In
music
Music is the arrangement of sound to create some combination of Musical form, form, harmony, melody, rhythm, or otherwise Musical expression, expressive content. Music is generally agreed to be a cultural universal that is present in all hum ...
, 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 ( 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 are sometime ...
in
twelve tone music, or a
melody
A melody (), also tune, voice, or line, is a linear succession of musical tones that the listener perceives as a single entity. In its most literal sense, a melody is a combination of Pitch (music), pitch and rhythm, while more figurativel ...
or
chord progression
In a musical composition, a chord progression or harmonic progression (informally chord changes, used as a plural, or simply changes) is a succession of chords. Chord progressions are the foundation of harmony in Western musical tradition from ...
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 the root of a triad with t ...
), 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 r ...
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 ...
,
performance
A performance is an act or process 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.
Performance has evolved glo ...
, 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 is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division (mathematics), division. The result of a multiplication operation is called a ''Product (mathem ...
,
rotation
Rotation or rotational/rotary motion is the circular movement of an object around a central line, known as an ''axis of rotation''. A plane figure can rotate in either a clockwise or counterclockwise sense around a perpendicular axis intersect ...
,
permutation
In mathematics, a permutation of a set can mean one of two different things:
* an arrangement of its members in a sequence or linear order, or
* the act or process of changing the linear order of an ordered set.
An example of the first mean ...
(i.e.
transposition,
inversion, and
retrograde),
prolation (
augmentation,
diminution
In Western culture, 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 (music), embellishment in whic ...
) and combinations thereof.
Transformations may also be applied to simpler or more complex variables such as
interval and
spectrum
A spectrum (: spectra or spectrums) is a set of related ideas, objects, or properties whose features overlap such that they blend to form a continuum. The word ''spectrum'' was first used scientifically in optics to describe the rainbow of co ...
or
timbre
In music, timbre (), also known as tone color or tone quality (from psychoacoustics), is the perceived sound of a musical note, sound or tone. Timbre distinguishes sounds according to their source, such as choir voices and musical instrument ...
.
See also
*
Developing variation
*
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 inst ...
*
Operation (music)
*
Permutation (music)
In music, a permutation (order) of a set (music), set is any ordering of the elements of that set. A specific arrangement of a set of discrete entities, or parameter (music), parameters, such as pitch (music), pitch, Dynamics (music), dynamics, o ...
*
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 Transformation (music), musical t ...
References
Musical techniques
{{Music-theory-stub