523edo
Theory
523et tempers out 2401/2400 in the 7-limit; 56723625/56689952, 26214400/26198073, 78675968/78594219, 759375/758912, 496125/495616, 6250/6237, 42875/42768, 19712/19683, 1479016/1476225, 16808715/16777216, 3294225/3294172, 43923/43904, 102487/102400 and 322102/321489 in the 11-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | +0.15 | -0.85 | -0.57 | -0.65 | -0.76 | +0.59 | +0.77 | +0.41 | +0.63 | -0.10 |
| Relative (%) | +0.0 | +6.5 | -36.8 | -24.7 | -28.3 | -33.0 | +25.7 | +33.4 | +17.7 | +27.6 | -4.5 | |
| Steps (reduced) |
523 (0) |
829 (306) |
1214 (168) |
1468 (422) |
1809 (240) |
1935 (366) |
2138 (46) |
2222 (130) |
2366 (274) |
2541 (449) |
2591 (499) | |
Subsets and supersets
523edo is the 99th prime edo.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [829 -523⟩ | [⟨523 829]] | -0.0468 | 0.0468 | 2.04 |
| 2.3.5 | 1600000/1594323, [-101 11 36⟩ | [⟨523 829 1214]] | +0.0901 | 0.1974 | 8.60 |
| 2.3.5.7 | 2401/2400, 1600000/1594323, 341796875/339738624 | [⟨523 829 1214 1468]] | +0.1180 | 0.1776 | 7.74 |
| 2.3.5.7.11 | 6250/6237, 2401/2400, 19712/19683, 166375/165888 | [⟨523 829 1214 1468 1809]] | +0.1319 | 0.1613 | 7.03 |
| 2.3.5.7.11.13 | 2080/2079, 625/624, 4459/4455, 19712/19683, 50193/50176 | [⟨523 829 1214 1468 1809 1935]] | +0.1440 | 0.1497 | 6.52 |
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated Ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 37\523 | 84.89 | 21/20 | Amicable |
| 1 | 52\523 | 119.31 | 15/14 | Septidiasemi |
| 1 | 148\523 | 339.58 | 243/200 | Amity |
* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct