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Text File | 1998-08-11 | 10.7 KB | 323 lines | [ TEXT/ScoM]
pcs type fn-name type - :integer :vector :symbol :pitch 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. In the examples below the composer may chose an type equivalent to those used by Forte but including SCOM's symbolic representation; :integer, :vector, :symbol :pitch. Pitch-class, one of the 12 pitch-classes designated by integers 0 11. Pitch-class 0 refers to all notated pitches C, B-sharp, D-double-flat. Pitch-class 1 refers to all notated pitches C-sharp, D-flat, B-double-sharp , and so on. The name of pcs consisting of two numerals separated by a hyphen. The numeral to th left of the hyphen is the cardinal-number of the set; the numeral to the right of the hyphen is the ordinal number of the set, its position on the list of prime-forms. (pcs :integer '6-Z10) => (0 1 3 4 5 7) (pcs :symbol '9-7) => (a b c d e f h i k) (pcs :vector '9-7) => (6 7 7 6 7 3) (pcs :pitch '6-Z10) => (c4 c#4 d#4 e4 f4 g4) The final parameter is an fname-list and expects the composer to make explicit reference to the Forte Notation name for a particular pitch-class set. Thus, the name 3-1 denotes a pitch class set of 0,1,2 and the interval vector, 210000, an ordered array of numerals representing the interval content of the pitch class set. (pcs :integer '(3-1 3-8)) => ((0 1 2) (0 2 6)) (pcs :symbol '(3-1 3-8)) => ((a b c) (a c g)) (pcs :vector '(3-1 3-8)) => ((2 1 0 0 0 0) (0 1 0 1 0 1)) (pcs :pitch '(3-1 3-8)) => ((c4 c#4 d4) (c4 d4 f#4)) Forte (pcs) Notation Reference: Prime Forms and Vectors of Pitch-Class Sets FN PCS Vector ------------------------------------- 2-1 (0 1) (1 0 0 0 0 0) 2-2 (0 2) (0 1 0 0 0 0) 2-3 (0 3) (0 0 1 0 0 0) 2-4 (0 4) (0 0 0 1 0 0) 2-5 (0 5) (0 0 0 0 1 0) 2-6 (0 6) (0 0 0 0 0 1) 3-1 (0 1 2) (2 1 0 0 0 0) 3-2 (0 1 3) (1 1 1 0 0 0) 3-3 (0 1 4) (1 0 1 1 0 0) 3-4 (0 1 5) (1 0 0 1 1 0) 3-5 (0 1 6) (1 0 0 0 1 1) 3-6 (0 2 