2520edo - 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"

2026-03-13T13:32:10Z

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 13:32, 13 March 2026
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	\| [[Barium]]		\| [[Barium]]
	\|}		\|}
	<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

	[[Category:Jacobin]]		[[Category:Jacobin]]

Francium: changed EDO intro to ED intro

2025-02-21T06:07:18Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:07, 21 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|2520~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 17:47, 15 January 2025

2025-01-15T17:47:49Z

← Older revision		Revision as of 17:47, 15 January 2025
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	In addition to being a highly composite number, 2520 is the least common multiple of numbers from 1 to 10, meaning 2520edo is the smallest superset of first 10 edos. Its subset edos are {{EDOs\| 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 56, 60, 63, 70, 72, 84, 90, 105, 120, 126, 140, 168, 180, 210, 252, 280, 315, 360, 420, 504, 630, 840, 1260 }}. It is a superabundant edo in addition to being highly composite, with abundancy index of 19/7 = 2.714.		In addition to being a highly composite number, 2520 is the least common multiple of numbers from 1 to 10, meaning 2520edo is the smallest superset of first 10 edos. Its subset edos are {{EDOs\| 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 56, 60, 63, 70, 72, 84, 90, 105, 120, 126, 140, 168, 180, 210, 252, 280, 315, 360, 420, 504, 630, 840, 1260 }}. It is a superabundant edo in addition to being highly composite, with abundancy index of {{nowrap\|19/7 {{=}} 2.714}}.

	Furthermore, one step of 2520edo is 8 pians ([[20160edo\|20160/8]]).		Furthermore, one step of 2520edo is 8 pians ([[20160edo\|20160/8]]).
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	\| [[Barium]]		\| [[Barium]]
	\|}		\|}
	<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

	[[Category:Jacobin]]		[[Category:Jacobin]]

ArrowHead294: Partial undo

2024-11-16T12:50:36Z

Partial undo

← Older revision		Revision as of 12:50, 16 November 2024
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	== 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
	\|-		\|-
	\| 9		\| 9
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	\| 4/3<br />(126/125)		\| 4/3<br />(126/125)
	\| [[Barium]]		\| [[Barium]]
	~~{{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

	[[Category:Jacobin]]		[[Category:Jacobin]]

ArrowHead294 at 03:47, 16 November 2024

2024-11-16T03:47:21Z

← Older revision		Revision as of 03:47, 16 November 2024
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	== 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~~
	\|-		\|-
	\| 9		\| 9
	\| 663\2520<br>(103\2520)		\| 663\2520<br />(103\2520)
	\| 315.714<br>(49.048)		\| 315.714<br />(49.048)
	\| 6/5<br>(36/35)		\| 6/5<br />(36/35)
	\| [[Ennealimmal]] (2520d)		\| [[Ennealimmal]] (2520d)
	\|-		\|-
	\| 18		\| 18
	\| 523\2520<br>(103\2520)		\| 523\2520<br />(103\2520)
	\| 249.047<br>(49.048)		\| 249.047<br />(49.048)
	\| 231/200<br>(99/98)		\| 231/200<br />(99/98)
	\| [[Hemiennealimmal]] (2520de)		\| [[Hemiennealimmal]] (2520de)
	\|-		\|-
	\| 56		\| 56
	\| 1046\2520<br>(11\2520)		\| 1046\2520<br />(11\2520)
	\| 498.095<br>(5.238)		\| 498.095<br />(5.238)
	\| 4/3<br>(126/125)		\| 4/3<br />(126/125)
	\| [[Barium]]		\| [[Barium]]
	\|}		{{rank-2 end}}
	~~<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}}

	[[Category:Jacobin]]		[[Category:Jacobin]]

FloraC: Linking

2023-10-30T10:32:22Z

Linking

← Older revision		Revision as of 10:32, 30 October 2023
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	== Theory ==		== Theory ==
	2520edo is the 18th [[highly composite edo]]. See Subsets and supersets section for the divisors.		2520edo is the 18th [[highly composite edo]]. See [[#Subsets and supersets]] section for the divisors.

