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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.
Because of this, music theorists often consider set classes basic objects of musical interest. There are two main conventions for naming equal-tempered set classes. One, known as the Forte number , derives from Allen Forte, whose The Structure of Atonal Music (1973), is one of the first works in musical set theory.
Motion between proximate harmonies is described by simple transformations. For example, motion between a C major and E minor triad, in either direction, is executed by an "L" transformation. Extended progressions of harmonies are characteristically displayed on a geometric plane, or map, which portrays the entire system of harmonic relations.
Godfried Toussaint (1944–2019) was a Belgian–Canadian computer scientist who worked as a professor of computer science for McGill University and New York University.His main professional expertise was in computational geometry, [2] but he was also a jazz drummer, [3] held a long-term interest in the mathematics of music and musical rhythm, and since 2005 held an affiliation as a researcher ...
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In music, an interval ratio is a ratio of the frequencies of the pitches in a musical interval. For example, a just perfect fifth (for example C to G) is 3:2 (Play ⓘ), 1.5, and may be approximated by an equal tempered perfect fifth (Play ⓘ) which is 2 7/12 (about 1.498).
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An example is where =, and , is the dot product. The musical isomorphisms are the global version of this isomorphism and its inverse for the tangent bundle and cotangent bundle of a (pseudo-)Riemannian manifold ( M , g ) {\displaystyle (M,g)} .