4) (0 2 0 1 0 0) 3-7 (0 2 5) (0 1 1 0 1 0) 3-8 (0 2 6) (0 1 0 1 0 1) 3-9 (0 2 7) (0 1 0 0 2 0) 3-10 (0 3 6) (0 0 2 0 0 1) 3-11 (0 3 7) (0 0 1 1 1 0) 3-12 (0 4 8) (0 0 0 3 0 0) 4-1 (0 1 2 3) (3 2 1 0 0 0) 4-2 (0 1 2 4) (2 2 1 1 0 0) 4-3 (0 1 3 4) (2 1 2 1 0 0) 4-4 (0 1 2 5) (2 1 1 1 1 0) 4-5 (0 1 2 6) (2 1 0 1 1 1) 4-6 (0 1 2 7) (2 1 0 0 2 1) 4-7 (0 1 4 5) (2 0 1 2 1 0) 4-8 (0 1 5 6) (2 0 0 1 2 1) 4-9 (0 1 6 7) (2 0 0 0 2 2) 4-10 (0 2 3 5) (1 2 2 0 1 0) 4-11 (0 1 3 5) (1 2 1 1 1 0) 4-12 (0 2 3 6) (1 1 2 1 0 1) 4-13 (0 1 3 6) (1 1 2 0 1 1) 4-14 (0 2 3 7) (1 1 1 1 2 0) 4-Z15 (0 1 4 6) (1 1 1 1 1 1) 4-16 (0 1 5 7) (1 1 0 1 2 1) 4-17 (0 3 4 7) (1 0 2 2 1 0) 4-18 (0 1 4 7) (1 0 2 1 1 1) 4-19 (0 1 4 8) (1 0 1 3 1 0) 4-20 (0 1 5 8) (1 0 1 2 2 0) 4-21 (0 2 4 6) (0 3 0 2 0 1) 4-22 (0 2 4 7) (0 2 1 1 2 0) 4-23 (0 2 5 7) (0 2 1 0 3 0) 4-24 (0 2 4 8) (0 2 0 3 0 1) 4-25 (0 2 6 8) (0 2 0 2 0 2) 4-26 (0 3 5 8) (0 1 2 1 2 0) 4-27 (0 2 5 8) (0 1 2 1 1 1) 4-28 (0 3 6 9) (0 0 4 0 0 2) 4-Z29 (0 1 3 7) (1 1 1 1 1 1) 5-1 (0 1 2 3 4) (4 3 2 1 0 0) 5-2 (0 1 2 3 5) (3 3 2 1 1 0) 5-3 (0 1 2 4 5) (3 2 2 2 1 0) 5-4 (0 1 2 3 6) (3 2 2 1 1 1) 5-5 (0 1 2 3 7) (3 2 1 1 2 1) 5-6 (0 1 2 5 6) (3 1 1 2 2 1) 5-7 (0 1 2 6 7) (3 1 0 1 3 2) 5-8 (0 2 3 4 6) (2 3 2 2 0 1) 5-9 (0 1 2 4 6) (2 3 1 2 1 1) 5-10 (0 1 3 4 6) (2 2 3 1 1 1) 5-11 (0 2 3 4 7) (2 2 2 2 2 0) 5-Z12 (0 1 3 5 6) (2 2 2 1 2 1) 5-13 (0 1 2 4 8) (2 2 1 3 1 1) 5-14 (0 1 2 5 7) (2 2 1 1 3 1) 5-15 (0 1 2 6 8) (2 2 0 2 2 2) 5-16 (0 1 3 4 7) (2 1 3 2 1 1) 5-Z17 (0 1 3 4 8) (2 1 2 3 2 0) 5-Z18 (0 1 4 5 7) (2 1 2 2 2 1) 5-19 (0 1 3 6 7) (2 1 2 1 2 2) 5-20 (0 1 3 7 8) (2 1 1 2 3 1) 5-21 (0 1 4 5 8) (2 0 2 4 2 0) 5-22 (0 1 4 7 8) (2 0 2 3 2 1) 5-23 (0 2 3 5 7) (1 3 2 1 3 0) 5-24 (0 1 3 5 7) (1 3 1 2 2 1) 5-25 (0 2 3 5 8) (1 2 3 1 2 1) 5-26 (0 2 4 5 8) (1 2 2 3 1 1) 5-27 (0 1 3 5 8) (1 2 2 2 3 0) 5-28 (0 2 3 6 8) (1 2 2 2 1 2) 5-29 (0 1 3 6 8) (1 2 2 1 3 1) 5-30 (0 1 4 6 8) (1 2 1 3 2 1) 5-31 (0 1 3 6 9) (1 1 4 1 1 2) 5-32 (0 1 4 6 