2-limit: Difference between revisions

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Not relevant here, and also incorrect (depending on who you ask, maybe)
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Sintel (talk | contribs)
remove more stuff that's irrelevant
Tag: Reverted
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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]].


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 [[1edo]].
 
It can be considered as a trivial rank-1 temperament, equivalent to 1et in the 2-limit, which is generated by only 2/1 and tempers out no commas. All equal temperaments with a mapping of 2/1 are weak extensions of it.  


== See also ==
== See also ==

Revision as of 21:27, 23 April 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 1edo.

See also