Dan and I were talking about tuning two instruments together, and how to listen for success.  I was getting concerned because the wave-beat thumping seemed to be getting louder when I thought was getting closer to the note, but this was counter-intuitive.  This is my attempt to explore what has happened.

This app shows the wavebeat effect of two notes close together being played together, such as when your teacher gives you an A and you are trying to match it.  As you get closer to the unison. (offset = zero in this app)  you may hear a thumping, or rough effect.  As you get close to the note the thumping may appear to get worse before it gets better, but what is really happening is that the pulses are becoming easier to hear.

Note: This does not work for violas.  See below for why.

The base note is open A (220 Hz) on a cello. The interval can be any number, but should be a small number (between -20 Hz and +20 Hz)  if you wish to see the effect on the graph.

In the app below, the thumping effect appears when the entire “wave envelope” is squeezed to zero. The notes are out of phase and are cancelling each other out instead of helping. This alternation of helping and cancelling is what causes the wave beat.

Another way to hear a wave beat is to drive in your car but open only ONE of the back windows.

Thanks to Wolfram Alpha for providing the widgetry to do this.

I wish I could find a way to put this app on my side-bar instead of on a post.

Some useful values to try for the interval

  • A half-semitone (based on equal temperament) : offset approx = 6.5 Hz
  • A cent (also based on ET) = 0.13 Hz
  • A semitone = 13.1

For more information on tuning systems, see the Wikipedia articles on Equal Temperament and Pythagorean tuning, or look these terms up in any music theory text.

Why does this not work for violas? Because of the old joke that says “What is a semitone? Two violists trying to play in unison”