144edo - 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"

2026-03-13T13:32:06Z

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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	\| [[Substitute harmonic#Dotcom\|Dotcom]]		\| [[Substitute harmonic#Dotcom\|Dotcom]]
	\|}		\|}
	<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

	== Music ==		== Music ==

Tristanbay: /* Approximation to φ */better wording

2025-10-25T11:10:46Z

Approximation to φ: better wording

← Older revision		Revision as of 11:10, 25 October 2025
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	=== Approximation to φ ===		=== Approximation to φ ===
	144edo is the 12th Fibonacci edo. As a consequence of being a Fibonacci edo, it ~~can produce~~ an extremely precise approximation of the [[Logarithmic phi\|logarithmic golden ratio]] at 89 steps. Coincidentally, it ''also'' excellently represents the [[Acoustic phi\|acoustic golden ratio]] by 100 steps.		144edo is the 12th Fibonacci edo. As a consequence of being a Fibonacci edo, it produces an extremely precise approximation of the [[Logarithmic phi\|logarithmic golden ratio]] at 89 steps. Coincidentally, it ''also'' excellently represents the [[Acoustic phi\|acoustic golden ratio]] by 100 steps.

	== Regular temperament properties ==		== Regular temperament properties ==

Tristanbay: /* Approximation to φ */Grammar fix

2025-10-25T11:10:02Z

Approximation to φ: Grammar fix

← Older revision		Revision as of 11:10, 25 October 2025
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	=== Approximation to φ ===		=== Approximation to φ ===
	144edo is the 12th Fibonacci edo. As a consequence of being a Fibonacci edo, it can produce extremely precise approximation of the [[Logarithmic phi\|logarithmic golden ratio]] at 89 steps. Coincidentally, it ''also'' excellently represents the [[Acoustic phi\|acoustic golden ratio]] by 100 steps.		144edo is the 12th Fibonacci edo. As a consequence of being a Fibonacci edo, it can produce an extremely precise approximation of the [[Logarithmic phi\|logarithmic golden ratio]] at 89 steps. Coincidentally, it ''also'' excellently represents the [[Acoustic phi\|acoustic golden ratio]] by 100 steps.

	== Regular temperament properties ==		== Regular temperament properties ==

Francium: changed EDO intro to ED intro

2025-02-19T17:57:18Z

changed EDO intro to ED intro

← Older revision		Revision as of 17:57, 19 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|144~~}}		{{ED intro}}

	144edo's step size is called a '''farab''' when used as an [[interval size unit]].<ref>http://tonalsoft.com/enc/f/farab.aspx</ref>		144edo's step size is called a '''farab''' when used as an [[interval size unit]].<ref>http://tonalsoft.com/enc/f/farab.aspx</ref>

ArrowHead294 at 19:53, 15 January 2025

2025-01-15T19:53:50Z

← Older revision		Revision as of 19:53, 15 January 2025
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	== Theory ==		== Theory ==
	144edo is closely related to [[72edo]], but the [[patent val]]s differ on the mapping for [[13/1\|13]] and [[17/1\|17]]. It is [[enfactoring\|enfactored]] in the 11-limit, [[tempering out]] [[225/224]], [[243/242]], [[385/384]], [[441/440]], and [[4000/3993]]. Using the [[patent val]], it tempers out [[847/845]], [[1188/1183]], 1701/1690, 1875/1859, and [[4225/4224]] in the 13-limit. It [[support]]s [[hemisecordite]], the 41 & 103 temperament, though [[103edo]] is better suited for this purpose.		144edo is closely related to [[72edo]], but the [[patent val]]s differ on the mapping for [[13/1\|13]] and [[17/1\|17]]. It is [[enfactoring\|enfactored]] in the 11-limit, [[tempering out]] [[225/224]], [[243/242]], [[385/384]], [[441/440]], and [[4000/3993]]. Using the [[patent val]], it tempers out [[847/845]], [[1188/1183]], 1701/1690, 1875/1859, and [[4225/4224]] in the 13-limit. It [[support]]s [[hemisecordite]], the {{nowrap\|41 & 103}} temperament, though [[103edo]] is better suited for this purpose.

