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In music, a pitch class (p.c. or pc) is a set of all pitches that are a whole number of octaves apart, e.g., the pitch class C consists of the Cs in all octaves. "The pitch class C stands for all possible Cs, in whatever octave position."〔Arnold Whittall, ''The Cambridge Introduction to Serialism'' (New York: Cambridge University Press, 2008): 276. ISBN 978-0-521-68200-8 (pbk).〕 Important to musical set theory, a pitch class is, "all pitches related to each other by octave, enharmonic equivalence, or both."〔Don Michael Randel, ed. (2003). "Set theory", ''The Harvard Dictionary of Music'', p.776. Harvard. ISBN 9780674011632.〕 Thus, using scientific pitch notation, the pitch class "C" is the set : = ; although there is no formal upper or lower limit to this sequence, only a limited number of these pitches are audible to the human ear. 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".〔Tymoczko, Dmitri (2011). ''A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice'', p.30. Oxford Studies in Music Theory. ISBN 9780199714353.〕 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.〔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."〕 Note that in standard Western equal temperament, distinct spellings can refer to the same sounding object: B3, C4, and D4 all refer to the same pitch, hence share the same chroma, and therefore belong to the same pitch class; a phenomenon called enharmonic equivalence. ==Integer notation== To avoid the problem of enharmonic spellings, theorists typically represent pitch classes using numbers beginning from zero, with each successively larger integer representing a pitch class that would be one semitone higher than the preceding one, if they were all realised as actual pitches in the same octave. Because octave-related pitches belong to the same class, when an octave is reached, the numbers begin again at zero. This cyclical system is referred to as modular arithmetic and, in the usual case of chromatic twelve-tone scales, pitch-class numbering is regarded as "modulo 12" (customarily abbreviated "mod 12" in the music-theory literature)—that is, every twelfth member is identical. One can map a pitch's fundamental frequency (measured in hertz) to a real number using the equation: : This creates a linear pitch space in which octaves have size 12, semitones (the distance between adjacent keys on the piano keyboard) have size 1, and middle C is assigned the number 60. Indeed, the mapping from pitch to real numbers defined in this manner forms the basis of the MIDI Tuning Standard, which uses the real numbers from 0 to 127 to represent the pitches C-2 to G8. To represent pitch ''classes'', we need to identify or "glue together" all pitches belonging to the same pitch class—i.e. all numbers ''p'' and ''p'' + 12. The result is a cyclical quotient group that musicians call pitch class space and mathematicians call R/12Z. Points in this space can be labelled using real numbers in the range 0 ≤ ''x'' < 12. These numbers provide numerical alternatives to the letter names of elementary music theory: :0 = C, 1 = C/D, 2 = D, 2.5 = "D quarter tone sharp", 3 = D/E, and so on. In this system, pitch classes represented by integers are classes of twelve-tone equal temperament (assuming standard concert A). In music, integer notation is the translation of pitch classes and/or interval classes into whole numbers.〔Whittall (2008), p.273.〕 Thus if C = 0, then C = 1 ... A = 10, B = 11, with "10" and "11" substituted by "t" and "e" in some sources,〔 ''A'' and ''B'' in others.〔Robert D. Morris, "Generalizing Rotational Arrays", ''Journal of Music Theory'' 32, no. 1 (Spring 1988): 75–132, citation on 83.〕 This allows the most economical presentation of information regarding post-tonal materials.〔 In the integer model of pitch, all pitch classes and intervals between pitch classes are designated using the numbers 0 through 11. It is not used to notate music for performance, but is a common analytical and compositional tool when working with chromatic music, including twelve tone, serial, or otherwise atonal music. Pitch classes can be notated in this way by assigning the number 0 to some note and assigning consecutive integers to consecutive semitones; so if 0 is C natural, 1 is C, 2 is D and so on up to 11, which is B. The C above this is not 12, but 0 again (12 − 12 = 0). Thus arithmetic modulo 12 is used to represent octave equivalence. One advantage of this system is that it ignores the "spelling" of notes (B, C and D are all 0) according to their diatonic functionality. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「pitch class」の詳細全文を読む スポンサード リンク
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