897edo

← 896edo

897edo

898edo →

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

• 13|3|23 by Francium