385edo
| ← 384edo | 385edo | 386edo → |
385 equal divisions of the octave (385edo), or 385-tone equal temperament (385tet), 385 equal temperament (385et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 385 equal parts of about 3.12 ¢ each.
Theory
385et tempers out following commas:
7-limit commas: 589824/588245, 134217728/133984375, 703125/702464, 1959552/1953125, 5250987/5242880, 200120949/200000000
11-limit commas: 1073741824/1071794405, 161280/161051, 25165824/25109315, 234375/234256, 2097152/2096325, 1366875/1362944, 166698/166375, 496125/495616, 151263/151250, 104857600/104825259, 540/539, 172032/171875, 369140625/369098752, 825000/823543, 180224/180075, 8019/8000, 160083/160000, 539055/537824, 766656/765625, 202397184/201768035, 43923/43904, 20614528/20588575, 39135393/39062500, 781258401/781250000
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +0.00 | -0.66 | +0.18 | +0.52 | +0.37 | +1.03 | +1.02 | -1.41 | +1.34 | -1.01 | -1.14 |
| relative (%) | +0 | -21 | +6 | +17 | +12 | +33 | +33 | -45 | +43 | -32 | -37 | |
| Steps (reduced) |
385 (0) |
610 (225) |
894 (124) |
1081 (311) |
1332 (177) |
1425 (270) |
1574 (34) |
1635 (95) |
1742 (202) |
1870 (330) |
1907 (367) | |
Subsets and supersets
385 factors into 5 x 7 x 11, with subset edos 5, 7, 11, 35, 55, and 77.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-122 77⟩ | ⟨385 610] | +0.2070 | 0.2071 | 6.64 |
| 2.3.5 | [-28 25 -5⟩, [38 -2 -15⟩ | ⟨385 610 894] | +0.1122 | 0.2158 | 6.92 |
| 2.3.5.7 | 19683/19600, 589824/588245, 703125/702464 | ⟨385 610 894 1081] | +0.0374 | 0.2274 | 7.30 |
| 2.3.5.7.11 | 540/539, 8019/8000, 496125/495616, 172032/171875 | ⟨385 610 894 1081 1332] | +0.0085 | 0.2114 | 6.78 |
| 2.3.5.7.11.13 | 540/539, 1716/1715, 8019/8000, 4096/4095, 81675/81536 | ⟨385 610 894 1081 1332 1425] | -0.0394 | 0.2207 | 7.08 |
| 2.3.5.7.11.13.17 | 540/539, 936/935, 1377/1375, 1716/1715, 4096/4095, 13365/13328 | ⟨385 610 894 1081 1332 1425 1574] | -0.0693 | 0.2171 | 6.97 |
Rank-2 temperaments
| Periods per 8ve |
Generator (Reduced) |
Cents (Reduced) |
Associated Ratio |
Temperaments |
|---|---|---|---|---|
| 1 | 62\385 | 193.247 | 4096/3645 | Luna |
| 1 | 162/385 | 504.935 | 4/3 | Countermeantone |
| 5 | 160\385 (6\385) |
498.701 (18.701) |
4/3 (81/80) |
Pental (5-limit) |