	Although the patent val comes out on top accuracy in the 13-limit, in the 17-limit 144 falls behind to 144g. The 144g val tempers out [[170/169]], [[289/288]], [[375/374]], [[561/560]], [[595/594]]. It supports [[semihemisecordite]], the 62 & 82f temperament. The patent val tempers out [[273/272]], [[715/714]], [[833/832]], 875/867, 891/884, and [[1275/1274]], supporting 17-limit hemisecordite. In the 19-limit the patent val tempers out 210/209, 325/323, [[343/342]], [[363/361]], [[400/399]], [[513/512]], and 665/663.		Although the patent val comes out on top accuracy in the 13-limit, in the 17-limit 144 falls behind to 144g. The 144g val tempers out [[170/169]], [[289/288]], [[375/374]], [[561/560]], [[595/594]]. It supports [[semihemisecordite]], the {{nowrap\|62 & 82f}} temperament. The patent val tempers out [[273/272]], [[715/714]], [[833/832]], 875/867, 891/884, and [[1275/1274]], supporting 17-limit hemisecordite. In the 19-limit the patent val tempers out 210/209, 325/323, [[343/342]], [[363/361]], [[400/399]], [[513/512]], and 665/663.

	Besides all these, the 144eff val supports hemimiracle, the 41 & 103e temperament. 144ee supports oracle, the 31 & 113e temperament. 144cf supports necromanteion, the 31 & 113cf temperament.		Besides all these, the 144eff val supports hemimiracle, the {{nowrap\|41 & 103e}} temperament. 144ee supports oracle, the {{nowrap\|31 & 113e}} temperament. 144cf supports necromanteion, the {{nowrap\|31 & 113cf}} temperament.

	=== Prime harmonics ===		=== Prime harmonics ===
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	\| [[Substitute harmonic#Dotcom\|Dotcom]]		\| [[Substitute harmonic#Dotcom\|Dotcom]]
	\|}		\|}
	<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

	== Music ==		== Music ==

ArrowHead294: Partial undo

2024-11-16T12:14:23Z

Partial undo

← Older revision		Revision as of 12:14, 16 November 2024
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	== Regular temperament properties ==		== Regular temperament properties ==
	{~~{comma basis begin}}~~		{\| class="wikitable center-4 center-5 center-6"
			\|-
			! rowspan="2" \| [[Subgroup]]
			! rowspan="2" \| [[Comma list]]
			! rowspan="2" \| [[Mapping]]
			! rowspan="2" \| Optimal<br />8ve stretch (¢)
			! colspan="2" \| Tuning error
			\|-
			! [[TE error\|Absolute]] (¢)
			! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
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	\| 0.596		\| 0.596
	\| 7.15		\| 7.15
	~~{{comma basis end}~~}		\|}

	=== 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
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	\| 129/128		\| 129/128
	\| [[Substitute harmonic#Dotcom\|Dotcom]]		\| [[Substitute harmonic#Dotcom\|Dotcom]]
	~~{{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

	== Music ==		== Music ==

ArrowHead294 at 05:16, 16 November 2024

2024-11-16T05:16:24Z

← Older revision		Revision as of 05:16, 16 November 2024
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	== Regular temperament properties ==		== Regular temperament properties ==
	{~~\| class="wikitable center-4 center-5 center-6"~~		{{comma basis begin}}
	~~! rowspan="2" \| [[Subgroup]]~~
	~~! rowspan="2" \| [[Comma list\|Comma List]]~~
	~~! rowspan="2" \| [[Mapping]]~~
	~~! rowspan="2" \| Optimal<br>8ve Stretch (¢)~~
	~~! colspan="2" \| Tuning Error~~
	\|-
	~~! [[TE error\|Absolute]] (¢)~~
	~~! [[TE simple badness\|Relative]] (%)~~
	\|-		\|-
	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
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	\| 0.595		\| 0.595
	\| 7.13		\| 7.13
	\|-style="border-top: double;"		\|- style="border-top: double;"
			\| 2.3.5.7.11.13.17
			\| 225/224, 243/242, 273/272, 325/324, 847/845, 875/867
			\| {{mapping\| 144 228 334 404 498 533 589 }} (144)
			\| +0.362
			\| 0.734
			\| 8.80
			\|- style="border-top: double;"
	\| 2.3.5.7.11.13.17		\| 2.3.5.7.11.13.17
	\| 170/169, 225/224, 243/242, 289/288, 375/374, 385/384		\| 170/169, 225/224, 243/242, 289/288, 375/374, 385/384
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	\| 0.596		\| 0.596
	\| 7.15		\| 7.15
	~~\|-style="border-top: double;"~~		{{comma basis end}}
	~~\| 2.3.5.7.11.13.17~~
	~~\| 225/224, 243/242, 273/272, 325/324, 847/845, 875/867~~
	\| {{~~mapping\| 144 228 334 404 498 533 589~~ }~~} (144)~~
	~~\| +0.362~~
	~~\| 0.734~~
	~~\| 8.80~~
	\|}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{~~\| class="wikitable center-all left-5"~~		{{rank-2 begin}}
	~~\|+Table of~~ rank-2 ~~temperaments by generator~~
	~~! Periods<br>per 8ve~~
	! Generator*
	! Cents*
	! Associated<br>Ratio*
	~~! Temperament~~
	\|-		\|-
	\| 1		\| 1
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	\| 129/128		\| 129/128
	\| [[Substitute harmonic#Dotcom\|Dotcom]]		\| [[Substitute harmonic#Dotcom\|Dotcom]]
	\|}		{{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}}

