2008andersonphd.pdf

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Anderson, Alasdair J. (2011)Analysis of musical structures: an approach

utilising monadic parser combinators.PhD thesis.

http://theses.gla.ac.uk/2353/

Copyright and moral rights for this thesis are retained by the author

A copy can be downloaded for personal non-commercial research or

study, without prior permission or charge

This thesis cannot be reproduced or quoted extensively from without firstobtaining permission in writing from the Author

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http://theses.gla.ac.uk/

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http://theses.gla.ac.uk/2353/http://theses.gla.ac.uk/2353/


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2424

8

24

8

24

24

8

8

6


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653

6

35

7

4

34

36

6

6

24


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4343

7

12

17


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3


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43

43

5


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UpperNeighbour

DoubleNeighbour

LowerNeighbour


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PassingNotes


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C

D


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a.f

f(x)

f(x) =x3 + 2x2 7x x.x3 + 2x2 7x

f(3) = 24 (x.x3 + 2x2 7x)3 = 24

a f


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2

[1] > (defun double(x)( 2x))

[2] > (double(double(double(double1))))16

[3] > (defun repeat(f n o)(if (zerop n)

o

(repeat f (1 n) (funcall f o))))[4] > (repeat#double4 1)16


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[5] > (repeat#(lambda(v) ( 2v)) 4 1)16

(p1 e1, , pn en)


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class Monad m where

(=) :: m a (a m b) m b() :: m a m b m breturn :: a m afail :: String m a

type TP a=String [(a, String)]

pass ::a TP apass a=inp [(a, inp)]

discard ::TP adiscard=inp [ ]

bind ::TP a (a TP b) TP bpbindf =inp concat[f v inp | (v, inp) p inp]


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item ::TP Charitem=inp caseinp of

[] [](x :xs) [(x, xs)]

satsify :: (Char Bool) TP Charsatisfy p =itembind

x ifp xthenpass xelsediscard

letter ::TP Charletter=satisfy isAlpha

space ::TP Charspace=satisfy isSpace


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alt ::TP a TP a TP apaltq=inp (p inp + +q inp)

choice ::TP a TP a TP apchoiceq=inp case(paltq)inp of

[ ](x : ) [x]

perhaps ::TParser a TParser[a]perhaps p =(some p) choicepass[]

some ::TParser a TParser[a]some p =pbind

x perhaps pbindxs pass(x :xs)

skip ::TParser a TParser b TParser apskipq=pbind

x perhaps qbind pass x

word ::TParser Stringword=some letter


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7 + (6 52 + 3)

7 + (6 52 + 3) =

= 7 + (6 25 + 3)

= 7 + (150 + 3)

= 7 + 153

= 160


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PRororganic or+ganic

PRorganorganic organ+ic

PRorganicorganic organic


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83


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Gott erhalte melody

Variation 2

3

Variation 3

3


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type Note=(Int, Int)

type B40 =Notetype B12 =Notetype B7 =Note


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x

Bx


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B/C/D Bx/C/D Cx/D/E D/E/F Dx/E/F E/F/G Ex/F/G Fx/G/A

G/A Gx/A/B A/B/C

Ax/B/C


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x


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type Crd = [Note]


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type Seq = [Crd]

C

E

C

D

E

F

Dx

C

E

D

E


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type Parser a = Seq [(a, Seq)]

noteitem ::Parser B40noteitem=inp caseinp of

[] [](x :xs) [(xel, xs) | xel x]


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cMapAll :: [a] [a] (a a Bool) BoolcMapAll c1c2f =and[ or[ f n1n2 | n2 c2] | n1 c1]

cMapAny :: [a] [a] (a a Bool) BoolcMapAny c1c2f =or[ or[ f n1n2 | n2 c2] | n1 c1]


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function ::B40 B40 Bool

notescan ::Parser B40notescan=inp caseinp of

[] [](x :xs) [(xel, x :xs) | xel x]

type TxtParser a=String [(a, String)]

itemscan ::TxtParser Charitemscan=inp caseinp of

[] [](x :xs) [(x, x :xs)]


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{ui : ui Z, un+1 un = 1}


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un+1 un = 1


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2n

2n+1


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un un+1 = 1


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seqsat ::Parser Seq (Seq Bool) ABParser Seqseqsat p c=pbindx ifc xthenalways xelsenever

somelap ::forall a.(Seq > [([a], Seq)]) > Seq > [([a], Seq)]somelap p =(ppseqmanylap p) usinglap

manylap ::forall a.(Seq > [([a], Seq)]) > Seq > [([a], Seq)]manylap p =(somelap p) choicealways[]

lap ::forall a.([a], [a]) > [a]lap(xh, []) =xhlap(xh, xt) =xh + + (tail xt)


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chordown ::Parser Seqchorddown=seqsat duplet seqstepdown

descent ::Parser Seqdescent=seqsat(somelap chorddown)length3


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43

ascent ::Parser Seqascent=seqsat(somelap chordup)length3


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43

neighbourup =((chorduppseqchorddown) usinglap) choicechorddownneighbourdown=((chorddownpseqchordup) usinglap) choicechordup


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neighbour ::Parser Seqneighbour=neighbourup choiceneighbourdown

43


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passingdown=(chorddownpseqchorddown) usinglappassingup =(chorduppseqchordup) usinglap

passing ::Parser Seqpassing=passingupchoicepassingdown


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alt ::Parser a Parser a Parser apaltq=inp (p inp ++ q inp)


