Missing Fundamental illusion

from Michael’s   Visual Phenomena & Optical Illusions

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What to do & hear

When you initially load this page, you will hear nothing. On pressing the “Missing Fund.” button, should hear a tone. [If not loud enough, use the Master volume, preset to only 10%.] Try to sing / hum it, and compare it with the sound from the “Normal tone” button. They sound different (in timbre), no doubt, but their pitch to many seems the same. This is surprising, because the “Missing Fund.” tone is missing the “fundamental”: the lowest sinewave that usually determines pitch. The mixture of all harmonics determines tone quality / timbre.

You can check with the “1 octave ↑” button – that indeed raises the pitch by one octave.

Changing the base frequency* to, say, 110 Hz, makes the effect stronger – at least with small speakers. Why? Because small speakers can’t reproduce bass well, it does not matter if the lower harmonic is there or not.
[*you need to “tab out of that field, or activate the master volume field, to make the computer notice you changed the frequency number.]

Comments

The sliders let you perform a Fourier synthesis: Fundamental (=1st harmonic), then 2nd harmonic at 2× the basic frequency, the next harmonic has 3× the frequency and so on. For the Normal tone I mix all harmonics in a slightly descending series (for insiders: amplitude 1 over the √ of the harmonic number, a bit spikier than a sawtooth).

Why do we hear the pitch of a fundamental, which is missing? The real answer is very complicated (see pertinent Wikipedia entry). But on this site we are already used to recognising that our brain reconstructs much from very little: The harmonic structure of the missing fundamental tone can only appear if it really were such a low tone – compare the mixture in the 1 octave up situation.

This also explains why we can hear the correct bass note even when using tinny speaker which cannot really reproduce it. It is also used with acoustic organs: If there is not enough space (or money) to add a 32’ register, let a 16’ and 10⅔’ sound at the same time, our brain invents a missing 32’.

I added note names below the harmonic sliders (C, c, g, …), assuming the fundamental were a C (at 523.25 Hz). These highlight an interesting aspect: the first 5 harmonics form a major chord! This may in part explain why the ionian scale sounds so “natural” – or is that culturally acquired?

Sources

Wikipedia: Missing fundamental