Val: Difference between revisions

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== Vals in regular temperaments ==

We write a tempered interval (an interval in a [[regular temperament]]) as a (generalized) monzo by taking a set of [[generator]]s (for rank-2 temperaments, this will be the period and the generator), then writing what JI ratio each generator approximates (distinguished from pure JI ~~intervals~~ by putting a tilde before it), followed by the number of that specified generator that the interval has. For example, the major third in [[meantone]] temperament can be written as {{monzo|~2: ‐2, ~3/2: 4}}, meaning "4 perfect fifths minus 2 octaves".

We write a tempered interval (an interval in a [[regular temperament]]) as a (generalized) monzo by taking a set of [[generator]]s (for rank-2 temperaments, this will be the period and the generator), then writing what JI ratio each generator approximates (distinguished from pure-JI subgroups by putting a tilde before it), followed by the number of that specified generator that the interval has. For example, the major third in [[meantone]] temperament can be written as {{monzo|~2: ‐2, ~3/2: 4}}, meaning "4 perfect fifths minus 2 octaves".

Similarly, edo tunings of a temperament can be given in terms of (a generalized version of) vals, by specifying how many edo steps are used for each generator of the temperament. For example, [[31edo]]'s tuning of meantone temperament can be written as {{val|~2: 31, ~3/2: 18}}.

== See also ==

* [[Mapping]]

@@ Line 56: / Line 56: @@
 == Vals in regular temperaments ==
-We write a tempered interval (an interval in a [[regular temperament]]) as a (generalized) monzo by taking a set of [[generator]]s (for rank-2 temperaments, this will be the period and the generator), then writing what JI ratio each generator approximates (distinguished from pure JI intervals by putting a tilde before it), followed by the number of that specified generator that the interval has. For example, the major third in [[meantone]] temperament can be written as {{monzo|~2: ‐2, ~3/2: 4}}, meaning "4 perfect fifths minus 2 octaves".
+We write a tempered interval (an interval in a [[regular temperament]]) as a (generalized) monzo by taking a set of [[generator]]s (for rank-2 temperaments, this will be the period and the generator), then writing what JI ratio each generator approximates (distinguished from pure-JI subgroups by putting a tilde before it), followed by the number of that specified generator that the interval has. For example, the major third in [[meantone]] temperament can be written as {{monzo|~2: ‐2, ~3/2: 4}}, meaning "4 perfect fifths minus 2 octaves".
 Similarly, edo tunings of a temperament can be given in terms of (a generalized version of) vals, by specifying how many edo steps are used for each generator of the temperament. For example, [[31edo]]'s tuning of meantone temperament can be written as {{val|~2: 31, ~3/2: 18}}.
 == See also ==
 * [[Mapping]]