CS100J Spring 2006 Assignment A5. Mozart's Musikalisches Würfelspiel. Due on the CMS at 11:59PM, Monday, 3 April
The inspiration for this assigment comes from a similar assignment given by Kevin Wayne and Robert Sedgewick in Computer Science and Princeton. The purpose of the assignment is to show you the use of two-dimensional arrays in an interesting setting, which also get you familar with random-number generation.
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 272 pre-composed musical elements at random. The waltz consists of two parts: a minuet and a trio. Each is composed of 16 measures, which are generated at random according to a fixed set of rules, as described below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
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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
17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
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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
Example. Here is a sample waltz generated using 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.
About this assignment. In this assignment, you will use a number of ideas for the first time: generation of random numbers, two-dimensional arrays, playing music stored in a .wav file, saving a double array that contains music in a file on your hard drive, and more. To help you learn all this and also to give you more advice on how to go about developing and testing programs, we lead you through this assignment in a series of steps. Please follow them carefully. When doing one step, don't go on to the next one until the current one is done and the method you wrote for it work!
Step 1. Download the following and place them all in a new folder for the assignment.
File StdAudio.java. Class StdAudio
contains methods for manipulating and playing music in wave (.wav) format.
File Mozart.java. You will be writing class Mozart.
We have provided you with a few components in it to help out.
File waves.zip (34MB) or waves.sitx (25MB).
After downloading a file, unpack it —into a folder waves that contains all the .wav files for the measures used in Mozart's Musikalisches Würfelspiel. If you are on a PC, you probably have to use waves.zip; mac people can use the smaller .sitx file. Put folder waves
in the folder with the two .java files.
Step 2. Generating rolls of a die. Your program will have to "roll a die" to
produce a random number in the range 1..6. At the beginning of class Mozart,
there is a declaration of a static Random variable generator. An object of class
generator has methods for generating "random" numbers. The one you will use is function
nextInt. Evaluation of a call generator.nextInt(t) yields an integer i
that satisfies 0 i < t.
You should use function nextInt to write a method with the following specification in class
Mozart:
/** = a roll of a die --an int in the range 1..6 */
private static int throwDie()
Class Random is in API package java.util. Use the link in the course webpage to
obtain the API spec for Random and spend some time becoming familiar with it.
Function throwDie seems extremely simple! Nevertheless,
it has to be tested to make sure that it will produce only integers in the range 1..6
and can produce all integers in that range. Test it! One way is to write a method that calls
the throwDie 50 times, each time printing the result in the interactions pane.
Then you can look at the values it produced.
Step 3. A method for printing a String array. Later, you will be writing a function that produces a
String array of file names corresponding to measures to be played.
In order to see that the method works, you have to see the array of Strings.
For that purpose, write and test the following function.
/** = a representation of array s --the list of Strings in the array, with each pair separated by ", " and the list delimited by "[" and "]".
Example: "[first, second, what]" */
public static String toString(String[] s)
Step 4. Generating a waltz. Before you work on creating a random waltz, first create a waltz assuming that each die thrown has the value 1, so that all the file names in row 2 of the minuet and row 1 of the trio are chosen. This will allow you to concentrate on the weird part of constructing a file name, as we discuss below. Thus, write a method with this specification:
/** = A String array that contains the names of all the files
described by row 2 of array minuet and row 1 of array trio.
The filenames must be of the form
"waves/M<integer>.wav" and
"waves/T<integer>.wav",
so the files are expected to be in directory waves.*/
public static String[] create1Spiel()
We have given you arrays minuet and trio in class
Mozart. Each element of of these arrays is an integer that indicates a file that represents a measure. For
example, minuet[2][1] = 96, which represents file waves/M96.wav. So, you have to put the
String "waves/M96.wav" into the array that this function returns.
minuet[2][1] is one of the musical phrases that can be used in measure 1 of the minuet part.
Note that "/" is used to separate
folder name waves from file name M96.wav. Even if you have a PC, you must use "/" and not a backslash.
After writing this function, you can check it out by executing
s= Mozart.create1Spiel() in the interactions pane and then displaying the contents of s
using Mozart.toString(s) and checking to make sure that the write file names
are displayed.
Step 5. Listen to the music! Now write the following method to play all the files whose names
are in an array such as that calculated by function createSpiel. Look in class
StdAudio for a method that will play the music in a file given by a file name.
You will notice that there is a pause between measures when the music is played. We'll investigate
eliminating the pauses later.
/** Play the music given by files whose names are in s, in order*/
public static void play(String[] s)
Playing your array should produce the same music as this file: mozart12.wav.
Step 6. Wouldn't you like to get rid of the pauses? One way to do this is to build a
single file that contains the music in the files given by an array like s in the past two steps. Write the following method:
/** Put the measures given by the file names in s into
a new array and return the new array */
public static double[] build(String[] s)
To do this, you have to know how to read a .wav file and place its contents into a
double array; find a method to do this in class StdAudio.
Your method should first of all determine the length of the output array --by reading all the files--,
then declare the output array, and finally copy the values of the .wav files given by s
into the output array,
one after the other. To help you out, we already placed a method
copy in class Mozart .
Step 7. Creating a Mozart Musikalisches Würfelspiel. Finally, write the following method:
/** = an array of random measure file names:16 for a minuet and 16 trios. The filenames are of
the form "waves/M<integer>.wav" and "waves/T<integer>.wav", so the files are expected
to be in directory waves, which should be in the same folder as this class. */
public static String[] createRandomSpiel()
This method should produce a random waltz as described at the beginning of this document. For this method, you can use method throwDie, which you wrote earlier,
to throw a die to get a number in the range 1..6. Also, use arrays
minuet and trio in class Mozart when generating random names of files,
as in method create1Spiel.
Step 8. Saving a file. You don't have to do anything for this step.
We just want to let you know that method StdAudio.save allows you to save a double
array in a .wav file, so that you can play it later if you want \or email it home to let your family know
that you have been turned on by classical music and Musikalisches Würfelspiel.
You can use any file name you want, as long as it ends in ".wav". The file will be stored on your desktop.
Step 9. Submitting your assignment. Submit your file Mozart
on the CMS by the due date: 11:59PM on Monday, 3 April. As usual, your methods should have precise and complete specifications, written as javadoc comments. There will be severe deductions if these javadoc comments are not suitable.