Date: Wed, 03 Mar 1999 15:59:58 -0600

Author: Clifford Bettis

Subject: Re: Missing Fundamental


Richard Berg wrote:

> I think this may not work the way you think with a square or triangular
> wave. Because they have only odd harmonics, the difference tone between
> adjacent harmonics is the second harmonic, not the fundamental. I suggest
> that you try a sawtooth, or better yet, a pulse train, both of which
> contain all harmonics.
> There is an effect called the "missing fundamental" that relies on your
> neural processing to insert the fundamental into a complex wave without
> the fundamental, but that is quite different from the difference tones
> that are produced by adjacent harmonics of a "loud" complex wave due to
> the non-linear response of the ear mechanism.
> If you really want to delve into this, I suggest getting a good book like
> Introduction to the Physics and Psychophysics of Music, by Juan
> Roederer, or better yet, The Physics of Sound, by Berg and Stork. It's a
> great bargain even at the price they are charging and I need the
> royalties.
> Dick Berg

Good point, Dick. You do need all the harmonics less the fundamental. I am
settling on using the Pasco Synthesizer. I set it so the harmonics are all at the
same level as measured by my spectrum analyzer. I have another oscillator that
iis connected to a different speaker and tuned to the fundamental. Both speakers
are keyed with a tap key. I have people listen first to a burst from the
oscillator and then to a burst from the synthesizer. I ask them if the pitches
are the same. I then repeat removing one or more of the lowest harmonics from the
synthesizer's output. If I listen to it enough, I could swear I hear the
fundamental even though I know it's not there as measured by my analyzer.