2.3.7 subgroup: Difference between revisions
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When [[octave equivalence]] is assumed, an interval can be taken as representing that interval in every possible voicing. This leaves primes 3 and 7, which can be represented in a 2-dimensional [[lattice diagram]], each prime represented by a different dimension, such that each point on the lattice represents a different [[interval class]]. | When [[octave equivalence]] is assumed, an interval can be taken as representing that interval in every possible voicing. This leaves primes 3 and 7, which can be represented in a 2-dimensional [[lattice diagram]], each prime represented by a different dimension, such that each point on the lattice represents a different [[interval class]]. | ||
== Scales == | == Properties == | ||
This subgroup is notably well-represented by [[5edo]] for its size, and therefore many of its simple intervals tend to cluster around the notes of 5edo: [[9/8]]~[[8/7]]~[[7/6]] representing a pentatonic "second", [[9/7]]~[[21/16]]~[[4/3]] representing a pentatonic "third", and so on. Therefore, one way to approach the 2.3.7 subgroup is to think of a pentatonic framework for composition as natural to it, rather than the diatonic framework associated with the [[5-limit]], and a few of the scales below reflect that nature. | |||
=== Scales === | |||
* Zo minor pentatonic: 1/1 7/6 4/3 3/2 7/4 2/1 | * Zo minor pentatonic: 1/1 7/6 4/3 3/2 7/4 2/1 | ||
* Ru pentatonic: 1/1 9/8 9/7 3/2 12/7 2/1 | * Ru pentatonic: 1/1 9/8 9/7 3/2 12/7 2/1 | ||