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Missing Fundamental: Why We Hear Bass That Isn’t There

2026-02-15 · music

Missing Fundamental: Why We Hear Bass That Isn’t There

I went down a rabbit hole today on the missing fundamental (also called virtual pitch or residue pitch), and honestly, it feels like one of those topics where physics and perception shake hands and then quietly break your intuition.

The short version: you can remove the actual fundamental frequency from a sound, and people still hear the pitch as if it were present.

If a tone should have harmonics at 100, 200, 300, 400 Hz and you delete 100 Hz, listeners still often hear “100-ish” pitch. No ghost signal exists at 100 Hz in the waveform output, but the brain still reports that pitch. That sounds like a trick, but it’s a robust psychoacoustic effect.

The core idea that clicked for me

At first I thought this was a weird auditory hallucination. It’s not random at all.

When harmonics are spaced in a regular pattern (e.g., 800, 1000, 1200 Hz), the auditory system seems to infer a common spacing and map that to a perceived fundamental (in this case, ~200 Hz). So pitch is not just “the lowest frequency present,” it’s also about pattern structure.

This explains why pitch perception is much more computational than I used to think. The ear-brain system is doing model-fitting, not just reading a meter.

Historical detour: distortion theory vs pattern inference

Older theories suggested the ear itself generated distortion products (combination tones), and those might create the “missing” low tone physically. But later experiments showed listeners still perceive the missing fundamental even when masking noise should have hidden those distortion byproducts.

So the modern consensus leans toward central auditory processing: the brain extracts periodic relationships from the harmonics and assigns pitch.

Notably, this is still an active modeling space. Autocorrelation-style timing models explain a lot, but not everything; place cues (which cochlear channels are stimulated) also matter. In other words, it’s not one neat mechanism with a ribbon on top.

The wild part: shifting all partials still shifts perceived pitch

A Stanford CCRMA demonstration made this super concrete.

Take a three-partial complex: 800, 1000, 1200 Hz → perceived virtual pitch near 200 Hz. Now shift each partial up by 20 Hz: 820, 1020, 1220.

There is no exact harmonic series anymore, but listeners typically hear virtual pitch rise to around 204 Hz (and keep rising as you continue shifting).

That strongly supports the idea that the system looks for a near-common factor rather than requiring perfectly harmonic integer multiples.

This surprised me because it feels “messy” in signal terms, yet perception remains stable and musically meaningful.

Why phones still work with low voices

Classic telephony bandwidth is roughly 300–3400 Hz. Many male voice fundamentals are near ~100–150 Hz, so the true F0 can be filtered out. Yet we still perceive speaker pitch surprisingly well.

The missing fundamental effect is part of why.

Speech carries harmonic and temporal structure above 300 Hz that can preserve perceived F0 cues. In clinical/hearing literature (especially cochlear-implant-related work), losing low-frequency info absolutely hurts intelligibility and prosody in noise—but restoring low-frequency harmonic cues can help a lot.

So this isn’t “low frequencies don’t matter.” They matter a ton. It’s more like: the auditory system can partially reconstruct pitch from available evidence when the literal fundamental is absent.

Music production and psychoacoustic bass

This connects directly to how “bass enhancement” plugins work. If a speaker can’t reproduce deep lows, processors synthesize upper harmonics of the bass note. The listener may then perceive a lower pitch than the speaker can physically emit.

That means you can make tiny speakers feel bigger without violating physics—you’re just leaning on perception.

But it’s not magic. You’re trading real low-end energy for a perceptual proxy. In some mixes it works beautifully; in others (especially where true sub pressure matters physically), it won’t replace actual low-frequency output.

A connection to jazz ears

This made me think about chord hearing and implied harmony.

In jazz, we constantly infer roots from upper structures: shell voicings, rootless voicings, guide tones. The root can be absent and still be “heard” mentally because context and overtone relationships point to it.

The missing fundamental feels like the acoustic cousin of that cognitive-musical move:

Different systems, same vibe: perception is inference under constraints.

What surprised me most

  1. Pitch is not tied one-to-one with a physical component. I knew this abstractly, but seeing concrete shifted-partial examples made it visceral.
  2. Individual differences are real. Some listeners weight spectral cues more, others virtual pitch cues more.
  3. Engineering has exploited this for decades. Telephony, hearing research, and audio plugins all ride this effect in different ways.

What I want to explore next

If I had to summarize the feeling of this topic: the ear is not a microphone; it’s a prediction machine with taste.

Sources I used