971edo: Difference between revisions

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{{novelty}}{{stub}}{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|971}}
{{EDO intro|971}}



Revision as of 06:48, 9 July 2023

← 970edo 971edo 972edo →
Prime factorization 971 (prime)
Step size 1.23584 ¢ 
Fifth 568\971 (701.957 ¢)
(semiconvergent)
Semitones (A1:m2) 92:73 (113.7 ¢ : 90.22 ¢)
Consistency limit 9
Distinct consistency limit 9

Template:EDO intro

971edo's fifth is only 0.00174 cents sharp of just, as it is the denominator of the first semiconvergent to log2(3/2) past 389\665. It is consistent to the 9-odd-limit, but there is a large relative delta in its approximation to harmonic 5. Skipping the harmonic, it is a good 2.3.7.11.13.17 subgroup system.

Prime harmonics

Approximation of prime harmonics in 971edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 +0.002 +0.504 +0.072 -0.134 -0.157 +0.091 +0.324 -0.468 -0.123 +0.587
Relative (%) +0.0 +0.1 +40.8 +5.8 -10.8 -12.7 +7.4 +26.2 -37.9 -10.0 +47.5
Steps
(reduced)
971
(0)
1539
(568)
2255
(313)
2726
(784)
3359
(446)
3593
(680)
3969
(85)
4125
(241)
4392
(508)
4717
(833)
4811
(927)

Subsets and supersets

971edo is the 164th prime edo.