hearing & deafness (4) pitch perception 1. pitch of pure tones 2. pitch of complex tones
TRANSCRIPT
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Hearing & Deafness (4)Pitch Perception
1. Pitch of pure tones
2. Pitch of complex tones
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Pitch of pure tones
Place theory
Place of maximum in basilar membrane excitation (excitation pattern) - which fibers excited
Timing theoryTemporal pattern of firing -
how are the fibers firing -
needs phase locking
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Phase Locking of Inner Hair Cells
Auditory nerve connected to inner hair cell tends to fire
at the same phase of the stimulating waveform.
QuickTime™ and aCinepak decompressor
are needed to see this picture.
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Phase-locking
-1
-0.5
0
0.5
1
0 0.2 0.4 0.6 0.8 1
Inter-spike IntervalsResponse to Low Frequency tones
time (t)
Response to High Frequency tones > 5kHz
Random intervals
time (t)
2 periods 1 periodnerve spike
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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)
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Frequency thresholds increase
above 4 kHz
BCJ Moore (1973)JASA.
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Pitch of complex tones: fundamental & harmonics
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Helmholtz’s place theory
Pitch = frequency of fundamental Coded by place of excitation
Peaks in excitation
high low
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Arguments against Helmholtz
1. Fundamental not necessary for pitch (Seebeck)
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Missing fundamental
No fundamental but you still hear the pitch at 200 HzTrack 37
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Same timbre - different pitch
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Distortion: Helmholtz fights back
Sound stimulus
Middle-eardistortion
Producesf2 - f1
600 - 400
Sound going into cochlea
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Against Helmholtz: Masking the fundamental
Unmasked complex still has a pitch of 200 Hz
Tracks 40-42
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200 850 1050 1250
200
amp
Against Helmholtz: Enharmonic sounds
Middle-ear distortion gives difference tone (1050 - 850 = 200)
BUT
Pitch heard is actually about 210
Tracks 38-39
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Schouten’s theory
Pitch due to beats of unresolved harmonics
Tracks 43-45
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Problems with Schouten’s theory (1)
1. Resolved harmonics dominant in pitch perception - not unresolved (Plomp)
“down”
frequency (Hz)200
1.0
400600 800 2000 2400
“down”
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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
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Against Schouten (3): Dichotic harmonics
• Pitch of complex tone still heard with one harmonic to each ear (Houtsma & Goldstein, 1972, JASA)
400 600
200 Hz pitch
No chance of distortion tones or physical beats
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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 phase-locked timing information near appropriate place.
• Then finds the best-fitting consecutive harmonic series to those numbers (eg 401 602 804) -> pitch of 200.5
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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
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Schouten’s + Goldstein's theories
-5.0
0.0
5.0
10.0
15.0
20.0
25.0
base apexlog (ish) frequency
2004001600
resolvedunresolved
600800
Output of 1600 Hz filter Output of 200 Hz filter
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
0 0.2 0.4 0.6 0.8 1
1/200s = 5ms
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
1/200s = 5ms
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input
AutocorrelatorMeddis, R. & O'Mard, L. 1997 A unitary model of pitch perception. J. Acoust. Soc. Am. 102, 1811-1820.
JCR Licklider
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QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
Summary autocorrelogram
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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
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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.
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Effect of SNHL
• Wider bandwidths, so fewer resolved harmonics
• Therefore more reliance on Schouten's mechanism - less musical pitch?
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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?
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Bach: Musical Offering (strings)
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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).
frequency (Hz)
400 800 1200 1600 2000 2400
200 Hz sieve spacing
0
blocked
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Mistuned harmonic’s contribution to pitch declines as Gaussian function of mistuning
• Experimental evidencefrom mistuning expts: Moore, Glasberg & Peters JASA (1985).
Darwin (1992). In M. E. H. Schouten (Ed). The auditory processing of speech: from sounds to words Berlin: Mouton de Gruyter
frequency (Hz)
400 800 1200 1600 2000 24000
Match low pitch
-1.5
-1
-0.5
0
0.5
1
1.5
540 560 580 600 620 640 660 680
∆F
0
(Hz)
Frequency of mistuned harmonic f (Hz)
∆Fo = a - k ∆f exp(-∆f
2 / 2 s
2)
s = 19.9
k = 0.073
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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.