971edo: Difference between revisions

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'''971EDO''' is the [[EDO|equal division of the octave]] into 971 parts of 1.23584 [[cent]]s each. It has a fifth which is only 0.00174 cents sharp. It is the denominator of the first semiconvergent to log<sub>2</sub>(3/2) past 389\665.
{{EDO intro|971}}


971EDO is the 164th [[prime EDO]].
971edo's fifth is only 0.00174 cents sharp of just, as it is the denominator of the first semiconvergent to log<sub>2</sub>(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.  


[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
=== Prime harmonics ===
[[Category:Prime EDO]]
{{Harmonics in equal|971}}
 
=== Subsets and supersets ===
971edo is the 164th [[prime edo]].

Revision as of 03:15, 27 May 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.