12-tone Terminology

source hexachord-reduce a collection of pitch class to normal form [arrange in ascending order from lowest to highest note; smallest intervalic compass]

all-combinatorial hexachord-the capacity of a collection to create aggregates with forms of itself and its complement under both transposition and inversion.

Such a collection is all-combinatorial in that it possess all four types of combinatoriality. source set must be symmetrical, self invertible, self- retrogradable

hexachordal combinatoriality-an ordered set segmented into 2 hexachords [also tetra-, tri- and di-; occasional is 5 + 7]

aggregate-a group that contains all twelve pitch classes (can be ordered or not)

degenerate set-set of which there are only 24 forms; middle interval must be IC6

a) R-degenerate-set in which there are only 24 forms rather than 48 (P, I, but 12 retrogrades are identical to 12 primes [another inverstion ])

b) RI degenerate-RI is same as prime

chromatic completion- “a sense of completion is felt when the entire chromatic palette is presented”

thus to delay the complete presentation is to suspend [i.e., prolong] completion

the overall pacing of a piece is determined by the completion of the large-scale structure

segmentation-dividing sets into subsets of adjacent notes

The division of a collection or set into two or more exclusive parts

notes usually not adjacent; deriving lines in a texture which are connected with each other

(M [Melby, Milton?] used extreme registral, timbral & dynamic differences)

77 combinations of partitioning 12 tones exist

centric-central pitch around which other pitches evolve; as opposed to tonal (bottom up)

time point system (Babbitt)-deals w/ points of attack within a measure; a ‘measure’ is one collection of 12 notes; not durations