CSCI 135 Online
Fundamentals of Computer Science I
Spring 2016

Montana Tech
Computer Science & Software Engineering

ASSIGNMENT 7 - Guitar Hero

In this assignment, you will be making a program that simulates the plucking of guitar strings. You will gain experience creating data types including a queue data type.

Write a program to simulate plucking a guitar string using the Karplus-Strong algorithm. This algorithm played a seminal role in the emergence of physically modeled sound synthesis (where a physical description of a musical instrument is used to synthesize sound electronically).

Digital audio. Before reading this assignment, review the StdAudio portion of section 1.5 of Introduction to Programming in Java or this page.

Simulate the plucking of a guitar string. When a guitar string is plucked, the string vibrates and creates sound. The length of the string determines its fundamental frequency of vibration. We model a guitar string by sampling its displacement (a real number between -1/2 and +1/2) at N equally spaced points (in time), where N equals the sampling rate (44,100) divided by the fundamental frequency (rounding the quotient to the nearest integer).
  Sampling from Karplus-Strong
Why it works? The two primary components that make the Karplus-Strong algorithm work are the ring buffer feedback mechanism and the averaging operation. Getting started You will be developing three classes in this assignment,,, and You will need to create these files from scratch implementing the APIs prescribed on this page. You will also need the support classes and

Ring buffer. Your first task is to create a data type to model the ring buffer. Write a class named RingBuffer that implements the following API:
public class RingBuffer
        RingBuffer(int capacity)  // create an empty ring buffer, with given max capacity
    int size()                    // return number of items currently in the buffer
boolean isEmpty()                 // is the buffer empty (size equals zero)?
boolean isFull()                  // is the buffer full  (size equals capacity)?
   void enqueue(double x)         // add item x to the end
 double dequeue()                 // delete and return item from the front
 double peek()                    // return (but do not delete) item from the front
Since the ring buffer has a known maximum capacity, implement it using a double array of that length. For efficiency, use cyclic wrap-around: Maintain one integer instance variable first that stores the index of the least recently inserted item; maintain a second integer instance variable last that stores the index one beyond the most recently inserted item. To insert an item, put it at index last and increment last. To remove an item, take it from index first and increment first. When either index equals capacity, make it wrap-around by changing the index to 0.

Implement RingBuffer to throw an exception if the client attempts to dequeue() or peek() from an empty buffer or enqueue() into a full buffer.
Ring buffer
You can test your RingBuffer data type on the following toy client, using the main() provided. It enqueues the numbers 1 through N, and then repeatedly dequeues the first two, and enqueues their sum.

  public static void main(String[] args) 
      int N = Integer.parseInt(args[0]);
      RingBuffer buffer = new RingBuffer(N);  
      for (int i = 1; i <= N; i++) 
      double t = buffer.dequeue();
      System.out.println("Size after wrap-around is " + buffer.size());
      while (buffer.size() >= 2) 
          double x = buffer.dequeue();
          double y = buffer.dequeue();
          buffer.enqueue(x + y);

% java RingBuffer 10
Size after wrap-around is 10

% java RingBuffer 100
Size after wrap-around is 100
Guitar string. Next, create a data type to model a vibrating guitar string. Write a class named GuitarString that implements the following API:
public class GuitarString
       GuitarString(double frequency)  // create a guitar string of the given frequency, using a sampling rate of 44,100
       GuitarString(double[] init)     // create a guitar string whose size and initial values are given by the array
  void pluck()                         // set the buffer to white noise
  void tic()                           // advance the simulation one time step
double sample()                        // return the current sample
   int time()                          // return number of tics
You can test your GuitarString data type with the following toy client, using the main() provided.

  public static void main(String[] args) 
      int N = Integer.parseInt(args[0]);
      double[] samples = { .2, .4, .5, .3, -.2, .4, .3, .0, -.1, -.3 };  
      GuitarString testString = new GuitarString(samples);
      for (int i = 0; i < N; i++) 
          int t = testString.time();
          double sample = testString.sample();
          System.out.printf("%6d %8.4f\n", t, sample);

% java GuitarString 25
     0   0.2000
     1   0.4000
     2   0.5000
     3   0.3000
     4  -0.2000
     5   0.4000
     6   0.3000
     7   0.0000
     8  -0.1000
     9  -0.3000
    10   0.2988
    11   0.4482
    12   0.3984
    13   0.0498
    14   0.0996
    15   0.3486
    16   0.1494
    17  -0.0498
    18  -0.1992
    19  -0.0006
    20   0.3720
    21   0.4216
    22   0.2232
    23   0.0744
    24   0.2232
Interactive guitar player. is a sample GuitarString client that plays the guitar in real-time, using the keyboard to input notes. When the user types the lowercase letter 'a' or 'c', the program plucks the corresponding string. Since the combined result of several sound waves is the superposition of the individual sound waves, we play the sum of all string samples.