9) (1 1 3 2 2 1) 5-33 (0 2 4 6 8) (0 4 0 4 0 2) 5-34 (0 2 4 6 9) (0 3 2 2 2 1) 5-35 (0 2 4 7 9) (0 3 2 1 4 0) 5-Z36 (0 1 2 4 7) (2 2 2 1 2 1) 5-Z37 (0 3 4 5 8) (2 1 2 3 2 0) 5-Z38 (0 1 2 5 8) (2 1 2 2 2 1) 6-1 (0 1 2 3 4 5) (5 4 3 2 1 0) 6-2 (0 1 2 3 4 6) (4 4 3 2 1 1) 6-Z3 (0 1 2 3 5 6) (4 3 3 2 2 1) 6-Z4 (0 1 2 4 5 6) (4 3 2 3 2 1) 6-5 (0 1 2 3 6 7) (4 2 2 2 3 2) 6-Z6 (0 1 2 5 6 7) (4 2 1 2 4 2) 6-7 (0 1 2 6 7 8) (4 2 0 2 4 3) 6-8 (0 2 3 4 5 7) (3 4 3 2 3 0) 6-9 (0 1 2 3 5 7) (3 4 2 2 3 1) 6-Z10 (0 1 3 4 5 7) (3 3 3 3 2 1) 6-Z11 (0 1 3 4 5 7) (3 3 3 3 2 1) 6-Z12 (0 1 2 4 6 7) (3 3 2 2 3 2) 6-Z13 (0 1 3 4 6 7) (3 2 4 2 2 2) 6-14 (0 1 3 4 5 8) (3 2 3 4 3 0) 6-15 (0 1 2 4 5 8) (3 2 3 4 2 1) 6-16 (0 1 4 5 6 8) (3 2 2 4 3 1) 6-Z17 (0 1 2 4 7 8) (3 2 2 3 3 2) 6-18 (0 1 2 5 7 8) (3 2 2 2 4 2) 6-Z19 (0 1 3 4 7 8) (3 1 3 4 3 1) 6-20 (0 1 4 5 8 9) (3 0 3 6 3 0) 6-21 (0 2 3 4 6 8) (2 4 2 4 1 2) 6-22 (0 1 2 4 6 8) (2 4 1 4 2 2) 6-Z23 (0 2 3 5 6 8) (2 3 4 2 2 2) 6-Z24 (0 1 3 4 6 8) (2 3 3 3 3 1) 6-Z25 (0 1 3 5 6 8) (2 3 3 2 4 2) 6-Z26 (0 1 3 5 7 8) (2 3 2 3 4 1) 6-27 (0 1 3 4 6 9) (2 2 5 2 2 2) 6-Z28 (0 1 3 5 6 9) (2 2 4 3 2 2) 6-Z29 (0 1 3 6 8 9) (2 2 4 2 3 2) 6-30 (0 1 3 6 7 9) (2 2 4 2 2 3) 6-31 (0 1 3 5 8 9) (2 2 3 4 3 1) 6-32 (0 2 4 5 7 9) (1 4 3 2 5 0) 6-33 (0 2 3 5 7 9) (1 4 3 2 4 1) 6-34 (0 1 3 5 7 9) (1 4 2 4 2 2) 6-35 (0 2 4 6 8 10) (0 6 0 6 0 3) 6-Z36 (0 1 2 3 4 7) (4 3 3 2 2 1) 6-Z37 (0 1 2 3 4 8) (4 3 2 3 2 1) 6-Z38 (0 1 2 3 7 8) (4 2 1 2 4 2) 6-Z39 (0 2 3 4 5 8) (3 3 3 3 2 1) 6-Z40 (0 1 2 3 5 8) (3 3 3 2 3 1) 6-Z41 (0 1 2 3 6 8) (3 3 2 2 3 2) 6-Z42 (0 1 2 3 6 9) (3 2 4 2 2 2) 6-Z43 (0 1 2 5 6 8) (3 2 2 3 3 2) 6-Z44 (0 1 2 5 6 9) (3 1 3 4 3 1) 6-Z45 (0 2 3 4 6 9) (2 3 4 2 2 2) 6-Z46 (0 1 2 4 6 9) (2 3 3 3 3 1) 6-Z47 (0 1 2 4 7 9) (2 3 3 2 4 1) 6-Z48 (0 1 2 5 7 9) (2 3 2 3 4 1) 6-Z49 (0 1 3 4 7 9) (2 2 4 3 2 2) 6-Z50 (0 1 4 6 7 9) (2 2 4 2 3 2) 7-1 (0 1 2 3 4 5 6) (6 5 4 3 2 1) 7-2 (0 1 2 3 4 5 7) (5 5 4 3 3 1) 7-3 (0 1 2 3 4 5 8) (5 4 4 4 3 1) 