2-limit - Revision history

FloraC: Re-add what it's equivalent to. These were all linked to each other so this page shouldn't be a dead end.

2025-05-21T10:32:18Z

Re-add what it's equivalent to. These were all linked to each other so this page shouldn't be a dead end.

← Older revision		Revision as of 10:32, 21 May 2025
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	Since humans tend to perceive notes an octave apart as having the same pitch class, the 2-limit is said to be "easy to collapse", with this collapse being generally implemented in lattices. This will reduce the dimensionality of the lattice by one, allowing the [[5-limit]] (whose intervals are represented by 3 coordinates corresponding to each prime) to be drawn in 2 dimensions, forming the familiar classical [[Tonnetz]].		Since humans tend to perceive notes an octave apart as having the same pitch class, the 2-limit is said to be "easy to collapse", with this collapse being generally implemented in lattices. This will reduce the dimensionality of the lattice by one, allowing the [[5-limit]] (whose intervals are represented by 3 coordinates corresponding to each prime) to be drawn in 2 dimensions, forming the familiar classical [[Tonnetz]].

	The 2-limit is equivalent to [[1edo]].		The 2-limit is equivalent to the [[1-odd-limit]], [[1edo]], and 1-''p''-fdo with arbitrary value of ''p'' (including [[AFDO\|1afdo]] and [[IFDO\|1ifdo]]).

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

Sintel: remove more stuff that's irrelevant

2025-04-23T21:27:28Z

remove more stuff that's irrelevant

← Older revision		Revision as of 21:27, 23 April 2025
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	Since humans tend to perceive notes an octave apart as having the same pitch class, the 2-limit is said to be "easy to collapse", with this collapse being generally implemented in lattices. This will reduce the dimensionality of the lattice by one, allowing the [[5-limit]] (whose intervals are represented by 3 coordinates corresponding to each prime) to be drawn in 2 dimensions, forming the familiar classical [[Tonnetz]].		Since humans tend to perceive notes an octave apart as having the same pitch class, the 2-limit is said to be "easy to collapse", with this collapse being generally implemented in lattices. This will reduce the dimensionality of the lattice by one, allowing the [[5-limit]] (whose intervals are represented by 3 coordinates corresponding to each prime) to be drawn in 2 dimensions, forming the familiar classical [[Tonnetz]].

	The 2-limit is equivalent to ~~the [[1-odd-limit]],~~ [[1edo]]~~, and 1-''p''-fdo with arbitrary value of ''p'' (including [[AFDO\|1afdo]] and [[IFDO\|1ifdo]]).~~		The 2-limit is equivalent to [[1edo]].

	It can be considered as a trivial rank-1 temperament, equivalent to 1et in the 2-limit, which is generated by only 2/1 and tempers out no commas. All equal temperaments with a mapping of 2/1 are weak extensions of it.

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

Sintel: Not relevant here, and also incorrect (depending on who you ask, maybe)

2025-04-23T21:24:06Z

Not relevant here, and also incorrect (depending on who you ask, maybe)

← Older revision		Revision as of 21:24, 23 April 2025
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	Since humans tend to perceive notes an octave apart as having the same pitch class, the 2-limit is said to be "easy to collapse", with this collapse being generally implemented in lattices. This will reduce the dimensionality of the lattice by one, allowing the [[5-limit]] (whose intervals are represented by 3 coordinates corresponding to each prime) to be drawn in 2 dimensions, forming the familiar classical [[Tonnetz]].		Since humans tend to perceive notes an octave apart as having the same pitch class, the 2-limit is said to be "easy to collapse", with this collapse being generally implemented in lattices. This will reduce the dimensionality of the lattice by one, allowing the [[5-limit]] (whose intervals are represented by 3 coordinates corresponding to each prime) to be drawn in 2 dimensions, forming the familiar classical [[Tonnetz]].

	Counterintuitively, applying octave-equivalence to a lattice is mathematically equivalent to [[tempering out]] 2/1 – a single interval is used to stand for all intervals an octave apart, just as in meantone, a single interval stands in for all intervals an 81/80 apart.

	The 2-limit is equivalent to the [[1-odd-limit]], [[1edo]], and 1-''p''-fdo with arbitrary value of ''p'' (including [[AFDO\|1afdo]] and [[IFDO\|1ifdo]]).		The 2-limit is equivalent to the [[1-odd-limit]], [[1edo]], and 1-''p''-fdo with arbitrary value of ''p'' (including [[AFDO\|1afdo]] and [[IFDO\|1ifdo]]).

FloraC: We don't accept new names for equal temps, thanks!

2025-04-20T11:50:21Z

We don't accept new names for equal temps, thanks!

