Map: Difference between revisions

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* 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]], 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 [[regular temperament theory]], the term "map" is used in the more specific sense of a [[Wikipedia:Linear_map|''linear'' map]], which, informally, can be thought of as a function that can be represented by a matrix. Examples include [[tuning map]]s, [[projection matrix|projection map]]s (sometimes 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 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.

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 * 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]], 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 [[regular temperament theory]], the term "map" is used in the more specific sense of a [[Wikipedia:Linear_map|''linear'' map]], which, informally, can be thought of as a function that can be represented by a matrix. Examples include [[tuning map]]s, [[projection matrix|projection map]]s (sometimes 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 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.