85/84 - Revision history

FloraC: - redundant parentheses (I was being dumb)

2026-05-19T07:36:13Z

- redundant parentheses (I was being dumb)

← Older revision		Revision as of 07:36, 19 May 2026
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	== Temperaments ==		== Temperaments ==
	It can be [[tempering out\|tempered out]] in the [[17-limit]], leading to a rank-6 temperament, or in the 2.3.5.7.17-subgroup, leading to a rank-4 temperament. However, 85/84 factors as ([[225/224]])⋅([[256/255]])⋅([[289/288]]), i.e. ({{S\|15}})⋅({{S\|16}})⋅({{S\|17}}), so that it is natural to temper out all of them, leading to the 2.3.5.7.17 version of [[pajara]] temperament, which also tempers out [[50/49]]. From there we can see that 50/49 = ([[99/98]])⋅([[100/99]]), and tempering both out leads to the 2.3.5.7.11.17-subgroup version of pajara. We find a factorization of 85/84 as ([[169/168]])⋅([[170/169]]), leading to an unnamed full 17-limit weak extension (34d & 44) that splits the fifth into two ~[[16/13]]'s. However, splitting the fifth doubles the [[generator complexity]] of every interval, greatly reducing the temperament's practicality.		It can be [[tempering out\|tempered out]] in the [[17-limit]], leading to a rank-6 temperament, or in the 2.3.5.7.17-subgroup, leading to a rank-4 temperament. However, 85/84 factors as ([[225/224]])⋅([[256/255]])⋅([[289/288]]), i.e. {{S\|15}}⋅{{S\|16}}⋅{{S\|17}}, so that it is natural to temper out all of them, leading to the 2.3.5.7.17 version of [[pajara]] temperament, which also tempers out [[50/49]]. From there we can see that 50/49 = ([[99/98]])⋅([[100/99]]), and tempering both out leads to the 2.3.5.7.11.17-subgroup version of pajara. We find a factorization of 85/84 as ([[169/168]])⋅([[170/169]]), leading to an unnamed full 17-limit weak extension (34d & 44) that splits the fifth into two ~[[16/13]]'s. However, splitting the fifth doubles the [[generator complexity]] of every interval, greatly reducing the temperament's practicality.

	== Etymology ==		== Etymology ==

Overthink: /* Temperaments / There is* a natural extension to 13, it seems.

2026-05-18T23:34:55Z

Temperaments: There *is* a natural extension to 13, it seems.

← Older revision		Revision as of 23:34, 18 May 2026
Line 10:		Line 10:

	== Temperaments ==		== Temperaments ==
	It can be [[tempering out\|tempered out]] in the [[17-limit]], leading to a rank-6 temperament, or in the 2.3.5.7.17-subgroup, leading to a rank-4 temperament. However, 85/84 factors as ([[225/224]])⋅([[256/255]])⋅([[289/288]]), i.e. ({{S\|15}})⋅({{S\|16}})⋅({{S\|17}}), so that it is natural to temper out all of them, leading to the 2.3.5.7.17 version of [[pajara]] temperament, which also tempers out [[50/49]]. From there we can see that 50/49 = ([[99/98]])⋅([[100/99]]), and tempering both out leads to the 2.3.5.7.11.17-subgroup version of pajara.		It can be [[tempering out\|tempered out]] in the [[17-limit]], leading to a rank-6 temperament, or in the 2.3.5.7.17-subgroup, leading to a rank-4 temperament. However, 85/84 factors as ([[225/224]])⋅([[256/255]])⋅([[289/288]]), i.e. ({{S\|15}})⋅({{S\|16}})⋅({{S\|17}}), so that it is natural to temper out all of them, leading to the 2.3.5.7.17 version of [[pajara]] temperament, which also tempers out [[50/49]]. From there we can see that 50/49 = ([[99/98]])⋅([[100/99]]), and tempering both out leads to the 2.3.5.7.11.17-subgroup version of pajara. We find a factorization of 85/84 as ([[169/168]])⋅([[170/169]]), leading to an unnamed full 17-limit weak extension (34d & 44) that splits the fifth into two ~[[16/13]]'s. However, splitting the fifth doubles the [[generator complexity]] of every interval, greatly reducing the temperament's practicality.

