8103edo
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Prime factorization
3 × 37 × 73
Step size
0.148093¢
Fifth
4740\8103 (701.962¢) (→1580\2701)
Semitones (A1:m2)
768:609 (113.7¢ : 90.19¢)
Consistency limit
21
Distinct consistency limit
21
| ← 8102edo | 8103edo | 8104edo → |
8103 equal divisions of the octave (abbreviated 8103edo or 8103ed2), also called 8103-tone equal temperament (8103tet) or 8103 equal temperament (8103et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 8103 equal parts of about 0.148 ¢ each. Each step represents a frequency ratio of 21/8103, or the 8103rd root of 2.
Theory
8103edo is consistent in the 21-odd-limit. In the 13-limit, it tempers out 123201/123200, and in the 17-limit, it tempers out 12376/12375.
It is divisible by 37, and inherits the precise 11th harmonic present in 37edo, although the error has accumulated up to 23% at this point.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0000 | +0.0072 | +0.0617 | +0.0005 | +0.0334 | +0.0499 | +0.0427 | +0.0064 | -0.0626 | -0.0326 | +0.0218 |
| Relative (%) | +0.0 | +4.9 | +41.7 | +0.3 | +22.6 | +33.7 | +28.9 | +4.3 | -42.3 | -22.0 | +14.7 | |
| Steps (reduced) |
8103 (0) |
12843 (4740) |
18815 (2609) |
22748 (6542) |
28032 (3723) |
29985 (5676) |
33121 (709) |
34421 (2009) |
36654 (4242) |
39364 (6952) |
40144 (7732) | |
Regular temperament properties
Rank-2 temperaments
| Periods per 8ve |
Generator (reduced) |
Cents (reduced) |
Associated ratio |
Temperaments |
|---|---|---|---|---|
| 111 | 3363\8103 (5\8103) |
498.0377 0.7405 |
4/3 (2657205/2656192) |
Roentgenium |