27/26 - Revision history

BudjarnLambeth at 07:21, 3 November 2024

2024-11-03T07:21:58Z

← Older revision		Revision as of 07:21, 3 November 2024
Line 25:		Line 25:
	[[Category:Chroma]]		[[Category:Chroma]]
	[[Category:Third tone]]		[[Category:Third tone]]
			[[Category:Commas named after their interval size]]

FloraC: Improve sectioning

2024-10-10T08:59:31Z

Improve sectioning

← Older revision		Revision as of 08:59, 10 October 2024
Line 7:		Line 7:
	In [[13-limit]] [[just intonation]], '''27/26''', the '''small tridecimal third tone''', appears as the interval between the Pythagorean major sixth ([[27/16]]) and the [[Octave reduction\|octave-reduced]] thirteenth [[harmonic]] ([[13/8]]). It measures about 65.3{{cent}}. It is close in size to another 13-limit microtone – [[26/25]]. These intervals differ by the [[superparticular]] ratio [[676/675]], about 2.6{{cent}}, the island comma; tempering it out produces temperaments associated with [[The Archipelago]].		In [[13-limit]] [[just intonation]], '''27/26''', the '''small tridecimal third tone''', appears as the interval between the Pythagorean major sixth ([[27/16]]) and the [[Octave reduction\|octave-reduced]] thirteenth [[harmonic]] ([[13/8]]). It measures about 65.3{{cent}}. It is close in size to another 13-limit microtone – [[26/25]]. These intervals differ by the [[superparticular]] ratio [[676/675]], about 2.6{{cent}}, the island comma; tempering it out produces temperaments associated with [[The Archipelago]].

	27/26 is significant in [[Helmholtz-Ellis notation]] as the tridecimal formal comma which translates a Pythagorean interval to a nearby tridecimal interval, analogous to [[64/63]] and [[33/32]] for septimal and undecimal, respectively. It is tempered out in the patent vals for edos 2, 5, 7, 9, 14, 16, 21, 23, 28 & 35~~. However, in the [[Functional Just System]], that role is taken by [[1053/1024]]~~.		== Temperaments ==
			27/26 is tempered out in the patent vals for edos 2, 5, 7, 9, 14, 16, 21, 23, 28 & 35.

	== Sagittal notation ==		== Notation ==
			27/26 is significant in [[Helmholtz-Ellis notation]] as the tridecimal formal comma which translates a Pythagorean interval to a nearby tridecimal interval, analogous to [[64/63]] and [[33/32]] for septimal and undecimal, respectively. However, in the [[Functional Just System]], that role is taken by [[1053/1024]].

			=== Sagittal notation ===
	In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented (in a secondary role) by the sagittal {{sagittal \| (!/ }} and is called the '''13 large diesis''', or '''13L''' for short, because the simplest interval it notates is 13/1 (equiv. 13/8), as for example in C-A{{nbhsp}}{{sagittal \| (!/ }}. The primary role of {{ sagittal \| (!/ }} is [[8505/8192#Sagittal notation \| 8192/8505]] (35L down). The upward version is called '''1/13L''' or '''13L up''' and is represented (in a secondary role) by {{sagittal\| (\|\ }}.		In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented (in a secondary role) by the sagittal {{sagittal \| (!/ }} and is called the '''13 large diesis''', or '''13L''' for short, because the simplest interval it notates is 13/1 (equiv. 13/8), as for example in C-A{{nbhsp}}{{sagittal \| (!/ }}. The primary role of {{ sagittal \| (!/ }} is [[8505/8192#Sagittal notation \| 8192/8505]] (35L down). The upward version is called '''1/13L''' or '''13L up''' and is represented (in a secondary role) by {{sagittal\| (\|\ }}.

Dave Keenan: /* Sagittal notation */ Changed "simplest ratio" to "simplest interval". Changed colons to slashes and dash. Gave the truly-simplest (2,3-free) interval in addition to the octave-reduced interval. Replaced hair-space with nbhsp template call.

2024-10-10T06:58:56Z

Sagittal notation: Changed "simplest ratio" to "simplest interval". Changed colons to slashes and dash. Gave the truly-simplest (2,3-free) interval in addition to the octave-reduced interval. Replaced hair-space with nbhsp template call.