7-4 (0 1 2 3 4 6 7) (5 4 4 3 3 2) 7-5 (0 1 2 3 5 6 7) (5 4 3 3 4 2) 7-6 (0 1 2 3 4 7 8) (5 3 3 4 4 2) 7-7 (0 1 2 3 6 7 8) (5 3 2 3 5 3) 7-8 (0 2 3 4 5 6 8) (4 5 4 4 2 2) 7-9 (0 1 2 3 4 6 8) (4 5 3 4 3 2) 7-10 (0 1 2 3 4 6 9) (4 4 5 3 3 2) 7-11 (0 1 3 4 5 6 8) (4 4 4 4 4 1) 7-Z12 (0 1 2 3 4 7 9) (4 4 4 3 4 2) 7-13 (0 1 2 4 5 6 8) (4 4 3 5 3 2) 7-14 (0 1 2 3 5 7 8) (4 4 3 3 5 2) 7-15 (0 1 2 4 6 7 8) (4 4 2 4 4 3) 7-16 (0 1 2 3 5 6 9) (4 3 5 4 3 2) 7-Z17 (0 1 2 4 5 6 9) (4 3 4 5 4 1) 7-Z18 (0 1 2 3 5 8 9) (4 3 4 4 4 2) 7-19 (0 1 2 3 6 7 9) (4 3 4 3 4 3) 7-20 (0 1 2 3 6 7 9) (4 3 4 3 4 3) 7-21 (0 1 2 4 5 8 9) (4 2 4 6 4 1) 7-22 (0 1 2 5 6 8 9) (4 2 4 5 4 2) 7-23 (0 2 3 4 5 7 9) (3 5 4 3 5 1) 7-24 (0 1 2 3 5 7 9) (3 5 3 4 4 2) 7-25 (0 2 3 4 6 7 9) (3 4 5 3 4 2) 7-26 (0 1 3 4 5 7 9) (3 4 4 5 3 2) 7-27 (0 1 2 4 5 7 9) (3 4 4 4 5 1) 7-28 (0 1 3 5 6 7 9) (3 4 4 4 3 3) 7-29 (0 1 2 4 6 7 9) (3 4 4 3 5 2) 7-30 (0 1 2 4 6 7 9) (3 4 4 3 5 2) 7-31 (0 1 3 4 6 7 9) (3 3 6 3 3 3) 7-32 (0 1 3 4 6 8 9) (3 3 5 4 4 2) 7-33 (0 1 2 4 6 8 10) (2 6 2 6 2 3) 7-34 (0 1 3 4 6 8 10) (2 5 4 4 4 2) 7-35 (0 1 3 5 6 8 10) (2 5 4 3 6 1) 7-Z36 (0 1 2 3 5 6 8) (4 4 4 3 4 2) 7-Z37 (0 1 3 4 5 7 8) (4 3 4 5 4 1) 7-Z38 (0 1 2 4 5 7 8) (4 3 4 4 4 2) 8-1 (0 1 2 3 4 5 6 7) (7 6 5 4 4 2) 8-2 (0 1 2 3 4 5 6 8) (6 6 5 5 4 2) 8-3 (0 1 2 3 4 5 6 9) (6 5 6 5 4 2) 8-4 (0 1 2 3 4 5 7 8) (6 5 5 5 5 2) 8-5 (0 1 2 3 4 6 7 8) (6 5 4 5 5 3) 8-6 (0 1 2 3 5 6 7 8) (6 5 4 4 6 3) 8-7 (0 1 2 3 4 5 8 9) (6 4 5 6 5 2) 8-8 (0 1 2 3 4 7 8 9) (6 4 4 5 6 3) 8-9 (0 1 2 3 6 7 8 9) (6 4 4 4 6 4) 8-10 (0 2 3 4 5 6 7 9) (5 6 6 4 5 2) 8-11 (0 1 2 3 4 5 7 9) (5 6 5 5 5 2) 8-12 (0 1 3 4 5 6 7 9) (5 5 6 5 4 3) 8-13 (0 1 2 3 4 6 7 9) (5 5 6 4 5 3) 8-14 (0 1 2 4 5 6 7 9) (5 5 5 5 6 2) 8-Z15 (0 1 2 3 4 6 8 9) (5 5 5 5 5 3) 8-16 (0 1 2 3 5 7 8 9) (5 5 4 5 6 3) 8-17 (0 1 3 4 5 6 8 9) (5 4 6 6 5 2) 8-18 (0 1 2 3 5 6 8 9) (5 4 6 5 5 3) 8-19 (0 1 2 4 5 6 8 9) (5 4 5 7 5 2) 8-20 (0 1 2 4 5 7 8 9) (5 4 5 6 6 2) 8-21 (0 1 2 3 4 