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]].

~~A '''~~2-limit~~''' interval~~ is ~~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 is fundamental~~ to ~~any sort of [[EDO]], and~~ in ~~fact~~, [[~~1edo~~]] ~~is basically the 2-limit in full, only with additional temperament properties for other primes~~.

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 [[~~Octave #Octave equivalence~~|~~octave equivalence~~]] ~~the 2-limit is also very valuable as a transparent extension to various prime axes~~.

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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[[Category:2-limit| ]]

[[Category:~~Prime~~ 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]].
-A '''2-limit''' interval is 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 is fundamental to any sort of [[EDO]], and in fact, [[1edo]] is basically the 2-limit in full, only with additional temperament properties for other primes.
+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 [[Octave #Octave equivalence|octave equivalence]] the 2-limit is also very valuable as a transparent extension to various prime axes.
+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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 [[Category:2-limit| ]] <!-- main article -->
-[[Category:Prime limit]]
+[[Category:1-odd-limit]]
+[[Category:1edo]]