Rank and codimension: Difference between revisions
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== Mathematical description == | == Mathematical description == | ||
Mathematically, | Mathematically, the rank of a regular temperament is the number of independent intervals, called ''generators'', which can be combined together to obtain any interval of the temperament. The terminology originally comes from group theory and linear algebra, although we are using the term "co-rank" slightly differently here. | ||
In the parlance of group theory, the intervals of a regular temperament comprise a [http://en.wikipedia.org/wiki/Free_abelian_group#Rank finitely generated free abelian group] with a rank equal to the number of generators. In the parlance of linear algebra, the rank of the temperament is also the rank of any mapping matrix defining the temperament. | In the parlance of group theory, the intervals of a regular temperament comprise a [http://en.wikipedia.org/wiki/Free_abelian_group#Rank finitely generated free abelian group] with a rank equal to the number of generators. In the parlance of linear algebra, the rank of the temperament is also the rank of any mapping matrix defining the temperament. | ||