2019edo - Revision history

FloraC: Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

2026-03-13T13:33:15Z

Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

← Older revision		Revision as of 13:33, 13 March 2026
Line 44:		Line 44:
	\| [[Domain]]		\| [[Domain]]
	\|}		\|}
	<nowiki />* [[Normal ~~lists~~\|Octave-reduced form]], reduced to the first half-octave, and [[~~Normal lists~~\|minimal form]] in parentheses if distinct		<nowiki />* [[Normal forms #Equave-reduced-generator form\|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form\|minimal form]] in parentheses if distinct

ArrowHead294 at 23:07, 20 February 2025

2025-02-20T23:07:39Z

← Older revision		Revision as of 23:07, 20 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|2019~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 15:59, 15 January 2025

2025-01-15T15:59:20Z

← Older revision		Revision as of 15:59, 15 January 2025
Line 44:		Line 44:
	\| [[Domain]]		\| [[Domain]]
	\|}		\|}
	<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

ArrowHead294: Partial undo

2024-11-16T13:22:28Z

Partial undo

← Older revision		Revision as of 13:22, 16 November 2024
Line 17:		Line 17:
	== Regular temperament properties ==		== Regular temperament properties ==
	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{{rank-2 ~~begin}}~~		{\| 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		\| 1
Line 36:		Line 43:
	\| 10/9		\| 10/9
	\| [[Domain]]		\| [[Domain]]
	~~{{rank-2 end}~~}		\|}
	~~{{orf}}~~		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

ArrowHead294 at 01:24, 16 November 2024

2024-11-16T01:24:59Z

← Older revision		Revision as of 01:24, 16 November 2024
Line 17:		Line 17:
	== Regular temperament properties ==		== Regular temperament properties ==
	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{~~\| class="wikitable center~~-~~all left-5"~~		{{rank-2 begin}}
	\|-
	~~! Periods<br />per 8ve~~
	! Generator*
	! Cents*
	! Associated<br />Ratio*
	~~! Temperaments~~
	\|-		\|-
	\| 1		\| 1
Line 42:		Line 36:
	\| 10/9		\| 10/9
	\| [[Domain]]		\| [[Domain]]
	\|}		{{rank-2 end}}
	{{orf}}		{{orf}}

ArrowHead294 at 00:43, 16 November 2024

2024-11-16T00:43:46Z

← Older revision		Revision as of 00:43, 16 November 2024
Line 18:		Line 18:
	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{\| class="wikitable center-all left-5"		{\| class="wikitable center-all left-5"
	! Periods<br>per 8ve		\|-
			! Periods<br />per 8ve
	! Generator*		! Generator*
	! Cents*		! Cents*
	! Associated<br>Ratio*		! Associated<br />Ratio*
	! Temperaments		! Temperaments
	\|-		\|-
Line 42:		Line 43:
	\| [[Domain]]		\| [[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~~		{{orf}}

Lériendil: /* Subsets and supersets */

2024-10-28T23:56:12Z

Subsets and supersets

← Older revision		Revision as of 23:56, 28 October 2024
Line 11:		Line 11:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 2019 factors into {{factorization\|2019}}, 2019 contains [[3edo]] and 673edo as subsets.		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 ==

FloraC: +subsets and supersets

2023-10-30T12:05:39Z

+subsets and supersets

← Older revision		Revision as of 12:05, 30 October 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|2019}}		{{EDO intro\|2019}}

	== 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]]. 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}.		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 ===		=== 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.

	== Regular temperament properties ==		== Regular temperament properties ==
Line 15:		Line 19:
	! Generator*		! Generator*
	! Cents*		! Cents*
	! Associated<br>Ratio		! Associated<br>Ratio*
	! Temperaments		! Temperaments
	\|-		\|-

FloraC: Cleanup; clarify the title row of the rank-2 temp table; -redundant categories

2023-10-15T13:47:01Z

Cleanup; clarify the title row of the rank-2 temp table; -redundant categories

← Older revision		Revision as of 13:47, 15 October 2023
Line 5:		Line 5:

	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}.		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}}
Line 12:		Line 13:
	{\| class="wikitable center-all left-5"		{\| class="wikitable center-all left-5"
	! Periods<br>per 8ve		! Periods<br>per 8ve
	! Generator~~<br>(Reduced)~~		! Generator*
	! Cents~~<br>(Reduced)~~		! Cents*
	! Associated<br>Ratio		! Associated<br>Ratio
	! Temperaments		! Temperaments
Line 20:		Line 21:
	\| 154\2019		\| 154\2019
	\| 91.530		\| 91.530
	\| ~~1953125000000000/1853020188851841~~		\| {{monzo\| 46 -7 -15 }}
	\| [[Gross]]		\| [[Gross]]
	\|-		\|-
Line 35:		Line 36:
	\| [[Domain]]		\| [[Domain]]
	\|}		\|}
	[[~~Category:Equal divisions of~~ the octave\|~~####~~]] ~~<!-- 4-digit number -->~~		<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

BudjarnLambeth at 06:59, 9 July 2023

2023-07-09T06:59:54Z

← Older revision		Revision as of 06:59, 9 July 2023
Line 1:		Line 1:
	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|2019}}		{{EDO intro\|2019}}
	== Theory ==		== Theory ==