159edo - 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"

2026-03-13T13:32:40Z

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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	\| [[Iodine]]		\| [[Iodine]]
	\|}		\|}
	<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

	== Instruments ==		== Instruments ==

Overthink: Sectioning

2026-02-21T04:25:56Z

Sectioning

← Older revision		Revision as of 04:25, 21 February 2026
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	{{ED intro}} The step size of this system is in between the sizes of [[243/242]] (the rastma) and [[225/224]] (the marvel comma).		{{ED intro}} The step size of this system is in between the sizes of [[243/242]] (the rastma) and [[225/224]] (the marvel comma).

	~~== Theory ==~~		== History ==
	~~A salient fact about 159edo is that {{nowrap\| 159 {{=}} 3 × 53 }}, and thus, this system has both [[3edo]] and [[53edo]] as subsets—the former subset being shared with [[12edo]].~~

	=== History ===
	Despite being none other than the tripled superset of the famous 53edo, and hence, one would think, fairly easy to find, it is a wonder that the first person to show theoretical interest in it was [[Ozan Yarman]]—specifically in terms of extracting a voluminous subset for representing maqamat—in late 2005 to early 2006.		Despite being none other than the tripled superset of the famous 53edo, and hence, one would think, fairly easy to find, it is a wonder that the first person to show theoretical interest in it was [[Ozan Yarman]]—specifically in terms of extracting a voluminous subset for representing maqamat—in late 2005 to early 2006.

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	Accordingly, it is no coincidence that [https://en.xen.wiki/index.php?title=159edo&type=revision&diff=5153&oldid=5154 the first records of 159edo on this Wiki from the days of Wikispaces] concern said 79-tone subset related to the [[Turkish maqam music temperaments\|yarman]] temperament which had been proposed by Yarman as a tuning standard for [[Arabic, Turkish, Persian music\|Arabic, Turkish and Persian music]]. Based on the information given by Ozan Yarman himself, his elder colleague [[M. Ugur Kececioglu]] first utilized 159edo in his revamped 2011 release of the [[Notist]] score editor and therein allowed the Arel-Ezgi-Uzdilek (AEU) accidentals to be bent by as little a detail as 1/3 of a single step of 53edo, while also mapping AEU altogether to a suitable subset of 53edo to allow transpositions throughout.		Accordingly, it is no coincidence that [https://en.xen.wiki/index.php?title=159edo&type=revision&diff=5153&oldid=5154 the first records of 159edo on this Wiki from the days of Wikispaces] concern said 79-tone subset related to the [[Turkish maqam music temperaments\|yarman]] temperament which had been proposed by Yarman as a tuning standard for [[Arabic, Turkish, Persian music\|Arabic, Turkish and Persian music]]. Based on the information given by Ozan Yarman himself, his elder colleague [[M. Ugur Kececioglu]] first utilized 159edo in his revamped 2011 release of the [[Notist]] score editor and therein allowed the Arel-Ezgi-Uzdilek (AEU) accidentals to be bent by as little a detail as 1/3 of a single step of 53edo, while also mapping AEU altogether to a suitable subset of 53edo to allow transpositions throughout.

			== Theory ==
			A salient fact about 159edo is that {{nowrap\| 159 {{=}} 3 × 53 }}, and thus, this system has both [[3edo]] and [[53edo]] as subsets—the former subset being shared with [[12edo]].

	=== Mappings and JI approximation quality ===		=== Mappings and JI approximation quality ===

Overthink: /* Commas */ update

2026-02-20T23:38:27Z

Commas: update

← Older revision		Revision as of 23:38, 20 February 2026
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	\| 2.2461		\| 2.2461
	\|		\|
	\| [[~~Tricot~~ comma]]		\| [[Alphatricot comma]]
	\|-		\|-
	\| 5		\| 5

Overthink: /* Commas */ fix this

2026-02-03T00:35:53Z

Commas: fix this

← Older revision		Revision as of 00:35, 3 February 2026
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	<references group="note" />		<references group="note" />

	In the 23-limit, with the 19-~~limit~~ skipped, this system is known to temper out [[392/391]], [[460/459]], [[507/506]], [[529/528]], [[897/896]], [[1105/1104]], [[1288/1287]], [[2024/2023]], [[2025/2024]], and [[2646/2645]] among others.		In the 23-limit, with the 19-prime skipped, this system is known to temper out [[392/391]], [[460/459]], [[507/506]], [[529/528]], [[897/896]], [[1105/1104]], [[1288/1287]], [[2024/2023]], [[2025/2024]], and [[2646/2645]] among others.

