1489edo
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Prime factorization
1489 (prime)
Step size
0.80591¢
Fifth
871\1489 (701.948¢)
Semitones (A1:m2)
141:112 (113.6¢ : 90.26¢)
Consistency limit
21
Distinct consistency limit
21
| ← 1488edo | 1489edo | 1490edo → |
1489 equal divisions of the octave (abbreviated 1489edo or 1489ed2), also called 1489-tone equal temperament (1489tet) or 1489 equal temperament (1489et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1489 equal parts of about 0.806 ¢ each. Each step represents a frequency ratio of 21/1489, or the 1489th root of 2.
Theory
1489edo is consistent to the 21-odd-limit. As an equal temperament, it tempers out 3025/3024 in the 11-limit; 4225/4224 and 256000/255879 in the 13-limit; 2500/2499, 5985/5984, and 57375/57344 in the 17-limit; 6175/6174 in the 19-limit. Using the 2.3.11.17.19.37 subgroup, it tempers out 3553/3552. It supports qak.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.007 | -0.283 | -0.122 | -0.075 | +0.036 | -0.187 | -0.132 | +0.335 | +0.376 | +0.163 |
| Relative (%) | +0.0 | -0.9 | -35.1 | -15.1 | -9.4 | +4.5 | -23.2 | -16.4 | +41.6 | +46.6 | +20.2 | |
| Steps (reduced) |
1489 (0) |
2360 (871) |
3457 (479) |
4180 (1202) |
5151 (684) |
5510 (1043) |
6086 (130) |
6325 (369) |
6736 (780) |
7234 (1278) |
7377 (1421) | |
Subsets and supersets
1489edo is the 237th prime edo.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-2360 1489⟩ | [⟨1489 2360]] | 0.0023 | 0.0023 | 0.29 |
| 2.3.5 | [54 -37 2⟩, [-73 -14 41⟩ | [⟨1489 2360 3457]] | 0.0422 | 0.0564 | 7.00 |
| 2.3.5.7 | 420175/419904, 703125/702464, [49 -27 7 -8⟩ | [⟨1489 2360 3457 4180]] | 0.0425 | 0.0488 | 6.06 |
| 2.3.5.7.11 | 3025/3024, 759375/758912, 420175/419904, 32768000000/32750405919 | [⟨1489 2360 3457 4180 5151]] | 0.0384 | 0.0444 | 5.51 |
| 2.3.5.7.11.13 | 3025/3024, 4225/4224, 91125/91091, 256000/255879, 420175/419904 | [⟨1489 2360 3457 4180 5151 5510]] | 0.0303 | 0.0444 | 5.51 |
| 2.3.5.7.11.13.17 | 3025/3024, 2500/2499, 4225/4224, 56595/56576, 57375/57344, 256000/255879 | [⟨1489 2360 3457 4180 5151 5510 6086]] | 0.0325 | 0.0414 | 5.14 |