Human pitch-perception is periodic: pitches separated by an integral number of octaves are perceived as having a similar "quality" or "color." Psychologists refer to the quality of a pitch as its "chroma." Music theorists typically use the term "pitch class" rather than "chroma." Pitch may refer to: Pitch is the property of a sound or musical tone measured by its perceived frequency Pitch, or tone of voice, refers to variation of tone in tonal language, and in languages with melodic accent Pitch, a throw of a baseball by a pitcher Pitch, part of...

There is a subtle difference between the concepts "chroma" and "pitch class." A "chroma" is an attribute of pitches, just like whiteness is an attribute of white things. A "pitch class" is a set of all pitches sharing the same chroma, just like "the set of all white things" is the collection of all white objects. Music theory's use of the term "pitch class" rather than "chroma" reflects the influence of logical positivism on its founders, particularly Milton Babbitt. Logical positivism (later referred to as logical empiricism, rational empiricism, and also neo-positivism) is a philosophy that originated in the Vienna Circle in the 1920s. ... Milton Byron Babbitt (born May 10, 1916) is an American composer. ...

The pitch class "C" is an infinite set containing all pitches with the chroma C, no matter what octave they are in. Thus, using scientific pitch notation it is the infinite set This article needs to be cleaned up to conform to a higher standard of quality. ...

{..., C-2, C-1, C0, C1, C2, C3 ...}

Note that in standard Western equal-temperament, distinct spellings can refer to the same sounding object: B#3, C4, and Dbb4 all refer to the same pitch, hence share the same chroma, and therefore belong to the same pitch class.

To avoid the problem of enharmonic spellings, theorists typically represent pitch classes using numbers. One can map a pitch's fundamental frequency f to a real number p using the equation

p = 69 + log₂(f / 440)

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. 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 circular quotient space that musicians call pitch class space and mathematicians call R/12Z. Points in this space provide numerical alternatives to the letter names of traditional music theory: 0 = C, 1 = C#/Db, 2 = D, 2.5 = "D quarter-tone sharp" and so on. To avoid confusing 10 with 1 and 0, some theorists assign pitch classes 10 and 11 the letters t and e, respectively (or A and B, as in the writings of Allen Forte and Robert Morris). In music pitch space is the modeling of pitch relationships, represented through mathematical models, most often multidimensional, describing how near or far pitches are from each other. ... In topology and related areas of mathematics, a quotient space (also called an identification space) is, intuitively speaking, the result of identifying or gluing together certain points of a given space. ... In musical set theory, pitch class space is the circular space that results when we ignore the difference between octave-related pitches. ... Allen Forte (born December 23, 1926) is a music theorist and musicologist. ... Robert Morris is a very common name, and unsurprisingly there are many famous individuals named Robert Morris, including: Robert Morris (merchant), financier of the American Revolution and signatory of three important founding documents of the US Robert Morris, minimalist artist Robert H. Morris, American cryptographer and former chief scientist of...

Other ways to label pitch classes

The system described above is flexible enough to describe any pitch class in any tuning system: for example, one can use the numbers {0, 2.4, 4.8, 7.2, 9.6} to refer to the five-tone scale that divides the octave evenly. However, in some contexts, it is convenient to use alternative labeling systems. For example, in just intonation, we may express pitch classes in terms of positive rational numbers p/q, expressed by reference to a 1 (often written "1/1") which represents a fixed pitch class. If a and b are two positive rational numbers, they belong to the same pitch class if and only if In music, Just intonation, also called rational intonation, is any musical tuning in which the frequencies of notes are related by whole number ratios; that is, by positive rational numbers. ...

a / b = 2ⁿ

for some integer n.

See also

• interval class
• pitch class space

In music, specifically, musical set theory an interval class, or unordered pitch-class interval, is an interval measured by the distance between its two pitch classes ordered so they are as close as possible. ... In musical set theory, pitch class space is the circular space that results when we ignore the difference between octave-related pitches. ...

References

• Rahn, John (1980). Basic Atonal Theory. ISBN 0028731603.