1911edo - 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"

2026-03-13T13:31:53Z

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 13:31, 13 March 2026
Line 40:		Line 40:
	\| [[Protactinium]]		\| [[Protactinium]]
	\|}		\|}
	<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

Overthink: /* Rank-2 temperaments */ + scandium

2026-01-15T05:27:57Z

Rank-2 temperaments: + scandium

← Older revision		Revision as of 05:27, 15 January 2026
Line 27:		Line 27:
	\| 4/3<br />(?)		\| 4/3<br />(?)
	\| [[Aluminium]]		\| [[Aluminium]]
			\|-
			\| 21
			\| 233\1911<br />(40\1911)
			\| 146.311<br />(25.118)
			\| 160/147<br />(?)
			\| [[21st-octave temperaments#Scandium\|Scandium]]
	\|-		\|-
	\| 91		\| 91

Francium: changed EDO intro to ED intro

2025-02-21T06:04:59Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:04, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|1911~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 16:05, 15 January 2025

2025-01-15T16:05:00Z

← Older revision		Revision as of 16:05, 15 January 2025
Line 34:		Line 34:
	\| [[Protactinium]]		\| [[Protactinium]]
	\|}		\|}
	<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

2024-11-16T13:22:54Z

Partial undo

← Older revision		Revision as of 13:22, 16 November 2024
Line 13:		Line 13:
	== 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
	\|-		\|-
	\| 13		\| 13
Line 26:		Line 33:
	\| 4/3<br />(176/175)		\| 4/3<br />(176/175)
	\| [[Protactinium]]		\| [[Protactinium]]
	~~{{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

2024-11-16T01:24:14Z

← Older revision		Revision as of 01:24, 16 November 2024
Line 13:		Line 13:
	== Regular temperament properties ==		== Regular temperament properties ==
	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{~~\| class="wikitable center-all left-5"~~		{{Rank-2 begin}}
	~~\|+ style="font-size: 105%;" \| Table of rank~~-2 ~~temperaments by generator~~
	\|-
	~~! Periods<br />per 8ve~~
	! Generator*
	! Cents*
	! Associated<br />Ratio*
	~~! Temperaments~~
	\|-		\|-
	\| 13		\| 13
Line 33:		Line 26:
	\| 4/3<br />(176/175)		\| 4/3<br />(176/175)
	\| [[Protactinium]]		\| [[Protactinium]]
	\|}		{{Rank-2 end}}
	{{orf}}		{{orf}}

ArrowHead294: Template

2024-11-16T00:42:12Z

Template

← Older revision		Revision as of 00:42, 16 November 2024
Line 14:		Line 14:
	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{\| class="wikitable center-all left-5"		{\| class="wikitable center-all left-5"
	\|+Table of rank-2 temperaments by generator		\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
	\|-		\|-
	! Periods<br>per 8ve		! Periods<br />per 8ve
	! Generator*		! Generator*
	! Cents*		! Cents*
	! Associated<br>Ratio*		! Associated<br />Ratio*
	! Temperaments		! Temperaments
	\|-		\|-
	\| 13		\| 13
	\| 793\1911<br>(58\1911)		\| 793\1911<br />(58\1911)
	\| 497.959<br>(36.421)		\| 497.959<br />(36.421)
	\| 4/3<br>(?)		\| 4/3<br />(?)
	\| [[Aluminium]]		\| [[Aluminium]]
	\|-		\|-
	\| 91		\| 91
	\| 793\1911<br>(16\1911)		\| 793\1911<br />(16\1911)
	\| 497.959<br>(10.047)		\| 497.959<br />(10.047)
	\| 4/3<br>(176/175)		\| 4/3<br />(176/175)
	\| [[Protactinium]]		\| [[Protactinium]]
	\|}		\|}
	~~<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}}

FloraC: Adopt template: Factorization; misc. cleanup

2023-10-30T12:23:54Z

Adopt template: Factorization; misc. cleanup

← Older revision		Revision as of 12:23, 30 October 2023
Line 3:		Line 3:

	== Theory ==		== Theory ==
	1911edo is [[consistent]] in the 11-limit ~~and~~ [[Tempering out\|tempers out]] the [[aluminium comma]] in the 5-limit~~. It~~ provides the [[optimal patent val]] for the [[protactinium]] temperament in the 17-limit. However as may stem from consistency only in the 11-limit, the 13th harmonic has a large relative error. As such, 1911edo is best considered as a 2.3.5.7.11.17.19 [[subgroup]] tuning.		1911edo is [[consistent]] in the [[11-odd-limit]]. The equal temperament [[Tempering out\|tempers out]] the [[aluminium comma]] in the 5-limit, and it provides the [[optimal patent val]] for the [[protactinium]] temperament in the 17-limit. However as may stem from consistency only in the 11-limit, the 13th harmonic has a large relative error. As such, 1911edo is best considered as a 2.3.5.7.11.17.19 [[subgroup]] tuning.

