Digital Music Programming: Programming Lab 3
Making an Oscillator



This lab demonstrates how to create a sinewave generating program in C/C++.

in Max/MSP, the cycle~ object is an oscillator which generates a sinewave as an output. It takes two inputs: (1) the frequency in Hertz of the sinewave, and (2) the phase of the sinewave. Here is a cycle~ object with the default frequency being 100 Hz:

Actually cycle~ is an interpolated wavetable which happens to have one cycle of a cosine in the contents of a 512 sample wavetable. But we will not worry about that.

An oscillator is generated from a sinewave which has the following mathematical equation: 

   cycle(frequency, phasor) 
                = cos(2 * pi (frequency * time + phasor))
                = cos(2 * pi * frequency * time + phase)

How can the cosine function be implemented as an oscillator which takes frequency and phase input? The phase increment must be calculated from the frequency like this: 

    phase_increment = 2 * pi * frequency / sample_rate
This value must then be added to the previous phase_position in the cosine cycle for each unit of time. Here is a C for-loop which can be used to calculate the oscillator: 

       sample_count  = 44100;   // one second of sound
   amplitude     = 0.5;
   sample_rate   = 44100.0;
   frequency     = 440.0;
   initial_phase = 0.0;
   sum = initial_phase;

   for (i=0; i<sample_count; i++) {
      output = amplitude * cos(sum);
      phase_increment = 2 * 3.14159265359 * frequency / sample_rate;
      sum = sum + phase_increment;
   }

Exercises

  1. Write a command-line program which generates a sinewave soundfile using the above code example as a guideline. Use the code from programming lab 2 as a program template.

  2. Add command-line frequency control to your program.
  3. Add command-line duration control to your program.
  4. Add command-line amplitude control to your program.
  5. What happens if you make the amplitude greater than 1.0?
  6. What is the highest frequency that you can hear with your program?
  7. Extra credit: Write a program that generates a sawtooth wave instead of sinewaves.