Psychoacoustics: How the Brain Interprets Sound

Introduction

You hear a violin playing a note, and you perceive not just a frequency but a pitch, not just an amplitude but a loudness, not just a spectrum but a timbre. The transformation from physical sound wave to subjective auditory experience is the domain of psychoacoustics — the study of how the human auditory system processes and interprets sound. This field reveals that hearing is not a passive recording of acoustic events but an active, constructive process that shapes our musical experience in profound ways.

The Ear as a Spectrum Analyzer

The human ear functions as a remarkably sophisticated frequency analyzer. Sound enters the ear canal and vibrates the eardrum, which transmits vibrations through the three tiny bones of the middle ear to the cochlea in the inner ear. The cochlea is a fluid-filled, spiral-shaped organ containing approximately 15,000 hair cells that convert mechanical vibrations into neural signals.

The cochlea performs a frequency-to-place transformation: high frequencies stimulate hair cells at the base of the cochlea, while low frequencies stimulate cells at the apex. This means the cochlea physically maps frequency onto position, functioning much like a biological Fourier transform. The brain reads this spatial map to determine the frequency content of incoming sound.

Critical Bands and Frequency Selectivity

The ear’s frequency analysis is not infinitely fine-grained. Instead, it divides the frequency spectrum into critical bands — ranges of frequencies that are processed together. The width of a critical band is approximately:

$$\Delta f \approx 25 + 75 \cdot f / 1000 \text{ Hz}$$

At low frequencies, critical bands are narrow (about 100 Hz at 500 Hz). At high frequencies, they widen (about 3,500 Hz at 15 kHz). This non-linear frequency resolution explains why we are more sensitive to frequency differences at low frequencies than at high frequencies.

The concept of critical bands explains many acoustic phenomena. Two tones falling within the same critical band produce roughness — a sensation of harshness or beating. Tones in different critical bands blend more smoothly. This is why consonant musical intervals correspond to frequency ratios that place the notes in separate critical bands, while dissonant intervals create roughness by falling within the same band.

Loudness Perception

The perception of loudness does not correspond linearly to physical intensity. The ear’s response is approximately logarithmic, which is why the decibel scale was developed. However, loudness perception also depends on frequency — the ear is most sensitive to frequencies between 1 and 4 kHz, where human speech falls.

The equal-loudness contours (Fletcher-Munson curves) show that a 100 Hz tone must be about 20 dB louder than a 1 kHz tone to be perceived as equally loud. This has practical implications: music sounds different at low volumes than at high volumes. Bass frequencies seem to disappear at low listening levels, which is why many amplifiers include a loudness compensation circuit that boosts bass and treble at low volumes.

The perception of loudness also depends on duration. Brief sounds (less than about 200 ms) are perceived as quieter than sustained sounds of the same intensity. This is why percussive attacks need to be physically louder than sustained notes to be perceived as equal in loudness.

Pitch Perception and Missing Fundamentals

The brain’s interpretation of pitch is remarkably sophisticated. When presented with a complex tone, the perceived pitch is usually that of the fundamental frequency, even if the fundamental is physically absent. This is the missing fundamental phenomenon.

For example, if you remove the fundamental from a complex tone at 200 Hz but leave the harmonics at 400, 600, 800 Hz, and so on, you will still perceive the pitch as 200 Hz. The brain infers the fundamental from the harmonic spacing. This is why small speakers that cannot reproduce low frequencies can still give the impression of bass — the brain reconstructs the missing fundamental from the audible harmonics.

Pitch perception is also influenced by context. The same frequency can be perceived as different pitches depending on the surrounding notes, the musical key, and the listener’s expectations. This context-dependent pitch perception is why musicians can use techniques like enhharmonic modulation to create surprising musical effects.

Auditory Masking

Auditory masking is the phenomenon where one sound renders another inaudible. When two sounds occur simultaneously, the louder sound can mask the softer one if they fall within the same critical band. This is the basis of lossy audio compression algorithms like MP3 and AAC.

An MP3 encoder analyzes the audio signal and identifies masked components — frequencies that are inaudible due to masking by louder nearby frequencies. These masked components can be discarded (or represented with fewer bits) without perceptible quality loss. The encoder allocates more bits to unmasked frequencies that are clearly audible, achieving compression ratios of 10:1 or more while maintaining perceived quality.

Forward masking occurs when a loud sound temporarily reduces sensitivity to softer sounds that follow. This temporal masking lasts for approximately 50-200 ms after the masking sound ends. Reverse masking (backward masking) occurs when a loud sound presented after a softer sound can mask it, though this effect is weaker and shorter.

Binaural Hearing and Spatial Perception

Humans hear with two ears, and the brain uses the differences between the two ear signals to determine the location of sound sources. Two key binaural cues are:

Interaural time difference (ITD): Sound arriving at the closer ear reaches it a few hundred microseconds before the opposite ear. The brain uses this delay to locate sounds on the horizontal plane.

Interaural level difference (ILD): The head creates an acoustic shadow that reduces the level of sound reaching the far ear, particularly at high frequencies. This level difference provides additional localization information.

These binaural cues explain why headphones can create a sense of space using binaural recording or processing techniques. They also explain why hearing loss in one ear significantly impairs the ability to locate sound sources.

Summary

Psychoacoustics reveals that hearing is an active, creative process — the brain does not merely record sound waves but constructs a rich perceptual experience from them. Critical bands shape our perception of harmony and dissonance, the missing fundamental allows us to perceive bass from tiny speakers, auditory masking enables efficient audio compression, and binaural processing creates our sense of acoustic space. Understanding these phenomena deepens our appreciation of both the power and the elegance of the human auditory system.