Temperament mapping matrix: Difference between revisions
Cmloegcmluin (talk | contribs) add Regular temperament theory category |
Cmloegcmluin (talk | contribs) make the basic take on this information more prominently linked, since we have a pattern going of pages with general versions and mathematical versions |
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This page gives a formal mathematical approach to [[RTT]] mapping. For a page with a simpler introduction, see [[mapping]]. | |||
=Basics= | =Basics= | ||
The multiplicative group generated by any finite set of rational numbers is an r-rank free abelian group. Thus, an [[Abstract_regular_temperament|abstract regular temperament]], can be represented by a group homomorphism '''T''': J → K from the group J of JI rationals to a quotient group K of tempered intervals. This homomorphism can also be represented by a integer matrix, called a '''temperament mapping matrix'''; when context is clear enough it's also sometimes just called a '''mapping matrix''' or even just a '''mapping''' for the temperament in question. (Note that many group homomorphisms can correspond to the same temperament, simply mapping to a different choice of tempered coordinates.) | The multiplicative group generated by any finite set of rational numbers is an r-rank free abelian group. Thus, an [[Abstract_regular_temperament|abstract regular temperament]], can be represented by a group homomorphism '''T''': J → K from the group J of JI rationals to a quotient group K of tempered intervals. This homomorphism can also be represented by a integer matrix, called a '''temperament mapping matrix'''; when context is clear enough it's also sometimes just called a '''mapping matrix''' or even just a '''mapping''' for the temperament in question. (Note that many group homomorphisms can correspond to the same temperament, simply mapping to a different choice of tempered coordinates.) | ||