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.
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971EDO is the 164th [[prime EDO]].
971edo's fifth is only 0.00174{{c}} 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]]
=== Prime harmonics ===
[[Category:Prime EDO]]
{{Harmonics in equal|971}}
 
=== Subsets and supersets ===
971edo is the 164th [[prime edo]].
 
== Music ==
; [[Francium]]
* "Todd Bonzalez" from ''Don't Give Your Kids These Names!'' (2025) − [https://open.spotify.com/track/6b3zWRAI12Vn2gwu5kwOML Spotify] | [https://francium223.bandcamp.com/track/todd-bonzalez Bandcamp] | [https://www.youtube.com/watch?v=AfFD4B5LeyM YouTube] − in Alexic, 971edo tuning

Latest revision as of 13:42, 31 March 2025

← 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

971 equal divisions of the octave (abbreviated 971edo or 971ed2), also called 971-tone equal temperament (971tet) or 971 equal temperament (971et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 971 equal parts of about 1.24 ¢ each. Each step represents a frequency ratio of 21/971, or the 971st root of 2.

971edo's fifth is only 0.00174 ¢ 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.

Music

Francium
  • "Todd Bonzalez" from Don't Give Your Kids These Names! (2025) − Spotify | Bandcamp | YouTube − in Alexic, 971edo tuning