897edo

This page presents a novelty topic. It may contain ideas which are less likely to find practical applications in music, or numbers or structures that are arbitrary or exceedingly small, large, or complex. Novelty topics are often developed by a single person or a small group. As such, this page may also contain idiosyncratic terms, notation, or conceptual frameworks.

This page is a stub. You can help the Xenharmonic Wiki by expanding it.

← 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

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 (%)	+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)

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