Rank-3 temperament: Difference between revisions

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	A '''rank-3 temperament''' is a [[regular temperament]] with three [[generator]]s. If one of the generators can be an [[~~2/1\|~~octave]], it is called a '''planar temperament''', though the word is sometimes applied to any rank-3 temperament. There are two interpretations for the name ''planar temperament'': first, the octave classes of notes of a planar temperament can be embedded in a plane as a [[lattice]]; and second, the set of all possible tunings of such a temperament is represented by a plane in a [[projective tuning space]] of three or more dimensions.		A '''rank-3 temperament''' is a [[regular temperament]] with three [[generator]]s. If one of the generators can be an [[octave]], it is called a '''planar temperament''', though the word is sometimes applied to any rank-3 temperament. There are two interpretations for the name ''planar temperament'': first, the octave classes of notes of a planar temperament can be embedded in a plane as a [[lattice]]; and second, the set of all possible tunings of such a temperament is represented by a plane in a [[projective tuning space]] of three or more dimensions.

	See [[Tour of regular temperaments #Rank-3 temperaments]] for a list of families, clans, and collections of rank-3 temperaments.		See [[Tour of regular temperaments #Rank-3 temperaments]] for a list of families, clans, and collections of rank-3 temperaments.