The Ear As a Frequency Analyzer

Reinier Plomp, 1976

Overview

• Ear As a Filter Bank

• How We Identify Sounds

• Detecting Partials: Multiple Approaches

• Masking

• Inverse Masking: Pulsation Threshold

• Lateral Suppression

• Conclusions

Ear as a Filter Bank

• Different parts of the Basilar Membrane oscillate at different frequencies

Ear as a Filter Bank

• Pitch and fundamental frequency

• We always perceive the fundamental – even where there is no energy there (demo)

How We Identify Sounds

• Trumpet at one octave above Middle C (523.25 Hz) and it’s Fourier transform

• Timbre: the psychoacoustician's waste-basket

How We Identify Sounds

• Ohm’s Acoustic Law: – Each tone of different pitch in a complex

sound originates from the objective existence of that freq in the Fourier analysis of the acoustic wave pattern

• So, can we always hear the partials?

Detecting Partials

• Helmholtz: – to determine whether a partial is present in a complex

sound, listen first to a tone of the same pitch as the partial, and then listen to the target

• Early difficulties:– Was this partial present?– How many tones made up this tone?

• Three position switch– Harmonic and inharmonic partials (demo)

Detecting Partials

Detecting Partials

• Identification of partials depends on:– Frequency– Frequency

Separation

Figure: Frequency difference between the harmonics of a complex tone, required to hear them separately, as a function of frequency.

Critical Bandwidth

• The difference in frequency between two pure tones at which the sensation of "roughness" disappears and the tones sound smooth is known as the critical band

• When two such frequencies lie within what has been termed a critical bandwidth, sensory dissonance is experienced

• (Demo)

Masking

• Masking:– Where one sound prevents another from

becoming audible• By playing at the same time (simultaneous

masking)• By playing beforehand (forward masking)

• Applications to digital watermarking

Masking

• Masking Threshold– The minimal sound pressure level of a

sinusoidal probe tone required to detect this tone in the presence of a masking stimulus

• Masking Pattern– The dependence of the masked threshold

upon the frequency of the probe tone

Masking and “The Auditory Filter”

• Simultaneous Masking Results– The closer the mask frequency is to the target

tone, the louder the target must be

• Problems close to the target tone– Beats (demo)– Combination tones (demo)

• “Noise Mask” alleviates these problems

Pulsation aka “Inverse Masking”

• “Inverse Masking”– Uses a non-simultaneous probe tone which is

longer in duration than the brief tone bursts in forward masking. Makes an nonexistent inaudible stimulus seem audible

– Think of it visually: • Figure vs. Ground • Occlusion

Pulsation Threshold

• The maximal level at which the probe tone still sounds continuous

• The general shape of the pulsation threshold pattern for a single pure tone doesn’t differ from the masking pattern, but for those probe tones coinciding in frequency with the harmonic, the threshold is much lower: it’s easier to hear it as pulsating

Lateral Suppression

• This can be considered lateral inhibition or lateral suppression– Like in vision, the edges of the filter (mach

bands) can be emphasized by contrast phenomena

– Non-simultaneous masking should be used; the masking contour will not show up when both the mask and the probe are subjected to the suppression process

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Lateral Suppression

• Edges are emphasized

Conclusions

• The ear can identify the partials of a complex sound, as long as the frequencies are separated by more than 15 to 20%, with a minimal frequency distance of about 60 Hz

• Non-simultaneous masking results in lateral suppression

• Auditory bandwidth will change depending on whether it’s measured with non-simultaneous probes or simultaneous probes

Picture Time

• Plaid – 3recurring “Rest Proof Clockwork”

Picture Time

• Venetian Snares' "Look"

Picture Time

• Aphex Twin – Windowlicker FFT