hmt-0.11: Music/Theory/Table.hs
-- | Set class tables and database.
module Music.Theory.Table where
import Data.List
import Data.Maybe
import Music.Theory.Prime
-- | Synonym for 'String'.
type SC_Name = String
-- | The set-class table (Forte prime forms).
sc_table :: (Integral a) => [(SC_Name,[a])]
sc_table =
[("0-1",[])
,("1-1",[0])
,("2-1",[0,1])
,("2-2",[0,2])
,("2-3",[0,3])
,("2-4",[0,4])
,("2-5",[0,5])
,("2-6",[0,6])
,("3-1",[0,1,2])
,("3-2",[0,1,3])
,("3-3",[0,1,4])
,("3-4",[0,1,5])
,("3-5",[0,1,6])
,("3-6",[0,2,4])
,("3-7",[0,2,5])
,("3-8",[0,2,6])
,("3-9",[0,2,7])
,("3-10",[0,3,6])
,("3-11",[0,3,7])
,("3-12",[0,4,8])
,("4-1",[0,1,2,3])
,("4-2",[0,1,2,4])
,("4-3",[0,1,3,4])
,("4-4",[0,1,2,5])
,("4-5",[0,1,2,6])
,("4-6",[0,1,2,7])
,("4-7",[0,1,4,5])
,("4-8",[0,1,5,6])
,("4-9",[0,1,6,7])
,("4-10",[0,2,3,5])
,("4-11",[0,1,3,5])
,("4-12",[0,2,3,6])
,("4-13",[0,1,3,6])
,("4-14",[0,2,3,7])
,("4-Z15",[0,1,4,6])
,("4-16",[0,1,5,7])
,("4-17",[0,3,4,7])
,("4-18",[0,1,4,7])
,("4-19",[0,1,4,8])
,("4-20",[0,1,5,8])
,("4-21",[0,2,4,6])
,("4-22",[0,2,4,7])
,("4-23",[0,2,5,7])
,("4-24",[0,2,4,8])
,("4-25",[0,2,6,8])
,("4-26",[0,3,5,8])
,("4-27",[0,2,5,8])
,("4-28",[0,3,6,9])
,("4-Z29",[0,1,3,7])
,("5-1",[0,1,2,3,4])
,("5-2",[0,1,2,3,5])
,("5-3",[0,1,2,4,5])
,("5-4",[0,1,2,3,6])
,("5-5",[0,1,2,3,7])
,("5-6",[0,1,2,5,6])
,("5-7",[0,1,2,6,7])
,("5-8",[0,2,3,4,6])
,("5-9",[0,1,2,4,6])
,("5-10",[0,1,3,4,6])
,("5-11",[0,2,3,4,7])
,("5-Z12",[0,1,3,5,6])
,("5-13",[0,1,2,4,8])
,("5-14",[0,1,2,5,7])
,("5-15",[0,1,2,6,8])
,("5-16",[0,1,3,4,7])
,("5-Z17",[0,1,3,4,8])
,("5-Z18",[0,1,4,5,7])
,("5-19",[0,1,3,6,7])
,("5-20",[0,1,3,7,8])
,("5-21",[0,1,4,5,8])
,("5-22",[0,1,4,7,8])
,("5-23",[0,2,3,5,7])
,("5-24",[0,1,3,5,7])
,("5-25",[0,2,3,5,8])
,("5-26",[0,2,4,5,8])
,("5-27",[0,1,3,5,8])
,("5-28",[0,2,3,6,8])
,("5-29",[0,1,3,6,8])
,("5-30",[0,1,4,6,8])
,("5-31",[0,1,3,6,9])
,("5-32",[0,1,4,6,9])
,("5-33",[0,2,4,6,8])
,("5-34",[0,2,4,6,9])
,("5-35",[0,2,4,7,9])
,("5-Z36",[0,1,2,4,7])
,("5-Z37",[0,3,4,5,8])
,("5-Z38",[0,1,2,5,8])
,("6-1",[0,1,2,3,4,5])
,("6-2",[0,1,2,3,4,6])
,("6-Z3",[0,1,2,3,5,6])
,("6-Z4",[0,1,2,4,5,6])
,("6-5",[0,1,2,3,6,7])
,("6-Z6",[0,1,2,5,6,7])
,("6-7",[0,1,2,6,7,8])
,("6-8",[0,2,3,4,5,7])
,("6-9",[0,1,2,3,5,7])
,("6-Z10",[0,1,3,4,5,7])
,("6-Z11",[0,1,2,4,5,7])
,("6-Z12",[0,1,2,4,6,7])
,("6-Z13",[0,1,3,4,6,7])
,("6-14",[0,1,3,4,5,8])
,("6-15",[0,1,2,4,5,8])
,("6-16",[0,1,4,5,6,8])
,("6-Z17",[0,1,2,4,7,8])
,("6-18",[0,1,2,5,7,8])
,("6-Z19",[0,1,3,4,7,8])
,("6-20",[0,1,4,5,8,9])
,("6-21",[0,2,3,4,6,8])
,("6-22",[0,1,2,4,6,8])
,("6-Z23",[0,2,3,5,6,8])
,("6-Z24",[0,1,3,4,6,8])
,("6-Z25",[0,1,3,5,6,8])
,("6-Z26",[0,1,3,5,7,8])
,("6-27",[0,1,3,4,6,9])
,("6-Z28",[0,1,3,5,6,9])
,("6-Z29",[0,1,3,6,8,9])