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===

FloraC: /* Music */ +1

2026-01-23T11:55:09Z

Music: +1

← Older revision		Revision as of 11:55, 23 January 2026
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	* [https://www.youtube.com/watch?v=niSgSld0lUA ''Foes and Forgiveness''] (2024)		* [https://www.youtube.com/watch?v=niSgSld0lUA ''Foes and Forgiveness''] (2024)
	* [https://www.youtube.com/watch?v=a2YLIxQZZPk ''Youthful Fun''] (2025)		* [https://www.youtube.com/watch?v=a2YLIxQZZPk ''Youthful Fun''] (2025)

			; [[Eufalesio]]
			* [https://soundcloud.com/eufalesio/transhypertonal-ai-megalomania ''TRANSHYPERTONAL AI MEGALOMANIA''] (2024)

	; [[Ozan Yarman]]		; [[Ozan Yarman]]

Lucius Chiaraviglio: /* Intervals */ Add 105/104 and 208/105

2025-11-16T10:20:55Z

Intervals: Add 105/104 and 208/105

← Older revision		Revision as of 10:20, 16 November 2025
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	\| ?		\| ?
	\| [[121/120]], [[100/99]]		\| [[121/120]], [[100/99]]
	\| [[144/143]]		\| [[144/143]], [[105/104]]
	\| [[120/119]]		\| [[120/119]]
	\|-		\|-
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	\| ?		\| ?
	\| [[240/121]], [[99/50]]		\| [[240/121]], [[99/50]]
	\| [[143/72]]		\| [[143/72]], [[208/105]]
	\| [[119/60]]		\| [[119/60]]
	\|-		\|-

Lucius Chiaraviglio: /* Mappings and JI approximation quality */ Add links to intervals that did not have them

2025-11-16T10:10:04Z

Mappings and JI approximation quality: Add links to intervals that did not have them

← Older revision		Revision as of 10:10, 16 November 2025
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	This system inherits its approximations of [[3/1\|3]], [[5/1\|5]], [[13/1\|13]], and [[19/1\|19]] from 53edo, however, the [[patent val]]s differ on the mappings for [[7/1\|7]], [[11/1\|11]] and [[17/1\|17]]—in fact, this edo has a very accurate 11 and an only slightly less accurate 17. Furthermore, 159edo demonstrates 3-to-2 [[telicity]], as despite being [[contorted]] in the 5-limit, it is the largest edo to temper out [[Mercator's comma]] in which said comma is less than half the size of a single edostep. This means, among other things, that there is a perfect match between the [[direct approximation]] and the more complicated traditional mapping for an [[octave-reduced]] stack of fifty-three tempered [[3/2]] perfect fifths—a complete [[circle of fifths]] for this edo.		This system inherits its approximations of [[3/1\|3]], [[5/1\|5]], [[13/1\|13]], and [[19/1\|19]] from 53edo, however, the [[patent val]]s differ on the mappings for [[7/1\|7]], [[11/1\|11]] and [[17/1\|17]]—in fact, this edo has a very accurate 11 and an only slightly less accurate 17. Furthermore, 159edo demonstrates 3-to-2 [[telicity]], as despite being [[contorted]] in the 5-limit, it is the largest edo to temper out [[Mercator's comma]] in which said comma is less than half the size of a single edostep. This means, among other things, that there is a perfect match between the [[direct approximation]] and the more complicated traditional mapping for an [[octave-reduced]] stack of fifty-three tempered [[3/2]] perfect fifths—a complete [[circle of fifths]] for this edo.

