128/125 - Revision history

FloraC: /* Temperaments */ link

2025-09-11T04:24:40Z

Temperaments: link

← Older revision		Revision as of 04:24, 11 September 2025
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	== Temperaments ==		== Temperaments ==
	=== As a comma ===		=== As a comma ===
	[[Tempering out]] this comma leads to [[augmented]] temperament. See [[~~augmented~~ family]] for the family where it is tempered out.		[[Tempering out]] this comma leads to [[augmented (temperament)\|augmented]] temperament. See [[Augmented family]] for the family where it is tempered out.

	=== As an interval ===		=== As an interval ===
	If the diesis is treated as a musical interval in its own right as opposed to tempering it out, it is approximately a quarter-tone and so can be used to introduce [[7-limit]] and [[11-limit]] harmony into 5-limit scales.		If the diesis is treated as a musical interval in its own right as opposed to tempering it out, it is approximately a quarter-tone and so can be used to introduce [[7-limit]] and [[11-limit]] harmony into 5-limit scales.

	== Trivia ==		== Trivia ==

BudjarnLambeth at 07:02, 3 November 2024

2024-11-03T07:02:05Z

← Older revision		Revision as of 07:02, 3 November 2024
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	[[Category:Augmented]]		[[Category:Augmented]]
	[[Category:Sonifications]]		[[Category:Sonifications]]
			[[Category:Commas named after their interval size]]

FloraC: Revert to original section order (I don't see anything wrong with this)

2024-01-04T07:39:09Z

Revert to original section order (I don't see anything wrong with this)

← Older revision		Revision as of 07:39, 4 January 2024
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	The 41.059-[[cent]] interval of '''128/125''' is called the '''diesis''' or '''augmented comma'''; it represents the gap between a stack of three [[5/4]] just major thirds and the [[octave]], or in other words 2/(5/4)<sup>3</sup>.		The 41.059-[[cent]] interval of '''128/125''' is called the '''diesis''' or '''augmented comma'''; it represents the gap between a stack of three [[5/4]] just major thirds and the [[octave]], or in other words 2/(5/4)<sup>3</sup>.

			== Approximations ==
			This interval is fairly accurately represented by a single step in [[28edo\|28-]], [[31edo\|31-]] or [[34edo]], and by two steps of [[53edo\|53-]], [[59edo\|59-]] or [[65edo]]. In any tuning with pure octaves and just major thirds, such as [[quarter-comma meantone]], it will be exact. Furthermore, in meantone it appears as the difference between sharps and flats, e.g. between D# and Eb. It is also called '''enharmonic diesis''' or '''enharmonic comma''' for this reason.

	== Temperaments ==		== Temperaments ==
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	=== As an interval ===		=== As an interval ===
	If the diesis is treated as a musical interval in its own right as opposed to tempering it out, it is approximately a quarter-tone and so can be used to introduce [[7-limit]] and [[11-limit]] harmony into 5-limit scales.		If the diesis is treated as a musical interval in its own right as opposed to tempering it out, it is approximately a quarter-tone and so can be used to introduce [[7-limit]] and [[11-limit]] harmony into 5-limit scales.

	~~== Approximations ==~~
	It is fairly accurately represented by a single step in [[28edo\|28-]], [[31edo\|31-]] or [[34edo]], and by two steps of [[53edo\|53-]], [[59edo\|59-]] or [[65edo]]. In any tuning with pure octaves and just major thirds, such as [[quarter-comma meantone]], it will be exact. Furthermore, in meantone it appears as the difference between sharps and flats, e.g. between D# and Eb. It is also called '''enharmonic diesis''' or '''enharmonic comma''' for this reason.

	== Trivia ==		== Trivia ==

FloraC: Add back original section titles; adopt template: Interwiki

2024-01-04T07:26:37Z

Add back original section titles; adopt template: Interwiki

← Older revision		Revision as of 07:26, 4 January 2024
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			{{Interwiki
			\| en = 128/125
			\| de = 128/125
			}}
	{{Infobox Interval		{{Infobox Interval
	\| Name = diesis, augmented comma, enharmonic diesis, enharmonic comma		\| Name = diesis, augmented comma, enharmonic diesis, enharmonic comma
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	}}		}}

	The 41.059 cent interval of '''128/125''' is called the '''diesis''' or '''augmented comma'''; it represents the gap between a stack of three [[5/4]] just major thirds and the [[octave]], or in other words 2/(5/4)<sup>3</sup>.		The 41.059-[[cent]] interval of '''128/125''' is called the '''diesis''' or '''augmented comma'''; it represents the gap between a stack of three [[5/4]] just major thirds and the [[octave]], or in other words 2/(5/4)<sup>3</sup>.

	== As a comma ==		== Temperaments ==
	Tempering out this comma leads to [[augmented]] temperament. See [[augmented family]] for the family where it is tempered out.		=== As a comma ===
			[[Tempering out]] this comma leads to [[augmented]] temperament. See [[augmented family]] for the family where it is tempered out.

