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The Ear As a Frequency Analyzer
Reinier Plomp, 1976
Overview
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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
_ can be emphasized
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bands)
by contrast
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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