Single-pitch tuning - Revision history

Lucius Chiaraviglio: /* Music */ Chris Vaisvil's ''0-EDO for Orchestra'' (2021): Really in 1edo, so moved there

2026-05-17T03:39:18Z

Music: Chris Vaisvil's ''0-EDO for Orchestra'' (2021): Really in 1edo, so moved there

← Older revision		Revision as of 03:39, 17 May 2026
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	; [[No Clue Music]]		; [[No Clue Music]]
	* [https://www.youtube.com/watch?v=g-WXe2mvAPk ''0 EDO Experiment''] (2024)		* [https://www.youtube.com/watch?v=g-WXe2mvAPk ''0 EDO Experiment''] (2024)

	~~; [[Chris Vaisvil]]~~
	* [https://www.youtube.com/watch?v=EAutHhRv3Gg ''0-EDO for Orchestra''] (2021)

	[[Category:Limiting cases]]		[[Category:Limiting cases]]
	[[Category:Trivial temperaments]]		[[Category:Trivial temperaments]]

Squib: /* In regular temperament theory */as a temperament of the empty subgroup

2026-01-11T20:02:02Z

In regular temperament theory: as a temperament of the empty subgroup

← Older revision		Revision as of 20:02, 11 January 2026
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	== In regular temperament theory ==		== In regular temperament theory ==
	Single-pitch tuning corresponds to the [[regular temperament]] in any given [[subgroup]] where all [[prime]]s in that subgroup are [[tempering out\|tempered out]], resulting in a rank-0 temperament with no [[generator]]. The mapping for this is the 0-val, {{val\| 0 0 … 0 }}, or more precisely, the rank-0 matrix, [ ].		Single-pitch tuning corresponds to the [[regular temperament]] in any given [[subgroup]] where all [[prime]]s in that subgroup are [[tempering out\|tempered out]], resulting in a rank-0 temperament with no [[generator]]. The mapping for this is the 0-val, {{val\| 0 0 … 0 }}, or more precisely, the rank-0 matrix, [ ]. Since it maps all intervals to the same pitch, it [[tempering out\|tempers out]] all commas and is [[consistent]] in all [[limit]]s.

	~~Being an example of~~ a [[~~trivial temperament~~]], single-pitch tuning ~~[[tempering out\|tempers out]] everything~~, ~~and~~ is ~~[[consistent]] in~~ all [[~~limit~~]]s.		Single-pitch tuning can also be considered a rank-0 temperament in the empty subgroup, which contains no primes. It tempers no commas and the pitch represents only the [[1/1\|unison]], so it is also empty-subgroup JI. (Tempering everything and tempering nothing are the same in this case, because there is nothing to temper.) This is closer to representing how single-pitch tuning is actually used, when it is used at all.

			Both are examples of [[trivial temperament]]s.

	== Music ==		== Music ==

Overthink: /* In equal tunings */ template is wrong

2026-01-02T19:56:12Z

In equal tunings: template is wrong

← Older revision		Revision as of 19:56, 2 January 2026
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	== In equal tunings ==		== In equal tunings ==
	{{Infobox ET\|0edo}}		{{Infobox ET\|0edo}}{{todo\|fix template\|description=The step size is wrong; it shouldn't be zero cents, but rather infinite or undefined.}}

	Single-pitch tuning can be specified as '''0 equal divisions of the octave''' ('''0edo'''), or 0 equal divisions of any finite interval.		Single-pitch tuning can be specified as '''0 equal divisions of the octave''' ('''0edo'''), or 0 equal divisions of any finite interval.

FloraC: /* In equal tunings */

2025-12-31T07:56:50Z

In equal tunings

← Older revision		Revision as of 07:56, 31 December 2025
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	{{Infobox ET\|0edo}}		{{Infobox ET\|0edo}}

	Single-pitch tuning can be specified as '''0 equal divisions of the octave''' ('''0edo'''), or 0 equal divisions of ~~anything~~.		Single-pitch tuning can be specified as '''0 equal divisions of the octave''' ('''0edo'''), or 0 equal divisions of any finite interval.

