Interval class: Difference between revisions

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''Interval class'' is used in ~~two different~~ ways~~. One~~, common in academic "set theory", defines it as the distance between two pitch classes, measured by the shortest distance. Thus C to G may be the interval of 7, but its interval class is 5. The largest interval class or "ic"--in [[~~12edo|~~12edo]]--is the tritone (6). This may be criticized on ~~two~~ grounds: it'~~s not~~ a class in the ~~vocabulary~~ of ~~mathematics~~, ~~and it'~~s ~~less useful than the second definition~~.

'''Interval class''' is used in the following ways:

# First, common in academic [[Wikipedia: Set theory (music)|set theory]], defines it as the [[Octave #Octave equivalence|octave-equivalent]] distance between two pitch classes, measured by the shortest distance. Thus C to G may be the interval of 7, but its interval class is 5. The largest interval class or "ic" – in [[12edo]] – is the tritone (6). This may be criticized on the grounds that it is less useful and less generalizable than the second definition.

# The second definition, used for example by [[Scala]], defines the ''interval class'', or the '''''generic interval''''', as the set of all specific intervals ([[interval qualities]]) at a certain number of scale steps apart. More formally, an interval class is the set of all intervals that occur in the scale as ''k''-step intervals, or ''k''-steps, for a specific fixed integer ''k''. For example, the interval class of 2-steps in the diatonic scale ([[5L 2s]]) is the set {2L, L + s} = {major third, minor third}.

~~The second definition, used for example by Scala, defines the interval~~ class ~~as the "generic interval" to which the specific intervals at a certain number of scale steps i apart belong. ''see also~~ [[~~Interval_size_measure|interval~~ size measure]], [[~~interval_measure|interval measure~~]]''

== See also ==

* [[Pitch class]]

* [[Interval size measure]]

* [[Interval region]]

* [[Functional systems]]

~~==Links==~~

[[Category:Interval]]

~~<ul><li>~~[~~http://solomonsmusic.net/setheory.htm#Basic%20Definition http://solomonsmusic.net/setheory.htm#Basic%20Definition]</li><li>~~[~~http~~:~~//en.wikipedia.org/wiki/Interval_class~~ Interval ~~class]</li></ul> [[Category:interval]]~~

~~[[Category:measure]]~~

~~[[Category:theory~~]]

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-''Interval class'' is used in two different ways. One, common in academic "set theory", defines it as the distance between two pitch classes, measured by the shortest distance. Thus C to G may be the interval of 7, but its interval class is 5. The largest interval class or "ic"--in [[12edo|12edo]]--is the tritone (6). This may be criticized on two grounds: it's not a class in the vocabulary of mathematics, and it's less useful than the second definition.
+{{Wikipedia|Interval class|Generic and specific intervals}}
+'''Interval class''' is used in the following ways:
+# First, common in academic [[Wikipedia: Set theory (music)|set theory]], defines it as the [[Octave #Octave equivalence|octave-equivalent]] distance between two pitch classes, measured by the shortest distance. Thus C to G may be the interval of 7, but its interval class is 5. The largest interval class or "ic" – in [[12edo]] – is the tritone (6). This may be criticized on the grounds that it is less useful and less generalizable than the second definition.
+# The second definition, used for example by [[Scala]], defines the ''interval class'', or the '''''generic interval''''', as the set of all specific intervals ([[interval qualities]]) at a certain number of scale steps apart. More formally, an interval class is the set of all intervals that occur in the scale as ''k''-step intervals, or ''k''-steps, for a specific fixed integer ''k''. For example, the interval class of 2-steps in the diatonic scale ([[5L 2s]]) is the set {2L, L + s} = {major third, minor third}.
-The second definition, used for example by Scala, defines the interval class as the "generic interval" to which the specific intervals at a certain number of scale steps i apart belong. ''see also [[Interval_size_measure|interval size measure]], [[interval_measure|interval measure]]''
+== See also ==
+* [[Pitch class]]
+* [[Interval size measure]]
+* [[Interval region]]
+* [[Functional systems]]
-==Links==
+[[Category:Interval]]
-<ul><li>[http://solomonsmusic.net/setheory.htm#Basic%20Definition http://solomonsmusic.net/setheory.htm#Basic%20Definition]</li><li>[http://en.wikipedia.org/wiki/Interval_class Interval class]</li></ul>      [[Category:interval]]
-[[Category:measure]]
-[[Category:theory]]