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 |
||
| (6 intermediate revisions by 3 users not shown) | |||
| Line 1: | Line 1: | ||
{{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, | 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]]. | ||
| Line 9: | Line 9: | ||
* [[Harmonic limit]] | * [[Harmonic limit]] | ||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
[[Category:2-limit| ]] <!-- main article --> | [[Category:2-limit| ]] <!-- main article --> | ||
[[Category:1-odd-limit]] | |||
[[Category:1edo]] | |||