	159edo is [[consistent]] up to the no-17's [[29-odd-limit]] or the no-19's [[27-odd-limit]] as 19/17, 29/17, and their [[octave complement]]s exhaust the inconsistently mapped interval pairs in the 29-odd-limit. Thus its full 29-limit interpretation using the [[patent val]] is obvious, albeit with the catch that it is less than ideal to use the 17-prime at the same time as either the 19-prime or the 29-prime. However, there is more to consider as the [[direct approximation]] and the val mapping for intervals such as [[49/32]], [[35/32]], and [[169/128]] do not match, and as a result, 159edo can be thought of as having a perfunctory [[7-limit]] that mainly serves to bridge to the [[11-limit]] and divide the nearly just 3/2 into three, as well as a similarly perfunctory [[13-limit]] that mainly serves to bridge to the 17-limit and to absorb complex combinations of 3 and 5.		159edo is [[consistent]] up to the no-17's [[29-odd-limit]] or the no-19's [[27-odd-limit]] as [[19/17]], [[29/17]], and their [[octave complement]]s exhaust the inconsistently mapped interval pairs in the 29-odd-limit. Thus its full 29-limit interpretation using the [[patent val]] is obvious, albeit with the catch that it is less than ideal to use the 17-prime at the same time as either the 19-prime or the 29-prime. However, there is more to consider as the [[direct approximation]] and the val mapping for intervals such as [[49/32]], [[35/32]], and [[169/128]] do not match, and as a result, 159edo can be thought of as having a perfunctory [[7-limit]] that mainly serves to bridge to the [[11-limit]] and divide the nearly just 3/2 into three, as well as a similarly perfunctory [[13-limit]] that mainly serves to bridge to the 17-limit and to absorb complex combinations of 3 and 5.

	Notably, 159edo provides the [[optimal patent val]] for 11-limit [[guiron]], 13-limit [[tritikleismic]], the 13-limit rank-3 temperament [[Gamelismic family #Portending\|portending]], as well as the 17-limit rank-6 temperament tempering out [[273/272]]. In addition to this, it also supports both forms of the yarman temperament, with a generator of 2\159 which can be taken as an approximate 105/104. Both have a [[mos]] of 79 or 80 notes to the octave, and have their optimal patent vals supplied by 159edo in 7-limit, 11-limit, 13-limit, 17-limit and even 19-limit forms. While the patent val [[support]]s both [[cartography]] and [[iodine]] temperaments, which are among the best 13-limit temperaments in the [[mercator family]], the 159d and 159f mappings support other members of this temperament family.		Notably, 159edo provides the [[optimal patent val]] for 11-limit [[guiron]], 13-limit [[tritikleismic]], the 13-limit rank-3 temperament [[Gamelismic family #Portending\|portending]], as well as the 17-limit rank-6 temperament tempering out [[273/272]]. In addition to this, it also supports both forms of the yarman temperament, with a generator of 2\159 which can be taken as an approximate [[105/104]]. Both have a [[mos]] of 79 or 80 notes to the octave, and have their optimal patent vals supplied by 159edo in 7-limit, 11-limit, 13-limit, 17-limit and even 19-limit forms. While the patent val [[support]]s both [[cartography]] and [[iodine]] temperaments, which are among the best 13-limit temperaments in the [[mercator family]], the 159d and 159f mappings support other members of this temperament family.

	=== Prime harmonics ===		=== Prime harmonics ===

Overthink: /* Intervals */ Linked 640/567

2025-11-16T03:47:25Z

Intervals: Linked 640/567

← Older revision		Revision as of 03:47, 16 November 2025
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	\| 211.3207547		\| 211.3207547
	\|		\|
	\| 640/567		\| [[640/567]]
	\| ?		\| ?
	\| [[44/39]]		\| [[44/39]]

Overthink: /* Intervals */ Added 567/320 and 640/567

2025-11-16T03:44:15Z

Intervals: Added 567/320 and 640/567

← Older revision		Revision as of 03:44, 16 November 2025
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	\| 211.3207547		\| 211.3207547
	\|		\|
	\| ?		\| 640/567
	\| ?		\| ?
	\| [[44/39]]		\| [[44/39]]
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	\| 988.6792458		\| 988.6792458
	\|		\|
	\| ?		\| [[567/320]]
	\| ?		\| ?
	\| [[39/22]]		\| [[39/22]]

BudjarnLambeth: /* Music */ add 1

2025-09-14T22:31:55Z

Music: add 1

← Older revision		Revision as of 22:31, 14 September 2025
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	== Music ==		== Music ==
	The songs below are written in 159edo, or, in approximations that differ from the actual 159edo by only fractions of a [[cent]].		The songs below are written in 159edo, or, in approximations that differ from the actual 159edo by only fractions of a [[cent]].

			; [[Back Of The Class]] & [[Dawson Berry]]
			* [https://soundcloud.com/backoftheclassss/embrace ''Embrace''] (2025)

	; [[Dawson Berry]]		; [[Dawson Berry]]