	== Etymology ==		== Etymology ==

FloraC: Re-organize, linking & style

2026-05-17T05:37:17Z

Re-organize, linking & style

← Older revision		Revision as of 05:37, 17 May 2026
Line 4:		Line 4:
	\| Comma = yes		\| Comma = yes
	}}		}}
	'''85/84''', the '''monk comma''', is a [[17-limit]] [[superparticular ~~interval~~]]. It is the difference between [[6/5]] and [[17/14]], as well as [[7/5]] and [[17/12]].		'''85/84''', the '''monk comma''', is a [[small comma\|small]] [[17-limit]] [[superparticular]] [[comma]] measuring about 20.5 [[cent]]s. It is the difference between [[6/5]] and [[17/14]], as well as [[7/5]] and [[17/12]].

	~~== Etymology ==~~
	The word ''monk'' for this comma was introduced by [[User:Xenllium\|Xenllium]] in 2023. It was translated from Japanese word <span style="font-family:san-serif" lang="ja">僧侶</span> (<span style="font-family:san-serif" lang="ja">そうりょ</span>, sōryo), a play of its [[Color notation\|color name]], ''soruyo'' (as resembling pronunciation).

	== Notation ==		== Notation ==
	This comma can be represented as a secondary comma for 5C ({{Sagittal\|\!}}) in Sagittal.		This comma can be represented as a secondary comma for 5C ({{Sagittal\|\!}}) in [[Sagittal]].

	== Temperaments ==		== Temperaments ==
	It can be [[tempering out\|tempered out]] in the [[17-limit]], leading to a rank-6 temperament, or in the 2.3.5.7.17-subgroup, leading to a rank-4 temperament. However, 85/84 factors as [[225/224]] * [[256/255]] * [[289/288]] ({{S\|15}} * {{S\|16}} * {{S\|17}}), so that it is natural to temper out all of them, leading to the 2.3.5.7.17 version of [[pajara]] temperament, which also tempers out [[50/49]]. From there we can see that 50/49 = [[99/98]] * [[100/99]], and tempering both out leads to the 2.3.5.7.11.17-subgroup version of pajara.		It can be [[tempering out\|tempered out]] in the [[17-limit]], leading to a rank-6 temperament, or in the 2.3.5.7.17-subgroup, leading to a rank-4 temperament. However, 85/84 factors as ([[225/224]])⋅([[256/255]])⋅([[289/288]]), i.e. ({{S\|15}})⋅({{S\|16}})⋅({{S\|17}}), so that it is natural to temper out all of them, leading to the 2.3.5.7.17 version of [[pajara]] temperament, which also tempers out [[50/49]]. From there we can see that 50/49 = ([[99/98]])⋅([[100/99]]), and tempering both out leads to the 2.3.5.7.11.17-subgroup version of pajara.

			== Etymology ==
			The word ''monk'' for this comma was introduced by [[Xenllium]] in 2023. It was translated from Japanese word <span style="font-family:san-serif" lang="ja">僧侶</span> (<span style="font-family:san-serif" lang="ja">そうりょ</span>, sōryo), a play of its [[Kite's color notation\|color name]], ''soruyo'' (as resembling pronunciation).

	== See also ==		== See also ==
	* [[Small comma]]
	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]

	[[Category:Commas named after their color name]]		[[Category:Commas named after their color name]]
	[[Category:Commas named by translating something into another language]]		[[Category:Commas named by translating something into another language]]

Overthink: temperaments

2026-05-16T17:45:02Z

temperaments

← Older revision		Revision as of 17:45, 16 May 2026
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	== Notation ==		== Notation ==
	This comma can be represented as a secondary comma for 5C ({{Sagittal\|\!}}) in Sagittal.		This comma can be represented as a secondary comma for 5C ({{Sagittal\|\!}}) in Sagittal.

			== Temperaments ==
			It can be [[tempering out\|tempered out]] in the [[17-limit]], leading to a rank-6 temperament, or in the 2.3.5.7.17-subgroup, leading to a rank-4 temperament. However, 85/84 factors as [[225/224]] * [[256/255]] * [[289/288]] ({{S\|15}} * {{S\|16}} * {{S\|17}}), so that it is natural to temper out all of them, leading to the 2.3.5.7.17 version of [[pajara]] temperament, which also tempers out [[50/49]]. From there we can see that 50/49 = [[99/98]] * [[100/99]], and tempering both out leads to the 2.3.5.7.11.17-subgroup version of pajara.

