2118edo: Difference between revisions
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== Theory == | == Theory == | ||
{{Harmonics in equal|2118}} | {{Harmonics in equal|2118}} | ||
Primes with less than 1 standard deviation in 2118edo are: 2, 3, 5, 7, 11, 19, 23, 29, 31, 43. | 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). In addition, it offers a 205-step generator "meantone secor" which is described by a 31 & 2118 temperament, and also offers a meantone fifth. | 2118edo provides a 43-limit approximation of [[secor]] with [[46/43]] (206 steps). 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. | ||
2118edo is 6 times the [[353edo]], meaning it can be used to play a compound of 6 chains of the [[Hemimean clan#Rectified Hebrew|Rectified Hebrew]] temperament. | 2118edo is 6 times the [[353edo]], meaning it can be used to play a compound of 6 chains of the [[Hemimean clan#Rectified Hebrew|Rectified Hebrew]] temperament. | ||
Revision as of 09:49, 11 May 2022
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). 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.
2118edo is 6 times the 353edo, meaning it can be used to play a compound of 6 chains of the Rectified Hebrew temperament.