# Interval class

In

musical set theory , an**interval class**(usual abbreviation:**ic**) is the shortest distance inpitch class space between two unorderedpitch class es. For example, the interval class between pitch classes 4 and 9 is 5 because 9 - 4 = 5 is less than 4 - 9 = -5 ≡ 7(mod 12). Seemodular arithmetic for more onmodulo 12.The largest interval class is 6 since any greater interval n may be reduced to 12 minus n.**Use of interval classes**The concept of interval class was created to account for

octave ,enharmonic , andinversional equivalency . Consider, for instance, the following passage:(To hear a MIDI realization, click the following: Audio|Octatonic_ic7.ogg|106 KB

In the example above, all four labeled pitch-pairs, or

dyad s, share a common "intervallic color." Inatonal theory, this similarity is denoted by interval class -- ic 5, in this case.Tonal theory, however, classifies the four intervals differently: interval 1 as perfect fifth; 2, perfect twelfth; 3, diminished sixth; and 4, perfect fourth. Thus we see that in adodecaphonic (i.e.,chromatic ) context, terminology tailored for the analysis ofheptatonic (i.e.,diatonic ) music is often no longer suitable.Incidentally, the example's pitch collection forms an

octatonic set.**Notation of interval classes**The

**unordered pitch class interval**"i" ("a","b") may be defined as::$i\; (a,b)\; =$ the smaller of $i,b>$ and $i,a>$, where "i" <"a","b"> is an ordered pitch class interval.While notating unordered intervals with parentheses, as in the example directly above, is perhaps the standard, some theorists, including Robert Morris (1991), prefer to use braces, as in "i" {"a","b}". Both notations are considered acceptable.

**Table of interval class equivalencies****ources***Morris, Robert (1991). "Class Notes for Atonal Music Theory". ASIN B0006DHW9I.

*Rahn, John (1980). "Basic Atonal Theory". ISBN 0-02-873160-3. For forumala definitions only.**Further reading***Friedmann, Michael (1990). "Ear Training for Twentieth Century Music". ISBN 0-300-04537-9.

**External links*** [

*http://solomonsmusic.net/setheory.htm#Basic%20Definition Solomon's Set Theory Primer*]

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### Look at other dictionaries:

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