← Older revision		Revision as of 11:50, 20 April 2025
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	Since humans tend to perceive notes an octave apart as having the same pitch class, the 2-limit is said to be "easy to collapse", with this collapse being generally implemented in lattices. This will reduce the dimensionality of the lattice by one, allowing the [[5-limit]] (whose intervals are represented by 3 coordinates corresponding to each prime) to be drawn in 2 dimensions, forming the familiar classical [[Tonnetz]].		Since humans tend to perceive notes an octave apart as having the same pitch class, the 2-limit is said to be "easy to collapse", with this collapse being generally implemented in lattices. This will reduce the dimensionality of the lattice by one, allowing the [[5-limit]] (whose intervals are represented by 3 coordinates corresponding to each prime) to be drawn in 2 dimensions, forming the familiar classical [[Tonnetz]].

	Counterintuitively, applying octave-equivalence to a lattice is mathematically equivalent to tempering out 2/1 - a single interval is used to stand for all intervals an octave apart, just as in meantone, a single interval stands in for all intervals an 81/80 apart.		Counterintuitively, applying octave-equivalence to a lattice is mathematically equivalent to [[tempering out]] 2/1 – a single interval is used to stand for all intervals an octave apart, just as in meantone, a single interval stands in for all intervals an 81/80 apart.

	The 2-limit is equivalent to the [[1-odd-limit]], [[1edo]], and 1-''p''-fdo with arbitrary value of ''p'' (including [[AFDO\|1afdo]] and [[IFDO\|1ifdo]]).		The 2-limit is equivalent to the [[1-odd-limit]], [[1edo]], and 1-''p''-fdo with arbitrary value of ''p'' (including [[AFDO\|1afdo]] and [[IFDO\|1ifdo]]).

	~~The 2-limit~~ can be considered as ~~the~~ trivial rank-1 temperament ~~'''binary'''~~, equivalent to ~~1-ET~~ in the 2-limit, which is generated by only 2/1 and tempers out no commas. All equal temperaments with a mapping of 2/1 are weak extensions of ~~binary~~.		It can be considered as a trivial rank-1 temperament, equivalent to 1et in the 2-limit, which is generated by only 2/1 and tempers out no commas. All equal temperaments with a mapping of 2/1 are weak extensions of it.

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

VectorGraphics at 09:28, 20 April 2025

2025-04-20T09:28:36Z

← Older revision		Revision as of 09:28, 20 April 2025
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	Since humans tend to perceive notes an octave apart as having the same pitch class, the 2-limit is said to be "easy to collapse", with this collapse being generally implemented in lattices. This will reduce the dimensionality of the lattice by one, allowing the [[5-limit]] (whose intervals are represented by 3 coordinates corresponding to each prime) to be drawn in 2 dimensions, forming the familiar classical [[Tonnetz]].		Since humans tend to perceive notes an octave apart as having the same pitch class, the 2-limit is said to be "easy to collapse", with this collapse being generally implemented in lattices. This will reduce the dimensionality of the lattice by one, allowing the [[5-limit]] (whose intervals are represented by 3 coordinates corresponding to each prime) to be drawn in 2 dimensions, forming the familiar classical [[Tonnetz]].

			Counterintuitively, applying octave-equivalence to a lattice is mathematically equivalent to tempering out 2/1 - a single interval is used to stand for all intervals an octave apart, just as in meantone, a single interval stands in for all intervals an 81/80 apart.

	The 2-limit is equivalent to the [[1-odd-limit]], [[1edo]], and 1-''p''-fdo with arbitrary value of ''p'' (including [[AFDO\|1afdo]] and [[IFDO\|1ifdo]]).		The 2-limit is equivalent to the [[1-odd-limit]], [[1edo]], and 1-''p''-fdo with arbitrary value of ''p'' (including [[AFDO\|1afdo]] and [[IFDO\|1ifdo]]).

			The 2-limit can be considered as the trivial rank-1 temperament '''binary''', equivalent to 1-ET in the 2-limit, which is generated by only 2/1 and tempers out no commas. All equal temperaments with a mapping of 2/1 are weak extensions of binary.

