Search results
Results from the WOW.Com Content Network
One branch of musical set theory deals with collections (sets and permutations) of pitches and pitch classes (pitch-class set theory), which may be ordered or unordered, and can be related by musical operations such as transposition, melodic inversion, and complementation.
This is a list of set classes, by Forte number. [1] In music theory, a set class (an abbreviation of pitch-class-set class) is an ascending collection of pitch classes, transposed to begin at zero. For a list of ordered collections, see this list of tone rows and series. Sets are listed with links to their complements.
A set (pitch set, pitch-class set, set class, set form, set genus, pitch collection) in music theory, as in mathematics and general parlance, is a collection of objects. In musical contexts the term is traditionally applied most often to collections of pitches or pitch-classes , but theorists have extended its use to other types of musical ...
Pages in category "Musical set theory" The following 23 pages are in this category, out of 23 total. This list may not reflect recent changes. ...
Set 3-1 has three possible rotations/inversions; the normal form (left) is the most compact, corresponding to the smallest sectorIn musical set theory, a Forte number is the pair of numbers Allen Forte assigned to the prime form of each pitch class set of three or more members in The Structure of Atonal Music (1973, ISBN 0-300-02120-8).
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. While music theory has no axiomatic foundation in modern mathematics, the basis of musical sound can be described mathematically (using acoustics) and exhibits "a remarkable array of ...
Pocket set theory; Positive set theory; S (Boolos 1989) Scott–Potter set theory; Tarski–Grothendieck set theory; Von Neumann–Bernays–Gödel set theory; Zermelo–Fraenkel set theory; Zermelo set theory; Set (mathematics) Set-builder notation; Set-theoretic topology; Simple theorems in the algebra of sets; Subset; Θ (set theory) Tree ...
"Mirror forms", P, R, I, and RI, of a tone row (from Arnold Schoenberg's Variations for Orchestra Op. 31, "Called mirror forms because...they are identical". [1]In music, a tone row or note row (German: Reihe or Tonreihe), also series or set, [2] is a non-repetitive ordering of a set of pitch-classes, typically of the twelve notes in musical set theory of the chromatic scale, though both ...