584edo
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Prime factorization
23 × 73
Step size
2.05479¢
Fifth
342\584 (702.74¢) (→171\292)
Semitones (A1:m2)
58:42 (119.2¢ : 86.3¢)
Dual sharp fifth
342\584 (702.74¢) (→171\292)
Dual flat fifth
341\584 (700.685¢)
Dual major 2nd
99\584 (203.425¢)
Consistency limit
5
Distinct consistency limit
5
| ← 583edo | 584edo | 585edo → |
584 equal divisions of the octave (584edo), or 584-tone equal temperament (584tet), 584 equal temperament (584et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 584 equal parts of about 2.05 ¢ each.
Theory
584et tempers out 48828125/48771072 and 67108864/66976875 in the 7-limit (hemiluna temperament), and 12005/11979, 131072/130977, 5632/5625, 537109375/536870912, 9453125/9437184, 160083/160000 and 391314/390625 in the 11-limit.
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +0.785 | -0.012 | -1.018 | -0.485 | -0.633 | -0.117 | +0.772 | -0.161 | +0.432 | -0.233 | +0.493 |
| relative (%) | +38 | -1 | -50 | -24 | -31 | -6 | +38 | -8 | +21 | -11 | +24 | |
| Steps (reduced) |
926 (342) |
1356 (188) |
1639 (471) |
1851 (99) |
2020 (268) |
2161 (409) |
2282 (530) |
2387 (51) |
2481 (145) |
2565 (229) |
2642 (306) | |
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [463 -292⟩ | ⟨584 926] | -0.2476 | 0.2475 | 12.05 |
| 2.3.5 | [3 -18 11⟩, [21 -20 4⟩ | ⟨584 926 1356] | -0.1633 | 0.2346 | 11.42 |
| 2.3.5.7 | 1500625/1492992, 1605632/1594323, 235298/234375 | ⟨584 926 1356 1639] | -0.0319 | 0.3052 | 14.85 |
| 2.3.5.7.11 | 5632/5625, 160083/160000, 26411/26244, 968000/964467 | ⟨584 926 1356 1639 2020] | +0.0111 | 0.2862 | 13.93 |
| 2.3.5.7.11.13 | 2080/2079, 1001/1000, 4096/4095, 85750/85293, 983125/979776 | ⟨584 926 1356 1639 2020 2161] | +0.0145 | 0.2613 | 12.72 |
Scales
Music
- Are You From The Moon? by Francium