Tuning map: Difference between revisions

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A '''tuning map''' represents the tuning of a [[regular temperament]]. It ~~is similar to a standard val, but it~~ specifies the tuning of a temperament in terms of logarithmic [[interval size unit]]s (such as [[cent]]s or [[octave]]s) rather than scale steps. It can take a vector representation of an interval ([[monzo]]) as input and outputs its tempered size.

A '''tuning map''' represents the tuning of a [[regular temperament]]. It specifies the tuning of a temperament in terms of logarithmic [[interval size unit]]s (such as [[cent]]s or [[octave]]s) rather than scale steps. It can take a vector representation of an interval ([[monzo]]) as input and outputs its tempered size.

A ~~standard~~ tuning map ~~(also called a subgroup tuning map)~~ has one entry for each [[basis element]] of the temperament's JI subgroup (e.g. 2, 9, 5 in a 2.9.5-subgroup temperament), giving its size in cents, octaves, or any other logarithmic interval size unit.

A tuning map has one entry for each [[basis element]] of the temperament's JI subgroup (e.g. 2, 9, 5 in a 2.9.5-subgroup temperament), giving its size in cents, octaves, or any other logarithmic interval size unit.

It may be helpful, then, to think of the units of each entry of a tuning map as <math>{\large\mathsf{¢}}\small /𝗽</math> (read "cents per prime"), <math>\small \mathsf{oct}/𝗽</math> (read "octaves per prime"), or any other logarithmic pitch unit per prime (for more information, see [[Dave Keenan & Douglas Blumeyer's guide to RTT/Units analysis]]).

== Generator tuning map ==

A '''generator tuning map''' is similar to a ~~(subgroup)~~ tuning map, but it specifies a tuning for a temperament by giving the sizes of its generators. Each entry of the generator tuning map gives the size of a different [[generator]]. It takes a vector in tempered interval space (a "[[tmonzos and tvals|tmonzo]]").

A '''generator tuning map''' is similar to a tuning map, but it specifies a tuning for a temperament by giving the sizes of its generators. Each entry of the generator tuning map gives the size of a different [[generator]]. It takes a vector in tempered interval space (a "[[tmonzos and tvals|tmonzo]]").

It may be helpful, then, to think of the units of each entry of a generator tuning map as <math>{\large\mathsf{¢}}\small /𝗴</math> (read "cents per generator"), <math>\small \mathsf{oct}/𝗴</math> (read "octaves per generator"), or any other logarithmic pitch unit per generator.

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-A '''tuning map''' represents the tuning of a [[regular temperament]]. It is similar to a standard val, but it specifies the tuning of a temperament in terms of logarithmic [[interval size unit]]s (such as [[cent]]s or [[octave]]s) rather than scale steps. It can take a vector representation of an interval ([[monzo]]) as input and outputs its tempered size.
+A '''tuning map''' represents the tuning of a [[regular temperament]]. It specifies the tuning of a temperament in terms of logarithmic [[interval size unit]]s (such as [[cent]]s or [[octave]]s) rather than scale steps. It can take a vector representation of an interval ([[monzo]]) as input and outputs its tempered size.
-A standard tuning map (also called a subgroup tuning map) has one entry for each [[basis element]] of the temperament's JI subgroup (e.g. 2, 9, 5 in a 2.9.5-subgroup temperament), giving its size in cents, octaves, or any other logarithmic interval size unit.
+A tuning map has one entry for each [[basis element]] of the temperament's JI subgroup (e.g. 2, 9, 5 in a 2.9.5-subgroup temperament), giving its size in cents, octaves, or any other logarithmic interval size unit.
 It may be helpful, then, to think of the units of each entry of a tuning map as <math>{\large\mathsf{¢}}\small /𝗽</math> (read "cents per prime"), <math>\small \mathsf{oct}/𝗽</math> (read "octaves per prime"), or any other logarithmic pitch unit per prime (for more information, see [[Dave Keenan & Douglas Blumeyer's guide to RTT/Units analysis]]).
 == Generator tuning map ==
-A '''generator tuning map''' is similar to a (subgroup) tuning map, but it specifies a tuning for a temperament by giving the sizes of its generators. Each entry of the generator tuning map gives the size of a different [[generator]]. It takes a vector in tempered interval space (a "[[tmonzos and tvals|tmonzo]]").
+A '''generator tuning map''' is similar to a tuning map, but it specifies a tuning for a temperament by giving the sizes of its generators. Each entry of the generator tuning map gives the size of a different [[generator]]. It takes a vector in tempered interval space (a "[[tmonzos and tvals|tmonzo]]").
 It may be helpful, then, to think of the units of each entry of a generator tuning map as <math>{\large\mathsf{¢}}\small /𝗴</math> (read "cents per generator"), <math>\small \mathsf{oct}/𝗴</math> (read "octaves per generator"), or any other logarithmic pitch unit per generator.