11-limit: Difference between revisions
Undo revision 193606 by VectorGraphics (talk). The sections are empty Tag: Undo |
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{{Prime limit navigation|11}} | {{Prime limit navigation|11}} | ||
The '''11-limit''' consists of all [[just intonation|justly tuned]] [[interval]]s whose [[ratio|numerators and denominators]] are both products of the [[prime]]s 2, 3, 5, 7 and 11. The 11-limit is the 5th [[prime limit]] and is a superset of the [[7-limit]] and a subset of the [[13-limit]]. Some examples of 11-limit intervals are [[14/11]], [[11/8]], [[27/22]] and [[99/98]]. | The '''11-limit''' consists of all [[just intonation|justly tuned]] [[interval]]s whose [[ratio|numerators and denominators]] are both products of the [[prime]]s 2, 3, 5, 7 and 11. The 11-limit is the 5th [[prime limit]] and is a superset of the [[7-limit]] and a subset of the [[13-limit]]. Some examples of 11-limit intervals are [[14/11]], [[11/8]], [[27/22]] and [[99/98]]. | ||
The 11-limit is a [[rank and codimension|rank-5]] system, and can be modeled in a 4-dimensional [[lattice]], with the primes 3, 5, 7, and 11 represented by each dimension. The prime 2 does not appear in the typical 11-limit lattice because [[octave equivalence]] is presumed. If octave equivalence is not presumed, a fifth dimension is needed. | |||
These things are contained by the 11-limit, but not the 7-limit: | These things are contained by the 11-limit, but not the 7-limit: | ||