	== Music ==		== Music ==
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	== References ==		== References ==
	<references/>		<references />

	== External links ==		== External links ==

Fredg999: Move farab to lead section, add reference

2024-07-06T05:24:30Z

Move farab to lead section, add reference

← Older revision		Revision as of 05:24, 6 July 2024
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	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|144}}		{{EDO intro\|144}}

			144edo's step size is called a '''farab''' when used as an [[interval size unit]].<ref>http://tonalsoft.com/enc/f/farab.aspx</ref>

	== Theory ==		== Theory ==
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	144edo is the square of world-dominant [[12edo]]~~. One step of it is called ''[[farab]]''~~.		144edo is the square of world-dominant [[12edo]].

	Since 144 factors into 2<sup>4</sup> × 3<sup>2</sup>, 144edo has subset edos {{EDOs\| 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, and 72 }}.		Since 144 factors into 2<sup>4</sup> × 3<sup>2</sup>, 144edo has subset edos {{EDOs\| 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, and 72 }}.
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	; [[Hideya]]		; [[Hideya]]
	* [https://www.youtube.com/watch?v=p71oF-A9gF8 ''Like an endless uphill''] (2022)		* [https://www.youtube.com/watch?v=p71oF-A9gF8 ''Like an endless uphill''] (2022)

			== References ==
			<references/>

	== External links ==		== External links ==

Fredg999: External link

2024-07-01T01:40:16Z

External link

← Older revision		Revision as of 01:40, 1 July 2024
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	; [[Hideya]]		; [[Hideya]]
	* [https://www.youtube.com/watch?v=p71oF-A9gF8 ''Like an endless uphill''] (2022)		* [https://www.youtube.com/watch?v=p71oF-A9gF8 ''Like an endless uphill''] (2022)

			== External links ==
			* [http://tonalsoft.com/enc/number/144edo.aspx 144-tone equal-temperament / 144-edo] on [[Tonalsoft Encyclopedia]]

	[[Category:Listen]]		[[Category:Listen]]

FloraC: Cleanup

2024-05-21T06:57:15Z

Cleanup

← Older revision		Revision as of 06:57, 21 May 2024
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	\| 0.595		\| 0.595
	\| 7.13		\| 7.13
	\|-		\|-style="border-top: double;"
	\| style="border-top: double;" \| 2.3.5.7.11.13.17		\| 2.3.5.7.11.13.17
	~~\| style="border-top: double;"~~ \| 170/169, 225/224, 243/242, 289/288, 375/374, 385/384		\| 170/169, 225/224, 243/242, 289/288, 375/374, 385/384
	~~\| style="border-top: double;"~~ \| {{mapping\| 144 228 334 404 498 533 588 }} (144g)		\| {{mapping\| 144 228 334 404 498 533 588 }} (144g)
	~~\| style="border-top: double;"~~ \| +0.653		\| +0.653
	~~\| style="border-top: double;"~~ \| 0.596		\| 0.596
	~~\| style="border-top: double;"~~ \| 7.15		\| 7.15
	\|-		\|-style="border-top: double;"
	\| style="border-top: double;" \| 2.3.5.7.11.13.17		\| 2.3.5.7.11.13.17
	~~\| style="border-top: double;"~~ \| 225/224, 243/242, 273/272, 325/324, 847/845, 875/867		\| 225/224, 243/242, 273/272, 325/324, 847/845, 875/867
	~~\| style="border-top: double;"~~ \| {{mapping\| 144 228 334 404 498 533 589 }} (144)		\| {{mapping\| 144 228 334 404 498 533 589 }} (144)
	~~\| style="border-top: double;"~~ \| +0.362		\| +0.362
	~~\| style="border-top: double;"~~ \| 0.734		\| 0.734
	~~\| style="border-top: double;"~~ \| 8.80		\| 8.80
	\|}		\|}

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	\|+Table of rank-2 temperaments by generator		\|+Table of rank-2 temperaments by generator
	! Periods<br>per 8ve		! Periods<br>per 8ve
	! Generator~~<br>(Reduced)~~		! Generator*
	! Cents~~<br>(Reduced)~~		! Cents*
	! Associated<br>Ratio		! Associated<br>Ratio*
	! Temperament		! Temperament
	\|-		\|-
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	\| [[Substitute harmonic#Dotcom\|Dotcom]]		\| [[Substitute harmonic#Dotcom\|Dotcom]]
	\|}		\|}
			<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

	== Music ==		== Music ==