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The fundamental concept of musical set theory is the (musical) set, which is an unordered collection of pitch classes. [4] More exactly, a pitch-class set is a numerical representation consisting of distinct integers (i.e., without duplicates). [5] The elements of a set may be manifested in music as simultaneous chords, successive tones (as in ...
The generative theory of tonal music (GTTM) is a system of music analysis developed by music theorist Fred Lerdahl and linguist Ray Jackendoff. [1] First presented in their 1983 book of the same title, it constitutes a "formal description of the musical intuitions of a listener who is experienced in a musical idiom" [1] with the aim of illuminating the unique human capacity for musical ...
In addition to S(2,3,9), Kramer and Mesner examined other systems that could be derived from S(5,6,12) and found that there could be up to 2 disjoint S(5,6,12) systems, up to 2 disjoint S(4,5,11) systems, and up to 5 disjoint S(3,4,10) systems. All such sets of 2 or 5 are respectively isomorphic to each other.
0 11 3 prime form, interval-vector = −1 +4 mod 12 0 1 9 inverse, interval-string = +1 −4 mod 12 + 1 1 1 ----- 1 2 10 Each of the four trichords (3-note sets) thus displays a relationship which can be made obvious by any of the four serial row operations, and thus creates certain invariances. These invariances in serial music are analogous ...
In music theory, complement refers to either traditional interval complementation, or the aggregate complementation of twelve-tone and serialism. In interval complementation a complement is the interval which, when added to the original interval, spans an octave in total. For example, a major 3rd is the complement of a minor 6th.
Harmonic Materials of Modern Music is a book on musical set theory by American composer Howard Hanson that overlaps significantly with composer Elliott Carter 's Harmony Book and theorist Allen Forte 's subsequent Structure of Atonal Music. Published in 1960, Hanson's theory was one of the first to examine all sets of pitches in terms of their ...
Berklee method. In music performance and education, the Berklee method is the music theory, terminology, and practice taught at Berklee College of Music, the largest independent college of contemporary music in the world. The "Berklee method" was founded by Lawrence Berk after study with Joseph Schillinger regarding the latter's "elaborate ...
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. Generally this requires symmetry. For instance, inverting an augmented triad or C4 interval cycle, 048, produces itself.