6 8 10) (4 7 4 6 4 3) 8-22 (0 1 2 3 5 6 8 10) (4 6 5 5 6 2) 8-23 (0 1 2 3 5 7 8 10) (4 6 5 4 7 2) 8-24 (0 1 2 4 5 6 8 10) (4 6 4 7 4 3) 8-25 (0 1 2 4 6 7 8 10) (4 6 4 6 4 4) 8-26 (0 1 2 4 5 7 9 10) (4 5 6 5 6 2) 8-27 (0 1 2 4 5 7 8 10) (4 5 6 5 5 3) 8-28 (0 1 3 4 6 7 9 10) (4 4 8 4 4 4) 8-Z29 (0 1 2 3 5 6 7 9) (5 5 5 5 5 3) 9-1 (0 1 2 3 4 5 6 7 8) (8 7 6 6 6 3) 9-2 (0 1 2 3 4 5 6 7 9) (7 7 7 6 6 3) 9-3 (0 1 2 3 4 5 6 8 9) (7 6 7 7 6 3) 9-4 (0 1 2 3 4 5 7 8 9) (7 6 6 7 7 3) 9-5 (0 1 2 3 4 6 7 8 9) (7 6 6 6 7 4) 9-6 (0 1 2 3 4 5 6 8 10) (6 8 6 7 6 3) 9-7 (0 1 2 3 4 5 7 8 10) (6 7 7 6 7 3) 9-8 (0 1 2 3 4 6 7 8 10) (6 7 6 7 6 4) 9-9 (0 1 2 3 5 6 7 8 10) (6 7 6 6 8 3) 9-10 (0 1 2 3 4 6 7 9 10) (6 6 8 6 6 4) 9-11 (0 1 2 3 5 6 7 9 10) (6 6 7 7 7 3) 9-12 (0 1 2 4 5 6 8 9 10) (6 6 6 9 6 3) 10-1 (0 1 2 3 4 5 6 7 8 9) (9 8 8 8 8 4) 10-2 (0 1 2 3 4 5 6 7 8 10) (8 9 8 8 8 4) 10-3 (0 1 2 3 4 5 6 7 9 10) (8 8 9 8 8 4) 10-4 (0 1 2 3 4 5 6 8 9 10) (8 8 8 9 8 4) 10-5 (0 1 2 3 4 5 7 8 9 10) (8 8 8 8 9 4) 10-6 (0 1 2 3 4 6 7 8 9 10) (8 8 8 8 8 5) F-Name P-Class-Sets Order No. ------------------------------------- a. 6-1 (0 1 2 3 4 5) 1st Order b. 6-8 (0 2 3 4 5 7) c. 6-32 (0 2 4 5 7 9) ------------------------------------- d. 6-7 (0 1 2 6 7 8) 2nd Order e. 6-20 (0 1 4 5 8 9) 3rd Order f. 6-35 (0 2 4 6 8 10) 6th Order Z-PAIRS F-Name Vector Name ------------------------------------- 4-Z15 (1 1 1 1 1 1) 4-Z29 5-Z12 (2 2 2 1 2 1) 5-Z36 5-Z17 (2 1 2 3 2 0) 5-Z37 5-Z18 (2 1 2 2 2 1) 5-Z38 6-Z3 (4 3 3 2 2 1) 6-Z36 6-Z4 (4 3 2 3 2 1) 6-Z37 6-Z6 (4 2 1 2 4 2) 6-Z38 6-Z10 (3 3 3 3 2 1) 6-Z39 6-Z11 (3 3 3 3 2 1) 6-Z40 6-Z12 (3 3 2 2 3 2) 6-Z41 6-Z13 (3 2 4 2 2 2) 6-Z42 6-Z17 (3 2 2 3 3 2) 6-Z43 6-Z19 (3 1 3 4 3 1) 6-Z44 6-Z23 (2 3 4 2 2 2) 6-Z45 6-Z24 (2 3 3 2 4 1) 6-Z46 6-Z25 (2 3 4 2 2 2) 6-Z47 6-Z26 (2 3 3 2 4 1) 6-Z48 6-Z28 (2 2 4 3 2 2) 6-Z49 6-Z29 (2 2 4 2 3 2) 6-Z50 7-Z12 (4 4 4 3 4 2) 7-Z36 7-Z17 (4 3 4 5 4 1) 7-Z37 7-Z18 (4 3 4 4 4 2) 7-Z38 8-Z15 (5 5 5 5 5 3) 8-Z29