2-limit: Difference between revisions

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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]].

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 ==

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== References ==

[[Category:2-limit| ]]

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 {{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]].
-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 ==
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 == References ==
-<references />
+<references/>
 [[Category:2-limit| ]] <!-- main article -->