2-limit: Difference between revisions
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Revision as of 10:02, 14 February 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).