← Older revision		Revision as of 06:58, 10 October 2024
Line 10:		Line 10:

	== Sagittal notation ==		== Sagittal notation ==
	In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented (in a secondary role) by the sagittal {{sagittal \| (!/ }} and is called the '''13 large diesis''', or '''13L''' for short, because the simplest ~~ratio~~ it notates is 8~~:13~~, as for example in C:A~~ ~~{{sagittal \| (!/ }}. The primary role of {{ sagittal \| (!/ }} is [[8505/8192#Sagittal notation \| 8192/8505]] (35L down). The upward version is called '''1/13L''' or '''13L up''' and is represented (in a secondary role) by {{sagittal\| (\|\ }}.		In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented (in a secondary role) by the sagittal {{sagittal \| (!/ }} and is called the '''13 large diesis''', or '''13L''' for short, because the simplest interval it notates is 13/1 (equiv. 13/8), as for example in C-A{{nbhsp}}{{sagittal \| (!/ }}. The primary role of {{ sagittal \| (!/ }} is [[8505/8192#Sagittal notation \| 8192/8505]] (35L down). The upward version is called '''1/13L''' or '''13L up''' and is represented (in a secondary role) by {{sagittal\| (\|\ }}.

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

Dave Keenan: /* Sagittal notation */ Added upward version

2024-10-09T12:44:40Z

Sagittal notation: Added upward version

← Older revision		Revision as of 12:44, 9 October 2024
Line 10:		Line 10:

	== Sagittal notation ==		== Sagittal notation ==
	In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented (in a secondary role) by the sagittal {{sagittal \| (!/ }} and is called the '''13 large diesis''', or '''13L''' for short, because the simplest ratio it notates is 8:13, as for example in C:A {{sagittal \| (!/ }}. The primary role of {{ sagittal \| (!/ }} is [[8505/8192#Sagittal notation \| 8192/8505]] (35L down).		In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented (in a secondary role) by the sagittal {{sagittal \| (!/ }} and is called the '''13 large diesis''', or '''13L''' for short, because the simplest ratio it notates is 8:13, as for example in C:A {{sagittal \| (!/ }}. The primary role of {{ sagittal \| (!/ }} is [[8505/8192#Sagittal notation \| 8192/8505]] (35L down). The upward version is called '''1/13L''' or '''13L up''' and is represented (in a secondary role) by {{sagittal\| (\|\ }}.

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

Yourmusic Productions: Where it is treated as a comma.

2024-10-09T11:30:06Z

Where it is treated as a comma.

← Older revision		Revision as of 11:30, 9 October 2024
Line 7:		Line 7:
	In [[13-limit]] [[just intonation]], '''27/26''', the '''small tridecimal third tone''', appears as the interval between the Pythagorean major sixth ([[27/16]]) and the [[Octave reduction\|octave-reduced]] thirteenth [[harmonic]] ([[13/8]]). It measures about 65.3{{cent}}. It is close in size to another 13-limit microtone – [[26/25]]. These intervals differ by the [[superparticular]] ratio [[676/675]], about 2.6{{cent}}, the island comma; tempering it out produces temperaments associated with [[The Archipelago]].		In [[13-limit]] [[just intonation]], '''27/26''', the '''small tridecimal third tone''', appears as the interval between the Pythagorean major sixth ([[27/16]]) and the [[Octave reduction\|octave-reduced]] thirteenth [[harmonic]] ([[13/8]]). It measures about 65.3{{cent}}. It is close in size to another 13-limit microtone – [[26/25]]. These intervals differ by the [[superparticular]] ratio [[676/675]], about 2.6{{cent}}, the island comma; tempering it out produces temperaments associated with [[The Archipelago]].

	27/26 is significant in [[Helmholtz-Ellis notation]] as the tridecimal formal comma which translates a Pythagorean interval to a nearby tridecimal interval, analogous to [[64/63]] and [[33/32]] for septimal and undecimal, respectively. However, in the [[Functional Just System]], that role is taken by [[1053/1024]].		27/26 is significant in [[Helmholtz-Ellis notation]] as the tridecimal formal comma which translates a Pythagorean interval to a nearby tridecimal interval, analogous to [[64/63]] and [[33/32]] for septimal and undecimal, respectively. It is tempered out in the patent vals for edos 2, 5, 7, 9, 14, 16, 21, 23, 28 & 35. However, in the [[Functional Just System]], that role is taken by [[1053/1024]].

	== Sagittal notation ==		== Sagittal notation ==

Dave Keenan: /* Sagittal notation */ Added a hair space between the nominal and the sagittal.