	== As an interval ==		=== As an interval ===
	If the diesis is treated as a musical interval in its own right as opposed to tempering it out, it is approximately a quarter-tone and so can be used to introduce [[7-limit]] and [[11-limit]] harmony into 5-limit scales.		If the diesis is treated as a musical interval in its own right as opposed to tempering it out, it is approximately a quarter-tone and so can be used to introduce [[7-limit]] and [[11-limit]] harmony into 5-limit scales.

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	It is fairly accurately represented by a single step in [[28edo\|28-]], [[31edo\|31-]] or [[34edo]], and by two steps of [[53edo\|53-]], [[59edo\|59-]] or [[65edo]]. In any tuning with pure octaves and just major thirds, such as [[quarter-comma meantone]], it will be exact. Furthermore, in meantone it appears as the difference between sharps and flats, e.g. between D# and Eb. It is also called '''enharmonic diesis''' or '''enharmonic comma''' for this reason.		It is fairly accurately represented by a single step in [[28edo\|28-]], [[31edo\|31-]] or [[34edo]], and by two steps of [[53edo\|53-]], [[59edo\|59-]] or [[65edo]]. In any tuning with pure octaves and just major thirds, such as [[quarter-comma meantone]], it will be exact. Furthermore, in meantone it appears as the difference between sharps and flats, e.g. between D# and Eb. It is also called '''enharmonic diesis''' or '''enharmonic comma''' for this reason.

	== ~~Relation to binary~~ ==		== Trivia ==
	This interval represents the amount by which the binary definition of kilobyte, 1024 bytes, exceeds the nominal definition of "kilo" prefix, 1000.		This interval represents the amount by which the binary definition of kilobyte, 1024 bytes, exceeds the nominal definition of "kilo" prefix, 1000.

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	[[Category:Augmented]]		[[Category:Augmented]]
	[[Category:Sonifications]]		[[Category:Sonifications]]

	~~<!-- interwiki: links are being placed in the sidebar -->~~
	~~[[https://de.xen.wiki/w/128/125]]~~
	~~[[Category:Augmented family]]~~

BudjarnLambeth: Add to category augmented family

2024-01-04T02:55:33Z

Add to category augmented family

← Older revision		Revision as of 02:55, 4 January 2024
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	<!-- interwiki: links are being placed in the sidebar -->		<!-- interwiki: links are being placed in the sidebar -->
	[[de:128/125]]		[[https://de.xen.wiki/w/128/125]]
			[[Category:Augmented family]]

BudjarnLambeth: Improved layout

2024-01-04T02:53:50Z

Improved layout

← Older revision		Revision as of 02:53, 4 January 2024
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	The 41.059 cent interval of '''128/125''' is called the '''diesis''' or '''augmented comma'''; it represents the gap between a stack of three [[5/4]] just major thirds and the [[octave]], or in other words 2/(5/4)<sup>3</sup>.		The 41.059 cent interval of '''128/125''' is called the '''diesis''' or '''augmented comma'''; it represents the gap between a stack of three [[5/4]] just major thirds and the [[octave]], or in other words 2/(5/4)<sup>3</sup>.

	== ~~Approximation~~ ==		== As a comma ==
			Tempering out this comma leads to [[augmented]] temperament. See [[augmented family]] for the family where it is tempered out.

			== As an interval ==
	If the diesis is treated as a musical interval in its own right as opposed to tempering it out, it is approximately a quarter-tone and so can be used to introduce [[7-limit]] and [[11-limit]] harmony into 5-limit scales.		If the diesis is treated as a musical interval in its own right as opposed to tempering it out, it is approximately a quarter-tone and so can be used to introduce [[7-limit]] and [[11-limit]] harmony into 5-limit scales.

			== Approximations ==
	It is fairly accurately represented by a single step in [[28edo\|28-]], [[31edo\|31-]] or [[34edo]], and by two steps of [[53edo\|53-]], [[59edo\|59-]] or [[65edo]]. In any tuning with pure octaves and just major thirds, such as [[quarter-comma meantone]], it will be exact. Furthermore, in meantone it appears as the difference between sharps and flats, e.g. between D# and Eb. It is also called '''enharmonic diesis''' or '''enharmonic comma''' for this reason.		It is fairly accurately represented by a single step in [[28edo\|28-]], [[31edo\|31-]] or [[34edo]], and by two steps of [[53edo\|53-]], [[59edo\|59-]] or [[65edo]]. In any tuning with pure octaves and just major thirds, such as [[quarter-comma meantone]], it will be exact. Furthermore, in meantone it appears as the difference between sharps and flats, e.g. between D# and Eb. It is also called '''enharmonic diesis''' or '''enharmonic comma''' for this reason.

