In
music
Music is generally defined as the art of arranging sound to create some combination of form, harmony, melody, rhythm or otherwise expressive content. Exact definitions of music vary considerably around the world, though it is an aspect ...
, a transformation consists of any operation or process that may apply to a musical variable (usually a
set
Set, The Set, SET or SETS may refer to:
Science, technology, and mathematics Mathematics
*Set (mathematics), a collection of elements
*Category of sets, the category whose objects and morphisms are sets and total functions, respectively
Electro ...
or
tone row
In music, a tone row or note row (german: Reihe or '), also series or set, is a non-repetitive ordering of a set of pitch-classes, typically of the twelve notes in musical set theory of the chromatic scale, though both larger and smaller sets ar ...
in
twelve tone music, or a
melody
A melody (from Greek language, Greek μελῳδία, ''melōidía'', "singing, chanting"), also tune, voice or line, is a Linearity#Music, linear succession of musical tones that the listener perceives as a single entity. In its most liter ...
or
chord progression
In a musical composition, a chord progression or harmonic progression (informally chord changes, used as a plural) is a succession of chords. Chord progressions are the foundation of harmony in Western musical tradition from the common practice ...
in
tonal music
Tonality is the arrangement of pitches and/or chords of a musical work in a hierarchy of perceived relations, stabilities, attractions and directionality. In this hierarchy, the single pitch or triadic chord with the greatest stability is cal ...
), or
rhythm
Rhythm (from Greek , ''rhythmos'', "any regular recurring motion, symmetry") generally means a " movement marked by the regulated succession of strong and weak elements, or of opposite or different conditions". This general meaning of regular recu ...
in
composition
Composition or Compositions may refer to:
Arts and literature
*Composition (dance), practice and teaching of choreography
*Composition (language), in literature and rhetoric, producing a work in spoken tradition and written discourse, to include v ...
,
performance
A performance is an act of staging or presenting a play, concert, or other form of entertainment. It is also defined as the action or process of carrying out or accomplishing an action, task, or function.
Management science
In the work place ...
, or
analysis
Analysis ( : analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (38 ...
. Transformations include
multiplication
Multiplication (often denoted by the cross symbol , by the mid-line dot operator , by juxtaposition, or, on computers, by an asterisk ) is one of the four elementary mathematical operations of arithmetic, with the other ones being additi ...
,
rotation
Rotation, or spin, is the circular movement of an object around a '' central axis''. A two-dimensional rotating object has only one possible central axis and can rotate in either a clockwise or counterclockwise direction. A three-dimensional ...
,
permutation
In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or proc ...
(i.e.
transposition,
inversion
Inversion or inversions may refer to:
Arts
* , a French gay magazine (1924/1925)
* ''Inversion'' (artwork), a 2005 temporary sculpture in Houston, Texas
* Inversion (music), a term with various meanings in music theory and musical set theory
* ...
, and
retrograde),
prolation (
augmentation,
diminution
In Western music and music theory, diminution (from Medieval Latin ''diminutio'', alteration of Latin ''deminutio'', decrease) has four distinct meanings. Diminution may be a form of embellishment in which a long note is divided into a series of ...
) and combinations thereof.
Transformations may also be applied to simpler or more complex variables such as
interval and
spectrum
A spectrum (plural ''spectra'' or ''spectrums'') is a condition that is not limited to a specific set of values but can vary, without gaps, across a continuum. The word was first used scientifically in optics to describe the rainbow of colors i ...
or
timbre
In music, timbre ( ), also known as tone color or tone quality (from psychoacoustics), is the perceived sound quality of a musical note, sound or musical tone, tone. Timbre distinguishes different types of sound production, such as choir voice ...
.
See also
*
Identity (music)
In post-tonal music theory, identity is similar to identity in universal algebra. An identity function is a permutation or transformation which transforms a pitch or pitch class set into itself. Generally this requires symmetry. For instance ...
*
Operation (music)
Musical set theory provides concepts for categorizing musical objects and describing their relationships. Howard Hanson first elaborated many of the concepts for analyzing tonal music. Other theorists, such as Allen Forte, further developed th ...
*
Permutation (music)
In music, a permutation (order) of a set is any ordering of the elements of that set. A specific arrangement of a set of discrete entities, or parameters, such as pitch, dynamics, or timbre. Different permutations may be related by transformati ...
*
Transformational theory
Transformational theory is a branch of music theory developed by David Lewin in the 1980s, and formally introduced in his 1987 work, ''Generalized Musical Intervals and Transformations''. The theory—which models musical transformations as ele ...
References
Musical techniques
{{Music-theory-stub