# 971edo

 ← 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 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.