Safe Haskell	Safe-Inferred
Language	Haskell2010

Music.Theory.Graph.Johnson_2014

Contents

Common
Map
Edge
Graph
P.12
P.14
P.31
P.114
P.125
P.131
P.148
P.162
P.172
P.177
P.178
P.196
P.201
P.205
IO

Description

Tom Johnson. Other Harmony: Beyond Tonal and Atonal. Editions 75, 2014.

Synopsis

type Z12 = Int8
dif :: Num a => (a, a) -> a
absdif :: Num a => (a, a) -> a
i_to_ic :: (Num a, Ord a) => a -> a
p2_and :: (t -> u -> Bool) -> (t -> u -> Bool) -> t -> u -> Bool
doi :: Eq t => [t] -> [t] -> Int
doi_of :: Eq t => Int -> [t] -> [t] -> Bool
loc_dif :: Num t => [t] -> [t] -> t
loc_dif_of :: (Eq t, Num t) => t -> [t] -> [t] -> Bool
loc_dif_in :: (Eq t, Num t) => [t] -> [t] -> [t] -> Bool
loc_dif_n :: (Eq t, Num i) => [t] -> [t] -> i
loc_dif_n_of :: Eq t => Int -> [t] -> [t] -> Bool
min_vl :: (Num a, Ord a) => [a] -> [a] -> a
min_vl_of :: (Num a, Ord a) => a -> [a] -> [a] -> Bool
min_vl_in :: (Num a, Ord a) => [a] -> [a] -> [a] -> Bool
combinations2 :: Ord t => [t] -> [(t, t)]
set_pp :: Show t => [t] -> String
tto_rel_to :: Integral t => Z t -> [t] -> [t] -> [Tto t]
set_pp_tto_rel :: (Integral t, Show t) => Z t -> [t] -> [t] -> String
m_get :: Ord k => Map k v -> k -> v
m_doi_of :: Map Int [Z12] -> Int -> Int -> Int -> Bool
e_add_id :: k -> [(t, u)] -> [((k, t), (k, u))]
gen_edges :: (t -> t -> Bool) -> [t] -> [(t, t)]
gen_u_edges :: Ord a => (a -> a -> Bool) -> [a] -> [(a, a)]
oh_def_opt :: [Dot_Meta_Attr]
gen_graph :: Ord v => [Dot_Meta_Attr] -> Graph_Pp v e -> [Edge_Lbl v e] -> [String]
gen_graph_ul :: Ord v => [Dot_Meta_Attr] -> (v -> String) -> [Edge v] -> [String]
gen_graph_ul_ty :: Ord v => String -> (v -> String) -> [Edge v] -> [String]
gen_flt_graph_pp :: Ord t => [Dot_Meta_Attr] -> ([t] -> String) -> ([t] -> [t] -> Bool) -> [[t]] -> [String]
gen_flt_graph :: (Ord t, Show t) => [Dot_Meta_Attr] -> ([t] -> [t] -> Bool) -> [[t]] -> [String]
circ_5 :: Integral a => Int -> a -> [a]
all_pairs :: [t] -> [u] -> [(t, u)]
adj :: [t] -> [(t, t)]
adj_cyc :: [t] -> [(t, t)]
p12_c5_eset :: [(Int, Int)]
e_add_label :: (Edge v -> l) -> [Edge v] -> [Edge_Lbl v l]
p12_c5_gr :: [String]
p12_euler_plane :: Euler_Plane Rational
p12_euler_plane_gr :: [String]
p14_eset :: ([(Int, Int)], [(Int, Int)], [(Int, Int)])
