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In music, especially folk and popular music, a matrix is an element of variations which does not change. [1] The term was derived from use in musical writings and from Arthur Koestler 's The Act of Creation , who defines creativity as the bisociation of two sets of ideas or matrices. [ 2 ]
Hexachordal combinatoriality is a concept in post-tonal theory that describes the combination of hexachords, often used in reference to the music of the Second Viennese school. In music that consistently utilizes all twelve chromatic tones (particularly twelve-tone and serial music ), the aggregate (collection of all 12 pitch classes) may be ...
Coltrane studied harmony with Dennis Sandole and at the Granoff School of Music in Philadelphia. He explored contemporary techniques and theory. He explored contemporary techniques and theory. He also studied the Thesaurus of Scales and Melodic Patterns by Nicolas Slonimsky (1947).
Music theory analyzes the pitch, timing, and structure of music. It uses mathematics to study elements of music such as tempo , chord progression , form , and meter . The attempt to structure and communicate new ways of composing and hearing music has led to musical applications of set theory , abstract algebra and number theory .
The Oxford Companion to Music describes three interrelated uses of the term "music theory": The first is the "rudiments", that are needed to understand music notation (key signatures, time signatures, and rhythmic notation); the second is learning scholars' views on music from antiquity to the present; the third is a sub-topic of musicology ...
The fundamental observation MUSIC and other subspace decomposition methods are based on is about the rank of the autocorrelation matrix which is related to number of signal sources as follows. If the sources are complex, then M > p {\displaystyle M>p} and the dimension of the signal subspace U S {\displaystyle {\mathcal {U}}_{S}} is p ...
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 musical transformations as elements of a mathematical group —can be used to analyze both tonal and atonal music .
The exponential of a Metzler (or quasipositive) matrix is a nonnegative matrix because of the corresponding property for the exponential of a nonnegative matrix. This is natural, once one observes that the generator matrices of continuous-time Markov chains are always Metzler matrices, and that probability distributions are always non-negative.