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
partitioning-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