Tempered monzos and vals: Difference between revisions

The generators need to be specified. *Mapping* is a clipping of *temperament mapping matrix*. Cleanup. +some links to Wikipedia
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This mapping represents meantone temperament. If we apply this mapping to the monzo {{monzo| 1 0 0 }}, representing 2/1, we get the tmonzo {{monzo| 1 0 }} (one tempered 2/1). If we instead apply it to {{monzo| -1 1 0 }}, we get the tmonzo {{monzo| 0 1 }} (one tempered 3/2). That 2/1 and 3/2 map to {{monzo| 1 0 }} and {{monzo| 0 1 }} respectively tell us that the tempered versions of these intervals can serve as a basis for meantone. If we now apply this mapping to the monzo {{monzo| -2 0 1 }}, representing 5/4, we get the tmonzo {{monzo| -2 4 }}, telling us that the tempered 5/4 maps to four tempered 3/2's minus two tempered 2/1's.  
This mapping represents meantone temperament. If we [[Mathematical guide/Matrix operations|apply]] this mapping to the monzo {{monzo| 1 0 0 }}, representing 2/1, we get the tmonzo {{monzo| 1 0 }} (one tempered 2/1). If we instead apply it to {{monzo| -1 1 0 }}, we get the tmonzo {{monzo| 0 1 }} (one tempered 3/2). That 2/1 and 3/2 map to {{monzo| 1 0 }} and {{monzo| 0 1 }} respectively tell us that the tempered versions of these intervals can serve as a basis for meantone. If we now apply this mapping to the monzo {{monzo| -2 0 1 }}, representing 5/4, we get the tmonzo {{monzo| -2 4 }}, telling us that the tempered 5/4 maps to four tempered 3/2's minus two tempered 2/1's.  


== See also ==
== See also ==