Music.Theory.Z12.Castren_1994

Marcus Castrén. RECREL: A Similarity Measure for Set-Classes. PhD thesis, Sibelius Academy, Helsinki, 1994.

Documentation

t_prime :: [Z12] -> [Z12]

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])

inv_sym :: [Z12] -> Bool

Is p symmetrical under inversion.

 map inv_sym (scs_n 2) == [True,True,True,True,True,True]
 map (fromEnum.inv_sym) (scs_n 3) == [1,0,0,0,0,1,0,0,1,1,0,1]

sc_t_ti :: [Z12] -> Maybe ([Z12], [Z12])

If p is not inv_sym then (p,invert 0 p) else Nothing.

 sc_t_ti [0,2,4] == Nothing
 sc_t_ti [0,1,3] == Just ([0,1,3],[0,2,3])

t_sc_table :: [(SC_Name, [Z12])]

Transpositional equivalence variant of Forte's sc_table. The inversionally related classes are distinguished by labels A and B; the class providing the best normal order (Forte 1973) is always the A class. If neither A nor B appears in the name of a set-class, it is inversionally symmetrical.

 (length sc_table,length t_sc_table) == (224,352)
 lookup "5-Z18B" t_sc_table == Just [0,2,3,6,7]

t_sc_name :: [Z12] -> SC_Name

Lookup a set-class name. The input set is subject to t_prime before lookup.

 t_sc_name [0,2,3,6,7] == "5-Z18B"
 t_sc_name [0,1,4,6,7,8] == "6-Z17B"

t_sc :: SC_Name -> [Z12]

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

 t_sc "6-Z17A" == [0,1,2,4,7,8]

t_scs :: [[Z12]]

List of set classes.

t_scs_n :: Integral i => i -> [[Z12]]

Cardinality n subset of t_scs.

 map (length . t_scs_n) [2..10] == [6,19,43,66,80,66,43,19,6]

t_subsets :: [Z12] -> [Z12] -> [[Z12]]

T-related q that are subsets of p.

 t_subsets [0,1,2,3,4] [0,1]  == [[0,1],[1,2],[2,3],[3,4]]
 t_subsets [0,1,2,3,4] [0,1,4] == [[0,1,4]]
 t_subsets [0,2,3,6,7] [0,1,4] == [[2,3,6]]

ti_subsets :: [Z12] -> [Z12] -> [[Z12]]

T/I-related q that are subsets of p.

 ti_subsets [0,1,2,3,4] [0,1]  == [[0,1],[1,2],[2,3],[3,4]]
 ti_subsets [0,1,2,3,4] [0,1,4] == [[0,1,4],[0,3,4]]
 ti_subsets [0,2,3,6,7] [0,1,4] == [[2,3,6],[3,6,7]]

rle :: (Eq a, Integral i) => [a] -> [(i, a)]

Trivial run length encoder.

 rle "abbcccdde" == [(1,'a'),(2,'b'),(3,'c'),(2,'d'),(1,'e')]

rle_decode :: Integral i => [(i, a)] -> [a]

Inverse of rle.

 rle_decode [(5,'a'),(4,'b')] == "aaaaabbbb"

rle_length :: Integral i => [(i, a)] -> i

Length of rle encoded sequence.

 rle_length [(5,'a'),(4,'b')] == 9

t_n_class_vector :: (Num a, Integral i) => i -> [Z12] -> [a]

T-equivalence n-class vector (subset-class vector, nCV).

 t_n_class_vector 2 [0..4] == [4,3,2,1,0,0]
 rle (t_n_class_vector 3 [0..4]) == [(1,3),(2,2),(2,1),(4,0),(1,1),(9,0)]
 rle (t_n_class_vector 4 [0..4]) == [(1,2),(3,1),(39,0)]

ti_n_class_vector :: (Num b, Integral i) => i -> [Z12] -> [b]

T/I-equivalence n-class vector (subset-class vector, nCV).

 ti_n_class_vector 2 [0..4] == [4,3,2,1,0,0]
 ti_n_class_vector 3 [0,1,2,3,4] == [3,4,2,0,0,1,0,0,0,0,0,0]
 rle (ti_n_class_vector 4 [0,1,2,3,4]) == [(2,2),(1,1),(26,0)]

dyad_class_percentage_vector :: Integral i => [Z12] -> [i]

icv scaled by sum of icv.

 dyad_class_percentage_vector [0,1,2,3,4] == [40,30,20,10,0,0]
 dyad_class_percentage_vector [0,1,4,5,7] == [20,10,20,20,20,10]

rel :: Integral i => [Z12] -> [Z12] -> Ratio i

rel metric.

 rel [0,1,2,3,4] [0,1,4,5,7] == 40
 rel [0,1,2,3,4] [0,2,4,6,8] == 60
 rel [0,1,4,5,7] [0,2,4,6,8] == 60