513/512 - Revision history

FloraC: Undevicesimal comma -> undevicesimal formal comma

2026-04-11T14:37:46Z

Undevicesimal comma -> undevicesimal formal comma

← Older revision		Revision as of 14:37, 11 April 2026
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	{{Infobox Interval		{{Infobox Interval
	\| Name = undevicesimal ~~comma~~, undevicesimal ~~schisma~~, Boethius' comma		\| Name = undevicesimal schisma, undevicesimal formal comma, Boethius' comma
	\| Color name = L19o1, lano 1sn, <br>Lano comma		\| Color name = L19o1, lano 1sn, <br>Lano comma
	\| Comma = yes		\| Comma = yes
	}}		}}
			'''513/512''', the '''undevicesimal schisma''', '''undevicesimal formal comma''' or '''Boethius' comma''', is an [[Unnoticeable comma\|unnoticeable]] [[19-limit]] (also 2.3.19 [[subgroup]]) comma. It is the amount by which [[19/16]] exceeds the [[32/27\|Pythagorean minor third (32/27)]] and by which [[24/19]] falls short of the [[81/64\|Pythagorean major third (81/64)]].
	'''513/512''', the '''undevicesimal ~~comma~~''', '''undevicesimal ~~schisma~~''' or '''Boethius' comma''', is an [[Unnoticeable comma\|unnoticeable]] [[19-limit]] (also 2.3.19 [[subgroup]]) comma. It is the amount by which [[19/16]] exceeds the [[32/27\|Pythagorean minor third (32/27)]] and by which [[24/19]] falls short of the [[81/64\|Pythagorean major third (81/64)]].

	== Temperaments ==		== Temperaments ==
	~~: ''"~~Boethius~~" redirects here. For~~ the medieval Roman platonist~~, see [[~~Anicius Manlius Severinus Boethius~~]].''~~		{{Redirect\|Boethius\|the medieval Roman platonist\|Anicius Manlius Severinus Boethius}}

	By tempering out this comma in the 19-limit is defined the '''boethius temperament''', or in the 2.3.19 subgroup, the '''boethian temperament'''. Both enable the [[boethius chords]]. See [[No-fives subgroup temperaments #Boethian]].		By tempering out this comma in the 19-limit is defined the '''boethius temperament''', or in the 2.3.19 subgroup, the '''boethian temperament'''. Both enable the [[boethius chords]]. See [[No-fives subgroup temperaments #Boethian]].

	== Notation ==		== Notation ==
	This comma is significant in [[Functional Just System]] and [[~~Helmholtz-Ellis~~ notation]] as the formal comma to translate a Pythagorean interval to a nearby undevicesimal interval.		This comma is significant in [[Functional Just System]] and [[Helmholtz–Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby undevicesimal interval.

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

Hotcrystal0: enables -> enable

2026-03-17T16:36:02Z

enables -> enable

← Older revision		Revision as of 16:36, 17 March 2026
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	: ''"Boethius" redirects here. For the medieval Roman platonist, see [[Anicius Manlius Severinus Boethius]].''		: ''"Boethius" redirects here. For the medieval Roman platonist, see [[Anicius Manlius Severinus Boethius]].''

	By tempering out this comma in the 19-limit is defined the '''boethius temperament''', or in the 2.3.19 subgroup, the '''boethian temperament'''. Both ~~enables~~ the [[boethius chords]]. See [[No-fives subgroup temperaments #Boethian]].		By tempering out this comma in the 19-limit is defined the '''boethius temperament''', or in the 2.3.19 subgroup, the '''boethian temperament'''. Both enable the [[boethius chords]]. See [[No-fives subgroup temperaments #Boethian]].

