Mozart’s Musikalisches Würfelspiel
Mozart’s Musikalisches Würfelspiel (score available on IMSLP) is a system to create a waltz by choosing each measure from a list of possibilities, with 759,499,667,166,482 possible waltzes in total. This is an implementation of the Würfelspiel using a bit of Scheme code to select the measures at random, producing a different waltz at each compilation. The code is an instructive example of creating music functions and manipulating music in Scheme.
\version "2.24"
rhMeasureEight = \relative {
\tag generation \alternative {
\volta 1 { <g' b d g>4 r8 }
\volta 2 { <g b d g>4 r8 }
}
\tag table {
<g b d g>4 r8
}
}
lhMeasureEight = \relative {
\tag generation \alternative {
\volta 1 { g,8 g'16 f! e d }
\volta 2 { g,8 b'16 g fis e }
}
\tag table {
<< { g,8^"Volta 2" b'16 g fis e } \\ { g,8_"Volta 1" g'16 f! e d } >>
}
}
rhData = \relative {
| f''8 d g
| a,8 fis16 g b g'
| g8 c, e
| g8 d4\trill
| \rhMeasureEight
| g,8 c e
| e16 c e g c g
| c,4 r8
| <c e>8 <b d> r8
| b16 a b c d b
| e16 c b a g fis
| <e c'>8 8 8
| c'8( g e)
| c'4 r8
| e8 g16 e c8
| a'8( fis d)
| c16 g c e g, c
| g8( c e)
| e16 c e8 g
| g8 b16 d d,8
| c16 e g d a fis'
| e8 c g
| f'16 e d e f g
| \rhMeasureEight
| d,16 fis a d fis a
| <c, e>8 8 8
| f16 e f d c b
| fis'16 d a a' fis d
| b16 d g d b8
| \rhMeasureEight
| e16[ c g8] e'
| g,8 c e
| \rhMeasureEight
| e16 c d b g8
| a8 d fis
| a,16 e' d g fis a
| g16 b g d b8
| c8 g e'
| g8 g, g
| c16 b c e g, c
| c16 b c e g,8
| b16 c d b a g
| g'8 f16 e d c
| a8 f'16 d a b
| c16 b c g e c
| g''8 b16 g d b
| g'8 g16 d b'8
| e,8 c16 e g c
| e,8( c g)
| c8 e16 c g8
| c16 g e' c g' e
| d16( cis) d f g, b
| <c e>8 16 <d f> <e g>8
| <e, c'>8 8 8
| g'8 b d,
| d16 b g8 r8
| e'8 c g
| g'8 e c
| g'8 c, e
| g8 f16 e d c
| c8 e16 c g'8
| e16 c b g a fis
| e'16 c b c g8
| e'16 g c g e c
| d16 a d8 fis
| fis8 a fis
| c16 b c e g, c
| g'8 b16 g d g
| g8( e c)
| fis8 a16 fis d fis
| g16 b d b g8
| f16 e d c b d
| g8 e c
| c'16 b c g e c
| <d fis>8 8 8
| c'16 b c g e c
| g'16 b g8 d
| c8 c, r
| c'4 r8
| d8 a\turn fis'
| \rhMeasureEight
| d16[ b g8] g'
| c,4 r8
| c16 g e' c g' e
| c8 e g,
| d'8 d16 g b8
| g8 c, e
| g16 d g b g d
| f16 e d8 g
| fis16 a d a fis a
| \rhMeasureEight
| <b, d>8 g'16 b d,8
| c4 r8
| \rhMeasureEight
| g'8 e c
| e8 c g
| g'16 fis g d b g
| c8 g e'
| fis8 a d,
| \rhMeasureEight
| e16 d e g c g
| fis16 d a8 fis'
| c16 e c g e8
| e'16 d e g c g
| fis8 a16 fis d fis
| a,8 d16 c b a
| \rhMeasureEight
| e'8( g c)
| d,16 f d f b, d
| <b d>16( <a c>) q( <g b>) q( <fis a>)
| c'4 r8
| e8 c g
| f'8 d b
| <b d>8 q q
| c16 g e' c g' e
| d16 f a f d b
| d16 a d fis a fis
| e16 a g b fis a
| e16 c g' e c' g
| d'8 a16 fis d a
| g'8 b16 g d8
| g16 fis g b d,8
| \rhMeasureEight
