534edo
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Prime factorization
2 × 3 × 89
Step size
2.24719¢
Fifth
312\534 (701.124¢) (→52\89)
Semitones (A1:m2)
48:42 (107.9¢ : 94.38¢)
Dual sharp fifth
313\534 (703.371¢)
Dual flat fifth
312\534 (701.124¢) (→52\89)
Dual major 2nd
91\534 (204.494¢)
Consistency limit
7
Distinct consistency limit
7
| ← 533edo | 534edo | 535edo → |
534 equal divisions of the octave (abbreviated 534edo or 534ed2), also called 534-tone equal temperament (534tet) or 534 equal temperament (534et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 534 equal parts of about 2.25 ¢ each. Each step represents a frequency ratio of 21/534, or the 534th root of 2.
534edo is consistent to the 7-odd-limit, but the error of harmonic 3 is quite large. The patent val tempers out 2401/2400 and 19683/19600 in the 7-limit and provides the optimal patent val for 7-limit harry temperament.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | -0.831 | +0.203 | -0.287 | +0.584 | -0.756 | -0.078 | -0.628 | +0.663 | -0.884 | -1.118 | +0.939 |
| relative (%) | -37 | +9 | -13 | +26 | -34 | -3 | -28 | +29 | -39 | -50 | +42 | |
| Steps (reduced) |
846 (312) |
1240 (172) |
1499 (431) |
1693 (91) |
1847 (245) |
1976 (374) |
2086 (484) |
2183 (47) |
2268 (132) |
2345 (209) |
2416 (280) | |
Subsets and supersets
Since 534 factors into 2 × 3 × 89, 534edo has subset edos 2, 3, 6, 89, 178, and 267.