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 ...
, especially
folk
Folk or Folks may refer to:
Sociology
*Nation
*People
* Folklore
** Folk art
** Folk dance
** Folk hero
** Folk horror
** Folk music
*** Folk metal
*** Folk punk
*** Folk rock
** Folk religion
* Folk taxonomy
Arts, entertainment, and media
* Fo ...
and
popular music
Popular music is music with wide appeal that is typically distributed to large audiences through the music industry. These forms and styles can be enjoyed and performed by people with little or no musical training.Popular Music. (2015). ''Fun ...
, a matrix is an element of
variations which does not change.
[
] The term was derived from use in musical writings and from
Arthur Koestler
Arthur Koestler (, ; ; ; 5 September 1905 – 1 March 1983) was an Austria-Hungary, Austro-Hungarian-born author and journalist. Koestler was born in Budapest, and was educated in Austria, apart from his early school years. In 1931, Koestler j ...
's ''
The Act of Creation'', 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
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 ...
— broken down into smaller ones. They are not necessarily intended by the composer or perceived by the listener, and they may be purposefully
ambiguous
Ambiguity is the type of meaning in which a phrase, statement, or resolution is not explicitly defined, making for several interpretations; others describe it as a concept or statement that has no real reference. A common aspect of ambiguit ...
.
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":
*
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
*three
primary triad
In music, a primary triad is one of the three triads, or three-note chords built from major or minor thirds, most important in tonal and diatonic music, as opposed to an auxiliary triad or secondary triad.
Each triad found in a diatonic key ...
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 (: matrices or matrixes) or MATRIX may refer to:
Science and mathematics
* Matrix (mathematics), a rectangular array of numbers, symbols or expressions
* Matrix (logic), part of a formula in prenex normal form
* Matrix (biology), the ...
are used in the visualization of all
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 ...
s or forms of a
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 ...
or
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 ...
in music written using the
twelve tone technique or
serialism
In music, serialism is a method of composition using series of pitches, rhythms, dynamics, timbres or other musical elements. Serialism began primarily with Arnold Schoenberg's twelve-tone technique, though some of his contemporaries were also ...
(
set-complex).
See also
*
Banjo roll
In bluegrass music, a banjo roll or roll is a pattern played by the banjo that uses a repeating eighth-note arpeggio – a broken chord – that by subdividing the beat 'keeps time'. "Each standard"roll pattern is a ''right hand'' fingerin ...
References
{{DEFAULTSORT:Matrix (Music)
Popular music
Folk music
Musical techniques