Safe Haskell | Safe |
---|---|
Language | Haskell98 |
Allen Forte. The Structure of Atonal Music. Yale University Press, New Haven, 1973.
- t_rotations :: [Z12] -> [[Z12]]
- ti_rotations :: [Z12] -> [[Z12]]
- forte_prime :: [Z12] -> [Z12]
- t_prime :: [Z12] -> [Z12]
- type SC_Name = SC_Name
- sc_table :: [(SC_Name, [Z12])]
- sc_name :: [Z12] -> SC_Name
- sc_name_long :: [Z12] -> SC_Name
- sc :: SC_Name -> [Z12]
- scs :: [[Z12]]
- scs_n :: Integral i => i -> [[Z12]]
- bip :: [Z12] -> [Z12]
- ic :: Z12 -> Z12
- icv :: Integral i => [Z12] -> [i]
- icv' :: [Z12] -> [Int]
- z_relation_of :: [Z12] -> Maybe [Z12]
Prime form
t_rotations :: [Z12] -> [[Z12]] Source #
T-related rotations of p.
t_rotations [0,1,3] == [[0,1,3],[0,2,11],[0,9,10]]
ti_rotations :: [Z12] -> [[Z12]] Source #
T/I-related rotations of p.
ti_rotations [0,1,3] == [[0,1,3],[0,2,11],[0,9,10] ,[0,9,11],[0,2,3],[0,1,10]]
forte_prime :: [Z12] -> [Z12] Source #
Forte prime form, ie. cmp_prime
of forte_cmp
.
forte_prime [0,1,3,6,8,9] == [0,1,3,6,8,9] forte_prime [0,2,3,6,7] == [0,1,4,5,7]
t_prime :: [Z12] -> [Z12] Source #
Transpositional equivalence prime form, ie. t_cmp_prime
of
forte_cmp
.
(forte_prime [0,2,3],t_prime [0,2,3]) == ([0,1,3],[0,2,3])
Set Class Table
sc_table :: [(SC_Name, [Z12])] Source #
The set-class table (Forte prime forms).
length sc_table == 224
sc_name :: [Z12] -> SC_Name Source #
Lookup a set-class name. The input set is subject to
forte_prime
before lookup.
sc_name [0,2,3,6,7] == "5-Z18" sc_name [0,1,4,6,7,8] == "6-Z17"
sc_name_long :: [Z12] -> SC_Name Source #
sc :: SC_Name -> [Z12] Source #
Lookup a set-class given a set-class name.
sc "6-Z17" == [0,1,2,4,7,8]
List of set classes (the set class universe).
