Hearing & Deafness (4)
Pitch Perception
1. Pitch of pure tones
2. Pitch of complex tones
Pitch of pure tones
Place theory
Place of maximum in basilar membrane excitation
(excitation pattern) - which fibers excited
Timing theory
Temporal pattern of firing how are the fibers firing needs phase locking
Phase Locking of Inner Hair Cells
Auditory nerve connected to inner hair cell tends to fire
at the same phase of the stimulating waveform.
Phase-locking
1
0.5
0
-0.5
0
0.2
0.4
0.6
0.8
1
-1
Response to Low Frequency tones
Inter-spike Intervals
2 periods
1 period
time (t)
Response to High Frequency tones > 5kHz
Random intervals
time (t)
nerve spike
Pure tones: place vs timing
Low frequency tones
Place & timing
High frequency tones
Place only
1. Phase locking only for tones below 4 kHz
2. Frequency difference threshold increases rapidly
above 4 kHz.
3. Musical pitch becomes absent above 4-5 kHz
(top of piano)
Frequency
thresholds
increase
above 4 kHz
BCJ Moore (1973)
JASA.
Pitch of complex tones:
fundamental & harmonics
4
pressure
3
2
1
0
1
-1
-2
amplitude
Fundamental =200 Hz
Harmonic spacing
= 200 Hz
1.0
-3
-4
time (t)
Period = 1/200 s = 5ms
200 400 600 800
frequency (Hz)
Helmholtz’s place theory
amplitude
Fundamental =200 Hz
Harmonic spacing
= 200 Hz
1.0
high
Peaks in
excitation
200 400 600 800
frequency (Hz)
Pitch = frequency of fundamental
Coded by place of excitation
low
Arguments against Helmholtz
1. Fundamental not necessary for pitch
(Seebeck)
Missing fundamental
Harmonic spacing
= 200 Hz
3
pressure
1
0
1
-1
-2
-3
amplitude
1.0
2
time (t)
200 400 600 800
frequency (Hz)
Period = 1/200 s = 5ms
No fundamental but you still hear the pitch at 200 Hz
Track 37
Same timbre - different pitch
Distortion: Helmholtz fights back
Sound stimulus
Sound going into cochlea
1.0
amplitude
Middle-ear
distortion
200 400 600 800
frequency (Hz)
Produces
f2 - f1
600 - 400
amplitude
Harmonic spacing
= 200 Hz
Fundamental =200 Hz
Harmonic spacing
= 200 Hz
1.0
200 400 600 800
frequency (Hz)
Against Helmholtz: Masking the
fundamental
Unmasked complex still
has a pitch of 200 Hz
amplitude
Fundamental =200 Hz
Harmonic spacing
= 200 Hz
1.0
Tracks 40-42
200 400 600 800
frequency (Hz)
amadeus
Against Helmholtz:
Enharmonic sounds
Middle-ear distortion
gives difference tone
(1050 - 850 = 200)
200
amp
BUT
Pitch heard is
actually about 210
Tracks 38-39
200
850 1050 1250
Schouten’s theory
Excitation pattern of complex tone on bm
unresolved
1600
resolved
800 600 400
25.0
b m vibration
200
20.0
15.0
10.0
5.0
base
Pitch due to
beats of
unresolved
harmonics
log (ish) frequency
Output of 1600 Hz filter
-5.0
1/200s = 5ms
1
0.8
1.5
0.6
1
0.4
0.5
0.2
0
-1
0.0
Output of 200 Hz filter
1/200s = 5ms
2
-0.5
apex
0
0
0.2
0.4
0.6
0.8
1
-0.2 0
-0.4
-0.6
-1.5
-0.8
-2
-1
0.2
0.4
0.6
0.8
1
Tracks 43-45
Problems with Schouten’s theory (1)
1. Resolved harmonics dominant in pitch perception not unresolved (Plomp)
“down”
“down”
1.0
200 400 600 800
frequency (Hz)
2000
2400
Problems with Schouten (2)
1. Musical pitch is weak for complex
sounds consisting only of unresolved
harmonics
2. Pitch difference harder to hear for
unresolved than resolved complexes
Against Schouten (3):
Dichotic harmonics
• Pitch of complex tone still heard with
one harmonic to each ear
(Houtsma & Goldstein, 1972, JASA)
200 Hz
pitch
400
600
No chance of distortion tones or physical beats
Goldstein’s theory
• Pitch based on resolved harmonics
• Brain estimates frequencies of resolved
harmonics (eg 402 597 806) - could be by a
place mechanism, but more likely through phaselocked timing information near appropriate place.
