Tuning map: Difference between revisions

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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.

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 ==

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A '''generator tuning map''' is like a (temperament) tuning map, but each entry gives the size in cents or octaves of a different [[generator]], rather than of a formal prime.

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

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.

From the generator tuning map <math>𝒈</math> and the mapping <math>M</math>, we can obtain the tuning map <math>𝒕</math> as <math>𝒈.M</math>.

@@ Line 3: / Line 3: @@
 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.
+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 ==
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 A '''generator tuning map''' is like a (temperament) tuning map, but each entry gives the size in cents or octaves of a different [[generator]], rather than of a formal prime.
-It may be helpful, then, to think of the units of each entry of a generator tuning map as c/g (read "cents per generator"), oct/g (read "octaves per generator"), or any other logarithmic pitch unit per generator.
+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.
 From the generator tuning map <math>𝒈</math> and the mapping <math>M</math>, we can obtain the tuning map <math>𝒕</math> as <math>𝒈.M</math>.