2019edo: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|2019}}
{{ED intro}}
 
== Theory ==
== Theory ==
2019edo is excellent in the 2.3.5.7 subgroup, and with such small errors it supports a noticeable amount of [[very high accuracy temperaments]].
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 ===
=== 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 ==
== Regular temperament properties ==
=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
{| class="wikitable center-all left-5"
! Periods<br>per 8ve
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
! Generator<br>(Reduced)
|-
! Cents<br>(Reduced)
! Periods<br />per 8ve
! Associated<br>Ratio
! Generator*
! Cents*
! Associated<br />ratio*
! Temperaments
! Temperaments
|-
|-
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| 154\2019
| 154\2019
| 91.530
| 91.530
| 1953125000000000/1853020188851841
| {{monzo| 46 -7 -15 }}
| [[Gross]]
| [[Gross]]
|-
|-
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| [[Domain]]
| [[Domain]]
|}
|}
[[Category:Equal divisions of the octave|####]] <!-- 4-digit number -->
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct