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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 music theorists 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 ...
In atonal, twelve tone, or musical set theory, a "pitch" is a specific frequency while a pitch class is all the octaves of a frequency. In many analytic discussions of atonal and post-tonal music, pitches are named with integers because of octave and enharmonic equivalency (for example, in a serial system, C ♯ and D ♭ are considered the ...
The fundamental concept of musical set theory is the (musical) set, which is an unordered collection of pitch classes. [4] More exactly, a pitch-class set is a numerical representation consisting of distinct integers (i.e., without duplicates). [5]
A set (pitch set, pitch-class set, set class, set form, set genus, pitch collection) in music theory, as in mathematics and general parlance, is a collection of objects. In musical contexts the term is traditionally applied most often to collections of pitches or pitch-classes , but theorists have extended its use to other types of musical ...
One branch of musical set theory deals with collections (sets and permutations) of pitches and pitch classes (pitch-class set theory), which may be ordered or unordered, and can be related by musical operations such as transposition, inversion, and complementation. The methods of musical set theory are sometimes applied to the analysis of ...
A pitch class is defined as the set of all pitches that share the same chroma. For example, using the scientific pitch notation, the pitch class corresponding to the chroma C is the set {..., C −2, C −1, C 0, C 1, C 2, C 3...} consisting of all pitches separated by an integer number of octaves.
Chromatic scale: every key of one octave on the piano keyboard. The chromatic scale (or twelve-tone scale) is a set of twelve pitches (more completely, pitch classes) used in tonal music, with notes separated by the interval of a semitone.
In music theory, pitch-class space is the circular space representing all the notes (pitch classes) in a musical octave. In this space, there is no distinction between tones separated by an integral number of octaves. For example, C4, C5, and C6, though different pitches, are represented by the same point in pitch class space.