let r = [("0-1",[0,0,0,0,0,0]) ,("1-1",[0,0,0,0,0,0]) ,("2-1",[1,0,0,0,0,0]) ,("2-2",[0,1,0,0,0,0]) ,("2-3",[0,0,1,0,0,0]) ,("2-4",[0,0,0,1,0,0]) ,("2-5",[0,0,0,0,1,0]) ,("2-6",[0,0,0,0,0,1]) ,("3-1",[2,1,0,0,0,0]) ,("3-2",[1,1,1,0,0,0]) ,("3-3",[1,0,1,1,0,0]) ,("3-4",[1,0,0,1,1,0]) ,("3-5",[1,0,0,0,1,1]) ,("3-6",[0,2,0,1,0,0]) ,("3-7",[0,1,1,0,1,0]) ,("3-8",[0,1,0,1,0,1]) ,("3-9",[0,1,0,0,2,0]) ,("3-10",[0,0,2,0,0,1]) ,("3-11",[0,0,1,1,1,0]) ,("3-12",[0,0,0,3,0,0]) ,("4-1",[3,2,1,0,0,0]) ,("4-2",[2,2,1,1,0,0]) ,("4-3",[2,1,2,1,0,0]) ,("4-4",[2,1,1,1,1,0]) ,("4-5",[2,1,0,1,1,1]) ,("4-6",[2,1,0,0,2,1]) ,("4-7",[2,0,1,2,1,0]) ,("4-8",[2,0,0,1,2,1]) ,("4-9",[2,0,0,0,2,2]) ,("4-10",[1,2,2,0,1,0]) ,("4-11",[1,2,1,1,1,0]) ,("4-12",[1,1,2,1,0,1]) ,("4-13",[1,1,2,0,1,1]) ,("4-14",[1,1,1,1,2,0]) ,("4-Z15",[1,1,1,1,1,1]) ,("4-16",[1,1,0,1,2,1]) ,("4-17",[1,0,2,2,1,0]) ,("4-18",[1,0,2,1,1,1]) ,("4-19",[1,0,1,3,1,0]) ,("4-20",[1,0,1,2,2,0]) ,("4-21",[0,3,0,2,0,1]) ,("4-22",[0,2,1,1,2,0]) ,("4-23",[0,2,1,0,3,0]) ,("4-24",[0,2,0,3,0,1]) ,("4-25",[0,2,0,2,0,2]) ,("4-26",[0,1,2,1,2,0]) ,("4-27",[0,1,2,1,1,1]) ,("4-28",[0,0,4,0,0,2]) ,("4-Z29",[1,1,1,1,1,1]) ,("5-1",[4,3,2,1,0,0]) ,("5-2",[3,3,2,1,1,0]) ,("5-3",[3,2,2,2,1,0]) ,("5-4",[3,2,2,1,1,1]) ,("5-5",[3,2,1,1,2,1]) ,("5-6",[3,1,1,2,2,1]) ,("5-7",[3,1,0,1,3,2]) ,("5-8",[2,3,2,2,0,1]) ,("5-9",[2,3,1,2,1,1]) ,("5-10",[2,2,3,1,1,1]) ,("5-11",[2,2,2,2,2,0]) ,("5-Z12",[2,2,2,1,2,1]) ,("5-13",[2,2,1,3,1,1]) ,("5-14",[2,2,1,1,3,1]) ,("5-15",[2,2,0,2,2,2]) ,("5-16",[2,1,3,2,1,1]) ,("5-Z17",[2,1,2,3,2,0]) ,("5-Z18",[2,1,2,2,2,1]) ,("5-19",[2,1,2,1,2,2]) ,("5-20",[2,1,1,2,3,1]) ,("5-21",[2,0,2,4,2,0]) ,("5-22",[2,0,2,3,2,1]) ,("5-23",[1,3,2,1,3,0]) ,("5-24",[1,3,1,2,2,1]) ,("5-25",[1,2,3,1,2,1]) ,("5-26",[1,2,2,3,1,1]) ,("5-27",[1,2,2,2,3,0]) ,("5-28",[1,2,2,2,1,2]) ,("5-29",[1,2,2,1,3,1]) ,("5-30",[1,2,1,3,2,1]) ,("5-31",[1,1,4,1,1,2]) ,("5-32",[1,1,3,2,2,1]) ,("5-33",[0,4,0,4,0,2]) ,("5-34",[0,3,2,2,2,1]) ,("5-35",[0,3,2,1,4,0]) ,("5-Z36",[2,2,2,1,2,1]) ,("5-Z37",[2,1,2,3,2,0]) ,("5-Z38",[2,1,2,2,2,1]) ,("6-1",[5,4,3,2,1,0]) ,("6-2",[4,4,3,2,1,1]) ,("6-Z3",[4,3,3,2,2,1]) ,("6-Z4",[4,3,2,3,2,1]) ,("6-5",[4,2,2,2,3,