2019edo: Difference between revisions

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== 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]]. While it is consistent in the 11-odd-limit, there is a large relative error on the representation of the 11th harmonic.

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}.

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=== Prime harmonics ===

=== 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"

! Periods<br>per 8ve

|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator

|-

! Periods<br />per 8ve

! Generator*

! Cents*

! Associated<br>~~Ratio~~

! Associated<br />ratio*

! Temperaments

|-

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| [[Domain]]

|}

<nowiki>*~~</nowiki>~~ [[Normal lists|~~octave~~-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if ~~it is~~ distinct

<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct

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 {{Infobox ET}}
-{{EDO intro|2019}}
+{{ED intro}}
 == Theory ==
-edo is excellent in the 2.3.5.7 subgroup, 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 11th harmonic.
+edo 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}.
@@ Line 8: / Line 9: @@
 === Prime harmonics ===
 {{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"
-! Periods<br>per 8ve
+|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
+|-
+! Periods<br />per 8ve
 ! Generator*
 ! Cents*
-! Associated<br>Ratio
+! Associated<br />ratio*
 ! Temperaments
 |-
@@ Line 36: / Line 44: @@
 | [[Domain]]
 |}
-<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
+<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct