Music.Theory.Z12.Forte_1973

Description

Allen Forte. The Structure of Atonal Music. Yale University Press, New Haven, 1973.

Synopsis

# 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 :: SC_Name -> [Z12] Source #

Lookup a set-class given a set-class name.

sc "6-Z17" == [0,1,2,4,7,8]

scs :: [[Z12]] Source #

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

ic :: Z12 -> Z12 Source #

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]

icv' :: [Z12] -> [Int] Source #

Type specialise...

# Z-relation

z_relation_of :: [Z12] -> Maybe [Z12] Source #

Locate Z relation of set class.

fmap sc_name (z_relation_of (sc "7-Z12")) == Just "7-Z36"