2118edo: Difference between revisions
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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. | ||
== Regular temperament properties == | |||
{| class="wikitable center-4 center-5 center-6" | |||
! rowspan="2" |Subgroup | |||
! rowspan="2" |[[Comma list]] | |||
! rowspan="2" |[[Mapping]] | |||
! rowspan="2" |Optimal | |||
8ve stretch (¢) | |||
! colspan="2" |Tuning error | |||
|- | |||
![[TE error|Absolute]] (¢) | |||
![[TE simple badness|Relative]] (%) | |||
|- | |||
|2.3.5 | |||
|{{monzo|38 -2 15}}, {{monzo| -11 130 -84}} | |||
|[{{val|2118 3357 4918}}] | |||
| -0.0186 | |||
|0.0156 | |||
| | |||
|- | |||
|2.3.5.7 | |||
|250047/250000,{{monzo|-1 -18 -3 13}}, {{monzo|38 -2 -15 0}} | |||
|[{{val|2118 3357 4918 5946}}] | |||
| -0.0150 | |||
|0.0148 | |||
| | |||
|- | |||
|2.3.5.7.11 | |||
|9801/9800, 250047/250000, {{monzo|25 1 -4 0 -5}}, {{monzo|16 -7 -9 2 3}} | |||
|[{{val|2118 3357 4918 5946 7927}}] | |||
|<nowiki>-0.0096</nowiki> | |||
|0.0172 | |||
| | |||
|} | |||
Revision as of 21:53, 13 May 2022
| ← 2117edo | 2118edo | 2119edo → |
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.
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 | |