897edo
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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
| ← 896edo | 897edo | 898edo → |
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.
| 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 |
Music
- 13|3|23 by Francium