Transformation (music)
Encyclopedia
In music
Music
Music is an art form whose medium is sound and silence. Its common elements are pitch , rhythm , dynamics, and the sonic qualities of timbre and texture...

, a transformation consists of any operation or process that may apply to a musical variable (usually a set
Set theory (music)
Musical set theory provides concepts for categorizing musical objects and describing their relationships. Many of the notions were first elaborated by Howard Hanson in connection with tonal music, and then mostly developed in connection with atonal music by theorists such as Allen Forte , drawing...

 or tone row
Tone row
In music, a tone row or note row , also series and set, refers to 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 sometimes found.-History and usage:Tone rows are the basis of...

 in twelve tone music, or a melody
Melody
A melody , also tune, voice, or line, is a linear succession of musical tones which is perceived as a single entity...

 or chord progression
Chord progression
A chord progression is a series of musical chords, or chord changes that "aims for a definite goal" of establishing a tonality founded on a key, root or tonic chord. In other words, the succession of root relationships...

 in tonal music
Tonality
Tonality is a system of music in which specific hierarchical pitch relationships are based on a key "center", or tonic. The term tonalité originated with Alexandre-Étienne Choron and was borrowed by François-Joseph Fétis in 1840...

) in composition
Musical composition
Musical composition can refer to an original piece of music, the structure of a musical piece, or the process of creating a new piece of music. People who practice composition are called composers.- Musical compositions :...

, performance
Musical performance
Musical performance may refer to:* Concert* Performance* Recital* Audition: a performance in front of a panel of judges* Concerto: a virtuoso solo work * Musical technique...

, or analysis
Musical analysis
Musical analysis is the attempt to answer the question how does this music work?. The method employed to answer this question, and indeed exactly what is meant by the question, differs from analyst to analyst, and according to the purpose of the analysis. According to Ian Bent , analysis is "an...

. Transformations include multiplication
Multiplication (music)
The mathematical operations of multiplication have several applications to music. Other than its application to the frequency ratios of intervals , it has been used in other ways for twelve-tone technique, and musical set theory...

, rotation
Rotation (disambiguation)
The term rotation can be used in several ways and includes various topics. Generally, it is used to denote the rotation of movement of a rigid body in such a way that any given point of that body remains at a constant distance from some fixed line .More specifically, it is applicable to:* Crop...

, permutation
Permutation (music)
In music, a permutation of a set is any ordering of the elements of that set. Different permutations may be related by transformation, through the application of zero or more of certain operations, such as transposition, inversion, retrogradation, circular permutation , or multiplicative operations...

 (i.e. transposition
Transposition (music)
In music transposition refers to the process, or operation, of moving a collection of notes up or down in pitch by a constant interval.For example, one might transpose an entire piece of music into another key...

, inversion
Inversion (music)
In music theory, the word inversion has several meanings. There are inverted chords, inverted melodies, inverted intervals, and inverted voices...

, and retrograde), and combinations thereof.

Transformations may also be applied to simpler or more complex variables such as interval
Interval (music)
In music theory, an interval is a combination of two notes, or the ratio between their frequencies. Two-note combinations are also called dyads...

 and spectrum
Harmonic series (music)
Pitched musical instruments are often based on an approximate harmonic oscillator such as a string or a column of air, which oscillates at numerous frequencies simultaneously. At these resonant frequencies, waves travel in both directions along the string or air column, reinforcing and canceling...

 or timbre
Timbre
In music, timbre is the quality of a musical note or sound or tone that distinguishes different types of sound production, such as voices and musical instruments, such as string instruments, wind instruments, and percussion instruments. The physical characteristics of sound that determine the...

.
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