503edo

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← 502edo503edo504edo →
Prime factorization 503 (prime)
Step size 2.38569¢ 
Fifth 294\503 (701.392¢)
Semitones (A1:m2) 46:39 (109.7¢ : 93.04¢)
Consistency limit 7
Distinct consistency limit 7

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

Approximation of prime harmonics in 503edo
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

Table of rank-2 temperaments by generator
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

Music

Francium