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

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.

~~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~~.

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]].

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