1794edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
1794edo is in[[consistent]] to the [[5-odd-limit]] and [[harmonic]]s [[3/1|3]], [[5/1|5]], and [[7/1|7]] are all about halfway between its steps. Otherwise it has decent approximations to [[9/1|9]], [[15/1|15]], [[17/1|17]], and [[21/1|21]], making it suitable for a 2.9.15.21.17 [[subgroup]] interpretation with an optional addition of either [[11/1|11]] or [[13/1|13]]. | |||
It | For higher harmonics, 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 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 === | ||
Since 1794 factors into {{factorization|1794}}, 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" | [[Comma list|Comma List]] | ||
! rowspan="2" | [[Mapping]] | |||
! rowspan="2" | Optimal<br>8ve Stretch (¢) | |||
! colspan="2" | Tuning Error | |||
|- | |- | ||
| | ! [[TE error|Absolute]] (¢) | ||
| | ! [[TE simple badness|Relative]] (%) | ||
|- | |- | ||
|2.11.17.19.29.31.47 | | 2.3 | ||
|9251/9248, 347072/346921, 492043/492032, 128116736/128086823, 151329376/151270111, 378544627/378535936 | | {{monzo| -2843 1794 }} | ||
|{{ | | {{mapping| 1794 2843 }} | ||
| | | +0.0892 | ||
|0.0259 | | 0.0892 | ||
|1.74 | | 5.97 | ||
|- | |||
| 2.11.17.19.29.31.47 | |||
| 9251/9248, 347072/346921, 492043/492032, 128116736/128086823, 151329376/151270111, 378544627/378535936 | |||
| {{mapping| 1794 6206 7333 7621 8715 8888 9965 }} | |||
| −0.0012 | |||
| 0.0259 | |||
| 1.74 | |||
|} | |} | ||
{{Todo| review }} | |||