20203edo
| ← 20202edo | 20203edo | 20204edo → |
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
| 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) | |