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 ...

, especially

folk Folk or Folks may refer to: Sociology *Nation *People * Folklore ** Folk art ** Folk dance ** Folk hero ** Folk music *** Folk metal *** Folk punk *** Folk rock ** Folk religion * Folk taxonomy Arts, entertainment, and media * Folk Plus or Fol ...

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 Variation or Variations may refer to: Science and mathematics * Variation (astronomy), any perturbation of the mean motion or orbit of a planet or satellite, particularly of the moon * Genetic variation, the difference in DNA among individuals ...

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

Arthur Koestler Arthur Koestler, (, ; ; hu, Kösztler Artúr; 5 September 1905 – 1 March 1983) was a Hungarian-born author and journalist. Koestler was born in Budapest and, apart from his early school years, was educated in Austria. In 1931, Koestler join ...

'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 may be intended by the composer and perceived by the listener, or they may not, and they may be purposefully

ambiguous Ambiguity is the type of meaning (linguistics), meaning in which a phrase, statement or resolution is not explicitly defined, making several interpretations wikt:plausible#Adjective, plausible. A common aspect of ambiguity is uncertainty. It ...

. 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" (Roud 5249) is a traditional English and American song, a country dance, nursery rhyme, and singing game that emerged in the mid-19th century. It is commonly used in Jack-in-the-box toys and for ice cream trucks. The song ...

": *

major mode The major scale (or Ionian mode) is one of the most commonly used musical scales, especially in Western music. It is one of the diatonic scales. Like many musical scales, it is made up of seven notes: the eighth duplicates the first at double ...

*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 In Western musical theory, a cadence (Latin ''cadentia'', "a falling") is the end of a phrase in which the melody or harmony creates a sense of full or partial resolution, especially in music of the 16th century onwards.Don Michael Randel (1999) ...

*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 co ...

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 most commonly refers to: * ''The Matrix'' (franchise), an American media franchise ** ''The Matrix'', a 1999 science-fiction action film ** "The Matrix", a fictional setting, a virtual reality environment, within ''The Matrix'' (franchis ...

are used in the visualization of all

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 ...

s or forms of a

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 ...

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 The twelve-tone technique—also known as dodecaphony, twelve-tone serialism, and (in British usage) twelve-note composition—is a method of musical composition first devised by Austrian composer Josef Matthias Hauer, who published his "law o ...

serialism In music, serialism is a method of Musical composition, composition using series of pitches, rhythms, dynamics, timbres or other elements of music, musical elements. Serialism began primarily with Arnold Schoenberg's twelve-tone technique, thou ...

( set-complex).

References

{{DEFAULTSORT:Matrix (Music) Popular music Folk music Musical techniques

Mathematical matrices in music

See also

References