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, 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]].

* 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). In the past, the terms "M-map" and "V-map" were also sometimes used to refer to temperament mappings and [[subgroup basis matrices]], although the terminology has since changed on this wiki. A rank-1 temperament mapping is also 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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 * 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, 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]].
+* 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). In the past, the terms "M-map"  and "V-map" were also sometimes used to refer to temperament mappings and [[subgroup basis matrices]], although the terminology has since changed on this wiki. A rank-1 temperament mapping is also 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.

Map: Difference between revisions

Mike Battaglia (talk | contribs)