COS 126

Plucking a Guitar String
Programming Assignment

This assignment allows optional partnering. If you choose to do this, you must follow the pair programming guidelines. Please note that writing code with a partner without following the pair programming instructions is a violation of the course collaboration policy. All writing of code, comments, the readme, and uploading to the dropbox should be done together from start to finish. If you come to office hours alone, you can get advice, but you may not change any code until both partners are together.

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 material in the textbook on digital audio (pp. 147–151, 202–206).

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. The integer N equals the sampling rate (44,100 Hz) divided by the desired fundamental frequency, rounded up to the next integer.

Why it works? The two primary components that make the Karplus-Strong algorithm work are the ring buffer feedback mechanism and the averaging operation.

From a mathematical physics viewpoint, the Karplus-Strong algorithm approximately solves the 1D wave equation, which describes the transverse motion of the string as a function of time.

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
 static void main(String[] args)  // test client, tests all methods
Since the ring buffer has a known maximum capacity, implement it using a double array of that length. For efficiency, use cyclic wrap-around: this ensures that each operation can be done in a constant amount of time. We recommend you 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 a run-time exception if the client attempts to enqueue() into a full buffer or call dequeue() or peek() on an empty buffer.

Ring buffer

Your test client may contain the tests we give you, ones you write yourself, or a combination thereof.

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()                         // pluck the guitar string by replacing the buffer with white noise
  void tic()                           // advance the simulation one time step
double sample()                        // return the current sample
   int time()                          // return number of times tic was called so far
static void main(String[] args)        // test client, tests all methods

Again, your test client may contain the tests we give you, ones you write yourself, or a combination thereof.

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.

  public class GuitarHeroLite {
      public static void main(String[] args) {

          // create two guitar strings, for concert A and C
          double CONCERT_A = 440.0;
          double CONCERT_C = CONCERT_A * Math.pow(2, 3.0/12.0); 
          GuitarString stringA = new GuitarString(CONCERT_A);
          GuitarString stringC = new GuitarString(CONCERT_C);

          while (true) {

              // check if the user has typed a key; if so, process it   
              if (StdDraw.hasNextKeyTyped()) {
                  char key = StdDraw.nextKeyTyped();
                  if      (key == 'a') { stringA.pluck(); }
                  else if (key == 'c') { stringC.pluck(); }

              // compute the superposition of samples
              double sample = stringA.sample() + stringC.sample();
              // play the sample on standard audio
              // advance the simulation of each guitar string by one step   

Write a program GuitarHero that is similar to GuitarHeroLite, but supports a total of 37 notes on the chromatic scale from 110Hz to 880Hz. Use the following 37 keys to represent the keyboard, from lowest note to highest note:
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 keyboard 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 pressed that does not correspond to one of your 37 notes.

Provided files.   In the Possible Progress Steps on the checklist we provide optional templates for RingBuffer and GuitarString. Here is a copy of which you will extend to create GuitarHero. Finally, we provide a readme.txt as well as an abbreviated partner readme.txt file — in each pair, one partner should submit the .java files and the long readme, and the other should submit only a short readme.

Submission.   Submit,,, and a completed readme.txt. (Or, if your partner is submitting the java files, just submit the completed partner readme.txt.) The names, logins, and precept numbers of both partners MUST appear at the top of every submitted file.

If you and your partner both do the extra credit separately, you are both allowed to upload .java files to facilitate testing.

Extra credit. There are two optional extra credit parts. You can do either one if you want or both. If working with a partner, you can do them together or alone — but decide before you start it.

Extra credit 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:

To get credit, your program must (1) draw something for every sample, (2) run smoothly in real-time with no effects on the audio, and (3) run at a minimum of 24 frames per second. Depending on your computer, you might be able to do 60 FPS or more, but this is not required. Part of what is necessary to accomplish this is the usage of animation mode as described in the StdDraw documentation, since deferring the on-screen display until an entire frame is complete helps make the StdDraw calls fast enough to not distort the audio. You can add extra embellishments if you like so long as your program satisfies all three aformentioned requirements.

Extra credit 2. Write a program that will automatically play a song with GuitarStrings. The song should be between 10 seconds and 2 minutes in length. It will be run with

% java-introcs AutoGuitar
It will make calls to but it must not make any other calls to the Std* libraries. In particular, make sure there are no calls to StdDraw, and that it works with no user input. Your main() must terminate; it cannot loop infinitely. To get the timing to work, either use the Stopwatch class, or use the fact that 1/44100 of a second elapses between calls to This will make it have consistent timing on different machines.

Use arrays, loops, conditionals, and randomization as you see fit. If you are interested, you can add chords, repetition, or different instruments (see below). You may submit additional classes, but don't modify your original classes (such as GuitarString).

If you find it helpful, you may submit a .txt file to be read with the In class, and you may hard-code the filename in your program.

Challenge for the bored. Here are suggestions on other effects and instruments to synthesize. Some come from the paper of Karplus and Strong.

This assignment was developed by Andrew Appel, Jeff Bernstein, Maia Ginsburg, Ken Steiglitz, Ge Wang, and Kevin Wayne.
Copyright © 2005