Allen Forte's unique notation system commonly known as Forte Notation has come to be recognised as one of the most successful attempts at providing a means of describing and analysing musical pitch structures that defy interpretation as tonal or 12-note serial systems. Thus, Forte's system is equally at home describing Ives and Stravinsky as it is Schoenberg and Webern.
Such a system able to deal with intervallic relationships from pitch class extrapolations of material has a potential within SCOM to be itself a generator of pitch series.
(pcs :integer '5-6)
=> (0 1 2 5 6)
(pcs-complement :integer 5 5 (pcs :integer '5-6))
=> (3 4 7 8 9 10 11)
This function is able to produce an output of 'complementary' symbols or intervals to that of the pcs generation. If for example, A is a pitch-class-set containing 4 elements (pc integers), then the complement of A is the set of 8 elements not contained in A.
(pcs-complement :symbol 0 5 (pcs :integer '5-6))
=> (d e h i j k l)
(pcs-complement :pitch 0 5 (pcs :integer '5-6))
=> (d#4 e4 g4 g#4 a4 a#4 b4)
(setq list1 (pcs :symbol '(6-7 5-7 4-5 2-1)))
=> ((a b c g h i) (a b c g h) (a b c g) (a b))
(pcs-complement :symbol 0 11 list1)
=> ((d e f j k l) (d e f i j k l)
(d e f h i j k l) (c d e f g h i j k l))
(pcs-complement :symbol 5 6 list1)
=> ((d e f j k l) (d e f i j k l) (a b c g) (a b))
