the missing fundamental
Psychoacoustics — when your auditory system infers a pitch that isn’t in the signal.
Play the 2nd, 3rd, and 4th harmonics of a 100 Hz tone — that’s 200, 300, and 400 Hz — and you’ll hear a pitch at 100 Hz. Look at the spectrum: 100 Hz isn’t there. Your cochlea never vibrated at that frequency. But the pitch is as clear as if it were.
This is the missing fundamental. Your auditory cortex doesn’t just passively report which frequencies are present. It asks a deeper question: what source would have produced these harmonics? The answer — the fundamental — is the generative cause of the harmonic series, and your brain recovers it even when the cause itself is absent from the evidence.
Toggle harmonics on and off below. Watch the spectrum. Listen for the pitch your brain constructs.
There is a temptation to call this an auditory illusion — to say the brain “hallucinates” a frequency that isn’t there. But that framing misses something important. The fundamental really is the generative cause of the harmonic series. The 2nd, 3rd, and 4th harmonics exist because of the fundamental. When your auditory system infers 100 Hz from its harmonics, it is recovering the causal structure of the signal. The inference is correct even though the direct evidence is absent.
This is what separates construction from confabulation. Not all things the brain builds are fictions. Some of them — the ones that track the causal structure of the world — are knowledge. The missing fundamental is not a bug in perception. It is perception doing exactly what it should: reasoning backward from effects to causes, and getting it right.