User:Overthink/202030edo
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Prime factorization
2 × 5 × 89 × 227
Step size
0.00593971 ¢
Fifth
118180\202030 (701.955 ¢) (→ 11818\20203)
Semitones (A1:m2)
19140:15190 (113.7 ¢ : 90.22 ¢)
Consistency limit
45
Distinct consistency limit
45
| ← 202029edo | 202030edo | 202031edo → |
202030 equal divisions of the octave (abbreviated 202030edo or 202030ed2), also called 202030-tone equal temperament (202030tet) or 202030 equal temperament (202030et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 202030 equal parts of about 0.00594 ¢ each. Each step represents a frequency ratio of 21/202030, or the 202030th root of 2.
Theory
202030edo is a very strong 43-limit system, distinctly consistent to the 45-odd-limit. Remarkably, it is also a multiple of 20203edo, which has a consistency limit just as high.
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00000 | +0.00015 | -0.00079 | +0.00051 | +0.00018 | +0.00097 | -0.00070 | +0.00121 | -0.00132 | +0.00059 | -0.00167 |
| Relative (%) | +0.0 | +2.6 | -13.3 | +8.5 | +3.0 | +16.4 | -11.8 | +20.4 | -22.2 | +10.0 | -28.1 | |
| Steps (reduced) |
202030 (0) |
320210 (118180) |
469099 (65039) |
567170 (163110) |
698909 (92819) |
747600 (141510) |
825790 (17670) |
858209 (50089) |
913895 (105775) |
981458 (173338) |
1000896 (192776) | |
| Harmonic | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00081 | -0.00138 | -0.00159 | +0.00246 | +0.00137 | -0.00223 | +0.00081 | +0.00001 | -0.00244 | -0.00152 | +0.00104 |
| Relative (%) | +13.7 | -23.1 | -26.8 | +41.4 | +23.1 | -37.5 | +13.6 | +0.1 | -41.1 | -25.6 | +17.5 | |
| Steps (reduced) |
1052466 (42316) |
1082386 (72236) |
1096268 (86118) |
1122194 (112044) |
1157212 (147062) |
1188470 (178320) |
1198187 (188037) |
1225532 (13352) |
1242433 (30253) |
1250530 (38350) |
1273553 (61373) | |