	The way to approach the idea of 0edo that leads to single-pitch tuning is to see what happens as ''n'' gets smaller in ''n''-edo. At 1-edo you have one note per octave. At 0.5-edo you have 1/0.5 which is one note every two octaves. As ''n'' gets smaller, steps become sparser, and in the limit, the steps go to infinity and only one pitch is left. It is thus a degenerate case.		The way to approach the idea of 0edo that leads to single-pitch tuning is to see what happens as ''n'' gets smaller in ''n''-edo. At 1-edo you have one note per octave. At 0.5-edo you have 1/0.5 which is one note every two octaves. As ''n'' gets smaller, steps become sparser, and in the limit, the steps go to infinity and only one pitch is left. It is thus a degenerate case.

Eufalesio: Degeneracy

2025-12-31T02:40:32Z

Degeneracy

← Older revision		Revision as of 02:40, 31 December 2025
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	{{Mathematical interest}}		{{Mathematical interest}}

	'''Single-pitch tuning''' is a [[tuning system]] that contains only a single pitch. It contrasts [[1edo]] because it does not even have [[2/1\|octaves]]. It also contrasts unpitched tuning, where no recognizable pitches exist. Single-pitch tuning can be described in terms of various models of tuning.		'''Single-pitch tuning''' is a [[tuning system]] that contains only a single pitch, and no single interval above or below it. It contrasts [[1edo]] because it does not even have [[2/1\|octaves]]. It also contrasts unpitched tuning, where no recognizable pitches exist. Single-pitch tuning can be described in terms of various models of tuning.

	== In equal tunings ==		== In equal tunings ==
	{{Infobox ET\|0edo}}		{{Infobox ET\|0edo}}

	Single-pitch tuning can be specified as '''0 equal divisions of the octave''' ('''0edo'''), or ~~0ed-''p'' for any positive, finite number ''p''~~.		Single-pitch tuning can be specified as '''0 equal divisions of the octave''' ('''0edo'''), or 0 equal divisions of anything.

	The way to approach the idea of 0edo that leads to single-pitch tuning is to see what happens as ''n'' gets smaller in ''n''-edo. At 1-edo you have one note per octave. At 0.5-edo you have 1/0.5 which is one note every two octaves. As ''n'' gets smaller ~~you reach a point where you only have one note within an audible octave range~~ and ~~any other notes outside of this range. Taking this~~ to ~~its conclusion,~~ and ~~assuming you want 0edo to be defined, you would conclude that 0edo is just~~ one pitch ~~without any octaves, which~~ is~~, arguably, pure rhythm~~.		The way to approach the idea of 0edo that leads to single-pitch tuning is to see what happens as ''n'' gets smaller in ''n''-edo. At 1-edo you have one note per octave. At 0.5-edo you have 1/0.5 which is one note every two octaves. As ''n'' gets smaller, steps become sparser, and in the limit, the steps go to infinity and only one pitch is left. It is thus a degenerate case.

	An alternative interpretation is that given that ''n''-edo means that you are dividing the octave into equal divisions with a logarithmic size of 1/''n'' octaves, and that [[1/0]] is sometimes considered undefined, it would follow that 0edo would be similarly undefined and thus ~~one could~~ not ~~use it as~~ a tuning system.		One musical application of 0edo is to use it with pure rhythm, or with change of timbre, though the latter can be disputed if harmonics are counted as distinct pitches. In the most purist sense, 0edo would be sonically similar to Morse code, only using one sinewave at a fixed frequency at different amplitudes with time.

			An alternative interpretation is that given that ''n''-edo means that you are dividing the octave into equal divisions with a logarithmic size of 1/''n'' octaves, and that [[1/0]] is sometimes considered undefined, it would follow that 0edo would be similarly undefined and thus not a tuning system.

