2-limit: Difference between revisions

Expand on the equivalence
Re-add what it's equivalent to. These were all linked to each other so this page shouldn't be a dead end.
Tag: Manual revert
 
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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 -->
[[Category:1-odd-limit]]
[[Category:1edo]]