	It is a good 2.3.5.11.13 [[subgroup]] tuning where it tempers out [[6656/6655]]. The 2520d val tempers out [[2401/2400]] and [[4375/4374]] and provides a tuning for the [[ennealimmal]] temperament and the rank-3 [[ennealimmic]] temperament. The 2520de val is a tuning for the [[hemiennealimmal]] temperament in the 11-limit. The 2520e val is a member of the [[optimal ET sequence]] for the [[tribilo]] temperament, the 2.3.11 rank-2 temperament tempering out 1771561/1769472.		It is a good 2.3.5.11.13 [[subgroup]] tuning where it tempers out [[6656/6655]]. The 2520d val tempers out [[2401/2400]] and [[4375/4374]] and provides a tuning for the [[ennealimmal]] temperament and the rank-3 [[ennealimmic]] temperament. The 2520de val is a tuning for the [[hemiennealimmal]] temperament in the 11-limit. The 2520e val is a member of the [[optimal ET sequence]] for the [[tribilo]] temperament, the 2.3.11 rank-2 temperament tempering out 1771561/1769472.
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	In addition to being a highly composite number, 2520 is the least common multiple of numbers from 1 to 10, meaning 2520edo is the smallest superset of first 10 edos.		In addition to being a highly composite number, 2520 is the least common multiple of numbers from 1 to 10, meaning 2520edo is the smallest superset of first 10 edos. Its subset edos are {{EDOs\| 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 56, 60, 63, 70, 72, 84, 90, 105, 120, 126, 140, 168, 180, 210, 252, 280, 315, 360, 420, 504, 630, 840, 1260 }}. It is a superabundant edo in addition to being highly composite, with abundancy index of 19/7 = 2.714.

	~~2520edo has~~ subset edos {{EDOs\|1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 56, 60, 63, 70, 72, 84, 90, 105, 120, 126, 140, 168, 180, 210, 252, 280, 315, 360, 420, 504, 630, 840, 1260}}. It is a superabundant edo in addition to being highly composite, with abundancy index of 19/7 = 2.714.

	Furthermore, one step of 2520edo is 8 pians ([[20160edo\|20160/8]]).		Furthermore, one step of 2520edo is 8 pians ([[20160edo\|20160/8]]).

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

2023-10-15T12:07:51Z

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

← Older revision		Revision as of 12:07, 15 October 2023
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	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|2520}}		{{EDO intro\|2520}}

	== Theory ==		== Theory ==
	2520edo is the 18th [[highly composite edo]]. See Subsets and supersets section for the divisors.		2520edo is the 18th [[highly composite edo]]. See Subsets and supersets section for the divisors.
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	It is a good 2.3.5.11.13 [[subgroup]] tuning where it tempers out [[6656/6655]]. The 2520d val tempers out [[2401/2400]] and [[4375/4374]] and provides a tuning for the [[ennealimmal]] temperament and the rank-3 [[ennealimmic]] temperament. The 2520de val is a tuning for the [[hemiennealimmal]] temperament in the 11-limit. The 2520e val is a member of the [[optimal ET sequence]] for the [[tribilo]] temperament, the 2.3.11 rank-2 temperament tempering out 1771561/1769472.		It is a good 2.3.5.11.13 [[subgroup]] tuning where it tempers out [[6656/6655]]. The 2520d val tempers out [[2401/2400]] and [[4375/4374]] and provides a tuning for the [[ennealimmal]] temperament and the rank-3 [[ennealimmic]] temperament. The 2520de val is a tuning for the [[hemiennealimmal]] temperament in the 11-limit. The 2520e val is a member of the [[optimal ET sequence]] for the [[tribilo]] temperament, the 2.3.11 rank-2 temperament tempering out 1771561/1769472.

	2520edo tempers out the [[barium comma]], setting [[81/80]] equal to 1/56th of the octave, and it tunes the [[barium]] temperament on the patent val upwards to the 13-limit. In addition, 2520edo tunes a variation of barium in the 2520d val for which has a comma basis of {[[~~vidar\|~~4225/4224, 4375/4374, 6656/6655]], ~~1116491110875/1115001192448~~} and reaches 7th harmonic in 9 generators instead of 5. Eliora proposes the name ''baridar'' for this temperament, being a portmanteau of 'barium' and 'vidar'. Overall, barium is best considered in 2520edo as a no-sevens temperament, where it has a comma basis {4225/4224, 6656/6655, ~~8862938119652501095929/8859136000000000000000~~}.		2520edo tempers out the [[barium comma]], setting [[81/80]] equal to 1/56th of the octave, and it tunes the [[barium]] temperament on the patent val upwards to the 13-limit. In addition, 2520edo tunes a variation of barium in the 2520d val for which has a comma basis of {[[4225/4224]], [[4375/4374]], [[6656/6655]], {{monzo\| -22 12 3 5 -2 -3 }}} and reaches the [[7/1\|7th harmonic]] in 9 generators instead of 5. [[Eliora]] proposes the name ''baridar'' for this temperament, being a portmanteau of 'barium' and 'vidar'. Overall, barium is best considered in 2520edo as a no-sevens temperament, where it has a comma basis {4225/4224, 6656/6655, {{monzo\| -24 46 -15 0 -3 -1 }}}.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|2520}}		{{Harmonics in equal\|2520}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
	In addition to being a highly composite number, 2520 is the least common multiple of numbers from 1 to 10, meaning 2520edo is the smallest superset of first 10 edos.		In addition to being a highly composite number, 2520 is the least common multiple of numbers from 1 to 10, meaning 2520edo is the smallest superset of first 10 edos.
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	Furthermore, one step of 2520edo is 8 pians ([[20160edo\|20160/8]]).		Furthermore, one step of 2520edo is 8 pians ([[20160edo\|20160/8]]).

