2019edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
2019edo is excellent in the 7-limit, and with such small errors it supports a noticeable amount of [[very high accuracy temperaments]]. While it is [[consistent]] in the [[11-odd-limit]], there is a large relative error on the representation of the [[11/1|11th harmonic]]. | |||
In higher limits, it tunes [[23/16]] and [[59/32]] with the comparable relative accuracy to the 2.3.5.7 subgroup (less than 7% error). A comma basis for the 2.3.5.7.23.59 subgroup is {14337/14336, 25921/25920, 250047/250000, 48234496/48234375, 843396867/843308032}. | |||
=== Prime harmonics === | |||
{{Harmonics in equal|2019}} | {{Harmonics in equal|2019}} | ||
== | === Subsets and supersets === | ||
Since 2019 factors into {{factorization|2019}}, 2019 contains [[3edo]] and 673edo as subsets. | |||
[[4038edo]], which doubles it, provides good corrections for a number of higher primes. | |||
== Regular temperament properties == | |||
=== Rank-2 temperaments === | |||
{| class="wikitable center-all left-5" | |||
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | |||
|- | |||
! Periods<br />per 8ve | |||
! Generator* | |||
! Cents* | |||
! Associated<br />ratio* | |||
! Temperaments | |||
|- | |||
| 1 | |||
| 154\2019 | |||
| 91.530 | |||
| {{monzo| 46 -7 -15 }} | |||
| [[Gross]] | |||
|- | |||
| 1 | |||
| 307\2019 | |||
| 182.467 | |||
| 10/9 | |||
| [[Minortone]] | |||
|- | |||
| 3 | |||
| 307\2019 | |||
| 182.467 | |||
| 10/9 | |||
| [[Domain]] | |||
|} | |||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | |||