Map - Revision history

Fredg999: /* Maps in regular temperament theory */ Add mapping to lattice

2026-07-28T05:23:05Z

Maps in regular temperament theory: Add mapping to lattice

← Older revision		Revision as of 05:23, 28 July 2026
Line 35:		Line 35:
	{{Main\|Projection matrix}}		{{Main\|Projection matrix}}
	A projection matrix (or rarely a projection map) uniquely identifies a specific tuning of a specific regular temperament.		A projection matrix (or rarely a projection map) uniquely identifies a specific tuning of a specific regular temperament.

			=== Lattice map ===
			{{Main\|Mapping to lattice}}
			A lattice map or mapping to lattice transforms intervals into their coordinates in a regularly tempered [[lattice]].

	== See also ==		== See also ==

Fredg999: Major rewrite

2026-07-28T03:59:51Z

Major rewrite

@@ Line 1: / Line 1: @@
-The word '''map''' could refer to:
+{{Wikipedia|Map (mathematics)}}
-* In general mathematics, a "map" is any function from one set to another. For more information, see [[Wikipedia: Map (mathematics)]].
+Various kinds of maps relevant to microtonal music theory are introduced below.
-* 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]].
+== Keyboard map ==
-* [[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 all occurrences at present on this wiki, as well as in Graham Breed's temperament finder, the term "map" (and not "mapping") consistently refers to a single-row mapping, so following this suggestion would be seamless moving forward. A "tuning map", which maps from generators to cents, is a map in "tuning space"; by analogy, a val is a map in "temperament space", and so it would be perfectly consistent with existing terminology to refer to a val as a "temperament map" as opposed to a "temperament mapping", and then when it is clear from the context that it is a ''temperament'' map, the qualifier "temperament" can be dropped, as is done with "temperament mapping matrix" being abbreviated to "mapping matrix". So the suggestion is equivalent to unqualified occurrences of "map" being assumed to be temperament maps, or in other words, synonymous with vals (except for the integer entry requirement), not tuning maps. Dave and Douglas recommend using "map" rather than "val", for two reasons. First, "map" is a basic linear algebra term with wide familiarity (being specialized for this purpose) while "val" is unnecessary jargon that creates a barrier to understanding by newcomers. Second, the coinage of "val" from the obscure mathematical term "valuation" is tenuous and unlikely to provide helpful insight: "p-adic valuation" is an obscure term for "prime count", which would be an element of a prime-count vector ("monzo"), not a map ("val").
+=== Musical instruments ===
-{{Disambiguation}}
+=== Computer keyboard bindings ===
 [[Category:Regular temperament theory]]

Fredg999 category edits: Move disambiguation template

2023-07-26T06:39:02Z

Move disambiguation template

← Older revision		Revision as of 06:39, 26 July 2023
Line 6:		Line 6:

	* [[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 all occurrences at present on this wiki, as well as in Graham Breed's temperament finder, the term "map" (and not "mapping") consistently refers to a single-row mapping, so following this suggestion would be seamless moving forward. A "tuning map", which maps from generators to cents, is a map in "tuning space"; by analogy, a val is a map in "temperament space", and so it would be perfectly consistent with existing terminology to refer to a val as a "temperament map" as opposed to a "temperament mapping", and then when it is clear from the context that it is a ''temperament'' map, the qualifier "temperament" can be dropped, as is done with "temperament mapping matrix" being abbreviated to "mapping matrix". So the suggestion is equivalent to unqualified occurrences of "map" being assumed to be temperament maps, or in other words, synonymous with vals (except for the integer entry requirement), not tuning maps. Dave and Douglas recommend using "map" rather than "val", for two reasons. First, "map" is a basic linear algebra term with wide familiarity (being specialized for this purpose) while "val" is unnecessary jargon that creates a barrier to understanding by newcomers. Second, the coinage of "val" from the obscure mathematical term "valuation" is tenuous and unlikely to provide helpful insight: "p-adic valuation" is an obscure term for "prime count", which would be an element of a prime-count vector ("monzo"), not a map ("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 all occurrences at present on this wiki, as well as in Graham Breed's temperament finder, the term "map" (and not "mapping") consistently refers to a single-row mapping, so following this suggestion would be seamless moving forward. A "tuning map", which maps from generators to cents, is a map in "tuning space"; by analogy, a val is a map in "temperament space", and so it would be perfectly consistent with existing terminology to refer to a val as a "temperament map" as opposed to a "temperament mapping", and then when it is clear from the context that it is a ''temperament'' map, the qualifier "temperament" can be dropped, as is done with "temperament mapping matrix" being abbreviated to "mapping matrix". So the suggestion is equivalent to unqualified occurrences of "map" being assumed to be temperament maps, or in other words, synonymous with vals (except for the integer entry requirement), not tuning maps. Dave and Douglas recommend using "map" rather than "val", for two reasons. First, "map" is a basic linear algebra term with wide familiarity (being specialized for this purpose) while "val" is unnecessary jargon that creates a barrier to understanding by newcomers. Second, the coinage of "val" from the obscure mathematical term "valuation" is tenuous and unlikely to provide helpful insight: "p-adic valuation" is an obscure term for "prime count", which would be an element of a prime-count vector ("monzo"), not a map ("val").

			{{Disambiguation}}

	[[Category:Regular temperament theory]]		[[Category:Regular temperament theory]]
Line 12:		Line 14:
	[[Category:Val]]		[[Category:Val]]
	[[Category:Mapping]]		[[Category:Mapping]]

	~~{{Disambiguation}}~~

Fredg999 category edits: Disambiguation template

2023-02-20T04:23:34Z

Disambiguation template

← Older revision		Revision as of 04:23, 20 February 2023
Line 7:		Line 7:
	* [[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 all occurrences at present on this wiki, as well as in Graham Breed's temperament finder, the term "map" (and not "mapping") consistently refers to a single-row mapping, so following this suggestion would be seamless moving forward. A "tuning map", which maps from generators to cents, is a map in "tuning space"; by analogy, a val is a map in "temperament space", and so it would be perfectly consistent with existing terminology to refer to a val as a "temperament map" as opposed to a "temperament mapping", and then when it is clear from the context that it is a ''temperament'' map, the qualifier "temperament" can be dropped, as is done with "temperament mapping matrix" being abbreviated to "mapping matrix". So the suggestion is equivalent to unqualified occurrences of "map" being assumed to be temperament maps, or in other words, synonymous with vals (except for the integer entry requirement), not tuning maps. Dave and Douglas recommend using "map" rather than "val", for two reasons. First, "map" is a basic linear algebra term with wide familiarity (being specialized for this purpose) while "val" is unnecessary jargon that creates a barrier to understanding by newcomers. Second, the coinage of "val" from the obscure mathematical term "valuation" is tenuous and unlikely to provide helpful insight: "p-adic valuation" is an obscure term for "prime count", which would be an element of a prime-count vector ("monzo"), not a map ("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 all occurrences at present on this wiki, as well as in Graham Breed's temperament finder, the term "map" (and not "mapping") consistently refers to a single-row mapping, so following this suggestion would be seamless moving forward. A "tuning map", which maps from generators to cents, is a map in "tuning space"; by analogy, a val is a map in "temperament space", and so it would be perfectly consistent with existing terminology to refer to a val as a "temperament map" as opposed to a "temperament mapping", and then when it is clear from the context that it is a ''temperament'' map, the qualifier "temperament" can be dropped, as is done with "temperament mapping matrix" being abbreviated to "mapping matrix". So the suggestion is equivalent to unqualified occurrences of "map" being assumed to be temperament maps, or in other words, synonymous with vals (except for the integer entry requirement), not tuning maps. Dave and Douglas recommend using "map" rather than "val", for two reasons. First, "map" is a basic linear algebra term with wide familiarity (being specialized for this purpose) while "val" is unnecessary jargon that creates a barrier to understanding by newcomers. Second, the coinage of "val" from the obscure mathematical term "valuation" is tenuous and unlikely to provide helpful insight: "p-adic valuation" is an obscure term for "prime count", which would be an element of a prime-count vector ("monzo"), not a map ("val").

