2019edo: Difference between revisions

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~~{{novelty}}{{stub}}~~{{Infobox ET}}

== 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}.

=== 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 per 8ve

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

! Generator~~ (Reduced)~~

|-

! Cents~~ (Reduced)~~

! Periods per 8ve

! Associated ~~Ratio~~

! Generator*

! Cents*

! Associated ratio*

! Temperaments

|-

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| 154\2019

| 91.530

| ~~1953125000000000/1853020188851841~~

| {{monzo| 46 -7 -15 }}

| [[Gross]]

|-

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| [[Domain]]

|}

[[~~Category:Equal divisions of~~ the octave|~~####~~]] ~~~~

<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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-{{novelty}}{{stub}}{{Infobox ET}}
+{{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}.
 === 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
-! Generator<br>(Reduced)
+|-
-! Cents<br>(Reduced)
+! Periods<br />per 8ve
-! Associated<br>Ratio
+! Generator*
+! Cents*
+! Associated<br />ratio*
 ! Temperaments
 |-
@@ Line 20: / Line 29: @@
 | 154\2019
 | 91.530
-| 1953125000000000/1853020188851841
+| {{monzo| 46 -7 -15 }}
 | [[Gross]]
 |-
@@ Line 35: / Line 44: @@
 | [[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