Map

The word map could refer to:

• In mathematics generally, any function from one set to another. See Wikipedia

• In regular temperament theory, at least on this wiki, the term "map" is often used to refer in particular to a linear map, such as a tuning map, a projection map, or Temperament mapping matrix. There are often some implicit restrictions - the term "mapping matrix" often assumes that we are mapping from JI to tempered intervals, for instance, which means that in the standard unweighted basis the entries are all integers. A mapping matrix with one row is called a val.

• In the past, the terms "M-map" and "V-map" were sometimes used to refer to Temperament mapping matrices and Subgroup basis matrices, as the former is a "map on monzos" and the latter a "map on vals" - the latter being an idea introduced later for subgroup calculations, which send vals to subgroup vals (or svals). The terminology has since changed on this Wiki, although it may be seen in various tuning archives and so on.

• In the writings of Douglas Blumeyer and Dave Keenan, the term "map" is primarily used in a much more specific sense as a synonym for a val, meaning a mapping matrix with one row and integer entries. In this terminological system, the term "mapping" is instead used in the broader sense to refer to temperament mapping matrices. In this usage, all "maps" are "mappings" but not all "mappings" are "maps" in this particular sense. The term "map" is also sometimes used to refer to things like tuning maps as well, which do not have integer coefficients. Thus, in this usage, we can identify it with a linear form, which is a function that can be represented by a covector, whereas in the broader usage within RTT we can identify it with a linear map. A simple tip to remember the difference between "map" and "mapping" in this usage is that the shorter word refers to the simpler object.