2]) ,("6-Z6",[4,2,1,2,4,2]) ,("6-7",[4,2,0,2,4,3]) ,("6-8",[3,4,3,2,3,0]) ,("6-9",[3,4,2,2,3,1]) ,("6-Z10",[3,3,3,3,2,1]) ,("6-Z11",[3,3,3,2,3,1]) ,("6-Z12",[3,3,2,2,3,2]) ,("6-Z13",[3,2,4,2,2,2]) ,("6-14",[3,2,3,4,3,0]) ,("6-15",[3,2,3,4,2,1]) ,("6-16",[3,2,2,4,3,1]) ,("6-Z17",[3,2,2,3,3,2]) ,("6-18",[3,2,2,2,4,2]) ,("6-Z19",[3,1,3,4,3,1]) ,("6-20",[3,0,3,6,3,0]) ,("6-21",[2,4,2,4,1,2]) ,("6-22",[2,4,1,4,2,2]) ,("6-Z23",[2,3,4,2,2,2]) ,("6-Z24",[2,3,3,3,3,1]) ,("6-Z25",[2,3,3,2,4,1]) ,("6-Z26",[2,3,2,3,4,1]) ,("6-27",[2,2,5,2,2,2]) ,("6-Z28",[2,2,4,3,2,2]) ,("6-Z29",[2,2,4,2,3,2]) ,("6-30",[2,2,4,2,2,3]) ,("6-31",[2,2,3,4,3,1]) ,("6-32",[1,4,3,2,5,0]) ,("6-33",[1,4,3,2,4,1]) ,("6-34",[1,4,2,4,2,2]) ,("6-35",[0,6,0,6,0,3]) ,("6-Z36",[4,3,3,2,2,1]) ,("6-Z37",[4,3,2,3,2,1]) ,("6-Z38",[4,2,1,2,4,2]) ,("6-Z39",[3,3,3,3,2,1]) ,("6-Z40",[3,3,3,2,3,1]) ,("6-Z41",[3,3,2,2,3,2]) ,("6-Z42",[3,2,4,2,2,2]) ,("6-Z43",[3,2,2,3,3,2]) ,("6-Z44",[3,1,3,4,3,1]) ,("6-Z45",[2,3,4,2,2,2]) ,("6-Z46",[2,3,3,3,3,1]) ,("6-Z47",[2,3,3,2,4,1]) ,("6-Z48",[2,3,2,3,4,1]) ,("6-Z49",[2,2,4,3,2,2]) ,("6-Z50",[2,2,4,2,3,2]) ,("7-1",[6,5,4,3,2,1]) ,("7-2",[5,5,4,3,3,1]) ,("7-3",[5,4,4,4,3,1]) ,("7-4",[5,4,4,3,3,2]) ,("7-5",[5,4,3,3,4,2]) ,("7-6",[5,3,3,4,4,2]) ,("7-7",[5,3,2,3,5,3]) ,("7-8",[4,5,4,4,2,2]) ,("7-9",[4,5,3,4,3,2]) ,("7-10",[4,4,5,3,3,2]) ,("7-11",[4,4,4,4,4,1]) ,("7-Z12",[4,4,4,3,4,2]) ,("7-13",[4,4,3,5,3,2]) ,("7-14",[4,4,3,3,5,2]) ,("7-15",[4,4,2,4,4,3]) ,("7-16",[4,3,5,4,3,2]) ,("7-Z17",[4,3,4,5,4,1]) ,("7-Z18",[4,3,4,4,4,2]) ,("7-19",[4,3,4,3,4,3]) ,("7-20",[4,3,3,4,5,2]) ,("7-21",[4,2,4,6,4,1]) ,("7-22",[4,2,4,5,4,2]) ,("7-23",[3,5,4,3,5,1]) ,("7-24",[3,5,3,4,4,2]) ,("7-25",[3,4,5,3,4,2]) ,("7-26",[3,4,4,5,3,2]) ,("7-27",[3,4,4,4,5,1]) ,("7-28",[3,4,4,4,3,3]) ,("7-29",[3,4,4,3,5,2]) ,("7-30",[3,4,3,5,4,2]) ,("7-31",[3,3,6,3,3,3]) ,("7-32",[3,3,5,4,4,2]) ,("7-33",[2,6,2,6,2,3]) ,("7-34",[2,5,4,4,4,2]) ,("7-35",[2,5,4,3,6,1]) ,("7-Z36