| <e, c'>8 8 8
| g'16 e d b g8
| c16 g c e g <c, e>
| \rhMeasureEight
| b8 d g
| a16 g fis g d8
| <e, c'>8 8 8
| c'4 r8
| <c e>8 <b d>16 <g b> g8
| d'8 g16 d b d
| a16 e' <b d> <a c> <g b> <fis a>
| fis'8 fis16 d a'8
| c16 b c g e c
| c8 g e'
| <a, d fis>8 fis'4\trill
| g16 b g b d,8
| a8 a16 d fis8
| d16 e f d c b
| c8 g e'
| g8 d16 b g8
| g'8 c, e
| d16 f a, d b d
| <fis, d'>8 <d' fis> <fis a>
| e16 c' b g a fis
| c'16 b c g e c
| f16 d a8 b
| <g c e>8 e'4\trill
| c4 r8
| g'8 f16 e d c
| d16 a fis' d a' fis
| d16 cis d fis a fis
| g16 b g d b g
| c16 g e' c g'8
| e16 d e g c g
| b,8 d16 b a g
| e'16 g d c b a
| c16 b c e g, c
| <fis, d'>8 8 8
| e'16 d e g c g
| g16 fis g d b g
| d'8 g,4
| d'8( b g)
| d'16 b' g d b8
| c8 c16 d e8
| g8 f16 e d c
| e16 g d g a, fis'
| c4 r8
| b16 c d e f d
| c4 r8
| f16 a a,8 b16 d
| g,8 c e
| e16 c b d g8
| a16 g b g d g
}
lhData = \relative {
| f8 d g
| <b, g'>4 r8
| <c e>4 r8
| g16 b g'8 b,
| \lhMeasureEight
| <c e>4 r8
| <c g'>4 r8
| c8 g c,
| g''4 g,8
| g'4 r8
| c,8 d d,
| c'8 8 8
| <e g>4 8
| c8 g c,
| <c' g'>4 <c e>8
| <d fis>4 <c fis>8
| <e g>4 r8
| <c e>4 <c g'>8
| <c g'>4 <c e>8
| b4 r8
| c8 d d,
| c'4 r8
| f16 e d e f g
| \lhMeasureEight
| d4 c8
| c16 e g e c' c,
| <g' b>4 r8
| <c, a'>4 r8
| g'4 g,8
| \lhMeasureEight
| <c g'>4 8
| <c e>4 r8
| \lhMeasureEight
| g'4 r8
| <d fis>4 <c a'>8
| c8 d d,
| <b' d>4 r8
| <c e>16 g' q g q g
| b,16 d g d b g
| <c e>4 r8
| <c e>4 r8
| g4 r8
| <c e>4 r8
| f4 g8
| <e g>4 r8
| <b d>4 r8
| q4 r8
| <c g'>4 <c e>8
| <c e>16 g' q g q g
| <e g>4 r8
| <c e>4 r8
| f4 g8
| c,4 r8
| c8 8 8
| <b d>4 r8
| <g g'>4 g'8
| <c, e>16 g' q g q g
| q16 g q g q g
| q16 g q g q g
| <c, e>4 r8
| <e g>4 r8
| c8 d d,
| c'4 r8
| <c g'>4 8
| <d fis>4 r8
| << { a'8 fis d } \\ { d8 d c } >>
| <c e>4 <e g>8
| b4 r8
| <c e>4 r8
| d4 c8
| <b d>4 8
| f'4 g8
| <c, e>16 g' q g q g
| <c, e>4 r8
| c8 8 8
| <c e>4 <c g'>8
| <b d>4 <b g'>8
| c4 c,8
| c'8 g c,
| c'4 r8
| \lhMeasureEight
| <b g'>4 <b d>8
| c8 g c,
| <c' e>4 r8
| <e g>4 r8
| <b g'>4 r8
| <c e>4 <c g'>8
| <b d>4 8
| f'16 e d8 g
| <c, a'>4 8
| \lhMeasureEight
| <g g'>4 g'8
| c,8 g c,
| \lhMeasureEight
| <c' e>4 r8
| c4 r8
| <b d>4 <b g'>8
| <c e>16 g' q g q g
| <c, a'>4 8
| \lhMeasureEight
| <c g'>4 <c e>8
| <c a'>4 8
| <e g>4 r8
| c4 r8
| c4 r8
| c8 d d,
| \lhMeasureEight
| <c' g'>4 <c e>8
| <f a>4 <g d'>8
| c,8 d d,
| c'8 g c,
| <c' e>16 g' q g q g
| <g b>4 r8
| g8 8 8
| <c, e>4 r8
| f4 g8
| <d fis>4 r8
| c8 d d,
| <c' e>4 r8
| <d fis>4 <c fis>8
| <b g'>4 r8
| <b d>8 8 <b g'>
| \lhMeasureEight
| c8 8 8
| g'8 g, r
| e'4 e16 c
| \lhMeasureEight
| g4 r8
| <b d>8 8 <b g'>
| c8 8 8
| c8 g c,
| g''8 g, r8
| <b g'>4 r8
| c8 d d,
| << { d'8 d d } \\ { c8 c c } >>
| << e4 \\ c4 >> r8
| <c e>16 g' q g q g
| d,16 d' cis d c d