	As a result of the step size of 0edo being infinite, the [[relative interval error\|relative error]] of all intervals is zero.		As a result of the step size of 0edo being infinite, the [[relative interval error\|relative error]] of all intervals is zero.
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	Single-pitch tuning corresponds to the [[regular temperament]] in any given [[subgroup]] where all [[prime]]s in that subgroup are [[tempering out\|tempered out]], resulting in a rank-0 temperament with no [[generator]]. The mapping for this is the 0-val, {{val\| 0 0 … 0 }}, or more precisely, the rank-0 matrix, [ ].		Single-pitch tuning corresponds to the [[regular temperament]] in any given [[subgroup]] where all [[prime]]s in that subgroup are [[tempering out\|tempered out]], resulting in a rank-0 temperament with no [[generator]]. The mapping for this is the 0-val, {{val\| 0 0 … 0 }}, or more precisely, the rank-0 matrix, [ ].

	Being an example of a [[trivial temperament]], single-pitch tuning [[tempering out\|tempers out]] ~~all [[comma]]s~~ and is [[consistent]] in all [[limit]]s.		Being an example of a [[trivial temperament]], single-pitch tuning [[tempering out\|tempers out]] everything, and is [[consistent]] in all [[limit]]s.

	== Music ==		== Music ==

FloraC: /* In regular temperament theory */ - duplicate stuff

2025-10-25T15:31:48Z

In regular temperament theory: - duplicate stuff

← Older revision		Revision as of 15:31, 25 October 2025
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	== In regular temperament theory ==		== In regular temperament theory ==
	Single-pitch tuning corresponds to the [[regular temperament]] in any given [[subgroup]] where all [[prime]]s in that subgroup are [[tempering out\|tempered out]], resulting in a rank-0 temperament with no [[generator]]~~. This is sometimes called the '''Om temperment'''~~. The mapping for this is the 0-val, {{val\| 0 0 … 0 }}, or more precisely, the rank-0 matrix, [ ].		Single-pitch tuning corresponds to the [[regular temperament]] in any given [[subgroup]] where all [[prime]]s in that subgroup are [[tempering out\|tempered out]], resulting in a rank-0 temperament with no [[generator]]. The mapping for this is the 0-val, {{val\| 0 0 … 0 }}, or more precisely, the rank-0 matrix, [ ].

	The name ''Om'' is a reference to {{w\|Om\|that syllable's use in Hindu meditation practices}}; [[Keenan Pepper]] gave it this name because there is only one temperament-distinct pitch in the whole system, in the same way that ''Om'' in the meditation sense is the only word you need to create the whole universe.

	Being an example of a [[trivial temperament]], single-pitch tuning [[tempering out\|tempers out]] all [[comma]]s and is [[consistent]] in all [[limit]]s.		Being an example of a [[trivial temperament]], single-pitch tuning [[tempering out\|tempers out]] all [[comma]]s and is [[consistent]] in all [[limit]]s.

FloraC: /* Music */ cleanup

2025-10-25T15:30:32Z

Music: cleanup

← Older revision		Revision as of 15:30, 25 October 2025
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	== Music ==		== Music ==
	~~; [[Chris Vaisvil]]~~
	* [https://www.youtube.com/watch?v=EAutHhRv3Gg ''0-EDO for Orchestra'']

	; [[Cryptovolans]], [[Reuben Gingrich]]		; [[Cryptovolans]], [[Reuben Gingrich]]
	* [https://soundcloud.com/sexytoadsandfrogsfriendcircle/0-cryptovolans-reuben ~~''Many Birds Pecking On Wood''~~] ~~(2021) (~~[https://sexytoadsandfrogsfriendcircle.bandcamp.com/album/staffcirc-vol-7-terra-octava Bandcamp])		* ''Many Birds Pecking On Wood'' (2021) – [https://soundcloud.com/sexytoadsandfrogsfriendcircle/0-cryptovolans-reuben SoundCloud] \| [https://sexytoadsandfrogsfriendcircle.bandcamp.com/album/staffcirc-vol-7-terra-octava Bandcamp]

	; [[Elliott Carter]]		; [[Elliott Carter]]
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	; [[No Clue Music]]		; [[No Clue Music]]
	* [https://www.youtube.com/watch?v=g-WXe2mvAPk ''0 EDO Experiment''] (2024)		* [https://www.youtube.com/watch?v=g-WXe2mvAPk ''0 EDO Experiment''] (2024)

			; [[Chris Vaisvil]]
			* [https://www.youtube.com/watch?v=EAutHhRv3Gg ''0-EDO for Orchestra''] (2021)

	[[Category:Limiting cases]]		[[Category:Limiting cases]]
	[[Category:Trivial temperaments]]		[[Category:Trivial temperaments]]

Osmiorisbendi: Added other 0-EDD music piece.

