Monzo: Difference between revisions

Line 83:

== Monzos in regular temperaments ==

Proposed notation: 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".

Proposed notation: 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 it in quotes), 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}}.

@@ Line 83: / Line 83: @@
 == Monzos in regular temperaments ==
-Proposed notation: 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".
+Proposed notation: 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 it in quotes), 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}}.