CS100J Spring 2007 Assignment A6. Mozart's Musikalisches Würfelspiel. Due at 11:59PM, Tuesday, 10 April
This assignment uses two-dimensional arrays abd random-number generation in an interesting setting. Inspiration for it comes from an assignment given by Kevin Wayne and Robert Sedgewick in Computer Science at Princeton.
In 1787, Wolfgang Amadeus Mozart created a dice game (Mozart's Musikalisches Würfelspiel). One composes 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.
Minuet. The minuet consists of 16 measures. The 176 possible Minuet measures are named M1.wav through M176.wav. To determine which one to play, roll two dice and use the following table. The dice roll (a row number) tells you what to play for a measure (a column number). For example, if you roll 11 for measure 3, then play wav file M165.wav.
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
Trio. The trio consists of 16 measures. The 96 possible Trio measures are named T1.wav through T96.wav. To determine which one to play, roll one die and use the following table. For example, if you roll 1 for measure 21, then play file T81.wav.
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
Example. Here is a sample waltz generated using this process and the accompanying musical score. There are 11^16 * 6^16 different possible Waltzes. Since this is over 10^23 different possibilities, each time you play the game you are likely to produce 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. To help you learn as much as possible in a short amount of time as possible, and also to give you advice on how to go about writing and testing programs, we lead you through this assignment in a series of steps. Please study the code we have given you; be conscious of style, specifications, etc.
Follow the directions carefully. Many people have had more points off because they failed to follow instructions than because of programming errors. 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 works!
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 WuerfelSpiel.java. You will be writing
class WuerfelSpiel. We have provided you with a few components in it to help
out.
File WuerfelSpielTester.java.
We have provided you with stubs of test methods and with some testing instructions
in the bodies.
File measures.zip (34MB).
After downloading this file, unzip it —into a folder measures that
contains all the .wav files for the measures used in Mozart's Musikalisches Würfelspiel.
Put folder measures in the folder with the two .java files.
Load StudioAudio.java into DrJava and become familiar with its
methods. Call method playScale just to see what
sounds come out.
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 WuerfelSpiel,
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.
Use function nextInt in writing the body of method WuerfelSpiel.throwDie.
The method body need be only a single return statement.
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 (1) it produces only integers in
the range 1..6 and (2) can produce all integers in 1..6. In order to help you
do this, we have written part of method WuerfelSpielTester.testThrowDie. Study
what we have written in the specification and the body of this method,
complete the method, and test throwDie.
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, we have partially written function toString(String[]).
Study what we have written in the specification and function body and complete
the function. Then test it by completing test method WuerfelSpielTester.testToString.
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 array minuet and row 1 of array trio
are chosen. This allows you to concentrate on the idea of constructing
a file name. To do this, write the body of function WuerfelSpiel.createSpiel().
We have given you arrays minuet and trio in class
WuerfelSpiel. Each element of these arrays is an integer that
indicates a file that represents a measure. For example, minuet[2][1]
= 96,
which represents file measures/M96.wav. So, you have to put the
String "measures/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 measures from file name M96.wav. Even
if you have a PC, you must use "/" and not a backslash.
After writing this function, complete procedure WuerfelSpiel.createSpiel().
We put in a test to make sure that the first aray element is correct so that
you have some idea how to do this. You must make sure that all array elements
are correct. You should also print the array of string in the interactions
pane, using function toString(String[]), so that you can see
it; this latter step is just for your benefit.
Step 5. Listen to the music! Complete procedure WuerfelSpiel.
play(String[]), which will
play all the files whose names are in an array such as that calculated by function createSpiel.
You
will notice a pause between measures when the music is played.
We'll investigate eliminating the pauses later. Playing your array should produce
the same music as this file:
mozart12.wav.
Step 6. We can get rid of the pause between measures by building
a single file that contains the music in the files given by an array
like s in the past two steps. To do this, complete the body of
function WuerfelSpiel.build(String).
To do this, you have to read a .wav file and place its contents
into a
double array; use function StdAudio.read(String) to
read one file at a time. To help you out, we gave an outline for the body of
WuerfelSpiel.build(String), and we also give you method WuerfelSpiel.copy.
You figure out how to check this function; as long at it is correct, we will
not look at your test cases.
Step 7. Creating a Mozart Musikalisches Würfelspiel. Finally,
write the the body of function WuerfelSpiel.createRandomSpiel(),
which will create a random waltz. It should produce a random waltz as described
at the beginning of this document. In this method, you can use 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 WuerfelSpiel when generating
random names of files, as in method createSpiel.
Step 8. Saving a file. You don't have to
do anything here. We want to know that method StdAudio.save allows
you to save a double
array in a .wav file, so that you can play it later ---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 file WuerfelSpiel.java and
WuerfelSpielTester.java on the CMS by the due date: 11:59PM on
Tueday, 10 April.