• Then finds the best-fitting consecutive
harmonic series to those numbers (eg 401
602 804) -> pitch of 200.5
Two pitch mechanisms ?
• Goldstein has difficulty with the fact that
unresolved harmonics have a pitch at all.
• So: Goldstein’s mechanism could be good as the
main pitch mechanism…
• …with Schouten’s being a separate (weaker)
mechanism for unresolved harmonics
Schouten’s + Goldstein's theories
unresolved
1600
resolved
800 600 400
25.0
200
20.0
15.0
10.0
5.0
base
log (ish) frequency
Output of 1600 Hz filter
0.4
0.5
-1.5
-2
1/200s = 5ms
0.8
0.6
1
-1
-5.0
1
1.5
0
-0.5 0
0.0
Output of 200 Hz filter
1/200s = 5ms
2
apex
0.2
0.2
0.4
0.6
0.8
1
0
-0.2 0
-0.4
-0.6
-0.8
-1
0.2
0.4
0.6
0.8
1
JCR Licklider
Autocorrelator
Meddis, R. & O'Mard, L. 1997 A
unitary model of pitch perception.
J. Acoust. Soc. Am. 102, 18111820.
input
Summary autocorrelogram
Some other sounds that give pitch
• SAM Noise: envelope timing - no spectral
– Sinusoidally amplitude modulated noise
• Rippled noise - envelope timing - spectral
– Comb-filter (f(t) + f(t-T)) -> sinusoidal
spectrum (high pass to remove resolved
spectral structure)
– Huygens @ the steps from a fountain
– Quetzal @ Chichen Itza
• Binaural interactions
Huygen’s repetition pitch
Christian Huygens in 1693 noted that the noise produced by a
fountain at the chateau of Chantilly de la Cour was reflected by a
stone staircase in such a way that it produced a musical tone. He
correctly deduced that this was due to the successively longer time
intervals taken for the reflections from each step to reach the
listener's ear.
Effect of SNHL
• Wider bandwidths, so fewer resolved
harmonics
• Therefore more reliance on Schouten's
mechanism - less musical pitch?
Problem we haven’t addressed
• What happens when you have two
simultaneous pitches - as with two voices or
two instruments - or just two notes on a
piano?
• How do you know which harmonic is from
which pitch?
Bach: Musical Offering (strings)
Harmonic Sieve
• Only consider frequencies that are close enough to
harmonic. Useful as front-end to a Goldstein-type model of
pitch perception.
Duifhuis, Willems & Sluyter JASA (1982).
blocked
200 Hz sieve spacing
0
400
800
1200
frequency (Hz)
1600
2000
2400
Mistuned harmonic’s contribution to pitch
declines as Gaussian function of mistuning
• Experimental evidence
from mistuning expts:
1.5
∆F = a - k ∆f exp(-∆f
1
Moore, Glasberg & Peters JASA
(1985).
(Hz)
∆F
0
800
2
/2s )
0
-0.5
s = 19.9
k = 0.073
-1
400
2
0.5
Match low pitch
0
o
1200
1600
frequency (Hz)
2000
2400
-1.5
540
560
580
600
620
640
660
680
Frequency of mistuned harmonic f (Hz)
Darwin (1992). In M. E. H. Schouten (Ed). The auditory processing of speech: from
sounds to words Berlin: Mouton de Gruyter
Is “harmonic sieve” necessary
with autocorrelation models?
•
Autocorrelation could in
principle explain mistuning
effect
–
mistuned harmonic
initially shifts
autocorrelation peak
– then produces its own peak
•
But the numbers do not
work out.
– Meddis & Hewitt model is
too tolerant of mistuning.
One pitch mechanism or two?
experimental evidence
• Ease of comparing two pitches:
– both resolved (best) - Goldstein
– both unresolved - Schouten
– one resolved, one unresolved (worst)
• So easier within than between mechanisms
• Carlyon, R. P. and Shackleton, T. M. (1994). J. Acoust.
Soc. Am. 95, 3541-3554.
• But see later paper for alternative explanation:
• Gockel, H., Carlyon, R. P. and Plack, C. J. (2004). J.
Acoust. Soc. Am. 116, 1092-104.
One pitch mechanism or two?
Efficiency
• Autocorrelation always detects evidence for
periodicity at F0 in each frequency channel.
• Goldstein uses evidence of periodicity at the
harmonic frequency. May be more
efficient.
General problems
• How to do deal with multiple sounds
• What is the physiological instantiation of
the long delays (c. 30 ms) necessary for
autocorrelation or for Schouten?