897edo

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← 896edo897edo898edo →
Prime factorization 3 × 13 × 23
Step size 1.33779¢
Fifth 525\897 (702.341¢) (→175\299)
Semitones (A1:m2) 87:66 (116.4¢ : 88.29¢)
Consistency limit 7
Distinct consistency limit 7

897 equal divisions of the octave (897edo), or 897-tone equal temperament (897tet), 897 equal temperament (897et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 897 equal parts of about 1.34 ¢ each.

Theory

897et tempers out 250047/250000 in the 7-limit; 100663296/100656875, 2097152/2096325, 131072/130977, 172032/171875, 5632/5625, 47265625/47258883, 3025/3024, 160083/160000, 102487/102400, 1771561/1769472 in the 11-limit.

Approximation of odd harmonics in 897edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error absolute (¢) +0.386 +0.308 -0.264 -0.566 -0.147 -0.394 -0.643 -0.608 -0.523 +0.122 +0.488
relative (%) +29 +23 -20 -42 -11 -29 -48 -45 -39 +9 +36
Steps
(reduced)
1422
(525)
2083
(289)
2518
(724)
2843
(152)
3103
(412)
3319
(628)
3504
(813)
3666
(78)
3810
(222)
3940
(352)
4058
(470)

Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.3 [474 -299 897 1422] -0.1218 0.1218 9.10
2.3.5 [33 -34 9, [70 -9 -24 897 ​1422​ 2083​] -0.1255 0.010 0.75
2.3.5.7 250047/250000, 67108864/66976875, 28824005/28697814 897​ 1422 ​2083 ​2518] -0.0706 0.1283 9.59
2.3.5.7.11 3025/3024, 5632/5625, 160083/160000, 28824005/28697814 897 ​1422​ 2083 ​2518 ​3103] -0.0480 0.1234 9.22
2.3.5.7.11.13 2080/2079, 1001/1000, 3025/3024, 4096/4095, 2058857500/2051893701 897​ 1422 ​2083 ​2518​ 3103​ 3319] -0.0222 0.1265 9.46

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator
(reduced)
Cents
(reduced)
Associated
ratio
Temperaments
1 419\897 560.535 864/625 Whoosh

Music