p14_mk_e :: [(Int, Int)] -> [(Key, Key)]
p14_edges_u :: [(Key, Key)]
p14_edges :: [(Key, Key)]
p14_mk_gr :: [Dot_Meta_Attr] -> [Edge Key] -> [String]
p14_gr_u :: [String]
p14_gr :: [String]
p14_gen_tonnetz_n :: Int -> [Int] -> [Int] -> [Int]
p14_gen_tonnetz_e :: Int -> [Int] -> [Int] -> [((Int, Int), Int)]
p14_nrt_gr :: [String]
p31_f_4_22 :: [Z12]
p31_e_set :: [([Z12], [Z12])]
p31_gr :: [String]
p114_f_3_7 :: [Z12]
p114_mk_o :: Show t => t -> [Dot_Meta_Attr]
p114_mk_gr :: Double -> ([Z12] -> [Z12] -> Bool) -> [String]
p114_f37_sc_pp :: [Z12] -> String
p114_g0 :: [String]
p114_g1 :: [String]
p114_gr_set :: [(String, [String])]
p125_gr :: [String]
p131_gr :: [String]
p148_mk_gr :: ([Int] -> [Int] -> Bool) -> [String]
p148_gr_set :: [(String, [String])]
p162_ch :: [[Int]]
p162_e :: [Edge [Int]]
p162_gr :: [String]
p172_nd_map :: Map Int [Z12]
p172_nd_e_set :: [(Int, Int)]
p172_nd_e_set_alt :: [Edge Int]
p172_gr :: Gr () ()
p172_set_pp :: Int -> String
p172_all_cyc :: ([[Int]], [[Int]])
p172_cyc0 :: [[Int]]
p172_g1 :: [String]
p172_g2 :: [String]
p172_g3 :: [String]
tto_tn :: Integral t => t -> Tto t
tto_tni :: Integral t => t -> Tto t
gen_tto_alt_seq :: Integral t => (t -> Tto t, t -> Tto t) -> Int -> t -> t -> t -> [Tto t]
gen_tni_seq :: Integral t => Int -> t -> t -> t -> [Tto t]
p172_c4 :: [[Tto Int]]
tto_seq_edges :: (Show t, Num t, Eq t) => [[Tto t]] -> [(String, String)]
p172_g4 :: [String]
p172_gr_set :: [(String, [String])]
partition_ic :: (Num t, Ord t, Show t) => t -> [t] -> ([t], [t])
p177_gr_set :: [(String, [String])]
type SC = [Int]
type PCSET = [Int]
ait :: [SC]
mk_bridge :: SC -> PCSET -> PCSET -> [PCSET]
mk_bridge_set :: [SC] -> PCSET -> PCSET -> [PCSET]
mk_bridge_set_seq :: [SC] -> [PCSET] -> [[PCSET]]
p178_i6_seq :: [PCSET]
p178_ch :: [(PCSET, [PCSET], PCSET)]
type ID = Char
p178_e :: [((ID, PCSET), (ID, PCSET))]
p178_gr_1 :: [String]
p178_gr_2 :: [String]
p196_gr :: [String]
type SET = [Int]
type E = (SET, SET)
bd_9_3_2_12 :: [SET]
p201_mk_e :: [Int] -> [E]
p201_e :: [[E]]
p201_o :: [Dot_Meta_Attr]
p201_gr_set :: [[String]]
p201_gr_join :: [String]
bd_9_3_2_34 :: [SET]
p205_mk_e :: [Int] -> [E]
p205_gr :: [String]
wr_graphs :: FilePath -> IO ()