	~~[[Category:Disambiguation pages]]~~
	[[Category:Regular temperament theory]]		[[Category:Regular temperament theory]]
	[[Category:Terms]]		[[Category:Terms]]
Line 13:		Line 12:
	[[Category:Val]]		[[Category:Val]]
	[[Category:Mapping]]		[[Category:Mapping]]

			{{Disambiguation}}

Cmloegcmluin: correction

2021-12-29T15:45:16Z

correction

← Older revision		Revision as of 15:45, 29 December 2021
Line 5:		Line 5:
	* 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]].		* 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 all occurrences at present on this wiki, as well as in Graham Breed's temperament finder~~, and also the Yahoo Groups tuning list archives~~, the term "map" (and not "mapping") consistently refers to a single-row mapping, so following this suggestion would be seamless moving forward. A "tuning map", which maps from generators to cents, is a map in "tuning space"; by analogy, a val is a map in "temperament space", and so it would be perfectly consistent with existing terminology to refer to a val as a "temperament map" as opposed to a "temperament mapping", and then when it is clear from the context that it is a ''temperament'' map, the qualifier "temperament" can be dropped, as is done with "temperament mapping matrix" being abbreviated to "mapping matrix". So the suggestion is equivalent to unqualified occurrences of "map" being assumed to be temperament maps, or in other words, synonymous with vals (except for the integer entry requirement), not tuning maps. Dave and Douglas recommend using "map" rather than "val", for two reasons. First, "map" is a basic linear algebra term with wide familiarity (being specialized for this purpose) while "val" is unnecessary jargon that creates a barrier to understanding by newcomers. Second, the coinage of "val" from the obscure mathematical term "valuation" is tenuous and unlikely to provide helpful insight: "p-adic valuation" is an obscure term for "prime count", which would be an element of a prime-count vector ("monzo"), not a map ("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 all occurrences at present on this wiki, as well as in Graham Breed's temperament finder, the term "map" (and not "mapping") consistently refers to a single-row mapping, so following this suggestion would be seamless moving forward. A "tuning map", which maps from generators to cents, is a map in "tuning space"; by analogy, a val is a map in "temperament space", and so it would be perfectly consistent with existing terminology to refer to a val as a "temperament map" as opposed to a "temperament mapping", and then when it is clear from the context that it is a ''temperament'' map, the qualifier "temperament" can be dropped, as is done with "temperament mapping matrix" being abbreviated to "mapping matrix". So the suggestion is equivalent to unqualified occurrences of "map" being assumed to be temperament maps, or in other words, synonymous with vals (except for the integer entry requirement), not tuning maps. Dave and Douglas recommend using "map" rather than "val", for two reasons. First, "map" is a basic linear algebra term with wide familiarity (being specialized for this purpose) while "val" is unnecessary jargon that creates a barrier to understanding by newcomers. Second, the coinage of "val" from the obscure mathematical term "valuation" is tenuous and unlikely to provide helpful insight: "p-adic valuation" is an obscure term for "prime count", which would be an element of a prime-count vector ("monzo"), not a map ("val").

	[[Category:Disambiguation pages]]		[[Category:Disambiguation pages]]

Cmloegcmluin: Sintel and I were chatting on Discord recently about this page, when he asked why Dave and I would recommend reserving "map" for one row of a mapping when the term "val" is already available for this purpose. This comment caused me to realize that an important element was missing from this page: our motivation for making this suggestion, namely, that we disapprove of the term "val". Without such a statement of purpose, I realized this recommendation came across as unjustified. So I've explained.

