Pitch class

${ \override Score.TimeSignature #'stencil = ##f \relative c' { \clef treble \key c \major \time 4/4 <c c'>1 } }$

Perfect octave

${ \override Score.TimeSignature #'stencil = ##f \new PianoStaff << \new Staff \relative c' { \clef treble \key c \major \time 4/4 <c' c' c'>1 \bar "|." } \new Staff \relative c' { \clef bass \key c \major \time 4/4 <c c, c, c,>1 } >> }$

All Cs from C₁ to C₇ inclusive

In music, a pitch class (p.c. or pc) is a set of all pitches that are a whole number of octaves 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."^[1] Important to musical set theory, a pitch class is "all pitches related to each other by octave, enharmonic equivalence, or both."^[2] Thus, using scientific pitch notation, the pitch class "C" is the set

{C_n : n is an integer} = {..., C₋₂, C₋₁, C₀, C₁, C₂, C₃ ...}.

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-perception is 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".^[3] 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.^[4]

In standard Western equal temperament, distinct spellings can refer to the same sounding object: B♯₃, C₄, and D₄ all refer to the same pitch, hence share the same chroma, and therefore belong to the same pitch class. This phenomenon is called enharmonic equivalence.

^ Arnold Whittall, The Cambridge Introduction to Serialism (New York: Cambridge University Press, 2008): 276. ISBN 978-0-521-68200-8 (pbk).
^ Don Michael Randel, ed. (2003). "Set theory", The Harvard Dictionary of Music, p.776. Harvard. ISBN 9780674011632.
^ Tymoczko, Dmitri (2011). A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice, p.30. Oxford Studies in Music Theory. ISBN 9780199714353.
^ 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."

[1] Arnold Whittall, The Cambridge Introduction to Serialism (New York: Cambridge University Press, 2008): 276. ISBN 978-0-521-68200-8 (pbk).

[2] Don Michael Randel, ed. (2003). "Set theory", The Harvard Dictionary of Music, p.776. Harvard. ISBN 9780674011632.

[3] Tymoczko, Dmitri (2011). A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice, p.30. Oxford Studies in Music Theory. ISBN 9780199714353.

[4] 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."

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Pitch class

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