897edo

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

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
Error	Relative (%)	+28.9	+23.0	-19.7	-42.3	-11.0	-29.4	-48.1	-45.4	-39.1	+9.1	+36.5
Steps (reduced)		1422 (525)	2083 (289)	2518 (724)	2843 (152)	3103 (412)	3319 (628)	3504 (813)	3666 (78)	3810 (222)	3940 (352)	4058 (470)

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	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

Table of rank-2 temperaments by generator
Periods per 8ve	Generator (reduced)	Cents (reduced)	Associated ratio	Temperaments
1	419\1200	560.535	864/625	Whoosh