1680edo
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Prime factorization
24 × 3 × 5 × 7
Step size
0.714286¢
Fifth
983\1680 (702.143¢)
Semitones (A1:m2)
161:125 (115¢ : 89.29¢)
Consistency limit
5
Distinct consistency limit
5
Special properties
| ← 1679edo | 1680edo | 1681edo → |
1680 equal divisions of the octave (abbreviated 1680edo or 1680ed2), also called 1680-tone equal temperament (1680tet) or 1680 equal temperament (1680et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1680 equal parts of about 0.714 ¢ each. Each step represents a frequency ratio of 21/1680, or the 1680th root of 2. 1680edo is the 17th highly composite edo.
1680edo is consistent in the 5-odd-limit.
1680d val is better tuned than the patent val and other vals as high as the 23-limit, and offers a good representation of the 17-limit in this regard. It tunes the 80th-octave temperament mercury in the 19-limit and the rank-3 temperament thor in the 11-limit.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +0.188 | +0.115 | -0.254 | -0.339 | +0.111 | +0.187 | +0.303 | +0.045 | +0.344 | -0.067 | +0.297 |
| relative (%) | +26 | +16 | -36 | -47 | +15 | +26 | +42 | +6 | +48 | -9 | +42 | |
| Steps (reduced) |
2663 (983) |
3901 (541) |
4716 (1356) |
5325 (285) |
5812 (772) |
6217 (1177) |
6564 (1524) |
6867 (147) |
7137 (417) |
7379 (659) |
7600 (880) | |