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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, such as Allen Forte, further developed the theory for analyzing atonal music, drawing on the twelve-tone theory of Milton Babbitt. The concepts of musical set theory are very general and can be applied to tonal and atonal styles in any equal temperament tuning system, and to some extent more generally than that. 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. Some theorists apply the methods of musical set theory to the analysis of rhythm as well. Mathematical set theory versus musical set theory Although musical set theory is often thought to involve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Z-relation Z17 Example
In Set theory (music), musical set theory, an interval vector is an array of natural numbers which summarize the Interval (music), intervals present in a Set (music), set of pitch classes. (That is, a set of Pitch (music), pitches where octaves are disregarded.) Other names include: ic vector (or interval-class vector), PIC vector (or pitch-class interval vector) and APIC vector (or absolute pitch-class interval vector, which Michiel Schuijer states is more proper.) While primarily an analytic tool, interval vectors can also be useful for composers, as they quickly show the sound qualities that are created by different collections of pitch class. That is, sets with high concentrations of conventionally dissonant intervals (i.e., seconds and sevenths) sound more dissonant, while sets with higher numbers of conventionally consonant intervals (i.e., thirds and sixths) sound more consonance and dissonance, consonant. While the actual perception of consonance and dissonance involv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