",[4,4,4,3,4,2]) ,("7-Z37",[4,3,4,5,4,1]) ,("7-Z38",[4,3,4,4,4,2]) ,("8-1",[7,6,5,4,4,2]) ,("8-2",[6,6,5,5,4,2]) ,("8-3",[6,5,6,5,4,2]) ,("8-4",[6,5,5,5,5,2]) ,("8-5",[6,5,4,5,5,3]) ,("8-6",[6,5,4,4,6,3]) ,("8-7",[6,4,5,6,5,2]) ,("8-8",[6,4,4,5,6,3]) ,("8-9",[6,4,4,4,6,4]) ,("8-10",[5,6,6,4,5,2]) ,("8-11",[5,6,5,5,5,2]) ,("8-12",[5,5,6,5,4,3]) ,("8-13",[5,5,6,4,5,3]) ,("8-14",[5,5,5,5,6,2]) ,("8-Z15",[5,5,5,5,5,3]) ,("8-16",[5,5,4,5,6,3]) ,("8-17",[5,4,6,6,5,2]) ,("8-18",[5,4,6,5,5,3]) ,("8-19",[5,4,5,7,5,2]) ,("8-20",[5,4,5,6,6,2]) ,("8-21",[4,7,4,6,4,3]) ,("8-22",[4,6,5,5,6,2]) ,("8-23",[4,6,5,4,7,2]) ,("8-24",[4,6,4,7,4,3]) ,("8-25",[4,6,4,6,4,4]) ,("8-26",[4,5,6,5,6,2]) ,("8-27",[4,5,6,5,5,3]) ,("8-28",[4,4,8,4,4,4]) ,("8-Z29",[5,5,5,5,5,3]) ,("9-1",[8,7,6,6,6,3]) ,("9-2",[7,7,7,6,6,3]) ,("9-3",[7,6,7,7,6,3]) ,("9-4",[7,6,6,7,7,3]) ,("9-5",[7,6,6,6,7,4]) ,("9-6",[6,8,6,7,6,3]) ,("9-7",[6,7,7,6,7,3]) ,("9-8",[6,7,6,7,6,4]) ,("9-9",[6,7,6,6,8,3]) ,("9-10",[6,6,8,6,6,4]) ,("9-11",[6,6,7,7,7,3]) ,("9-12",[6,6,6,9,6,3]) ,("10-1",[9,8,8,8,8,4]) ,("10-2",[8,9,8,8,8,4]) ,("10-3",[8,8,9,8,8,4]) ,("10-4",[8,8,8,9,8,4]) ,("10-5",[8,8,8,8,9,4]) ,("10-6",[8,8,8,8,8,5]) ,("11-1",[10,10,10,10,10,5]) ,("12-1",[12,12,12,12,12,6])] in let icvs = map icv scs in zip (map sc_name scs) icvs == r
scs_n :: Integral i => i -> [[Z12]] Source #
Cardinality n subset of scs
.
map (length . scs_n) [1..11] == [1,6,12,29,38,50,38,29,12,6,1]
BIP Metric
bip :: [Z12] -> [Z12] Source #
Basic interval pattern, see Allen Forte "The Basic Interval Patterns" JMT 17/2 (1973):234-272
>>>
pct bip 0t95728e3416
11223344556
bip [0,10,9,5,7,2,8,11,3,4,1,6] == [1,1,2,2,3,3,4,4,5,5,6] bip (pco "0t95728e3416") == [1,1,2,2,3,3,4,4,5,5,6]
ICV Metric
Interval class of Z12 interval i.
map ic [5,6,7] == [5,6,5] map ic [-13,-1,0,1,13] == [1,1,0,1,1]
icv :: Integral i => [Z12] -> [i] Source #
Forte notation for interval class vector.
icv [0,1,2,4,7,8] == [3,2,2,3,3,2]