2024-10-09T06:34:11Z

Sagittal notation: Added a hair space between the nominal and the sagittal.

← Older revision		Revision as of 06:34, 9 October 2024
Line 10:		Line 10:

	== Sagittal notation ==		== Sagittal notation ==
	In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented (in a secondary role) by the sagittal {{sagittal \| (!/ }} and is called the '''13 large diesis''', or '''13L''' for short, because the simplest ratio it notates is 8:13, as for example in C:A{{sagittal \| (!/ }}. The primary role of {{ sagittal \| (!/ }} is [[8505/8192#Sagittal notation \| 8192/8505]] (35L down).		In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented (in a secondary role) by the sagittal {{sagittal \| (!/ }} and is called the '''13 large diesis''', or '''13L''' for short, because the simplest ratio it notates is 8:13, as for example in C:A {{sagittal \| (!/ }}. The primary role of {{ sagittal \| (!/ }} is [[8505/8192#Sagittal notation \| 8192/8505]] (35L down).

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

Cmloegcmluin: add section for this comma's use in Sagittal notation

2024-10-09T05:17:26Z

add section for this comma's use in Sagittal notation

← Older revision		Revision as of 05:17, 9 October 2024
Line 8:		Line 8:

	27/26 is significant in [[Helmholtz-Ellis notation]] as the tridecimal formal comma which translates a Pythagorean interval to a nearby tridecimal interval, analogous to [[64/63]] and [[33/32]] for septimal and undecimal, respectively. However, in the [[Functional Just System]], that role is taken by [[1053/1024]].		27/26 is significant in [[Helmholtz-Ellis notation]] as the tridecimal formal comma which translates a Pythagorean interval to a nearby tridecimal interval, analogous to [[64/63]] and [[33/32]] for septimal and undecimal, respectively. However, in the [[Functional Just System]], that role is taken by [[1053/1024]].

			== Sagittal notation ==
			In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented (in a secondary role) by the sagittal {{sagittal \| (!/ }} and is called the '''13 large diesis''', or '''13L''' for short, because the simplest ratio it notates is 8:13, as for example in C:A{{sagittal \| (!/ }}. The primary role of {{ sagittal \| (!/ }} is [[8505/8192#Sagittal notation \| 8192/8505]] (35L down).

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

Plumtree: Normalising usage of Infobox Interval

2022-10-25T14:43:10Z

Normalising usage of Infobox Interval

← Older revision		Revision as of 14:43, 25 October 2022
Line 1:		Line 1:
	{{Infobox Interval		{{Infobox Interval
	~~\| Ratio = 27/26~~
	~~\| Monzo = -1 3 0 0 0 -1~~
	~~\| Cents = 65.33734~~
	\| Name = small tridecimal third tone		\| Name = small tridecimal third tone
	\| Color name = 3u1, thu unison		\| Color name = 3u1, thu unison
	~~\| FJS name = A1<sub>13</sub>~~
	\| Sound = jid_27_26_pluck_adu_dr220.mp3		\| Sound = jid_27_26_pluck_adu_dr220.mp3
			\| Comma = yes
	}}		}}
	In [[13-limit]] [[just intonation]], '''27/26''', the '''small tridecimal third tone''', appears as the interval between the Pythagorean major sixth ([[27/16]]) and the [[Octave reduction\|octave-reduced]] thirteenth [[harmonic]] ([[13/8]]). It measures about 65.3{{cent}}. It is close in size to another 13-limit microtone – [[26/25]]. These intervals differ by the [[superparticular]] ratio [[676/675]], about 2.6{{cent}}, the island comma; tempering it out produces temperaments associated with [[The Archipelago]].		In [[13-limit]] [[just intonation]], '''27/26''', the '''small tridecimal third tone''', appears as the interval between the Pythagorean major sixth ([[27/16]]) and the [[Octave reduction\|octave-reduced]] thirteenth [[harmonic]] ([[13/8]]). It measures about 65.3{{cent}}. It is close in size to another 13-limit microtone – [[26/25]]. These intervals differ by the [[superparticular]] ratio [[676/675]], about 2.6{{cent}}, the island comma; tempering it out produces temperaments associated with [[The Archipelago]].
Line 19:		Line 16:
	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]

