Formalized Music
Formalized Music: Thought and Mathematics in Composition is a book by Greek composer, architect, and engineer Iannis Xenakis in which he explains his motivation, philosophy, and technique for composin
The Complexity of Songs
"The Complexity of Songs" is a scholarly article by computer scientist Donald Knuth in 1977, as an in-joke about computational complexity theory. The article capitalizes on the tendency of popular son
Neo-Riemannian theory
Neo-Riemannian theory is a loose collection of ideas present in the writings of music theorists such as David Lewin, Brian Hyer, Richard Cohn, and Henry Klumpenhouwer. What binds these ideas is a cent
Swing (jazz performance style)
In music, the term swing has two main uses. Colloquially, it is used to describe the propulsive quality or "feel" of a rhythm, especially when the music prompts a visceral response such as foot-tappin
Three-gap theorem
In mathematics, the three-gap theorem, three-distance theorem, or Steinhaus conjecture states that if one places n points on a circle, at angles of θ, 2θ, 3θ, ... from the starting point, then there w
Størmer's theorem
In number theory, Størmer's theorem, named after Carl Størmer, gives a finite bound on the number of consecutive pairs of smooth numbers that exist, for a given degree of smoothness, and provides a me
Music and mathematics
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 communic
Serialism
In music, serialism is a method of composition using series of pitches, rhythms, dynamics, timbres or other musical elements. Serialism began primarily with Arnold Schoenberg's twelve-tone technique,
Abacus Harmonicus
Abacus Harmonicus, or Abacum Arithmetico-Harmonicum is a table and tabular method described in Athanasius Kircher's comprehensive 1650 work on music, the Musurgia Vniversalis. The purpose is to genera
Regular number
Regular numbers are numbers that evenly divide powers of 60 (or, equivalently, powers of 30). Equivalently, they are the numbers whose only prime divisors are 2, 3, and 5. As an example, 602 = 3600 =
Transformational theory
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