Editing Pitch class (section)

{{Short description|Set of all pitches that are a whole number of octaves apart}}

{{Image frame|content=<score sound="1">  {
\override Score.TimeSignature #'stencil = ##f
\relative c' {
  \clef treble \key c \major \time 4/4
  <c c'>1
} }
</score>|width=300|caption=Perfect octave}}

{{Image frame|content=<score sound="1">  {
\override Score.TimeSignature #'stencil = ##f
\new PianoStaff <<
\new Staff \relative c' {
  \clef treble \key c \major \time 4/4
  <c' c' c'>1 \bar "|."
}

\new Staff \relative c' {
  \clef bass \key c \major \time 4/4
  <c c, c, c,>1
} >> }
</score>|width=300|caption=All Cs from C<sub>1</sub> to C<sub>7</sub> inclusive}}

In [[music]], a '''pitch class''' ('''p.c.''' or '''pc''') is a [[set (music)|set]] of all [[Pitch (music)|pitches]] that are a whole number of [[octave]]s apart; for example, the pitch class C consists of the Cs in all octaves. "The pitch class C stands for all possible Cs, in whatever octave position."<ref>[[Arnold Whittall]], ''The Cambridge Introduction to Serialism'' (New York: Cambridge University Press, 2008): 276. {{ISBN|978-0-521-68200-8}} (pbk).</ref> Important to [[musical set theory]], a pitch class is "all pitches related to each other by octave, [[Enharmonic|enharmonic equivalence]], or both."<ref>Don Michael Randel, ed. (2003). "Set theory", ''The Harvard Dictionary of Music'', p.776. Harvard. {{ISBN|9780674011632}}.</ref> Thus, using [[scientific pitch notation]], the pitch class "C" is the set

:{C<sub>''n''</sub> : ''n'' is an [[integer]]} = {..., C<sub>−2</sub>, C<sub>−1</sub>, C<sub>0</sub>, C<sub>1</sub>, C<sub>2</sub>, C<sub>3</sub>, ...}.

Although there is no formal upper or lower limit to this sequence, only a few of these pitches are audible to humans. 
Pitch class is important because human [[Pitch (psychophysics)|pitch-perception]] is [[Periodic function|periodic]]: pitches belonging to the same pitch class are perceived as having a similar quality or color, a property called "[[octave equivalence]]".

Psychologists refer to the quality of a pitch as its "chroma".<ref>[[Dmitri Tymoczko|Tymoczko, Dmitri]] (2011). ''A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice'', p.30. Oxford Studies in Music Theory. {{ISBN|9780199714353}}.</ref> A ''chroma'' is an attribute of pitches (as opposed to ''tone height''), just like [[hue]] is an attribute of [[color]]. A ''pitch class'' is a set of all pitches that share the same chroma, just like "the set of all white things" is the collection of all white objects.<ref>Müller, Meinard (2007). ''Information Retrieval for Music and Motion'', p.60. {{ISBN|9783540740483}}. "A pitch class is defined to be the set of all pitches that share the same chroma."</ref>

In standard Western [[equal temperament]], distinct spellings can refer to the same sounding object: B{{music|sharp}}<sub>3</sub>, C<sub>4</sub>, and D{{music|bb}}<sub>4</sub> all refer to the same pitch, hence share the same chroma, and therefore belong to the same pitch class. This phenomenon is called [[Enharmonic|enharmonic equivalence]].