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...

, especially folk

Folk music

Folk music is an English term encompassing both traditional folk music and contemporary folk music. The term originated in the 19th century. Traditional folk music has been defined in several ways: as music transmitted by mouth, as music of the lower classes, and as music with unknown composers....

 and popular music

Popular music

Popular music belongs to any of a number of musical genres "having wide appeal" and is typically distributed to large audiences through the music industry. It stands in contrast to both art music and traditional music, which are typically disseminated academically or orally to smaller, local...

, a matrix is an element of variations

Variation (music)

In music, variation is a formal technique where material is repeated in an altered form. The changes may involve harmony, melody, counterpoint, rhythm, timbre, orchestration or any combination of these.-Variation form:...

 which does not change. The term was derived from use in musical writings and from Arthur Koestler

Arthur Koestler

Arthur Koestler CBE was a Hungarian author and journalist. Koestler was born in Budapest and, apart from his early school years, was educated in Austria...

's The Act of Creation

The Act of Creation

The Act of Creation is a 1964 book by Arthur Koestler. It is a study of the processes of discovery, invention, imagination and creativity in humor, science, and the arts...

, who defines creativity as the bisociation of two sets of ideas or matrices. Musical matrices may be combined in any number, usually more than two, and may be — and must be for 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...

 — broken down into smaller ones. They may be intended by the composer and perceived by the listener, or they may not, and they may be purposefully ambiguous.

The simplest examples given by van der Merwe are fixed notes, definite intervals, and regular beats, while the most complex given are the Baroque fugue, Classical tonality, and Romantic chromaticism. The following examples are some matrices which are part of "Pop Goes the Weasel

Pop Goes the Weasel

"Pop! Goes the Weasel" is an English language nursery rhyme and singing game. It has a Roud Folk Song Index number of 5249.-Lyrics:There are many different versions of the lyrics to the song...

":

• major mode
• 6/8 time
• four-bar phrasing
• regular beat
• rhyming tune structure
• ending both halves of the tune with the same figure
• melodic climax
• perfect cadence
  Cadence (music)
  In Western musical theory, a cadence is, "a melodic or harmonic configuration that creates a sense of repose or resolution [finality or pause]." A harmonic cadence is a progression of two chords that concludes a phrase, section, or piece of music...
  
  
• three primary triad
  Primary triad
  In music, a primary triad is a one of the three triads, or three note chord built from thirds, most important in tonal and diatonic music, as opposed to an auxiliary triad or secondary triad....
  
  s implied

Co-ordinated matrices may possess "bound-upness" or "at-oddness", depending on the degree to which they are connected to each other or go their separate ways, respectively, and are more or less easy to reconcile. The matrices of the larger matrix known as sonata rondo form are more bound up than the matrices of rondo form, while African and Indian music feature more rhythmic at-oddness than European music's coinciding beats, and European harmony features more at-oddness (between the melody and bass) than the preceding organum. At-oddness is a matter of degree, and almost all at odd matrices are partially bound up.

Mathematical matrices in music

Mathematical matrices

Matrix (mathematics)

In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions. The individual items in a matrix are called its elements or entries. An example of a matrix with six elements isMatrices of the same size can be added or subtracted element by element...

are used in the visualization of all permutation

Permutation

In mathematics, the notion of permutation is used with several slightly different meanings, all related to the act of permuting objects or values. Informally, a permutation of a set of objects is an arrangement of those objects into a particular order...

s or forms of a 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...

 or 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...

 in music written using the twelve tone technique or serialism

Serialism

In music, serialism is a method or technique of composition that uses a series of values to manipulate different musical elements. Serialism began primarily with Arnold Schoenberg's twelve-tone technique, though his contemporaries were also working to establish serialism as one example of...

.