,("6-30",[0,1,3,6,7,9])
,("6-31",[0,1,3,5,8,9])
,("6-32",[0,2,4,5,7,9])
,("6-33",[0,2,3,5,7,9])
,("6-34",[0,1,3,5,7,9])
,("6-35",[0,2,4,6,8,10])
,("6-Z36",[0,1,2,3,4,7])
,("6-Z37",[0,1,2,3,4,8])
,("6-Z38",[0,1,2,3,7,8])
,("6-Z39",[0,2,3,4,5,8])
,("6-Z40",[0,1,2,3,5,8])
,("6-Z41",[0,1,2,3,6,8])
,("6-Z42",[0,1,2,3,6,9])
,("6-Z43",[0,1,2,5,6,8])
,("6-Z44",[0,1,2,5,6,9])
,("6-Z45",[0,2,3,4,6,9])
,("6-Z46",[0,1,2,4,6,9])
,("6-Z47",[0,1,2,4,7,9])
,("6-Z48",[0,1,2,5,7,9])
,("6-Z49",[0,1,3,4,7,9])
,("6-Z50",[0,1,4,6,7,9])
,("7-1",[0,1,2,3,4,5,6])
,("7-2",[0,1,2,3,4,5,7])
,("7-3",[0,1,2,3,4,5,8])
,("7-4",[0,1,2,3,4,6,7])
,("7-5",[0,1,2,3,5,6,7])
,("7-6",[0,1,2,3,4,7,8])
,("7-7",[0,1,2,3,6,7,8])
,("7-8",[0,2,3,4,5,6,8])
,("7-9",[0,1,2,3,4,6,8])
,("7-10",[0,1,2,3,4,6,9])
,("7-11",[0,1,3,4,5,6,8])
,("7-Z12",[0,1,2,3,4,7,9])
,("7-13",[0,1,2,4,5,6,8])
,("7-14",[0,1,2,3,5,7,8])
,("7-15",[0,1,2,4,6,7,8])
,("7-16",[0,1,2,3,5,6,9])
,("7-Z17",[0,1,2,4,5,6,9])
,("7-Z18",[0,1,2,3,5,8,9])
,("7-19",[0,1,2,3,6,7,9])
,("7-20",[0,1,2,4,7,8,9])
,("7-21",[0,1,2,4,5,8,9])
,("7-22",[0,1,2,5,6,8,9])
,("7-23",[0,2,3,4,5,7,9])
,("7-24",[0,1,2,3,5,7,9])
,("7-25",[0,2,3,4,6,7,9])
,("7-26",[0,1,3,4,5,7,9])
,("7-27",[0,1,2,4,5,7,9])
,("7-28",[0,1,3,5,6,7,9])
,("7-29",[0,1,2,4,6,7,9])
,("7-30",[0,1,2,4,6,8,9])
,("7-31",[0,1,3,4,6,7,9])
,("7-32",[0,1,3,4,6,8,9])
,("7-33",[0,1,2,4,6,8,10])
,("7-34",[0,1,3,4,6,8,10])
,("7-35",[0,1,3,5,6,8,10])
,("7-Z36",[0,1,2,3,5,6,8])
,("7-Z37",[0,1,3,4,5,7,8])
,("7-Z38",[0,1,2,4,5,7,8])
,("8-1",[0,1,2,3,4,5,6,7])
,("8-2",[0,1,2,3,4,5,6,8])
,("8-3",[0,1,2,3,4,5,6,9])
,("8-4",[0,1,2,3,4,5,7,8])
,("8-5",[0,1,2,3,4,6,7,8])
,("8-6",[0,1,2,3,5,6,7,8])
,("8-7",[0,1,2,3,4,5,8,9])
,("8-8",[0,1,2,3,4,7,8,9])
,("8-9",[0,1,2,3,6,7,8,9])
,("8-10",[0,2,3,4,5,6,7,9])
,("8-11",[0,1,2,3,4,5,7,9])
,("8-12",[0,1,3,4,5,6,7,9])
,("8-13",[0,1,2,3,4,6,7,9])
,("8-14",[0,1,2,4,5,6,7,9])
,("8-Z15",[0,1,2,3,4,6,8,9])
,("8-16",[0,1,2,3,5,7,8,9])
,("8-17",[0,1,3,4,5,6,8,9])
,("8-18",[0,1,2,3,5,6,8,9])
,("8-19",[0,1,2,4,5,6,8,9])
,("8-20",[0,1,2,4,5,7,8,9])
,("8-21",[0,1,2,3,4,6,8,10])
,("8-22",[0,1,2,3,5,6,8,10])
,("8-23",[0,1,2,3,5,7,8,10])
,("8-24",[0,1,2,4,5,6,8,10])
,("8-25",[0,1,2,4,6,7,8,10])
,("8-26",[0,1,2,4,5,7,9,10])
,("8-27",[0,1,2,4,5,7,8,10])
,("8-28",[0,1,3,4,6,7,9,10])
,("8-Z29",[0,1,2,3,5,6,7,9])
,("9-1",[0,1,2,3,4,5,6,7,8])
,("9-2",[0,1,2,3,4,5,6,7,9])
,("9-3",[0,1,2,3,4,5,6,8,9])
,("9-4",[0,1,2,3,4,5,7,8,9])
,("9-5",[0,1,2,3,4,6,7,8,9])
,("9-6",[0,1,2,3,4,5,6,8,10])
,("9-7",[0,1,2,3,4,5,7,8,10])
,("9-8",[0,1,2,3,4,6,7,8,10])
,("9-9",[0,1,2,3,5,6,7,8,10])
,("9-10",[0,1,2,3,4,6,7,9,10])
,("9-11",[0,1,2,3,5,6,7,9,10])
,("9-12",[0,1,2,4,5,6,8,9,10])
,("10-1",[0,1,2,3,4,5,6,7,8,9])
