4190edo: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
The '''4190 equal temperament''' divides the octave into 4190 equal parts of 0.2864 cents each. It is notable for being a [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta gap edo]]. It is fairly strong in the 13-limit and the 4190g val does well if not outstandingly in a number of higher limits.
{{EDO intro|4190}}


[[Category:Equal divisions of the octave|####]] <!-- 4-digit number -->
4190edo is notable for being a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta gap edo]]. It is fairly strong in the 13-limit and the 4190g val does well if not outstandingly in a number of higher limits.
 
=== Prime harmonics ===
{{Harmonics in equal|4190}}
 
=== Divisors ===
Since 4190 factors into 2 × 5 × 419, 4190edo has subset edos 2, 5, 10, 419, 838, and 2095.

Revision as of 14:58, 31 January 2023

← 4189edo 4190edo 4191edo →
Prime factorization 2 × 5 × 419
Step size 0.286396 ¢ 
Fifth 2451\4190 (701.957 ¢)
Semitones (A1:m2) 397:315 (113.7 ¢ : 90.21 ¢)
Consistency limit 15
Distinct consistency limit 15

Template:EDO intro

4190edo is notable for being a zeta gap edo. It is fairly strong in the 13-limit and the 4190g val does well if not outstandingly in a number of higher limits.

Prime harmonics

Approximation of prime harmonics in 4190edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 +0.002 +0.035 +0.052 -0.005 +0.045 -0.134 +0.053 +0.079 +0.017 -0.024
Relative (%) +0.0 +0.7 +12.1 +18.3 -1.8 +15.8 -46.9 +18.4 +27.5 +6.0 -8.3
Steps
(reduced)
4190
(0)
6641
(2451)
9729
(1349)
11763
(3383)
14495
(1925)
15505
(2935)
17126
(366)
17799
(1039)
18954
(2194)
20355
(3595)
20758
(3998)

Divisors

Since 4190 factors into 2 × 5 × 419, 4190edo has subset edos 2, 5, 10, 419, 838, and 2095.