Map

The word map could refer to:

• In general mathematics, a "map" is any function from one set to another. For more information, see Wikipedia:Map (mathematics).

• In regular temperament theory, the term "map" is used in the more specific sense of a linear map, which, informally, can be thought of as a function that can be represented by a matrix. Examples include tuning maps, projection maps (sometimes called projection matrices), and temperament maps (usually called "temperament mapping matrices", or "mapping matrices" or even just "mappings" for short). There may be implicit restrictions; for instance, mappings are often assumed to map from JI to tempered intervals, which means that in the standard unweighted basis the entries are all integers. A mapping matrix with all integer entries and one row is called a val.

• Douglas Blumeyer and Dave Keenan recommend reserving the word "map" for a mapping with one row, so that all maps are mappings but not all mappings are maps; a simple tip to remember this usage is that the shorter word refers to the simpler object.

• In the past, the terms "M-map" and "V-map" were sometimes used to refer to mappings and subgroup basis matrices, respectively, as the former is a "map on monzos" and the latter is a "map on vals". V-maps were 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.