	~~[[Category:13-limit]]~~
	[[Category:Chroma]]		[[Category:Chroma]]
	[[Category:Third tone]]		[[Category:Third tone]]
	~~[[Category:Medium commas]]~~
	~~[[Category:Superparticular]]~~

Fredg999: Improved phrasing

2022-03-22T13:57:37Z

Improved phrasing

← Older revision		Revision as of 13:57, 22 March 2022
Line 8:		Line 8:
	\| Sound = jid_27_26_pluck_adu_dr220.mp3		\| Sound = jid_27_26_pluck_adu_dr220.mp3
	}}		}}
	In [[13-limit]] [[just intonation]], '''27/26''', the '''small tridecimal third tone''', appears as the interval between the Pythagorean major sixth of [[27/16]] and the thirteenth harmonic of [[13/8]]. It measures about 65.3{{cent}}. It is close in size to another 13-limit microtone – [[26/25]]. These intervals differ by the [[superparticular]] ratio [[676/675]], about 2.6{{cent}}, the island comma; tempering it out produces temperaments associated with [[The Archipelago]].		In [[13-limit]] [[just intonation]], '''27/26''', the '''small tridecimal third tone''', appears as the interval between the Pythagorean major sixth ([[27/16]]) and the [[Octave reduction\|octave-reduced]] thirteenth [[harmonic]] ([[13/8]]). It measures about 65.3{{cent}}. It is close in size to another 13-limit microtone – [[26/25]]. These intervals differ by the [[superparticular]] ratio [[676/675]], about 2.6{{cent}}, the island comma; tempering it out produces temperaments associated with [[The Archipelago]].

	27/26 is significant in [[Helmholtz-Ellis notation]] as the tridecimal formal comma which translates a Pythagorean interval to a nearby tridecimal interval, analogous to [[64/63]] and [[33/32]] for septimal and undecimal, respectively. However, in the [[Functional Just System]], that role is taken by [[1053/1024]].		27/26 is significant in [[Helmholtz-Ellis notation]] as the tridecimal formal comma which translates a Pythagorean interval to a nearby tridecimal interval, analogous to [[64/63]] and [[33/32]] for septimal and undecimal, respectively. However, in the [[Functional Just System]], that role is taken by [[1053/1024]].

Fredg999: Added link to large third tone, misc. edits

2022-03-22T13:55:40Z

Added link to large third tone, misc. edits

← Older revision		Revision as of 13:55, 22 March 2022
Line 8:		Line 8:
	\| Sound = jid_27_26_pluck_adu_dr220.mp3		\| Sound = jid_27_26_pluck_adu_dr220.mp3
	}}		}}
			In [[13-limit]] [[just intonation]], '''27/26''', the '''small tridecimal third tone''', appears as the interval between the Pythagorean major sixth of [[27/16]] and the thirteenth harmonic of [[13/8]]. It measures about 65.3{{cent}}. It is close in size to another 13-limit microtone – [[26/25]]. These intervals differ by the [[superparticular]] ratio [[676/675]], about 2.6{{cent}}, the island comma; tempering it out produces temperaments associated with [[The Archipelago]].

	In [[13-limit]] [[just intonation]], '''27/26''', the '''small tridecimal third tone''', appears as the interval between the Pythagorean major sixth of [[27/16]] and the thirteenth harmonic of [[13/8]]. It measures about 65.3¢. It is close in size to another 13-limit microtone – [[26/25]]. These intervals differ by the [[superparticular]] ratio [[676/675]], about 2.6¢, the island comma; tempering it out produces temperaments associated with [[The Archipelago]].		27/26 is significant in [[Helmholtz-Ellis notation]] as the tridecimal formal comma which translates a Pythagorean interval to a nearby tridecimal interval, analogous to [[64/63]] and [[33/32]] for septimal and undecimal, respectively. However, in the [[Functional Just System]], that role is taken by [[1053/1024]].

	27/26 is significant in [[Helmholtz-Ellis notation]] as the tridecimal formal comma which translates a Pythagorean interval to a nearby tridecimal interval, analogous to [[64/63]] and [[33/32]] for septimal and undecimal, respectively. However, in [[Functional Just System]], that role is taken by [[1053/1024]].

	== See also ==		== See also ==
	* [[52/27]] – its [[octave complement]]		* [[52/27]] – its [[octave complement]]
	* [[13/9]] – its [[fifth complement]]		* [[13/9]] – its [[fifth complement]]
			* [[26/25]] - the large tridecimal third tone
	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]
	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]