Common

type Z12 = Int8 Source #

dif :: Num a => (a, a) -> a Source #

absdif :: Num a => (a, a) -> a Source #

i_to_ic :: (Num a, Ord a) => a -> a Source #

interval (0,11) to interval class (0,6)

p2_and :: (t -> u -> Bool) -> (t -> u -> Bool) -> t -> u -> Bool Source #

doi :: Eq t => [t] -> [t] -> Int Source #

degree of intersection

doi_of :: Eq t => Int -> [t] -> [t] -> Bool Source #

loc_dif :: Num t => [t] -> [t] -> t Source #

The sum of the pointwise absolute difference.

loc_dif_of :: (Eq t, Num t) => t -> [t] -> [t] -> Bool Source #

loc_dif_in :: (Eq t, Num t) => [t] -> [t] -> [t] -> Bool Source #

loc_dif_n :: (Eq t, Num i) => [t] -> [t] -> i Source #

The number of places that are, pointwise, not equal.

loc_dif_n "test" "pest" == 1

loc_dif_n_of :: Eq t => Int -> [t] -> [t] -> Bool Source #

min_vl :: (Num a, Ord a) => [a] -> [a] -> a Source #

min_vl_of :: (Num a, Ord a) => a -> [a] -> [a] -> Bool Source #

min_vl_in :: (Num a, Ord a) => [a] -> [a] -> [a] -> Bool Source #

combinations2 :: Ord t => [t] -> [(t, t)] Source #

set_pp :: Show t => [t] -> String Source #

tto_rel_to :: Integral t => Z t -> [t] -> [t] -> [Tto t] Source #

set_pp_tto_rel :: (Integral t, Show t) => Z t -> [t] -> [t] -> String Source #

Map

m_get :: Ord k => Map k v -> k -> v Source #

m_doi_of :: Map Int [Z12] -> Int -> Int -> Int -> Bool Source #

degree of intersection

Edge

e_add_id :: k -> [(t, u)] -> [((k, t), (k, u))] Source #

Add k as prefix to both left and right hand sides of edge.

gen_edges :: (t -> t -> Bool) -> [t] -> [(t, t)] Source #

gen_u_edges :: Ord a => (a -> a -> Bool) -> [a] -> [(a, a)] Source #

Graph

oh_def_opt :: [Dot_Meta_Attr] Source #

gen_graph :: Ord v => [Dot_Meta_Attr] -> Graph_Pp v e -> [Edge_Lbl v e] -> [String] Source #

gen_graph_ul :: Ord v => [Dot_Meta_Attr] -> (v -> String) -> [Edge v] -> [String] Source #

gen_graph_ul_ty :: Ord v => String -> (v -> String) -> [Edge v] -> [String] Source #

gen_flt_graph_pp :: Ord t => [Dot_Meta_Attr] -> ([t] -> String) -> ([t] -> [t] -> Bool) -> [[t]] -> [String] Source #

gen_flt_graph :: (Ord t, Show t) => [Dot_Meta_Attr] -> ([t] -> [t] -> Bool) -> [[t]] -> [String] Source #