	== See also ==		== See also ==

MisterShafXen at 21:05, 21 August 2025

2025-08-21T21:05:54Z

← Older revision		Revision as of 21:05, 21 August 2025
Line 8:		Line 8:
	== Etymology ==		== Etymology ==
	The word ''monk'' for this comma was introduced by [[User:Xenllium\|Xenllium]] in 2023. It was translated from Japanese word <span style="font-family:san-serif" lang="ja">僧侶</span> (<span style="font-family:san-serif" lang="ja">そうりょ</span>, sōryo), a play of its [[Color notation\|color name]], ''soruyo'' (as resembling pronunciation).		The word ''monk'' for this comma was introduced by [[User:Xenllium\|Xenllium]] in 2023. It was translated from Japanese word <span style="font-family:san-serif" lang="ja">僧侶</span> (<span style="font-family:san-serif" lang="ja">そうりょ</span>, sōryo), a play of its [[Color notation\|color name]], ''soruyo'' (as resembling pronunciation).

			== Notation ==
			This comma can be represented as a secondary comma for 5C ({{Sagittal\|\!}}) in Sagittal.

	== See also ==		== See also ==

BudjarnLambeth at 00:24, 16 November 2024

2024-11-16T00:24:23Z

← Older revision		Revision as of 00:24, 16 November 2024
Line 12:		Line 12:
	* [[Small comma]]		* [[Small comma]]
	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]

			[[Category:Commas named after their color name]]
			[[Category:Commas named by translating something into another language]]

Xenllium at 01:42, 29 April 2024

2024-04-29T01:42:40Z

← Older revision		Revision as of 01:42, 29 April 2024
Line 7:		Line 7:

	== Etymology ==		== Etymology ==
	The word ''monk'' for this comma was introduced by [[User:Xenllium\|Xenllium]] in 2023. It was translated from Japanese word <span style="font-family:~~Yu Gothic UI~~">僧侶</span> (<span style="font-family:~~Yu Gothic UI~~">そうりょ</span>, sōryo), a play of its [[Color notation\|color name]], ''soruyo'' (as resembling pronunciation).		The word ''monk'' for this comma was introduced by [[User:Xenllium\|Xenllium]] in 2023. It was translated from Japanese word <span style="font-family:san-serif" lang="ja">僧侶</span> (<span style="font-family:san-serif" lang="ja">そうりょ</span>, sōryo), a play of its [[Color notation\|color name]], ''soruyo'' (as resembling pronunciation).

	== See also ==		== See also ==
	* [[Small comma]]		* [[Small comma]]
	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]

Xenllium at 13:09, 11 December 2023

2023-12-11T13:09:17Z

← Older revision		Revision as of 13:09, 11 December 2023
Line 7:		Line 7:

	== Etymology ==		== Etymology ==
	The ~~name~~ ''monk'' was ~~named~~ by [[User:Xenllium\|Xenllium]] in 2023. It was translated from Japanese word <span style="font-family:Yu Gothic UI">僧侶</span> (<span style="font-family:Yu Gothic UI">そうりょ</span>, sōryo), a play of its [[Color notation\|color name]], ''soruyo'' (as resembling pronunciation).		The word ''monk'' for this comma was introduced by [[User:Xenllium\|Xenllium]] in 2023. It was translated from Japanese word <span style="font-family:Yu Gothic UI">僧侶</span> (<span style="font-family:Yu Gothic UI">そうりょ</span>, sōryo), a play of its [[Color notation\|color name]], ''soruyo'' (as resembling pronunciation).

	== See also ==		== See also ==
	* [[Small comma]]		* [[Small comma]]
	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]

Xenllium: Created page with "{{Infobox Interval | Name = monk comma | Color name = 17ory1, soruyo 1sn,
Soruyo comma | Comma = yes }} '''85/84''', the '''monk comma''', is a 17-limit superparticu..."

2023-08-16T13:51:24Z

Created page with "{{Infobox Interval | Name = monk comma | Color name = 17ory1, soruyo 1sn, Soruyo comma | Comma = yes }} '''85/84''', the '''monk comma''', is a 17-limit superparticu..."

New page

{{Infobox Interval
| Name = monk comma
| Color name = 17ory1, soruyo 1sn, Soruyo comma
| Comma = yes
}}
'''85/84''', the '''monk comma''', is a [[17-limit]] [[superparticular interval]]. It is the difference between [[6/5]] and [[17/14]], as well as [[7/5]] and [[17/12]].

== Etymology ==
The name ''monk'' was named by [[User:Xenllium|Xenllium]] in 2023. It was translated from Japanese word 僧侶 (そうりょ, sōryo), a play of its [[Color notation|color name]], ''soruyo'' (as resembling pronunciation).

== See also ==
* [[Small comma]]
* [[List of superparticular intervals]]