# 203edo

 ← 202edo 203edo 204edo →
Prime factorization 7 × 29
Step size 5.91133¢
Fifth 119\203 (703.448¢) (→17\29)
Semitones (A1:m2) 21:14 (124.1¢ : 82.76¢)
Consistency limit 3
Distinct consistency limit 3

203 equal divisions of the octave (abbreviated 203edo or 203ed2), also called 203-tone equal temperament (203tet) or 203 equal temperament (203et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 203 equal parts of about 5.91 ¢ each. Each step represents a frequency ratio of 21/203, or the 203rd root of 2.

203 = 7 × 29, and 203edo shares its fifth with 29edo. It is inconsistent to the 5-odd-limit and higher limits, with two mappings possible for the 7-limit: 203 322 471 570] (patent val), 203 322 472 570] (203c). Using the patent val, it tempers out 2109375/2097152 (semicomma) and [4 -23 14 in the 5-limit; 4000/3969, 10976/10935, and 2100875/2097152 in the 7-limit; 385/384, 1331/1323, and 4000/3993 in the 11-limit; 352/351, 676/675, 1573/1568, and 1625/1617 in the 13-limit. Using the 203c val, it tempers out 78732/78125 (sensipent comma) in the 5-limit; 5120/5103, 50421/50000, and 110592/109375 in the 7-limit; 176/175, 1331/1323, 8019/8000, and 26411/26244 in the 11-limit. The alternative 203cef val is also worth considering, which tempers out 441/440, 896/891, and 3388/3375 in the 11-limit; and 196/195, 352/351, 364/363, and 676/675 in the 13-limit.

### Odd harmonics

Approximation of odd harmonics in 203edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +1.49 -2.08 +0.63 -2.92 -1.56 -1.12 -0.58 +1.45 -1.95 +2.13 -1.67
Relative (%) +25.3 -35.1 +10.7 -49.5 -26.5 -18.9 -9.9 +24.5 -32.9 +36.0 -28.3
Steps
(reduced)
322
(119)
471
(65)
570
(164)
643
(34)
702
(93)
751
(142)
793
(184)
830
(18)
862
(50)
892
(80)
918
(106)

### Subsets and supersets

Since 203 factors into 7 × 29, 203edo contains 7edo and 29edo as its subsets.