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choice ::Parser a Parser a Parser apchoiceq=inp case(paltq)inp of

[] [](x :xs) [x]


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pllel :: [Parser a] Parser apllel ap=case(length ap)of

2 (head ap) choice (last ap)otherwise (head ap) choice (pllel(tail ap))

43


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many ::Parser a Parser[a]many p =(some p) choicealways[]

some ::Parser a Parser[a]some p =pbindx

many pbindxs always(x :xs)


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seqitem ::Parser Seqseqitem=inp caseinp of

[] [](x :xs) [([x], xs)]

43


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A

D

D

43

A


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interesting :: [Parser Seq] Parser Seqinteresting p =seqsat(pnone p)length3


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pnone :: [Parser Seq] Parser Seqpnone p =inp case((pllel p)inp)of

[] noneagain p inpotherwise always[] inp

noneagain :: [Parser Seq] > Parser Seqnoneagain p =seqitembindy

(pnone p) bindz always(y+ +z)


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A

I

I

43

D

I

A

I

D 4

A A


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pedalpoint ::Parser Seqpedalpoint=seqsat tripletnote pedalBin

pedal ::Parser Seqpedal=seqsat(somelap pedalpoint)length5


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type N5 = (Int, Int, Int, Int, Int)

type Crd =[N5]type HSlice=[N5]type VSlice=[N5]

type Seq =[[N5]]type HSlab =[VSlice]type VSlab =[HSlice]


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op :: (Parser Seq, String) Parser Token Parser Token(p, t) opxs=(ptokt) altxs

combiner :: [(Parser Seq, String)] Parser[Token]

combiner l inp| inp == [] = [([(End, inp)], inp)]| otherwise = case(foldr op never l inp) of

[] combiner l(tail inp)x concat[tokenjoin(t, s, l) | (t, s) x]

tokenjoin :: (Token, Seq, [(Parser Seq, String)]) [([Token, Seq)]tokenjoin(t, s, l) =[(t :t, s) | (t, s) (combiner l s)]


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Al

Al

N

Al

N

N

I

N

Al

Al

I

Al


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Al

Al

Al

Al

2

Al

3

Al

4

Al

Al

5

Ne St

Al


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Al

7

St

Ne

Al

Al

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Al

St

St

9

St

St

St

10

St


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Ne

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Ne

Al

St

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StSt

St

13

Al

St

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Ne

Ne

15

Al


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Al

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Al

Al

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Al

Al

Al

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19

St

Ne


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St

St

20

St

St

St

St

21

St

St

St

22

St

23

St


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St

St

St

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St

St

St

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St

St

St

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St

St

St

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Ne


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St28

Ne

St

St

29

St

St

30

St31

Al

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AlSt


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Nb

Ig

Alt

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Ig

2

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Ig

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Nb


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AltNb

Alt

St

5

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Nb

Alt

Ig

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Nb

Nb

Alt

St

Ig

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Nb

Nb


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St St

St

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Alt

St

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Nb

Alt

Ig

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Nb

Nb

Nb

Alt

Nb

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Ig

Nb


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AltNb

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Ig

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Ig

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Alt

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St

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Ig St

Ig

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St


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Ig St

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St


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StSt

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AltSt

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Alt37

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Alt


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0

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Al

Al

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IgAl

1

Nb

Ig

Ig

Ig

IgAl

Ig

Al

Al

Nb

Ig

Al

Ig

Ig

Al


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Al

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Ig

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Ig

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Al

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Al

Al

Nb

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Al

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Al

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Nb

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14

Ig

Al

Al

Al

Al


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Al

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Ig

Al

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Al

Al

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Ig

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Al

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0

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Nb

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1

Nb

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Al


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Ig

Al

Al

Al

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Nb

Al

Al

Ig

Ig

Ig

10

Al

Nb

Nb

Nb

Al

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Al

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13

Nb

Al

Nb

Al

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8

11

9

12


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always :: a Parser a

always a = inp [(a, inp)]

never :: Parser a

never = inp []

duplet ::Parser Seqduplet=chorditembindx

chordscanbindy

always(x : [y])


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chorditem :: Parser Crd

chorditem = inp caseinp of

[] []

(x :xs) [(x, xs)]

chordscan :: Parser Crd

chordscan = inp caseinp of

[] []

(x :xs) [(x, x :xs)]

notestepup :: B40 B40 Bool

notestepup n1n2 = case((forty2Seven n1) b7Interval (forty2Seven n2))of

1 True

otherwiseFalse

notestepdown :: B40 B40 Bool

notestepdown n1n2 = notestepup n2n1

chordstepdown :: Crd Crd Bool

chordstepdown c1c2 = cMapAny c1c2notestepdown

seqstepdown :: Seq > Bool

seqstepdown[] = True

seqstepdown s@(c: cs)


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| (chordstepdown c(head cs)) == True=(seqstepup (tail cs))

| otherwise =False

bind :: Parser a (a Parser b) Parser b

pbindf = inp concat[f v inp | (v, inp) p inp]

tripletnote ::Parser Seq

tripletnote=noteitembindx

noteitembindy

notescanbindz

always([x] : [y] : [[z]])

pedalBin seq | (length seq) > 2 = chordpedal(seq!!0) (seq!!2)

| otherwise = False

chordpedal c1c2 =cMapAny c1c2

notepedal notepedal n1n2 =n1 nexactn2

mlex:: [(Parser Seq, String)] Parser[Token]

mlex=many.(foldr op never)


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many ::Parser a Parser[a]

many p =(some p) choicealways[]


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