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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.
A collection of texts on applications of stochastic processes, game theory and computer programming in music, it was later revised, expanded and translated into English as Formalized Music: Thought and Mathematics in Composition (1971) during Xenakis's tenure at Indiana University. Xenakis was an atheist.
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.
Algorithmic composition is the technique of using algorithms to create music. Algorithms (or, at the very least, formal sets of rules) have been used to compose music for centuries; the procedures used to plot voice-leading in Western counterpoint , for example, can often be reduced to algorithmic determinacy.
Although musical set theory is often thought to involve the application of mathematical set theory to music, there are numerous differences between the methods and terminology of the two. For example, musicians use the terms transposition and inversion where mathematicians would use translation and reflection .
When that video raked up hundreds of thousands of views in a matter of days, it inspired him to reimagine other ways to teach math, including using the tune to Swift's "Anti-Hero" to help students ...
The use of computers in order to study and analyze music generally began in the 1960s, [3] although musicians have been using computers to assist them in the composition of music beginning in the 1950s. Today, computational musicology encompasses a wide range of research topics dealing with the multiple ways music can be represented. [4]
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. It was proposed in 2000 by Elaine Chew in her MIT doctoral thesis Toward a Mathematical Model of Tonality ...