2021-12-24T17:10:59Z

Sintel and I were chatting on Discord recently about this page, when he asked why Dave and I would recommend reserving "map" for one row of a mapping when the term "val" is already available for this purpose. This comment caused me to realize that an important element was missing from this page: our motivation for making this suggestion, namely, that we disapprove of the term "val". Without such a statement of purpose, I realized this recommendation came across as unjustified. So I've explained.

← Older revision		Revision as of 17:10, 24 December 2021
Line 5:		Line 5:
	* 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]].		* 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.		* [[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 all occurrences at present on this wiki, as well as in Graham Breed's temperament finder, and also the Yahoo Groups tuning list archives, the term "map" (and not "mapping") consistently refers to a single-row mapping, so following this suggestion would be seamless moving forward. A "tuning map", which maps from generators to cents, is a map in "tuning space"; by analogy, a val is a map in "temperament space", and so it would be perfectly consistent with existing terminology to refer to a val as a "temperament map" as opposed to a "temperament mapping", and then when it is clear from the context that it is a ''temperament'' map, the qualifier "temperament" can be dropped, as is done with "temperament mapping matrix" being abbreviated to "mapping matrix". So the suggestion is equivalent to unqualified occurrences of "map" being assumed to be temperament maps, or in other words, synonymous with vals (except for the integer entry requirement), not tuning maps. Dave and Douglas recommend using "map" rather than "val", for two reasons. First, "map" is a basic linear algebra term with wide familiarity (being specialized for this purpose) while "val" is unnecessary jargon that creates a barrier to understanding by newcomers. Second, the coinage of "val" from the obscure mathematical term "valuation" is tenuous and unlikely to provide helpful insight: "p-adic valuation" is an obscure term for "prime count", which would be an element of a prime-count vector ("monzo"), not a map ("val").

	[[Category:Disambiguation pages]]		[[Category:Disambiguation pages]]

FloraC: Simplify categories

2021-12-21T13:13:16Z

Simplify categories

← Older revision		Revision as of 13:13, 21 December 2021
Line 1:		Line 1:
	The word '''map''' could refer to:		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)\|~~Wikipedia:Map (mathematics)]].		* 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 [[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]].		* 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]].
Line 7:		Line 7:
	* [[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.		* [[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.

			[[Category:Disambiguation pages]]
	[[Category:~~Temperament~~]]
	[[Category:Regular temperament theory]]		[[Category:Regular temperament theory]]
	~~[[Category:Theory]]~~
	[[Category:Terms]]		[[Category:Terms]]
	[[Category:Math]]		[[Category:Math]]
	[[Category:Val]]		[[Category:Val]]
	[[Category:Mapping]]		[[Category:Mapping]]
	~~[[Category:Tuning]]~~

Mike Battaglia: Shorten some stufd

2021-12-21T04:52:58Z

Shorten some stufd

← Older revision		Revision as of 04:52, 21 December 2021
Line 3:		Line 3:
	* In general mathematics, a "map" is any function from one set to another. For more information, see [[Wikipedia:Map_(mathematics)\|Wikipedia:Map (mathematics)]].		* 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.		* [[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.

Mike Battaglia: Small edits

2021-12-21T04:34:37Z

Small edits

← Older revision		Revision as of 04:34, 21 December 2021
Line 3:		Line 3:
	* In general mathematics, a "map" is any function from one set to another. For more information, see [[Wikipedia:Map_(mathematics)\|Wikipedia:Map (mathematics)]].		* 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.		* [[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.

Cmloegcmluin: clean up, and restore some aspects from recent edits of mine that had been lost

2021-12-21T04:04:36Z

clean up, and restore some aspects from recent edits of mine that had been lost

← Older revision		Revision as of 04:04, 21 December 2021
Line 1:		Line 1:
	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]]