P.12

circ_5 :: Integral a => Int -> a -> [a] Source #

all_pairs :: [t] -> [u] -> [(t, u)] Source #

adj :: [t] -> [(t, t)] Source #

adj_cyc :: [t] -> [(t, t)] Source #

p12_c5_eset :: [(Int, Int)] Source #

e_add_label :: (Edge v -> l) -> [Edge v] -> [Edge_Lbl v l] Source #

p12_c5_gr :: [String] Source #

p12_euler_plane :: Euler_Plane Rational Source #

p12_euler_plane_gr :: [String] Source #

P.14

p14_eset :: ([(Int, Int)], [(Int, Int)], [(Int, Int)]) Source #

p14_mk_e :: [(Int, Int)] -> [(Key, Key)] Source #

p14_edges_u :: [(Key, Key)] Source #

p14_edges :: [(Key, Key)] Source #

p14_mk_gr :: [Dot_Meta_Attr] -> [Edge Key] -> [String] Source #

p14_gr_u :: [String] Source #

p14_gr :: [String] Source #

p14_gen_tonnetz_n :: Int -> [Int] -> [Int] -> [Int] Source #

p14_gen_tonnetz_e :: Int -> [Int] -> [Int] -> [((Int, Int), Int)] Source #

p14_nrt_gr :: [String] Source #

P.31

p31_f_4_22 :: [Z12] Source #

p31_e_set :: [([Z12], [Z12])] Source #

p31_gr :: [String] Source #

P.114

p114_f_3_7 :: [Z12] Source #

p114_mk_o :: Show t => t -> [Dot_Meta_Attr] Source #

p114_mk_gr :: Double -> ([Z12] -> [Z12] -> Bool) -> [String] Source #

p114_f37_sc_pp :: [Z12] -> String Source #

p114_g0 :: [String] Source #

p114_g1 :: [String] Source #

p114_gr_set :: [(String, [String])] Source #

P.125

p125_gr :: [String] Source #

P.131

p131_gr :: [String] Source #

P.148

p148_mk_gr :: ([Int] -> [Int] -> Bool) -> [String] Source #

p148_gr_set :: [(String, [String])] Source #

P.162

p162_ch :: [[Int]] Source #

p162_e :: [Edge [Int]] Source #

p162_gr :: [String] Source #

P.172

p172_nd_map :: Map Int [Z12] Source #

p172_nd_e_set :: [(Int, Int)] Source #

p172_nd_e_set_alt :: [Edge Int] Source #

p172_gr :: Gr () () Source #

p172_set_pp :: Int -> String Source #

p172_all_cyc :: ([[Int]], [[Int]]) Source #

p172_cyc0 :: [[Int]] Source #

p172_g1 :: [String] Source #

p172_g2 :: [String] Source #

p172_g3 :: [String] Source #

tto_tn :: Integral t => t -> Tto t Source #

Tto Tn.

tto_tni :: Integral t => t -> Tto t Source #

Tto TnI.

gen_tto_alt_seq :: Integral t => (t -> Tto t, t -> Tto t) -> Int -> t -> t -> t -> [Tto t] Source #

gen_tni_seq :: Integral t => Int -> t -> t -> t -> [Tto t] Source #

k is length of the T & I sequences, n is the T & I sequence interval, m is the interval between the T & I sequence.

r = ["T0 T5I T3 T8I T6 T11I T9 T2I","T1 T6I T4 T9I T7 T0I T10 T3I"]
map (unwords . map T.tto_pp . gen_tni_seq 4 3 5) [0,1] == r

p172_c4 :: [[Tto Int]] Source #

tto_seq_edges :: (Show t, Num t, Eq t) => [[Tto t]] -> [(String, String)] Source #

p172_g4 :: [String] Source #

p172_gr_set :: [(String, [String])] Source #

P.177

partition_ic :: (Num t, Ord t, Show t) => t -> [t] -> ([t], [t]) Source #

p177_gr_set :: [(String, [String])] Source #

P.178

type SC = [Int] Source #

type PCSET = [Int] Source #

ait :: [SC] Source #

mk_bridge :: SC -> PCSET -> PCSET -> [PCSET] Source #

List of pcsets s where prime(p+s)=r and prime(q+s)=r. #p and #q must be equal, and less than #r.

mk_bridge (T.sc "4-Z15") [0,6] [1,7] == [[2,5],[8,11]]
mk_bridge (T.sc "4-Z29") [0,6] [1,7] == [[2,11],[5,8]]

mk_bridge_set :: [SC] -> PCSET -> PCSET -> [PCSET] Source #

concatMap of mk_bridge.

mk_bridge_set ait [0,6] [1,7] == [[2,5],[8,11],[2,11],[5,8]]

mk_bridge_set_seq :: [SC] -> [PCSET] -> [[PCSET]] Source #

p178_i6_seq :: [PCSET] Source #

p178_ch :: [(PCSET, [PCSET], PCSET)] Source #

type ID = Char Source #

p178_e :: [((ID, PCSET), (ID, PCSET))] Source #

Add ID to vertices, the 2,11 the is between 0,6 and 1,7 is not the same 2,11 that is between 3,9 and 4,10.

p178_gr_1 :: [String] Source #

p178_gr_2 :: [String] Source #

P.196

p196_gr :: [String] Source #

P.201

type SET = [Int] Source #

type E = (SET, SET) Source #

bd_9_3_2_12 :: [SET] Source #

p201_mk_e :: [Int] -> [E] Source #

p201_e :: [[E]] Source #

p201_o :: [Dot_Meta_Attr] Source #

p201_gr_set :: [[String]] Source #

p201_gr_join :: [String] Source #

P.205

bd_9_3_2_34 :: [SET] Source #

p205_mk_e :: [Int] -> [E] Source #

p205_gr :: [String] Source #

IO

wr_graphs :: FilePath -> IO () Source #