Write a program GuitarHero that is similar to GuitarHeroLite, but supports a total of 37 notes on the chromatic scale from 110Hz to 880Hz. In general, make the ith character of the string
String keyboard = "q2we4r5ty7u8i9op-[=zxdcfvgbnjmk,.;/' ";
This keyboard arrangement imitates a piano keyboard: The "white keys" are on the qwerty and zxcv rows and the "black keys" on the 12345 and asdf rows of the keyboard.
Piano keyboard
The ith character of the string corresponds to a frequency of 440 × 2(i - 24) / 12, so that the character 'q' is 110Hz, 'i' is 220Hz, 'v' is 440Hz, and ' ' is 880Hz. Don't even think of including 37 individual GuitarString variables or a 37-way if statement! Instead, create an array of 37 GuitarString objects and use keyboard.indexOf(key) to figure out which key was typed. Make sure your program does not crash if a key is played that is not one of your 37 notes. You can test your GuitarHero program by typing the following into your guitar to get the beginning of Led Zeppelin's Stairway to Heaven. Multiple notes in a column are dyads and chords.
                                              w q q
        8       u       7       y             o p p
i p z v b z p b n z p n d [ i d z p i p z p i u i i
What is this familiar melody?
nn//SS/ ..,,mmn //..,,m //..,,m nn//SS/ ..,,mmn   (S = space)

Do I need to follow the prescribed API? Yes, we will be testing the methods in the API directly. If your method has a different signature or does not behave as specified, you will lose a substantial number of points. You may not add public methods to the API; however, you may add private methods (which are only accessible in the class in which they are declared).

Where do I enter keystrokes in GuitarHeroLite and GuitarHero? Be sure that the standard draw window has focus by clicking in it. Then, type the keystrokes.

Is the size of a RingBuffer equal to the number of nonzeros? No. Some of the elements in the buffer can be zero. To get an accurate count, increment the instance variable size each time you call enqueue() and decrement it each time you call dequeue().

How do I throw a RuntimeException? See the examples in (but you'll need to pick your own short description string).

When generating random values between -0.5 and +0.5 in should I include the endpoints? You are free to choose whatever convention you find most convenient. The inclusion or exclusion of the endpoints makes no humanly discernable difference in the sound, but the inclusion of exactly one endpoint makes the implementation of the method very simple.

How do I round a double to the nearest int? See the toGray() method in (Program 3.1.3).

What should RingBuffer do if the client attempts to dequeue() from an empty buffer or enqueue() into a full buffer? You should throw an exception to indicate the error. This is easy to do, here is an example: throw new RuntimeException("Ring buffer overflow");

What happens if I call where x is greater than 1 or less than -1? The value is clipped—it is replaced by the value 1.0 or -1.0, respectively.

I get an ArrayOutOfBounds or NullPointerException error in RingBuffer. What could cause this? Does your constructor correctly initialize all of the instance variables? Did you allocate memory for your array? Did you inadvertently redeclare an instance variable in a method or constructor, thereby shadowing the instance variable with the same name?

I get a Ring buffer underflow error in GuitarHeroLite before I type any keystrokes. Why? Did you forget to initialize the ring buffer to contain N zeros in your GuitarString constructor?

When I run GuitarHeroLite for the first time, I hear no sound. What am I doing wrong? Make sure you have tested with the main() provided for GuitarString. If that works, it is likely something wrong with pluck() since the main() provided for GuitarString does not test that method. To diagnose the problem, print out the values of sample() and check that they become nonzero after you type lower case characters 'a' and 'c'.

When I run GuitarHeroLite, I hear static (either just one click, and then silence or continual static). What am I doing wrong? It's likely that pluck() is working, but tic() is not. The best test is to run the main() provided for GuitarString.

How do I use keyboard.indexOf(key)? If keyboard is a String and key is a character, then keyboard.indexOf(key) return the integer index of the first occurrence of the character key in the string keyboard (or -1 if it does not occur).

Should I hardwire the constants 44,100, 110.0, 440.0, 880.0, and 37 in my program? No, in general, we will deduct if you use an unnamed constant (such as 37) in your program more than once. We recommend using the name SAMPLING_RATE for 44,100 and CONCERT_A for 440. But you need not name all of the constants in the formula 2(i - 24) / 12.

Extra credit performance At the beginning of the next lab, perform a piece for your classmates (on my laptop, your laptop, or a lab computer). Partners may perform a duet and both will receive extra credit, or a solo for individual extra credit.

Extra credit idea 1. Write a program (by modifying that plots the sound wave in real-time, as the user is playing the keyboard guitar. The output should look something like this, but change over time.

  Sampling from Karplus-Strong

Extra credit idea 2. Modify the Karplus-Strong algorithm to synthesize a different instrument. Consider changing the excitation of the string (from white-noise to something more structured) or changing the averaging formula (from the average of the first two samples to a more complicated rule) or anything else you might imagine.

Extra credit idea 3. Make an actual game similar to the real Guitar Hero game. The game should indicate what keys to play and the timing of the notes. The video to the right shows the game one previous student came up with.

Submission. Submit your programs,, and Be sure each submitted source file has the required header with your name, email address, and a description of the program. If you did the extra-credit, submit a single zip file containing all the files required to run your creation.
This assignment was originally developed by these folks at Princeton: Andrew Appel, Jeff Bernstein, Maia Ginsburg, Ken Steiglitz, Ge Wang, and Kevin Wayne.

Page last updated: January 21, 2015