In 1787, Wolfgang Amadeus Mozart created a dice game (Mozart's Musikalisches Würfelspiel). In the game, you compose a two part waltz by pasting together 32 of 292 pre-composed musical elements at random using a table of rules.

The waltz. The waltz consists of two parts - the minuet and the trio. Each is comprised of 16 measures, which are generated at random according to a fixed set of rules.

• Minuet. The minuet consists of 16 measures. There are 196 possible Minuet measures, named M1.wav through M196.wav. To determine which one to play, roll two fair dice, and use the following table.

         1    2    3    4    5    6    7    8    9   10   11   12   13   14   15   16
  -----------------------------------------------------------------------------------
    2   96   22  141   41  105  122   11   30   70  121   26    9  112   49  109   14
    3   32    6  128   63  146   46  134   81  117   39  126   56  174   18  116   83
    4   69   95  158   13  153   55  110   24   66  139   15  132   73   58  145   79
    5   40   17  113   85  161    2  159  100   90  176    7   34   67  160   52  170
    6  148   74  163   45   80   97   36  107   25  143   64  125   76  136    1   93
    7  104  157   27  167  154   68  118   91  138   71  150   29  101  162   23  151
    8  152   60  171   53   99  133   21  127   16  155   57  175   43  168   89  172
    9  119   84  114   50  140   86  169   94  120   88   48  166   51  115   72  111
   10   98  142   42  156   75  129   62  123   65   77   19   82  137   38  149    8
   11    3   87  165   61  135   47  147   33  102    4   31  164  144   59  173   78
   12   54  130   10  103   28   37  106    5   35   20  108   92   12  124   44  131
  

  For example, if you roll an 11 for measure 3, then play measure 165.

• Trio. The trio consists of 16 measures. There are 96 possible Trio measures named T1.wav through T96.wav. To determine which one to play, roll one fair die, and use the following table.

      17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32
  ------------------------------------------------------------------
   1  72   6  59  25  81  41  89  13  36   5  46  79  30  95  19  66
   2  56  82  42  74  14   7  26  71  76  20  64  84   8  35  47  88
   3  75  39  54   1  65  43  15  80   9  34  93  48  69  58  90  21
   4  40  73  16  68  29  55   2  61  22  67  49  77  57  87  33  10
   5  83   3  28  53  37  17  44  70  63  85  32  96  12  23  50  91
   6  18  45  62  38   4  27  52  94  11  92  24  86  51  60  78  31
  

Part 1: generating the waltz. For this part, your goal is to generate a random sequence of measures according to the rules described above. Initialize a 13-by-17 array minuet so that minuet[i][j] is the musical element to play in measure j if you roll i. Initialize a 6-by-17 array trio so that trio[i][j] is the musical element to play in measure j+16 if you roll i.

Part 2: playing the waltz. Crude approach: play each measure in turn using StdAudio.play. Not ideal because there is a slight, but annoying, pause between each measure. Instead, concatenate all of the measures together, overlapping each pair of successive ones by a small amount.

Composition. Here is a sample waltz generated from this process and the accompanying musical score. There are 11^16 * 6^16 different possible results, some of which are more likely than others. Since this is over 10^23 different possibilities, each time you play the game you are likely to compose a piece of music that has never been heard before! Mozart carefully constructed the measures to obey a rigid harmonic structure, so each waltz reflects Mozart's distinct style. Unfortunately, due to the rigidly, the process never results in anything truly extraordinary.