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, 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 is fundamental to any sort of [[edo]]~~, ~~with~~ [[~~1edo~~]] ~~being the easiest and simplest to grasp~~.

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]].

Due to the human ability to perceive notes an octave apart as having the same pitch class, the 2-limit also collapses very easily, with this collapse being generally implemented in lattices. This collapse is helpful to understanding the pitches involved in other prime axes within the space of a single octave, should you add other primes to the mix.

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]].

== See also ==

* [[Harmonic limit]]

* [[Gallery of just intervals]]

~~== References ==~~

~~<references />~~

[[Category:2-limit| ]]

[[Category:1-odd-limit]]

[[Category:1edo]]

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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, 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 is fundamental to any sort of [[edo]], with [[1edo]] being the easiest and simplest to grasp.
+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]].
-Due to the human ability to perceive notes an octave apart as having the same pitch class, the 2-limit also collapses very easily, with this collapse being generally implemented in lattices.  This collapse is helpful to understanding the pitches involved in other prime axes within the space of a single octave, should you add other primes to the mix.
+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]].
 == See also ==
 * [[Harmonic limit]]
 * [[Gallery of just intervals]]
-== References ==
-<references />
 [[Category:2-limit| ]] <!-- main article -->
+[[Category:1-odd-limit]]
+[[Category:1edo]]