Tuning map: Difference between revisions

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A '''tuning map''' represents the tuning of a [[regular temperament]]. It can take a vector representation of an interval ([[monzo]]) as input and outputs its pitch, usually measured in cents or octaves.

A tuning map has one entry for each [[~~formal prime~~]] of the temperament, giving its size in cents or octaves (or any other logarithmic pitch unit).

A tuning map has one entry for each [[basis element]] of the temperament, giving its size in cents or octaves (or any other logarithmic pitch unit).

It may be helpful, then, to think of the units of each entry of a tuning map as c/p (read "cents per prime"), oct/p (read "octaves per prime"), or any other logarithmic pitch unit per prime.

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== With respect to the JIP ==

[[JI]] can be conceptualized as the temperament where nothing is [[tempered out]], and as such, the untempered primes can be thought of as its generators, or of course its ~~formal primes~~. So, JI subgroups have generators tuning maps and tuning maps too; the generators tuning maps and tuning maps are always the same thing as each other, and they are all subsets of the entries of the [[JIP]].

[[JI]] can be conceptualized as the temperament where nothing is [[tempered out]], and as such, the untempered primes can be thought of as its generators, or of course its basis elements. So, JI subgroups have generators tuning maps and tuning maps too; the generators tuning maps and tuning maps are always the same thing as each other, and they are all subsets of the entries of the [[JIP]].

== With respect to linear algebra ==

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 A '''tuning map''' represents the tuning of a [[regular temperament]]. It can take a vector representation of an interval ([[monzo]]) as input and outputs its pitch, usually measured in cents or octaves.
-A tuning map has one entry for each [[formal prime]] of the temperament, giving its size in cents or octaves (or any other logarithmic pitch unit).
+A tuning map has one entry for each [[basis element]] of the temperament, giving its size in cents or octaves (or any other logarithmic pitch unit).
 It may be helpful, then, to think of the units of each entry of a tuning map as c/p (read "cents per prime"), oct/p (read "octaves per prime"), or any other logarithmic pitch unit per prime.
@@ Line 26: / Line 26: @@
 == With respect to the JIP ==
-[[JI]] can be conceptualized as the temperament where nothing is [[tempered out]], and as such, the untempered primes can be thought of as its generators, or of course its formal primes. So, JI subgroups have generators tuning maps and tuning maps too; the generators tuning maps and tuning maps are always the same thing as each other, and they are all subsets of the entries of the [[JIP]].
+[[JI]] can be conceptualized as the temperament where nothing is [[tempered out]], and as such, the untempered primes can be thought of as its generators, or of course its basis elements. So, JI subgroups have generators tuning maps and tuning maps too; the generators tuning maps and tuning maps are always the same thing as each other, and they are all subsets of the entries of the [[JIP]].
 == With respect to linear algebra ==