A synthesizer plays a tone containing harmonics at 200 Hz, 300 Hz, and 400 Hz, but no 100 Hz component. What pitch does a listener most likely perceive?
A200 Hz — the lowest frequency actually present in the signal
B300 Hz — the middle harmonic, which dominates the blend
C100 Hz — the missing fundamental inferred from the harmonic pattern
DNo definite pitch — without the fundamental, pitch cannot be perceived
This is the 'missing fundamental' effect: the auditory system recognizes that 200, 300, and 400 Hz are the 2nd, 3rd, and 4th harmonics of 100 Hz, and reconstructs a perceived pitch at 100 Hz — even though that frequency is physically absent. This is a cognitive reconstruction, not a passive readout of the acoustic signal. It proves that pitch is not simply 'the lowest frequency present' but a property inferred by the auditory system from the harmonic pattern.
Question 2 Multiple Choice
Two partials in a complex tone fall within the same critical band. What is the perceptual consequence?
AThe two partials are heard as separate pitches, making the chord sound richer
BThe partials fuse into a single perceived component, and if close in frequency, may produce beating or roughness
CThe higher partial masks the lower one completely, so only one pitch is heard
DThe two partials combine constructively, increasing perceived loudness
Critical bands are frequency regions (roughly 1/3 of an octave wide) within which the cochlea cannot resolve individual partials — they fuse into a single perceived component. Two partials within the same critical band interact and can produce 'beating' (amplitude fluctuations at a rate equal to their frequency difference) or 'roughness' (if the difference exceeds ~20 Hz). This explains why certain chord voicings sound rough: harmonics collide within critical bands, while spacing partials across different bands produces smoother sounds.
Question 3 True / False
Pitch perception scales logarithmically with frequency, which is why musical intervals are defined by frequency ratios rather than differences.
TTrue
FFalse
Answer: True
Doubling frequency (a 2:1 ratio) always corresponds to one octave, regardless of the starting pitch. The octave from 220–440 Hz sounds the same as 440–880 Hz, even though the second involves twice the physical frequency difference. This logarithmic scaling means equal-ratio intervals (perfect 5th = 3:2, octave = 2:1) are perceptually uniform, while equal-difference intervals would sound increasingly small as pitch rises. Equal temperament and all standard musical notation are built on this logarithmic property.
Question 4 True / False
Removing the fundamental frequency from a recording of a cello note will eliminate the listener's perception of its pitch.
TTrue
FFalse
Answer: False
This is exactly what the missing fundamental effect disproves. The auditory system infers the fundamental from the pattern of harmonics present. A cello note with its fundamental removed will still be perceived at the same pitch — because the 2nd, 3rd, 4th harmonics remain, and their pattern unambiguously implies the fundamental. This effect is exploited by small loudspeakers that cannot physically reproduce low bass frequencies: the brain fills in the perceived bass from the harmonics the speaker can produce.
Question 5 Short Answer
What does the 'missing fundamental' effect reveal about the nature of pitch perception?
Think about your answer, then reveal below.
Model answer: It shows that pitch is a cognitive reconstruction, not a direct readout of the lowest frequency present in the sound. The auditory system analyzes the pattern of harmonics in a complex tone and infers what fundamental frequency they imply — even when that fundamental is absent from the physical signal. Pitch is a perceptual property computed by the brain, not simply a physical property of the sound wave.
This finding has broad implications: it means the gap between acoustic stimulus and perceptual experience is real and systematic. The auditory system doesn't passively register frequencies — it actively reconstructs a pitch. This is why psychoacoustics is essential to music theory: the relationship between what is in the score or signal and what the listener hears is mediated by cognitive processing that can produce perceptions of things that aren't physically there.