	== 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		! Generator*
	! Cents		! Cents*
	! Associated<br>Ratio		! Associated<br>Ratio
	! Temperaments		! Temperaments
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	\| [[Barium]]		\| [[Barium]]
	\|}		\|}
			<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

	[[Category:Jacobin]]		[[Category:Jacobin]]

BudjarnLambeth at 07:01, 9 July 2023

2023-07-09T07:01:49Z

← Older revision		Revision as of 07:01, 9 July 2023
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	~~{{novelty}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|2520}}		{{EDO intro\|2520}}
	== Theory ==		== Theory ==

BudjarnLambeth at 04:37, 9 July 2023

2023-07-09T04:37:11Z

← Older revision		Revision as of 04:37, 9 July 2023
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	{{Infobox ET}}		{{novelty}}{{Infobox ET}}
	{{EDO intro\|2520}}		{{EDO intro\|2520}}
	== Theory ==		== Theory ==

Cmloegcmluin: "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence

2023-05-07T17:53:24Z

"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence

← Older revision		Revision as of 17:53, 7 May 2023
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	2520edo is the 18th [[highly composite edo]]. See Subsets and supersets section for the divisors.		2520edo is the 18th [[highly composite edo]]. See Subsets and supersets section for the divisors.

	It is a good 2.3.5.11.13 [[subgroup]] tuning where it tempers out [[6656/6655]]. The 2520d val tempers out [[2401/2400]] and [[4375/4374]] and provides a tuning for the [[ennealimmal]] temperament and the rank-3 [[ennealimmic]] temperament. The 2520de val is a tuning for the [[hemiennealimmal]] temperament in the 11-limit. The 2520e val is a member of the [[optimal ~~GPV~~ sequence]] for the [[tribilo]] temperament, the 2.3.11 rank-2 temperament tempering out 1771561/1769472.		It is a good 2.3.5.11.13 [[subgroup]] tuning where it tempers out [[6656/6655]]. The 2520d val tempers out [[2401/2400]] and [[4375/4374]] and provides a tuning for the [[ennealimmal]] temperament and the rank-3 [[ennealimmic]] temperament. The 2520de val is a tuning for the [[hemiennealimmal]] temperament in the 11-limit. The 2520e val is a member of the [[optimal ET sequence]] for the [[tribilo]] temperament, the 2.3.11 rank-2 temperament tempering out 1771561/1769472.

	2520edo tempers out the [[barium comma]], setting [[81/80]] equal to 1/56th of the octave, and it tunes the [[barium]] temperament on the patent val upwards to the 13-limit. In addition, 2520edo tunes a variation of barium in the 2520d val for which has a comma basis of {[[vidar\|4225/4224, 4375/4374, 6656/6655]], 1116491110875/1115001192448} and reaches 7th harmonic in 9 generators instead of 5. Eliora proposes the name ''baridar'' for this temperament, being a portmanteau of 'barium' and 'vidar'. Overall, barium is best considered in 2520edo as a no-sevens temperament, where it has a comma basis {4225/4224, 6656/6655, 8862938119652501095929/8859136000000000000000}.		2520edo tempers out the [[barium comma]], setting [[81/80]] equal to 1/56th of the octave, and it tunes the [[barium]] temperament on the patent val upwards to the 13-limit. In addition, 2520edo tunes a variation of barium in the 2520d val for which has a comma basis of {[[vidar\|4225/4224, 4375/4374, 6656/6655]], 1116491110875/1115001192448} and reaches 7th harmonic in 9 generators instead of 5. Eliora proposes the name ''baridar'' for this temperament, being a portmanteau of 'barium' and 'vidar'. Overall, barium is best considered in 2520edo as a no-sevens temperament, where it has a comma basis {4225/4224, 6656/6655, 8862938119652501095929/8859136000000000000000}.