In
music theory
Music theory is the study of the practices and possibilities of music. ''The Oxford Companion to Music'' describes three interrelated uses of the term "music theory". The first is the "rudiments", that are needed to understand music notation (ke ...
, pitch-class space is the circular
space
Space is the boundless three-dimensional extent in which objects and events have relative position and direction. In classical physics, physical space is often conceived in three linear dimensions, although modern physicists usually consider ...
representing all the
note
Note, notes, or NOTE may refer to:
Music and entertainment
* Musical note, a pitched sound (or a symbol for a sound) in music
* ''Notes'' (album), a 1987 album by Paul Bley and Paul Motian
* ''Notes'', a common (yet unofficial) shortened version ...
s (
pitch class
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 positio ...
es) in a musical
octave
In music, an octave ( la, octavus: eighth) or perfect octave (sometimes called the diapason) is the interval between one musical pitch and another with double its frequency. The octave relationship is a natural phenomenon that has been refer ...
.
In this space, there is no distinction between tones that are 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.
Since pitch-class space is a circle, we return to our starting point by taking a series of steps in the same direction: beginning with C, we can move "upward" in pitch-class space, through the pitch classes C♯, D, D♯, E, F, F♯, G, G♯, A, A♯, and B, returning finally to C. By contrast,
pitch space
In music theory, pitch spaces model relationships between pitches. These models typically use distance to model the degree of relatedness, with closely related pitches placed near one another, and less closely related pitches placed farther apa ...
is a linear space: the more steps we take in a single direction, the further we get from our starting point.
Tonal pitch-class space
, and
Lerdahl and Jackendoff (1983) use a "reductional format" to represent the perception of pitch-class relations in tonal contexts. These two-dimensional models resemble bar graphs, using height to represent a pitch class's degree of importance or centricity. Lerdahl's version uses five levels: the first (highest) contains only the
tonic, the second contains tonic and
dominant, the third contains tonic,
mediant In music, the mediant (''Latin'': to be in the middle) is the third scale degree () of a diatonic scale, being the note halfway between the tonic and the dominant.Benward & Saker (2003), p.32. In the movable do solfège system, the mediant note i ...
, and dominant, the fourth contains all the notes of the
diatonic scale
In music theory, a diatonic scale is any heptatonic scale that includes five whole steps (whole tones) and two half steps (semitones) in each octave, in which the two half steps are separated from each other by either two or three whole steps, ...
, and the fifth contains the
chromatic scale
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. Chromatic instruments, such as the piano, are made to produce the ...
. In addition to representing centricity or importance, the individual levels are also supposed to represent "alphabets" that describe the melodic possibilities in tonal music . The model asserts that tonal melodies will be cognized in terms of one of the five levels ''a''-''e'':
::
Note that Lerdahl's model is meant to be cyclical, with its right edge identical to its left. One could therefore display Lerdahl's graph as a series of five concentric circles representing the five melodic "alphabets." In this way one could unite the circular representation depicted at the beginning of this article with Lerdahl's flat two-dimensional representation depicted above.
According to David , "Harmonic space, or tonal space as defined by Fred Lerdahl, is the abstract nexus of possible normative harmonic connections in a system, as opposed to the actual series of temporal connections in a realized work, linear or otherwise."
See also
*
Pitch circularity
Pitch circularity is a fixed series of tones that are perceived to ascend or descend endlessly in pitch. It's an example of an auditory illusion. Explanation
Pitch is often defined as extending along a one-dimensional continuum from high to l ...
*
Pitch interval
In musical set theory, a pitch interval (PI or ip) is the number of semitones that separates one pitch from another, upward or downward.Schuijer, Michiel (2008). ''Analyzing Atonal Music: Pitch-Class Set Theory and Its Contexts'', Eastman Studie ...
*
Scientific pitch notation
Scientific pitch notation (SPN), also known as American standard pitch notation (ASPN) and international pitch notation (IPN), is a method of specifying musical pitch by combining a musical note name (with accidental if needed) and a number ide ...
*
Pitch constellation
The chromatic circle is a clock diagram for displaying relationships among the 12 equal-tempered pitch classes making up the familiar chromatic scale on a circle.
Explanation
If one starts on any equal-tempered pitch and repeatedly ascends by th ...
Sources
Full Text*
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Further reading
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{{DEFAULTSORT:Pitch Class Space
Musical set theory
Pitch space