,("10-2",[0,1,2,3,4,5,6,7,8,10])
,("10-3",[0,1,2,3,4,5,6,7,9,10])
,("10-4",[0,1,2,3,4,5,6,8,9,10])
,("10-5",[0,1,2,3,4,5,7,8,9,10])
,("10-6",[0,1,2,3,4,6,7,8,9,10])
,("11-1",[0,1,2,3,4,5,6,7,8,9,10])
,("12-1",[0,1,2,3,4,5,6,7,8,9,10,11])]
-- | Lookup a set-class name. The input set is subject to
-- 'forte_prime' before lookup.
--
-- > sc_name [0,1,4,6,7,8] == "6-Z17"
sc_name :: (Integral a) => [a] -> SC_Name
sc_name p =
let n = find (\(_,q) -> forte_prime p == q) sc_table
in fst (fromJust n)
-- | Lookup a set-class given a set-class name.
--
-- > sc "6-Z17" == [0,1,2,4,7,8]
sc :: (Integral a) => SC_Name -> [a]
sc n = snd (fromJust (find (\(m,_) -> n == m) sc_table))
-- | List of set classes.
scs :: (Integral a) => [[a]]
scs = map snd sc_table
-- | Set class database with descriptors for historically and
-- theoretically significant set classes.
--
-- > lookup "6-Z17" sc_db == Just "All-Trichord Hexachord"
-- > lookup "7-35" sc_db == Just "diatonic collection (d)"
sc_db :: [(SC_Name,String)]
sc_db =
[ ("4-Z15","All-Interval Tetrachord (see also 4-Z29)")
,("4-Z29","All-Interval Tetrachord (see also 4-Z15)")
,("6-Z17","All-Trichord Hexachord")
,("8-Z15","All-Tetrachord Octochord (see also 8-Z29)")
,("8-Z29","All-Tetrachord Octochord (see also 8-Z15)")
,("6-1","A-Type All-Combinatorial Hexachord")
,("6-8","B-Type All-Combinatorial Hexachord")
,("6-32","C-Type All-Combinatorial Hexachord")
,("6-7","D-Type All-Combinatorial Hexachord")
,("6-20","E-Type All-Combinatorial Hexachord")
,("6-35","F-Type All-Combinatorial Hexachord")
,("7-35","diatonic collection (d)")
,("7-34","ascending melodic minor collection")
,("8-28","octotonic collection (Messiaen Mode II)")
,("6-35","wholetone collection")
,("3-10","diminished triad")
,("3-11","major/minor triad")
,("3-12","augmented triad")
,("4-19","minor major-seventh chord")
,("4-20","major-seventh chord")
,("4-25","french augmented sixth chord")
,("4-28","dimished-seventh chord")
,("4-26","minor-seventh chord")
,("4-27","half-dimished seventh(P)/dominant-seventh(I) chord")
,("6-30","Petrushka Chord {0476a1},3-11 at T6")
,("6-34","Mystic Chord {06a492}")
,("6-Z44","Schoenberg Signature Set,3-3 at T5 or T7")
,("6-Z19","complement of 6-Z44,3-11 at T1 or TB")
,("9-12","Messiaen Mode III (nontonic collection)")
,("8-9","Messian Mode IV")
,("7-31","The only seven-element subset of 8-28. ")
,("5-31","The only five-element superset of 4-28.")
,("5-33","The only five-element subset of 6-35.")
,("7-33","The only seven-element superset of 6-35.")
,("5-21","The only five-element subset of 6-20.")
,("7-21","The only seven-element superset of 6-20.")
,("5-25","The only five-element subset of both 7-35 and 8-28.")
,("6-14","Any non-intersecting union of 3-6 and 3-12.") ]