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

FloraC: +categories (since they exist)

2025-02-14T10:02:00Z

+categories (since they exist)

← Older revision		Revision as of 10:02, 14 February 2025
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	[[Category:2-limit\| ]] <!-- main article -->		[[Category:2-limit\| ]] <!-- main article -->
			[[Category:1-odd-limit]]
			[[Category:1edo]]

FloraC: No point to reference here

2025-02-14T09:59:39Z

No point to reference here

← Older revision		Revision as of 09:59, 14 February 2025
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	{{Prime limit navigation\|2}}		{{Prime limit navigation\|2}}
	The '''2-limit''' consists of [[interval]]s that are either an integer whose only prime factor is 2, or the reciprocal of such an integer. Naturally, since [[2/1]] is the octave, this limits us to unisons,~~<ref>[http://www.tonalsoft.com/enc/l/limit.aspx#MainContent Tonalsoft Encylopedia \| ''limit'']</ref>~~ octaves and stacks of octaves. The 2-limit can be represented by any [[edo]].		The '''2-limit''' consists of [[interval]]s that are either an integer whose only prime factor is 2, or the reciprocal of such an integer. Naturally, since [[2/1]] is the octave, this limits us to unisons, octaves and stacks of octaves. The 2-limit can be represented by any [[edo]].

	Since humans tend to perceive notes an octave apart as having the same pitch class, the 2-limit is said to be "easy to collapse", with this collapse being generally implemented in lattices. This will reduce the dimensionality of the lattice by one, allowing the [[5-limit]] (whose intervals are represented by 3 coordinates corresponding to each prime) to be drawn in 2 dimensions, forming the familiar classical [[Tonnetz]].		Since humans tend to perceive notes an octave apart as having the same pitch class, the 2-limit is said to be "easy to collapse", with this collapse being generally implemented in lattices. This will reduce the dimensionality of the lattice by one, allowing the [[5-limit]] (whose intervals are represented by 3 coordinates corresponding to each prime) to be drawn in 2 dimensions, forming the familiar classical [[Tonnetz]].
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	* [[Harmonic limit]]		* [[Harmonic limit]]
	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]

	~~== References ==~~
	~~<references/>~~

	[[Category:2-limit\| ]] <!-- main article -->		[[Category:2-limit\| ]] <!-- main article -->

FloraC: Expand on the equivalence

2025-02-14T09:59:10Z

Expand on the equivalence

← Older revision		Revision as of 09:59, 14 February 2025
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	{{Prime limit navigation\|2}}		{{Prime limit navigation\|2}}
			The '''2-limit''' consists of [[interval]]s that are either an integer whose only prime factor is 2, or the reciprocal of such an integer. Naturally, since [[2/1]] is the octave, this limits us to unisons,<ref>[http://www.tonalsoft.com/enc/l/limit.aspx#MainContent Tonalsoft Encylopedia \| ''limit'']</ref> octaves and stacks of octaves. The 2-limit can be represented by any [[edo]].
	The '''2-limit''' consists of [[interval]]s that are either an integer whose only prime factor is 2, or the reciprocal of such an integer. Naturally, since [[2/1]] is the octave, this limits us to unisons,<ref>[http://www.tonalsoft.com/enc/l/limit.aspx#MainContent Tonalsoft Encylopedia \| ''limit'']</ref> octaves and stacks of octaves. The 2-limit can be represented by any [[edo]]~~, and is in fact equivalent to [[1edo]], which is a subset of all other edos~~.

	Since humans tend to perceive notes an octave apart as having the same pitch class, the 2-limit is said to be "easy to collapse", with this collapse being generally implemented in lattices. This will reduce the dimensionality of the lattice by one, allowing the [[5-limit]] (whose intervals are represented by 3 coordinates corresponding to each prime) to be drawn in 2 dimensions, forming the familiar classical [[Tonnetz]].		Since humans tend to perceive notes an octave apart as having the same pitch class, the 2-limit is said to be "easy to collapse", with this collapse being generally implemented in lattices. This will reduce the dimensionality of the lattice by one, allowing the [[5-limit]] (whose intervals are represented by 3 coordinates corresponding to each prime) to be drawn in 2 dimensions, forming the familiar classical [[Tonnetz]].

	The 2-limit is equivalent to the [[1-odd-limit]].		The 2-limit is equivalent to the [[1-odd-limit]], [[1edo]], and 1-''p''-fdo with arbitrary value of ''p'' (including [[AFDO\|1afdo]] and [[IFDO\|1ifdo]]).

	== See also ==		== See also ==
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	== References ==		== References ==
	<references />		<references/>

	[[Category:2-limit\| ]] <!-- main article -->		[[Category:2-limit\| ]] <!-- main article -->

Lériendil at 03:09, 26 August 2024

2024-08-26T03:09:21Z

← Older revision		Revision as of 03:09, 26 August 2024
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	[[Category:2-limit\| ]] <!-- main article -->		[[Category:2-limit\| ]] <!-- main article -->
	~~[[Category:Prime limit]]~~

Lériendil at 03:05, 26 August 2024

2024-08-26T03:05:38Z

← Older revision		Revision as of 03:05, 26 August 2024
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	[[Category:2-limit\| ]] <!-- main article -->		[[Category:2-limit\| ]] <!-- main article -->
			[[Category:Prime limit]]