:Equal divisions of the octave|#####]] <!-- 5-digit number -->
14348edo is a strong 17-limit system, with a lower 17-limit [[relative error]] than any smaller edo aside from [[7033edo|7033]]. It is also distinctly [[consistent]] in the 29-odd-limit, and has a lower 23-limit relative error than any lower division aside from [[2460edo|2460]], [[8269edo|8269]], [[8539edo|8539]] and [[11664edo|11664]]. Besides all that it is a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak, integral and gap edo]]. It factors as 2<sup>2</sup> × 17 × 211, so [[17edo|17]], [[34edo|34]], [[68edo|68]] and [[422edo|422]] are all divisors.
 
=== Prime harmonics ===
{{Harmonics in equal|14348}}

Revision as of 11:21, 7 January 2023

← 14347edo 14348edo 14349edo →
Prime factorization 22 × 17 × 211
Step size 0.0836353 ¢ 
Fifth 8393\14348 (701.951 ¢)
Semitones (A1:m2) 1359:1079 (113.7 ¢ : 90.24 ¢)
Consistency limit 29
Distinct consistency limit 29

Template:EDO intro

14348edo is a strong 17-limit system, with a lower 17-limit relative error than any smaller edo aside from 7033. It is also distinctly consistent in the 29-odd-limit, and has a lower 23-limit relative error than any lower division aside from 2460, 8269, 8539 and 11664. Besides all that it is a zeta peak, integral and gap edo. It factors as 22 × 17 × 211, so 17, 34, 68 and 422 are all divisors.

Prime harmonics

Approximation of prime harmonics in 14348edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.0000 -0.0035 -0.0020 +0.0060 +0.0063 +0.0076 +0.0070 -0.0221 -0.0056 -0.0260 +0.0160
Relative (%) +0.0 -4.2 -2.4 +7.2 +7.5 +9.1 +8.3 -26.4 -6.7 -31.1 +19.1
Steps
(reduced)
14348
(0)
22741
(8393)
33315
(4619)
40280
(11584)
49636
(6592)
53094
(10050)
58647
(1255)
60949
(3557)
64904
(7512)
69702
(12310)
71083
(13691)