| b4 r8
| <c fis>8 8 <c a'>
| <b g'>4 g8
| <c e>4 r8
| <b d>4 8
| <c e>16 g' q g q g
| f4 g8
| c,8 8 8
| c8 d d,
| <c' e>4 r8
| f4 g8
| c,16 b c d e fis
| c8 g c,
| <c' e>4 r8
| c4 r8
| c4 r8
| <b d>4 r8
| <e g>4 r8
| c4 r8
| g4 r8
| c8 d d,
| <c' e>4 8
| c8 8 8
| <c g'>4 <c e>8
| <b d>4 r8
| g'16 fis g d b g
| b4 r8
| <g' b>4 r8
| <c, e>4 r8
| <c e>4 <e g>8
| c8 d d,
| c'8 g c,
| <g' g'>4 <b g'>8
| c8 g c,
| f'4 g8
| <c, e>16 g' q g q g
| g8 g, r8
| <b d>4 8
}
table = #'(
#(96 32 69 40 148 104 152 119 98 3 54)
#(22 6 95 17 74 157 60 84 142 87 130)
#(141 128 158 113 163 27 171 114 42 165 10)
#(41 63 13 85 45 167 53 50 156 61 103)
#(105 146 153 161 80 154 99 140 75 135 28)
#(122 46 55 2 97 68 133 86 129 47 37)
#(11 134 110 159 36 118 21 169 62 147 106)
#(30 81 24 100 107 91 127 94 123 33 5)
#(70 117 66 90 25 138 16 120 65 102 35)
#(121 39 139 176 143 71 155 88 77 4 20)
#(26 126 15 7 64 150 57 48 19 31 108)
#(9 56 132 34 125 29 175 166 82 164 92)
#(112 174 73 67 76 101 43 51 137 144 12)
#(49 18 58 160 136 162 168 115 38 59 124)
#(109 116 145 52 1 23 89 72 149 173 44)
#(14 83 79 170 93 151 172 111 8 78 131)
)
#(define choices
(map (lambda (possibilities)
(1- (vector-ref possibilities (random 11))))
table))
#(define (split-measures music)
(let ((elements (ly:music-property
(ly:music-property music 'element)
'elements)))
(let loop ((elts (reverse elements))
(measure '())
(measures '()))
(cond
((null? elts)
(list->vector measures))
((or (music-is-of-type? (car elts) 'bar-check) ;; until 2.25.5
(music-is-of-type? (car elts) 'bar-check-event)) ;; since 2.25.6
(let ((measure-music (make-sequential-music measure)))
(loop (cdr elts) '() (cons measure-music measures))))
(else
(loop (cdr elts) (cons (car elts) measure) measures))))))
applyChoices =
#(define-music-function (music) (ly:music?)
(let* ((measures (split-measures music))
(chosen-measures
(map (lambda (i) (vector-ref measures i))
choices))
(first-part (make-sequential-music (take chosen-measures 8)))
(second-part (make-sequential-music (drop chosen-measures 8))))
#{
\repeat volta 2 { #first-part }
\repeat volta 2 { #second-part }
#}))
\header {
title = "Valse"
composer = "Mozart"
}
randomWaltz =
\keepWithTag generation
\new PianoStaff <<
\new Staff {
\time 3/8
\applyChoices \rhData
}
\new Staff {
\clef bass
\applyChoices \lhData
}
>>
\score {
\layout { }
\randomWaltz
}
\score {
\midi { }
\unfoldRepeats \randomWaltz
}
% Uncomment to display the table of all possible measures ("Notentafel")
%{
\score {
\layout {
\context {
\Score
barNumberVisibility = #all-bar-numbers-visible
\override BarNumber.break-visibility = #end-of-line-invisible
centerBarNumbers = ##t
}
}
\keepWithTag table <<
\new Staff {
\time 3/8
\rhData
}
\new Staff {
\clef bass
\lhData
}
>>
}
%}