	== Notation ==		== Notation ==

Lucius Chiaraviglio: Add the corresponding major third

2026-03-06T06:14:48Z

Add the corresponding major third

← Older revision		Revision as of 06:14, 6 March 2026
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	}}		}}

	'''513/512''', the '''undevicesimal comma''', '''undevicesimal schisma''' or '''Boethius' comma''', is an [[Unnoticeable comma\|unnoticeable]] [[19-limit]] (also 2.3.19 [[subgroup]]) comma. It is the amount by which [[19/16]] exceeds the [[32/27\|Pythagorean minor third (32/27)]].		'''513/512''', the '''undevicesimal comma''', '''undevicesimal schisma''' or '''Boethius' comma''', is an [[Unnoticeable comma\|unnoticeable]] [[19-limit]] (also 2.3.19 [[subgroup]]) comma. It is the amount by which [[19/16]] exceeds the [[32/27\|Pythagorean minor third (32/27)]] and by which [[24/19]] falls short of the [[81/64\|Pythagorean major third (81/64)]].

	== Temperaments ==		== Temperaments ==

FloraC: Undo revision 192393 by Sintel (talk). This one doesn't have alt names, unlike helmholtz!

2025-04-17T12:03:45Z

Undo revision 192393 by Sintel (talk). This one doesn't have alt names, unlike helmholtz!

← Older revision		Revision as of 12:03, 17 April 2025
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	== Temperaments ==		== Temperaments ==
			: ''"Boethius" redirects here. For the medieval Roman platonist, see [[Anicius Manlius Severinus Boethius]].''

	By tempering out this comma in the 19-limit is defined the '''boethius temperament''', or in the 2.3.19 subgroup, the '''boethian temperament'''. Both enables the [[boethius chords]]. See [[No-fives subgroup temperaments #Boethian]].		By tempering out this comma in the 19-limit is defined the '''boethius temperament''', or in the 2.3.19 subgroup, the '''boethian temperament'''. Both enables the [[boethius chords]]. See [[No-fives subgroup temperaments #Boethian]].

Sintel: /* Temperaments */ Fix note since Boethius redirect changed

2025-04-16T15:00:45Z

Temperaments: Fix note since Boethius redirect changed

← Older revision		Revision as of 15:00, 16 April 2025
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	== Temperaments ==		== Temperaments ==
	~~: ''"Boethius" redirects here. For the medieval Roman platonist, see [[Anicius Manlius Severinus Boethius]].''~~

	By tempering out this comma in the 19-limit is defined the '''boethius temperament''', or in the 2.3.19 subgroup, the '''boethian temperament'''. Both enables the [[boethius chords]]. See [[No-fives subgroup temperaments #Boethian]].		By tempering out this comma in the 19-limit is defined the '''boethius temperament''', or in the 2.3.19 subgroup, the '''boethian temperament'''. Both enables the [[boethius chords]]. See [[No-fives subgroup temperaments #Boethian]].

BudjarnLambeth at 02:11, 16 November 2024

2024-11-16T02:11:15Z

← Older revision		Revision as of 02:11, 16 November 2024
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	[[Category:Boethius]]		[[Category:Boethius]]
			[[Category:Commas named after their interval size]]
			[[Category:Commas named after polymaths]]

BudjarnLambeth: /* Temperaments */

2024-11-06T01:00:29Z

Temperaments

← Older revision		Revision as of 01:00, 6 November 2024
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	== Temperaments ==		== Temperaments ==
	: ''"Boethius" redirects here. For the medieval Roman platonist, see [[~~Wikipedia:~~ Boethius]].''		: ''"Boethius" redirects here. For the medieval Roman platonist, see [[Anicius Manlius Severinus Boethius]].''

	By tempering out this comma in the 19-limit is defined the '''boethius temperament''', or in the 2.3.19 subgroup, the '''boethian temperament'''. Both enables the [[boethius chords]]. See [[No-fives subgroup temperaments #Boethian]].		By tempering out this comma in the 19-limit is defined the '''boethius temperament''', or in the 2.3.19 subgroup, the '''boethian temperament'''. Both enables the [[boethius chords]]. See [[No-fives subgroup temperaments #Boethian]].

	== Notation ==		== Notation ==

FloraC: +link to data for boethian

2024-10-20T08:11:32Z

+link to data for boethian

← Older revision		Revision as of 08:11, 20 October 2024
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	: ''"Boethius" redirects here. For the medieval Roman platonist, see [[Wikipedia: Boethius]].''		: ''"Boethius" redirects here. For the medieval Roman platonist, see [[Wikipedia: Boethius]].''

