2190edo
|
This page presents a novelty topic.
It may contain ideas which are less likely to find practical applications in music, or numbers or structures that are arbitrary or exceedingly small, large, or complex. Novelty topics are often developed by a single person or a small group. As such, this page may also contain idiosyncratic terms, notation, or conceptual frameworks. |
|
This page is a stub. You can help the Xenharmonic Wiki by expanding it. |
| ← 2189edo | 2190edo | 2191edo → |
Template:EDO intro It is is a very strong 13-limit system; no smaller division has a smaller 13-limit relative error, and nothing beats it until 2684. A basis for the 13-limit commas is {9801/9800, 10648/10647, 105644/105625, 140625/140608, 196625/196608}; also tempered out are 123201/123200 and 151263/151250. It is not as impressive beyond the 13-limit, though it does well in the 2.3.5.7.11.13.19.29 subgroup.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.037 | -0.012 | -0.059 | -0.085 | +0.020 | +0.250 | +0.021 | +0.219 | +0.012 | +0.170 |
| Relative (%) | +0.0 | -6.8 | -2.3 | -10.7 | -15.5 | +3.7 | +45.6 | +3.9 | +39.9 | +2.2 | +31.0 | |
| Steps (reduced) |
2190 (0) |
3471 (1281) |
5085 (705) |
6148 (1768) |
7576 (1006) |
8104 (1534) |
8952 (192) |
9303 (543) |
9907 (1147) |
10639 (1879) |
10850 (2090) | |
Subsets and supersets
2190 factors as 2 × 3 × 5 × 73; among its divisors is the Woolhouse unit system, 730.
4380edo, which doubles 2190edo, provides a good correction to the harmonics 17 and 23.