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The word '''map''' could refer to:
The word '''map''' could refer to:


* In mathematics generally, any function from one set to another. See [https://en.wikipedia.org/wiki/Map_(mathematics) Wikipedia]
* In general mathematics, a "map" is any function from one set to another. For more information, see [[Wikipedia:Map_(mathematics)|Wikipedia:Map (mathematics)]].


* 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 [[regular temperament theory]], the term "map" is used in the more specific sense of a [[Wikipedia:Linear_map|''linear'' map]], which means a function that can be represented by a matrix. Examples include [[tuning map]]s, [[projection matrix|projection map]]s (usually called "projection matrices"), and [[temperament mapping matrix|temperament map]]s (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 with all integer entries and 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.
* [[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.


* 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 [[Wikipedia:Linear_form|linear form]], which is a function that can be represented by a [[Wikipedia:Covector|covector]], whereas in the broader usage within RTT we can identify it with a [[Wikipedia:Linear_map|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.


[[Category:Temperament]]
[[Category:Temperament]]

Revision as of 04:04, 21 December 2021

The word map could refer to:

  • In regular temperament theory, the term "map" is used in the more specific sense of a linear map, which means a function that can be represented by a matrix. Examples include tuning maps, projection maps (usually 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 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.
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