8. Psychoacoustics (Perception Layer) · Concept 10 of 18
Missing Fundamental
Your brain hearing a low bass note even when the actual low frequency is not there.
Small box drops the 100 Hz fundamental, but the brain reads the 100 Hz spacing of the harmonics and hears the bass anyway.
What it is
Your brain reconstructs a low bass note from its upper harmonics even when the actual fundamental frequency is absent.
Key facts
Harmonic series: a note at fundamental f0 also contains overtones at 2f0, 3f0, 4f0, 5f0 (integer multiples)
Missing fundamental: remove f0 but keep 2f0, 3f0, 4f0 and the brain still hears pitch f0
Mechanism = the harmonics share a common spacing of f0 Hz; brain locks to that spacing (periodicity pitch)
f0 = the greatest common divisor (GCD) of the surviving harmonics, e.g. 200, 300, 400 Hz all spaced 100 Hz to f0 = 100 Hz
Period formula: T = 1 / f0, where T = repeat time in seconds and f0 = fundamental in hertz (Hz)
Low E bass string = 41.2 Hz fundamental, but its 2nd-6th harmonics sit at 82, 124, 165, 206, 247 Hz
A typical small PA box / phone speaker rolls off below 100-150 Hz, so f0 of bass is often physically absent
Speed of sound in air = 343 m/s at 20 degrees C (metres travelled per second)
Wavelength formula: lambda = c / f, lambda = wavelength (m), c = 343 m/s, f = frequency (Hz)
41.2 Hz fundamental = 8.3 m wavelength, needs a huge cone/horn; its 200 Hz harmonic = only 1.7 m, easy for a small box
How it works
A bass note is played: it contains a fundamental f0 plus harmonics at 2f0, 3f0, 4f0.
Small speaker physically cannot reproduce the low f0 and rolls it off.
Only the higher harmonics (2f0, 3f0, 4f0) actually leave the speaker.
Ear sends these spaced tones to the brainstem and auditory cortex.
Brain measures the common spacing between harmonics = f0 Hz.
Brain reports pitch at f0 even though no energy exists at f0 - you 'hear' the bass.
Real examples
Phone or laptop speaker seeming to play a kick drum it can't physically move air for
Telephone passes only 300-3400 Hz yet a male voice still sounds full-pitched (its ~120 Hz fundamental is gone)
Cheap earbuds making a 40 Hz bass line audible by reproducing its harmonics
A small 8-inch club speaker delivering convincing bass guitar
Church organ 'acoustic bass' stops that combine two higher pipes to fake a deep 16-foot note
How it helps in live sound
On small tops with no sub, boost the upper-bass harmonics around 80-250 Hz to fake low-end fullness
Use a 'harmonic bass exciter' / psychoacoustic enhancer (e.g. Waves MaxxBass, RBass) to synth harmonics of frequencies below the box's limit
High-pass small boxes at 100-120 Hz so you stop wasting headroom on f0 they can't reproduce anyway
Set the HPF just above the speaker's roll-off, then add 2-4 dB around 150-200 Hz to restore perceived weight
Don't chase real 40 Hz on a 10-inch box - feed it the harmonics instead and let the listener's brain fill in the root
For voice clarity on tiny speakers, protect 150-300 Hz so the fundamental's harmonics survive and pitch stays solid
Everyday analogy
Like seeing only the top of a person's head over a fence and your brain still 'knowing' a whole body is standing there.
Watch out
Myth: you must reproduce the actual low frequency to be heard as bass. Truth: the brain infers pitch from harmonic spacing, so the fundamental itself can be totally absent.
Fun fact
A telephone deliberately throws away the ~120 Hz fundamental of a male voice (it only passes 300-3400 Hz), yet you never notice the voice 'went up' in pitch - your brain rebuilds it for free.
Key takeaways
Pitch comes from harmonic spacing, not necessarily from energy at the fundamental
f0 = greatest common divisor of the present harmonics
Small/cheap speakers exploit this to 'fake' bass they cannot physically produce
Boost upper-bass harmonics (80-250 Hz) to add felt weight on tiny PA boxes
High-pass below the box's limit - you lose nothing the ear was using anyway