1794edo: Difference between revisions
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The best subgroup for 1794 is 2.11.17.19.29.31.47. Notably, it offers a 1794 & [[2016edo|2016]] temperament, and the years 1794 and 2016 are known for having rather grotesque historical events in proportion to their era (see below). | The best subgroup for 1794 is 2.11.17.19.29.31.47. Notably, it offers a 1794 & [[2016edo|2016]] temperament, and the years 1794 and 2016 are known for having rather grotesque historical events in proportion to their era (see below). | ||
It | It is possible to interpret 1794edo as an intersection of 26edo and 69edo. Using the {{val| 1794 2834 4160 5037 }} val in the 7-limit, which takes 5-limit from 69edo and 7/4 from 26edo, produces a comma basis 81/80, {{monzo| -41 1 17 0 }}, {{monzo| 20 13 14 -26 }}. | ||
Nonetheless, 1794edo does offer some simpler interpretations. | Nonetheless, 1794edo does offer some simpler interpretations. | ||
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Remarkably, using the patent val, 1794edo tempers out the [[schisma]]. | Remarkably, using the patent val, 1794edo tempers out the [[schisma]]. | ||
=== | === Odd harmonics === | ||
{{Harmonics in equal|1794}} | {{Harmonics in equal|1794}} | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
1794edo has subset edos {{EDOs| 2, 3, 6, 13, 23, 26, 39, 46, 69, 78, 138, 299, 598, and 897 }}. | |||
1794edo has subset edos {{EDOs|2, 3, 6, 13, 23, 26, 39, 46, 69, 78, 138, 299, 598, and 897 }}. | |||
== Regular temperament properties == | == Regular temperament properties == | ||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
! rowspan="2" |Subgroup | ! rowspan="2" | [[Subgroup]] | ||
! rowspan="2" |[[Comma list]] | ! rowspan="2" | [[Comma list|Comma List]] | ||
! rowspan="2" |[[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" |Optimal | ! rowspan="2" | Optimal<br>8ve stretch (¢) | ||
8ve stretch (¢) | ! colspan="2" | Tuning Error | ||
! colspan="2" |Tuning | |||
|- | |- | ||
![[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
![[TE simple badness|Relative]] (%) | ! [[TE simple badness|Relative]] (%) | ||
|- | |- | ||
|2.3 | | 2.3 | ||
|{{monzo|-2843 | | {{monzo| -2843 1794 }} | ||
|{{ | | {{mapping| 1794 2843 }} | ||
|0.0892 | | 0.0892 | ||
|0.0892 | | 0.0892 | ||
|5.97 | | 5.97 | ||
|- | |- | ||
|2.11.17.19.29.31.47 | | 2.11.17.19.29.31.47 | ||
|9251/9248, 347072/346921, 492043/492032, 128116736/128086823, 151329376/151270111, 378544627/378535936 | | 9251/9248, 347072/346921, 492043/492032, 128116736/128086823, 151329376/151270111, 378544627/378535936 | ||
|{{ | | {{mapping| 1794 6206 7333 7621 8715 8888 9965 }} | ||
| -0.0012 | | -0.0012 | ||
|0.0259 | | 0.0259 | ||
|1.74 | | 1.74 | ||
|} | |} | ||
{{Todo| review }} | |||