3-7 Missing Fundamental

What is a missing fundamental?

A missing fundamental is similar to a combination tone in that it is a sound our ear perceives which is not actually produced by the sound source.

Whereas a combination tone is a sound we hear by combining two tones, a missing fundamental is when we hear a sound which is missing from a set of tones.

For example, complex tones of frequency f would have the harmonies 2f, 3f, 4f, 5f, etc. If we take away the original frequency tone (1f) but play the tones that precede it, our ear will imagine the original tone even though it is not being played. Since we are hearing a pitch which doesn't actually exist, these missing fundamentals are also referred to as phantom fundamentals or suppressed fundamentals.

Who discovered the missing fundamental?

Mathematician/ physician, Fourier, is praised for discovering the missing fundamental. Fourier realized that the harmonic frequencies to the original frequency will have the same period. This doesn't change no matter how many harmonics have been added! Since the frequencies are all the same, the resultant wave will be perceived to have the same pitch. (This is why when even the original frequency has been removed we can still "hear" the sound.)

This can be seen here:

How do you find the missing fundamental?

    missing fundamental = f2-f1

Musical Interval	f1	f2	Frequency of "Missing Fundamental"
Octave	f	2f	f
Fifth	f	3/2f	1/2f
Fourth	f	5/3f	1/3f
Third	f	5/4f	1/4f
Sixth	f	5/3f	1/3f

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