1

Hearing & Deafness (4)Pitch Perception

1. Pitch of pure tones

2. Pitch of complex tones

2

Pitch of pure tones

Place theoryPlace of maximum in basilar membrane excitation(excitation pattern) - which fibers excited

Timing theoryTemporal pattern of firing -how are the fibers firing -needs phase locking

3

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

4

Pure tones: place vs timingLow frequency tones

Place & timing

High frequency tones

Place only

1. Phase locking only for tones below 4 kHz

2. Frequency difference threshold increases rapidlyabove 4 kHz.

3. Musical pitch absent above 4 kHz (top of piano)

5

Frequencythresholdsincrease

above 4 kHz

B C J Moore (1973)JASA.

Phase-lock?Yes No

6

Pitch of complex tones:fundamental & harmonics

time (t)

pres

sure

-4-3-2-1

01234

1

Period = 1/200 s = 5msfrequency (Hz)

ampl

itude

200

1.0

400 600 800

Harmonic spacing = 200 Hz

Fundamental =200 Hz

7

Helmholtz’s place theory

frequency (Hz)

amp

litu

de

200

1.0

400 600 800

Harmonic spacing = 200 Hz

Fundamental =200 Hz

Pitch = frequency of fundamentalCoded by place of excitation

Peaks in excitation

8

Arguments against Helmholtz

1. Fundamental not necessary for pitch(Seebeck)

9

Missing fundamental

time (t)

pre

ssur

e

-3

-2

-1

0

1

2

3

1

Period = 1/200 s = 5ms frequency (Hz)

ampl

itude

200

1.0

400 600 800

Harmonic spacing = 200 Hz

No fundamental but you still hear the pitch at 200 HzTrack 37

10

Distortion: Helmholtz fights back

frequency (Hz)

amp

litu

de

200

1.0

400 600 800

Harmonic spacing = 200 Hz

Sound stimulus

frequency (Hz)

amp

litu

de

200

1.0

400 600 800

Harmonic spacing = 200 Hz

Fundamental =200 Hz

Middle-eardistortion

Producesf2 - f1

600 - 400

Sound going into cochlea

11

Against Helmholtz: Masking thefundamental

frequency (Hz)

amp

litu

de

200

1.0

400 600 800

Harmonic spacing = 200 Hz

Fundamental =200 Hz

Unmasked complex still has a pitch of 200 Hz

Tracks 40-42

12

200 850 1050 1250

200

amp

Against Helmholtz:Enharmonic sounds

Middle-ear distortiongives difference tone(1050 - 850 = 200)

BUT

Pitch heard isactually about 210

Tracks 38-39

13

Schouten’s theory

Excitation pattern of complex tone on bm

-5.0

0.0

5.0

10.0

15.0

20.0

25.0

b m

vib

rati

on

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

Pitch due tobeats ofunresolvedharmonics

Tracks 43-45

14

Problems with Schouten’s theory (1)1. Resolved harmonics dominant in pitch perception -not unresolved (Plomp, 1967)

“down”

frequency (Hz)200

1.0

400 600 800 2000 2400

“down”

15

Problems with Schouten (2)2. Pitch discrimination much worse for unresolved than

resolved (Houtsma & Smurzynski (1990, JASA).res --> unres

good

bad

16

Problems with Schouten (3)

3. Musical pitch is weak for complexsounds consisting only of unresolvedharmonics (Houtsma, 1984, MusicPerception)

17

Against Schouten (4):Dichotic harmonics

• Pitch of complex tone still heard withone harmonic to each ear(Houtsma & Goldstein, 1972)

400 600

200 Hzpitch

No chance of distortion tones or physical beats

18

Goldstein’s theory

• Pitch based on resolved harmonics• Brain estimates frequencies of resolved harmonics

(eg 402 597 806) - could be by a placemechanism, but more likely through phase-lockedtiming information.

• Then finds the best-fitting consecutive harmonicseries to those numbers (eg 401 602 804) -> pitchof 200.5

19

Two pitch mechanisms ?

• Goldstein has difficulty with the fact thatunresolved harmonics have a pitch at all.

• So: Goldstein’s mechanism could be goodas the main pitch mechanism

• With Schouten’s being a separate (weaker)mechanism for unresolved harmonics

20

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

11.5

2

0 0.2 0.4 0.6 0.8 1

1/200s = 5ms

-1

-0.8-0.6-0.4-0.2

00.20.40.60.8

1

0 0.2 0.4 0.6 0.8 1

1/200s = 5ms

21

Some other sounds that givepitch

• SAM Noise: envelope timing - not spectral– Sinusoidally amplitude modulated noise

• Rippled noise - envelope timing & spectral– Comb-filter (f(t) + f(t-T)) -> sinusoidal spectrum– Huygens @ the steps from a fountain– Quetzal @ Chichen Itza

• Binaural interactions

100 200

22

Huygen’s repetition pitch

Christian Huygens in 1693 noted that the noise produced by afountain at the chateau of Chantilly de la Cour was reflected by astone staircase in such a way that it produced a musical tone. Hecorrectly deduced that this was due to the successively longer timeintervals taken for the reflections from each step to reach thelistener's ear.

23

24

Effect of SNHL

• Wider bandwidths, so fewer resolvedharmonics

• Therefore more reliance on Schouten'smechanism - less musical pitch?

25

Problem we haven’t addressed

• What happens when you have twosimultaneous pitches - as with two voices ortwo instruments - or just two notes on apiano?

• How do you know which harmonic is fromwhich pitch?