Plücker coordinates: Difference between revisions

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 == Definition ==
-A temperament on a JI subgroup with some number of primes can be viewed as a point in a space representing all possible temperaments sharing the temperament's rank and tempering a JI subgroup with the same number of primes. This is called a Grassmannian variety, written as <math>\mathrm{Gr} (k, n)</math>, where k is the rank of the temperament and n is the rank of the JI subgroup.
+A temperament can be viewed as a point in what is called a Grassmannian variety, written as <math>\mathrm{Gr} (k, n)</math>.
+This variety contains all possible k-dimensional subspaces of <math>\mathbb{R}^n</math>.
-Because temperaments can be treated as linear mappings, this variety thus contains all possible k-dimensional subspaces of <math>\mathbb{R}^n</math>.
+In musical terms, k represents the rank of the temperament (how many independent generators it has), and n is the number of primes we're considering in our [[just intonation subgroup]].
 Let <math>M</math> be an element of <math>\mathrm{Gr} (k, n)</math>, spanned by basis vectors <math>m_1, \ldots, m_k</math>.