2118edo
|
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. |
Theory
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.028 | +0.089 | +0.013 | -0.043 | +0.266 | -0.140 | -0.063 | +0.054 | -0.115 | +0.007 |
| Relative (%) | +0.0 | +4.9 | +15.6 | +2.2 | -7.6 | +46.9 | -24.6 | -11.0 | +9.6 | -20.4 | +1.2 | |
| Steps (reduced) |
2118 (0) |
3357 (1239) |
4918 (682) |
5946 (1710) |
7327 (973) |
7838 (1484) |
8657 (185) |
8997 (525) |
9581 (1109) |
10289 (1817) |
10493 (2021) | |
Primes with less than 1 standard deviation in 2118edo are: 2, 3, 5, 7, 11, 19, 23, 29, 31, 43. Overall, it offers excellent double-13s 31-limit harmony, as both mappings of 13 (2118 and 2118f vals) have useful interpretations.
2118edo provides a 43-limit approximation of secor with 46/43 (206 steps), however this reduces to 103\1059, meaning that it is a compound of two circles of such secor. In addition, it offers a 205-step generator "meantone secor" which is described by a 31 & 2118 temperament, also in the 2.3.5.7.11.23.43 subgroup, and also offers a meantone fifth. The comma basis for the "meantone secor" temperament is 5376/5375, 9317/9315, 25921/25920, 151263/151250, and 10551296/10546875.
2118edo is 6 times the 353edo, meaning it can be used to play a compound of 6 chains of the Rectified Hebrew temperament.
Regular temperament properties
| Subgroup | Comma list | Mapping | Optimal
8ve stretch (¢) |
Tuning error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3.5 | [38 -2 15⟩, [-11 130 -84⟩ | [⟨2118 3357 4918]] | -0.0186 | 0.0156 | |
| 2.3.5.7 | 250047/250000,[-1 -18 -3 13⟩, [38 -2 -15 0⟩ | [⟨2118 3357 4918 5946]] | -0.0150 | 0.0148 | |
| 2.3.5.7.11 | 9801/9800, 250047/250000, [25 1 -4 0 -5⟩, [16 -7 -9 2 3⟩ | [⟨2118 3357 4918 5946 7927]] | -0.0096 | 0.0172 | |