Schoenberg hexachord
6-Z44 (012569), known as the Schoenberg hexachord, is Arnold Schoenberg's signature hexachord, as one transposition contains the pitches [A], Es, C, H, B, E, G (A. Schoenberg), E♭, B, and B♭ being Es,
Identity (music)
In post-tonal music theory, identity is similar to identity in universal algebra. An identity function is a permutation or transformation which transforms a pitch or pitch class set into itself. Gener
List of set classes
This is a list of set classes by Forte number. For a list of ordered collections, see: list of tone rows and series. Sets are listed next to their complements. Inversions are marked "B" (sets not mark
Interval vector
In musical set theory, an interval vector is an array of natural numbers which summarize the intervals present in a set of pitch classes. (That is, a set of pitches where octaves are disregarded.) Oth
Chromatic hexachord
In music theory, the chromatic hexachord is the hexachord consisting of a consecutive six-note segment of the chromatic scale. It is the first hexachord as ordered by Forte number, and its complement
Rothenberg propriety
In diatonic set theory, Rothenberg propriety is an important concept, lack of contradiction and ambiguity, in the general theory of musical scales which was introduced by in a seminal series of papers
"Ode-to-Napoleon" hexachord
In music, the "Ode-to-Napoleon" hexachord (also magic hexachord and hexatonic collection or hexatonic set class) is the hexachord named after its use in the twelve-tone piece Ode to Napoleon Buonapart
Projected set
In music a projected set is a technique where a collection of pitches or pitch classes is extended in a texture through the emphasized simultaneous statement of a set followed or preceded by a success
Pitch class
In music, a pitch class (p.c. or pc) is a set of all pitches that are a whole number of octaves apart; for example, the pitch class C consists of the Cs in all octaves. "The pitch class C stands for a
Interval class
In musical set theory, an interval class (often abbreviated: ic), also known as unordered pitch-class interval, interval distance, undirected interval, or "(even completely incorrectly) as 'interval m
Pitch class space
In music theory, pitch-class space is the circular space representing all the notes (pitch classes) in a musical octave. In this space, there is no distinction between tones that are separated by an i
Forte number
In 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-
Sacher hexachord
The Sacher hexachord (6-Z11, musical cryptogram on the name of Swiss conductor Paul Sacher) is a hexachord notable for its use in a set of twelve compositions (12 Hommages à Paul Sacher) created at th
All-trichord hexachord
In music, the all-trichord hexachord is a unique hexachord that contains all twelve trichords, or from which all twelve possible trichords may be derived. The prime form of this set class is {012478}
Viennese trichord
In music theory, a Viennese trichord (also Viennese fourth chord and tritone-fourth chord), named for the Second Viennese School, is a pitch set with prime form (0,1,6). Its Forte number is 3-5. The s
Permutation (music)
In music, a permutation (order) of a set is any ordering of the elements of that set. A specific arrangement of a set of discrete entities, or parameters, such as pitch, dynamics, or timbre. Different
Equivalence class (music)
In music theory, equivalence class is an equality (=) or equivalence between properties of sets (unordered) or twelve-tone rows (ordered sets). A relation rather than an operation, it may be contraste
All-interval tetrachord
An all-interval tetrachord is a tetrachord, a collection of four pitch classes, containing all six interval classes. There are only two possible all-interval tetrachords (to within inversion), when ex
Set theory (music)
Musical set theory provides concepts for categorizing musical objects and describing their relationships. Howard Hanson first elaborated many of the concepts for analyzing tonal music. Other theorists
Set (music)
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 i
Pitch interval
In musical set theory, a pitch interval (PI or ip) is the number of semitones that separates one pitch from another, upward or downward. They are notated as follows: PI(a,b) = b − a For example C4 to
Similarity relation (music)
In music, a similarity relation or pitch-class similarity is a comparison between sets of the same cardinality (two sets containing the same number of pitch classes), based upon shared pitch class and