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 ( 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

Identification of partials depends on: –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

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