	=== Odd harmonics ===		=== Odd harmonics ===
Line 9:		Line 9:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 1911 factors into ~~3 × 7<sup>2</sup> × 13~~, 1911edo has subset edos {{EDOs\| 3, 7, 13, 21, 39, 49, 91, 147, 273, 637 }}.		Since 1911 factors into {{factorization\|1911}}, 1911edo has subset edos {{EDOs\| 3, 7, 13, 21, 39, 49, 91, 147, 273, 637 }}.

	== Regular temperament properties ==		== Regular temperament properties ==
	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{\| class="wikitable center-all left-5"		{\| class="wikitable center-all left-5"
			\|+Table of rank-2 temperaments by generator
			\|-
	! Periods<br>per 8ve		! Periods<br>per 8ve
	! Generator*		! Generator*
	! Cents*		! Cents*
	! Associated<br>Ratio		! Associated<br>Ratio*
	! Temperaments		! Temperaments
	\|-		\|-

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

2023-10-15T14:10:10Z

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

← Older revision		Revision as of 14:10, 15 October 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|1911}}		{{EDO intro\|1911}}

	== Theory ==		== Theory ==
	1911edo is consistent in the 11-limit and tempers out the [[aluminium comma]] in the 5-limit. It provides the [[optimal patent val]] for the [[protactinium]] temperament in the 17-limit. However as may stem from consistency only in the 11-limit, the 13th harmonic has a large relative error. As such, 1911edo is best considered as a 2.3.5.7.11.17.19 subgroup tuning.		1911edo is [[consistent]] in the 11-limit and [[Tempering out\|tempers out]] the [[aluminium comma]] in the 5-limit. It provides the [[optimal patent val]] for the [[protactinium]] temperament in the 17-limit. However as may stem from consistency only in the 11-limit, the 13th harmonic has a large relative error. As such, 1911edo is best considered as a 2.3.5.7.11.17.19 [[subgroup]] tuning.

	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|1911}}		{{Harmonics in equal\|1911}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
	1911edo has subset edos {{EDOs\|1, 3, 7, 13, 21, 39, 49, 91, 147, 273, 637}}.		Since 1911 factors into 3 × 7<sup>2</sup> × 13, 1911edo has subset edos {{EDOs\| 3, 7, 13, 21, 39, 49, 91, 147, 273, 637 }}.

	== 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		! Periods<br>per 8ve
	!Generator~~<br>(Reduced)~~		! Generator*
	!Cents~~<br>(Reduced)~~		! Cents*
	!Associated<br>Ratio		! Associated<br>Ratio
	!Temperaments		! Temperaments
	\|-		\|-
	\|13		\| 13
	\|793\1911<br>(58\1911)		\| 793\1911<br>(58\1911)
	\|497.959<br>(36.421)		\| 497.959<br>(36.421)
	\|4/3<br>(?)		\| 4/3<br>(?)
	\|[[Aluminium]]		\| [[Aluminium]]
	\|-		\|-
	\|91		\| 91
	\|793\1911<br>(16\1911)		\| 793\1911<br>(16\1911)
	\|497.959<br>(10.047)		\| 497.959<br>(10.047)
	\|4/3<br>(176/175)		\| 4/3<br>(176/175)
	\|[[Protactinium]]		\| [[Protactinium]]
	\|}		\|}
			<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

Eliora: style

2023-07-17T21:20:15Z

style

← Older revision		Revision as of 21:20, 17 July 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|1911}}		{{EDO intro\|1911}}
			== Theory ==
	1911edo is consistent in the 11-limit and tempers out the [[aluminium comma]] in the 5-limit. It provides the [[optimal patent val]] for the [[protactinium]] temperament in the 17-limit. However as may stem from consistency only in the 11-limit, the 13th harmonic has a large relative error. As such, 1911edo is best considered as a 2.3.5.7.11.17.19 subgroup tuning.		1911edo is consistent in the 11-limit and tempers out the [[aluminium comma]] in the 5-limit. It provides the [[optimal patent val]] for the [[protactinium]] temperament in the 17-limit. However as may stem from consistency only in the 11-limit, the 13th harmonic has a large relative error. As such, 1911edo is best considered as a 2.3.5.7.11.17.19 subgroup tuning.
	=== Odd harmonics ===		=== Odd harmonics ===
Line 13:		Line 13:
	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{\| class="wikitable center-all left-5"		{\| class="wikitable center-all left-5"
	!Periods		!Periods<br>per 8ve
	per 8ve		!Generator<br>(Reduced)
	!Generator		!Cents<br>(Reduced)
	(Reduced)		!Associated<br>Ratio
	!Cents
	(Reduced)
	!Associated
	Ratio
	!Temperaments		!Temperaments
	\|-		\|-
	\|13		\|13
	\|793\1911		\|793\1911<br>(58\1911)
	(58\1911)		\|497.959<br>(36.421)
	\|497.959		\|4/3<br>(?)
	(36.421)
	\|4/3
	(?)
	\|[[Aluminium]]		\|[[Aluminium]]
	\|-		\|-
	\|91		\|91
	\|793\1911		\|793\1911<br>(16\1911)
	(16\1911)		\|497.959<br>(10.047)
	\|497.959		\|4/3<br>(176/175)
	(10.047)
	\|4/3
	(176/175)
	\|[[Protactinium]]		\|[[Protactinium]]
	\|}		\|}