Did you ever play duets with your teacher or a friend and you heard a third note in your head? Well guess what…. It was “All in your head!” That doesn’t mean you are crazy, it’s just a phenomenon that occurs on our eardrums called the “difference tone”.
Scientifically, the difference tone is the number of wave lengths found between two different frequencies. For instance: 600 hz (waves per second) minus 500 hz equals 100 hz (the difference between the two original pitches played).
When we apply this concept to the harmonic series an extremely cool thing happens. But first, a little about the series.
A harmonic series is the sequence of sounds where the base frequency of each sound is an integer multiple of the lowest base frequency.
You start with the fundamental, followed by the first octave, then the 5th, then the 4th higher (the second octave), next is the 3rd, the flat 3rd, the second etc.
If the fundamental is 100 hz, each consecutive note in the series will be 100 hz greater than the last note. Example:
Fundamental 100…..octave 200….5th 300….4th 400….3rd 500 hz. and so on. Do the math. It works.
Here’s what happens. Play the 1st octave and the 5th. The DT (Difference Tone) will be the fundamental. Add the 4th over the 5th….there’s another DT equal to the first DT. Get where I’m going. Each pair of consecutive harmonic notes reinforces the fundamental. After about 10 or more notes of the series, the only note will you hear is the fundamental which is the only note you didn’t play. This is the “Chord of Nature”!………ONE NOTE.
In college, I did a demonstration in a small auditorium. By the time I was through, the auditorium was filled with one overwhelming note. That note was one I wasn’t actually playing. The difference tone was overpowering every other note that was physically being played. The other students’ jaws were dropped to the floor.
One caveat, this can not be accomplished on an equal temperament piano. Our ears are trained to accept slightly out of tune music. However, this concept is used commonly and naturally in every day life. High frequency overtones are transmitted and received by tiny earbuds and somehow we still hear the bass notes. Hmmmmm….
Image by: Hyacinth at the English language Wikipedia, CC BY-SA 3.0, source