509edo
| ← 508edo | 509edo | 510edo → |
Theory
509et tempers out 134217728/133984375, 29360128/29296875 and 2401/2400 in the 7-limit and 1073741824/1071794405, 1019215872/1019046875, 151263/151250, 226492416/226474325, 2359296/2358125, 1953125/1948617, 172032/171875, 4302592/4296875, 5767168/5764801, 180224/180075, 5632/5625, 422576/421875, 3025/3024, 41503/41472, 1362944/1361367, 42592/42525, 456533/455625, 322102/321489 and 781258401/781250000 in the 11-limit. It provides the optimal patent val for the temperaments Eir (in the 17-limit), Petrtri and Orthocanousmic.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.60 | +0.33 | +0.13 | -1.16 | +0.35 | +1.12 | +0.93 | +1.13 | -0.46 | +0.73 | -1.16 |
| Relative (%) | +25.4 | +13.9 | +5.6 | -49.2 | +14.9 | +47.6 | +39.3 | +48.1 | -19.5 | +31.0 | -49.3 | |
| Steps (reduced) |
807 (298) |
1182 (164) |
1429 (411) |
1613 (86) |
1761 (234) |
1884 (357) |
1989 (462) |
2081 (45) |
2162 (126) |
2236 (200) |
2302 (266) | |
Subsets and supersets
509 is the 97th prime EDO.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [807 -509⟩ | ⟨509 807] | -0.1890 | 0.1889 | 8.01 |
| 2.3.5 | [9 -13 5⟩, [93 -3 -38⟩ | ⟨509 807 1182] | -0.1729 | 0.1559 | 6.61 |
| 2.3.5.7 | 2401/2400, 1600000/1594323, 4802000/4782969 | ⟨509 807 1182 1429] | -0.1415 | 0.1456 | 6.18 |
| 2.3.5.7.11 | 2401/2400, 3025/3024, 5632/5625, 41503/41472 | ⟨509 807 1182 1429 1761] | -0.1335 | 0.1312 | 5.57 |
| 2.3.5.7.11.13 | 2080/2079, 2200/2197, 3025/3024, 4459/4455, 5632/5625 | ⟨509 807 1182 1429 1761 1884] | -0.1618 | 0.1354 | 5.74 |
| 2.3.5.7.11.13.17 | 1225/1224, 2080/2079, 2431/2430, 7744/7735, 12376/12375, 14161/14157 | ⟨509 807 1182 1429 1761 1884 2081] | -0.1784 | 0.1318 | 5.59 |
Rank-2 temperaments
| Periods per 8ve |
Generator (reduced) |
Cents (reduced) |
Associated ratio |
Temperaments |
|---|---|---|---|---|
| 1 | 36\509 | 84.87 | 21/20 | Amicable |
| 1 | 115\509 | 271.12 | 1024/875 | Quasiorwell |
| 1 | 144\509 | 339.49 | 243/200 | Amity |