2118edo: Difference between revisions
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{{ | {{Infobox ET}} | ||
{{ED intro}} | |||
== Theory == | == Theory == | ||
Primes approximated with less than 1 standard deviation in 2118edo are: 2, 3, 5, 7, 11, 19, 23, 29, 31, 43. Overall, it offers excellent double-13's 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 {{nowrap|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. | |||
=== Prime harmonics === | |||
{{Harmonics in equal|2118}} | {{Harmonics in equal|2118}} | ||
2118edo | === Subsets and supersets === | ||
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|Comma List]] | |||
! rowspan="2" | [[Mapping]] | |||
! rowspan="2" | Optimal<br>8ve Stretch (¢) | |||
! colspan="2" | Tuning Error | |||
|- | |||
! [[TE error|Absolute]] (¢) | |||
! [[TE simple badness|Relative]] (%) | |||
|- | |||
| 2.3.5 | |||
| {{monzo| 38 -2 15 }}, {{monzo| -11 130 -84 }} | |||
| {{mapping| 2118 3357 4918 }} | |||
| −0.0186 | |||
| 0.0156 | |||
| | |||
|- | |||
| 2.3.5.7 | |||
| 250047/250000, {{monzo| -1 -18 -3 13 }}, {{monzo| 38 -2 -15 }} | |||
| {{mapping| 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 }} | |||
| {{mapping| 2118 3357 4918 5946 7927 }} | |||
| −0.0096 | |||
| 0.0172 | |||
| | |||
|} | |||