503edo
| ← 502edo | 503edo | 504edo → |
503 equal divisions of the octave (abbreviated 503edo or 503ed2), also called 503-tone equal temperament (503tet) or 503 equal temperament (503et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 503 equal parts of about 2.39 ¢ each. Each step represents a frequency ratio of 21/503, or the 503rd root of 2.
Theory
503et tempers out 2401/2400 in the 7-limit; 56723625/56689952, 100663296/100656875, 10333575/10307264, 46656/46585, 166698/166375, 759375/758912, 496125/495616, 226492416/226474325, 2359296/2358125, 172032/171875, 369140625/369098752, 4302592/4296875, 24057/24010, 8019/8000, 16808715/16777216, 766656/765625, 391314/390625, 3294225/3294172, 43923/43904 and 102487/102400 in the 11-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | -0.56 | +0.17 | -0.24 | -0.22 | -0.77 | +0.01 | +0.70 | -0.84 | +1.04 | +0.09 |
| Relative (%) | +0.0 | -23.6 | +7.0 | -10.0 | -9.4 | -32.1 | +0.6 | +29.2 | -35.2 | +43.6 | +3.9 | |
| Steps (reduced) |
503 (0) |
797 (294) |
1168 (162) |
1412 (406) |
1740 (231) |
1861 (352) |
2056 (44) |
2137 (125) |
2275 (263) |
2444 (432) |
2492 (480) | |
Subsets and supersets
503edo is the 96th prime edo.
Regular temperament properties
| Subgroup | Comma list | Mapping | Optimal 8ve stretch (¢) |
Tuning error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-797 503⟩ | ⟨503 797] | 0.1777 | 0.1777 | 7.45 |
| 2.3.5 | [38 -2 -15⟩, [-5 31 -19⟩ | ⟨503 797 1168] | 0.0944 | 0.1869 | 7.83 |
| 2.3.5.7 | 2401/2400, 1959552/1953125, 26873856/26796875 | ⟨503 797 1168 1412] | 0.0920 | 0.1619 | 6.79 |
| 2.3.5.7.11 | 2401/2400, 8019/8000, 24057/24010, 43923/43904 | ⟨503 797 1168 1412 1740] | 0.0866 | 0.1452 | 6.09 |
| 2.3.5.7.11.13 | 729/728, 1001/1000, 1716/1715, 4225/4224, 6656/6655 | ⟨503 797 1168 1412 1740 1861] | 0.1066 | 0.1400 | 5.87 |
| 2.3.5.7.11.13.17 | 729/728, 936/935, 1001/1000, 1716/1715, 2401/2400, 2601/2600 | ⟨503 797 1168 1412 1740 1861 2056] | 0.0909 | 0.1352 | 5.67 |
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 11\503 | 26.24 | 1594323/1562500 | Sfourth (5-limit) |
| 1 | 50\503 | 119.28 | 15/14 | Septidiasemi |
| 1 | 81\503 | 193.24 | 262144/234375 | Luna |
| 1 | 127\503 | 302.98 | 25/21 | Quinmite |
| 1 | 146\503 | 348.31 | 57344/46875 | Subneutral |
* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct