20203edo

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← 20202edo20203edo20204edo →
Prime factorization 89 × 227
Step size 0.0593971¢ 
Fifth 11818\20203 (701.955¢)
Semitones (A1:m2) 1914:1519 (113.7¢ : 90.22¢)
Consistency limit 45
Distinct consistency limit 45

20203 equal divisions of the octave (abbreviated 20203edo or 20203ed2), also called 20203-tone equal temperament (20203tet) or 20203 equal temperament (20203et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 20203 equal parts of about 0.0594 ¢ each. Each step represents a frequency ratio of 21/20203, or the 20203rd root of 2.

20203edo is a very strong high-limit system, and specializes in the 17- and 19-limit, with a lower 17- and 19-limit relative error than any smaller edo until 102557 and 128215, respectively. It is also distinctly consistent through the 45-odd-limit, and has a lower relative error than any smaller distinctly consistent 41-limit patent val except 17461. It tempers out 47151/47150, 52326/52325, 69875/69874, 81796/81795, 111112/111111, 127281/127280, 156520/156519, 315495/315491, 395200/395199, 728365/728364, 1324323/1324300, 1518804/1518803, and 3845961/3845920 in the 43-limit.

Prime harmonics

Approximation of prime harmonics in 20203edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47
Error Absolute (¢) +0.0000 +0.0002 +0.0051 +0.0005 +0.0061 +0.0010 -0.0007 +0.0072 +0.0284 +0.0125 +0.0221 +0.0246 +0.0224 +0.0103 -0.0213
Relative (%) +0.0 +0.3 +8.7 +0.9 +10.3 +1.6 -1.2 +12.0 +47.8 +21.0 +37.2 +41.4 +37.7 +17.3 -35.9
Steps
(reduced)
20203
(0)
32021
(11818)
46910
(6504)
56717
(16311)
69891
(9282)
74760
(14151)
82579
(1767)
85821
(5009)
91390
(10578)
98146
(17334)
100090
(19278)
105247
(4232)
108239
(7224)
109627
(8612)
112219
(11204)