2025-10-25T09:56:14Z

Added other 0-EDD music piece.

← Older revision		Revision as of 09:56, 25 October 2025
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	== Music ==		== Music ==
			; [[Chris Vaisvil]]
			* [https://www.youtube.com/watch?v=EAutHhRv3Gg ''0-EDO for Orchestra'']

	; [[Cryptovolans]], [[Reuben Gingrich]]		; [[Cryptovolans]], [[Reuben Gingrich]]
	* [https://soundcloud.com/sexytoadsandfrogsfriendcircle/0-cryptovolans-reuben ''Many Birds Pecking On Wood''] (2021) ([https://sexytoadsandfrogsfriendcircle.bandcamp.com/album/staffcirc-vol-7-terra-octava Bandcamp])		* [https://soundcloud.com/sexytoadsandfrogsfriendcircle/0-cryptovolans-reuben ''Many Birds Pecking On Wood''] (2021) ([https://sexytoadsandfrogsfriendcircle.bandcamp.com/album/staffcirc-vol-7-terra-octava Bandcamp])

Dummy index: /* In regular temperament theory */

2025-10-19T08:58:15Z

In regular temperament theory

← Older revision		Revision as of 08:58, 19 October 2025
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	== In regular temperament theory ==		== In regular temperament theory ==
	Single-pitch tuning corresponds to the [[regular temperament]] in any given [[subgroup]] where all [[prime]]s in that subgroup are [[tempering out\|tempered out]], resulting in a rank-0 temperament with no [[generator]]. This is sometimes called the '''Om temperment'''. The mapping for this is the 0-val, {{val\| 0 0 … 0 }}.		Single-pitch tuning corresponds to the [[regular temperament]] in any given [[subgroup]] where all [[prime]]s in that subgroup are [[tempering out\|tempered out]], resulting in a rank-0 temperament with no [[generator]]. This is sometimes called the '''Om temperment'''. The mapping for this is the 0-val, {{val\| 0 0 … 0 }}, or more precisely, the rank-0 matrix, [ ].

	The name ''Om'' is a reference to {{w\|Om\|that syllable's use in Hindu meditation practices}}; [[Keenan Pepper]] gave it this name because there is only one temperament-distinct pitch in the whole system, in the same way that ''Om'' in the meditation sense is the only word you need to create the whole universe.		The name ''Om'' is a reference to {{w\|Om\|that syllable's use in Hindu meditation practices}}; [[Keenan Pepper]] gave it this name because there is only one temperament-distinct pitch in the whole system, in the same way that ''Om'' in the meditation sense is the only word you need to create the whole universe.

	Being an example of a [[trivial temperament]], single-pitch tuning [[tempering out\|tempers out]] all [[comma]]s and is [[consistent]] in all [[limit]]s.		Being an example of a [[trivial temperament]], single-pitch tuning [[tempering out\|tempers out]] all [[comma]]s and is [[consistent]] in all [[limit]]s.

	== Music ==		== Music ==

BudjarnLambeth: Mathematical interest

2025-08-10T22:29:43Z

Mathematical interest

← Older revision		Revision as of 22:29, 10 August 2025
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	\| ro = Sistem monocord		\| ro = Sistem monocord
	}}		}}
	{{~~Niche~~}}		{{Mathematical interest}}

	'''Single-pitch tuning''' is a [[tuning system]] that contains only a single pitch. It contrasts [[1edo]] because it does not even have [[2/1\|octaves]]. It also contrasts unpitched tuning, where no recognizable pitches exist. Single-pitch tuning can be described in terms of various models of tuning.		'''Single-pitch tuning''' is a [[tuning system]] that contains only a single pitch. It contrasts [[1edo]] because it does not even have [[2/1\|octaves]]. It also contrasts unpitched tuning, where no recognizable pitches exist. Single-pitch tuning can be described in terms of various models of tuning.