	== ~~Temperaments ==~~		== Relation to binary ==
	~~Tempering out this comma leads~~ to ~~[[augmented]] temperament. See [[augmented family]] for the family where it is tempered out.~~

	~~== Trivia~~ ==
	This interval represents the amount by which the binary definition of kilobyte, 1024 bytes, exceeds the nominal definition of "kilo" prefix, 1000.		This interval represents the amount by which the binary definition of kilobyte, 1024 bytes, exceeds the nominal definition of "kilo" prefix, 1000.

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	<!-- interwiki: links are being placed in the sidebar -->		<!-- interwiki: links are being placed in the sidebar -->
	[[de:128/125]]		[[de:128/125]]

	~~[[Category:Todo:improve layout]]~~

FloraC: Undo. More names not accepted for this comma and its corresponding temperament

2023-12-15T08:05:25Z

Undo. More names not accepted for this comma and its corresponding temperament

← Older revision		Revision as of 08:05, 15 December 2023
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	{{Infobox Interval		{{Infobox Interval
	\| Name = diesis, augmented comma, enharmonic diesis, enharmonic comma~~, cyberisma~~		\| Name = diesis, augmented comma, enharmonic diesis, enharmonic comma
	\| Color name = g<sup>3</sup>2, trigu 2nd,<br>Trigu comma		\| Color name = g<sup>3</sup>2, trigu 2nd,<br>Trigu comma
	\| Comma = yes		\| Comma = yes
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	== Temperaments ==		== Temperaments ==
	Tempering out this comma leads to [[augmented]] temperament. See [[augmented family]] for the family where it is tempered out.		Tempering out this comma leads to [[augmented]] temperament. See [[augmented family]] for the family where it is tempered out.

	~~=== Walker temperament ===~~
	Walker temperament flattens the octave in order to temper out the difference between 2^10 and 10^3, which is an occurrence of the diesis. [[40ed10]] is an example of Walker temperament. It was created by Vector Graphics (Jay Walker) before he even knew what temperament was, as an attempt to align powers of 2 and powers of 10. In the context of Walker temperament, the augmented comma can be called the '''cyberisma,''' after its appearance in computing.

	== Trivia ==		== Trivia ==
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	<!-- interwiki: links are being placed in the sidebar -->		<!-- interwiki: links are being placed in the sidebar -->
	[[~~https~~:~~//de.xen.wiki/w/~~128/125]]		[[de:128/125]]

	[[Category:Todo:improve layout]]		[[Category:Todo:improve layout]]

VectorGraphics at 07:51, 15 December 2023

2023-12-15T07:51:37Z

← Older revision		Revision as of 07:51, 15 December 2023
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	{{Infobox Interval		{{Infobox Interval
	\| Name = diesis, augmented comma, enharmonic diesis, enharmonic comma		\| Name = diesis, augmented comma, enharmonic diesis, enharmonic comma, cyberisma
	\| Color name = g<sup>3</sup>2, trigu 2nd,<br>Trigu comma		\| Color name = g<sup>3</sup>2, trigu 2nd,<br>Trigu comma
	\| Comma = yes		\| Comma = yes
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	== Temperaments ==		== Temperaments ==
	Tempering out this comma leads to [[augmented]] temperament. See [[augmented family]] for the family where it is tempered out.		Tempering out this comma leads to [[augmented]] temperament. See [[augmented family]] for the family where it is tempered out.

			=== Walker temperament ===
			Walker temperament flattens the octave in order to temper out the difference between 2^10 and 10^3, which is an occurrence of the diesis. [[40ed10]] is an example of Walker temperament. It was created by Vector Graphics (Jay Walker) before he even knew what temperament was, as an attempt to align powers of 2 and powers of 10. In the context of Walker temperament, the augmented comma can be called the '''cyberisma,''' after its appearance in computing.

	== Trivia ==		== Trivia ==
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	<!-- interwiki: links are being placed in the sidebar -->		<!-- interwiki: links are being placed in the sidebar -->
	[[de:128/125]]		[[https://de.xen.wiki/w/128/125]]

	[[Category:Todo:improve layout]]		[[Category:Todo:improve layout]]

FloraC: Recategorize

2023-08-08T07:31:10Z

Recategorize

← Older revision		Revision as of 07:31, 8 August 2023
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	[[Category:Augmented]]		[[Category:Augmented]]
	[[Category:~~Real-life sonifications~~]]		[[Category:Sonifications]]

	<!-- interwiki: links are being placed in the sidebar -->		<!-- interwiki: links are being placed in the sidebar -->

BudjarnLambeth: Added enharmonic diesis and enharmonic comma to the list of names in the infobox

2023-06-29T13:33:49Z

Added enharmonic diesis and enharmonic comma to the list of names in the infobox

← Older revision		Revision as of 13:33, 29 June 2023
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	{{Infobox Interval		{{Infobox Interval
	\| Name = diesis, augmented comma		\| Name = diesis, augmented comma, enharmonic diesis, enharmonic comma
	\| Color name = g<sup>3</sup>2, trigu 2nd,<br>Trigu comma		\| Color name = g<sup>3</sup>2, trigu 2nd,<br>Trigu comma
	\| Comma = yes		\| Comma = yes