	By tempering out this comma in the 19-limit is defined the '''boethius temperament''', or in the 2.3.19 subgroup, the '''boethian temperament'''. Both enables the [[boethius chords]].		By tempering out this comma in the 19-limit is defined the '''boethius temperament''', or in the 2.3.19 subgroup, the '''boethian temperament'''. Both enables the [[boethius chords]]. See [[No-fives subgroup temperaments #Boethian]].

	== Notation ==		== Notation ==

FloraC: Merge notation into one section. -see-also link to unnoticeable comma (linked in the intro)

2024-10-20T08:06:52Z

Merge notation into one section. -see-also link to unnoticeable comma (linked in the intro)

← Older revision		Revision as of 08:06, 20 October 2024
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	}}		}}

	'''513/512''', the '''undevicesimal comma''', '''undevicesimal schisma''' or '''Boethius' comma''', is an [[Unnoticeable comma\|unnoticeable]] [[19-limit]] (also 2.3.19 [[subgroup]]) comma. It is the amount by which [[19/16]] exceeds the [[32/27\|Pythagorean minor third (32/27)]]~~. It is significant in [[Functional Just System]] and [[Helmholtz-Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby undevicesimal interval~~.		'''513/512''', the '''undevicesimal comma''', '''undevicesimal schisma''' or '''Boethius' comma''', is an [[Unnoticeable comma\|unnoticeable]] [[19-limit]] (also 2.3.19 [[subgroup]]) comma. It is the amount by which [[19/16]] exceeds the [[32/27\|Pythagorean minor third (32/27)]].

	== Temperaments ==		== Temperaments ==
Line 12:		Line 12:
	By tempering out this comma in the 19-limit is defined the '''boethius temperament''', or in the 2.3.19 subgroup, the '''boethian temperament'''. Both enables the [[boethius chords]].		By tempering out this comma in the 19-limit is defined the '''boethius temperament''', or in the 2.3.19 subgroup, the '''boethian temperament'''. Both enables the [[boethius chords]].

	== Sagittal notation ==		== Notation ==
			This comma is significant in [[Functional Just System]] and [[Helmholtz-Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby undevicesimal interval.

			=== Sagittal notation ===
	In the [[Sagittal]] system, this comma (possibly tempered) is represented by the sagittal {{sagittal \| )\| }} and is called the '''19 schisma''', or '''19s''' for short, because the simplest interval it notates is 19/1 (equiv 19/16), as for example in D-F{{nbhsp}}{{sagittal \| )\| }}. The downward version is called '''1/19s''' or '''19s down''' and is represented by {{sagittal\| )! }}.		In the [[Sagittal]] system, this comma (possibly tempered) is represented by the sagittal {{sagittal \| )\| }} and is called the '''19 schisma''', or '''19s''' for short, because the simplest interval it notates is 19/1 (equiv 19/16), as for example in D-F{{nbhsp}}{{sagittal \| )\| }}. The downward version is called '''1/19s''' or '''19s down''' and is represented by {{sagittal\| )! }}.

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

	[[Category:Boethius]]		[[Category:Boethius]]

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.

2024-10-10T07:01:14Z

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 07:01, 10 October 2024
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	== Sagittal notation ==		== Sagittal notation ==
	In the [[Sagittal]] system, this comma (possibly tempered) is represented by the sagittal {{sagittal \| )\| }} and is called the '''19 schisma''', or '''19s''' for short, because the simplest ~~ratio~~ it notates is 16~~:19~~, as for example in D:F~~ ~~{{sagittal \| )\| }}. The downward version is called '''1/19s''' or '''19s down''' and is represented by {{sagittal\| )! }}.		In the [[Sagittal]] system, this comma (possibly tempered) is represented by the sagittal {{sagittal \| )\| }} and is called the '''19 schisma''', or '''19s''' for short, because the simplest interval it notates is 19/1 (equiv 19/16), as for example in D-F{{nbhsp}}{{sagittal \| )\| }}. The downward version is called '''1/19s''' or '''19s down''' and is represented by {{sagittal\| )! }}.

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