2-limit: Difference between revisions
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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, 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]]. | |||
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 == | == See also == | ||
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[[Category:2-limit| ]] <!-- main article --> | [[Category:2-limit| ]] <!-- main article --> | ||
[[Category: | [[Category:1-odd-limit]] | ||
[[Category:1edo]] | |||
Latest revision as of 10:32, 21 May 2025
The 2-limit consists of intervals 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.
The 2-limit is equivalent to the 1-odd-limit, 1edo, and 1-p-fdo with arbitrary value of p (including 1afdo and 1ifdo).