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
|
This page presents a topic of primarily mathematical interest.
While it is derived from sound mathematical principles, its applications in terms of utility for actual music may be limited, highly contrived, or as yet unknown. |
| ← 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) | |