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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.
The use of mathematical models to solve problems in business or military operations is a large part of the field of operations research. Mathematical models are also used in music, [3] linguistics, [4] and philosophy (for example, intensively in analytic philosophy). A model may help to explain a system and to study the effects of different ...
Computer music systems and approaches are now ubiquitous, and so firmly embedded in the process of creating music that we hardly give them a second thought: computer-based synthesizers, digital mixers, and effects units have become so commonplace that use of digital rather than analog technology to create and record music is the norm, rather ...
Formal methods and databases — applications of automated music identification and recognition, such as score following, automatic accompaniment, routing and filtering for music and music queries, query languages, standards and other metadata or protocols for music information handling and retrieval, multi-agent systems, distributed search)
The Society for Mathematics and Computation in Music (SMCM) was founded in 2006 as an International Forum for researchers and musicians working in the trans-disciplinary field at the intersection of music, mathematics and computation. The SMCM is registered in the USA.
Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical science and specialized knowledge.
The mathematical operations of multiplication have several applications to music. Other than its application to the frequency ratios of intervals (for example, Just intonation , and the twelfth root of two in equal temperament ), it has been used in other ways for twelve-tone technique , and musical set theory .
In music theory, the spiral array model is an extended type of pitch space.A mathematical model involving concentric helices (an "array of spirals"), it represents human perceptions of pitches, chords, and keys in the same geometric space.