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]]. | ||
== Chords and harmony == | |||
There are a number of ways to approach harmony in this subgroup, most of which are discussed in [[Superpyth #Chords and harmony]]. The basic forms of chords include the triad [[6:7:9]], the tetrad [[6:7:8:9]], and their utonal inverses. Similarly, the fourth-spanning triad [[6:7:8]] and [[21:24:28]] can be used, as well as their wide voicing 4:7:12 and 7:12:21. Examples of extensions of these chords are [[12:14:18:21]] and [[14:18:21:24]]. Like in [[5-limit]] [[JI]], one quickly runs into [[wolf interval]]s without care, but the 2.3.7 wolf being [[21/16]] or [[32/21]] may be considered less discordant, and useful in its own ways. | |||
== Properties == | == Properties == | ||