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Human Hearing
Time to read Chapter 6.1 and
6.2 of Berg & Stork
3.2 mm2
55 mm2
Ossicles
Pretty small …
Uncoiled cochlea (schematic)
stiffer
http://www.howstuffworks.com/hearing1.htm
limber
Cross section of cochlea
Two theories
for the
vibrations
inside the
cochlea
inner hair cell
outer hair cell
Loss of OHCs: incomplete deafness and hearing aids
From cochlea to the brain
An animation may help:
http://www.maxanim.com/physiology/Cochlear%20Structures/Cochle
ar%20Structures.htm
length
along
basilar
membrane
Two frequencies f and 2f
(one octave)
3.5 mm
“same” interval corresponds
to the same frequency ratio
(fixed distance along the
cochlea)
Weber-Fletcher Law
625 Hz
 1.25
500 Hz
781.25 Hz
 1.25
625 Hz
976.56 Hz
 1.25
781.25 Hz
feels like the same
interval
sine wave excites
about 1.2 mm of the
basilar membrane
overlap for
frequencies
differing by less
than about 15%
(minor third)
excited hair
cells
distance along the
basilar membrane
sharpening
The amount of sharpening determined
the just noticeable difference in
frequencies
JND in pitch:
0.5%
2%
frequency up and down
by 0.001 = 0.1%
frequency up and down
by 0.005 = 0.5%
Periodicity pitch and fundamental tracking
(This is not Physics, it’s psychology)
An overtone series like 2f, 3f, 4f, … which
is missing the fundamental has a pitch equal
to the f, 2f, 3f, 4f, … series (the brain
“adds” the fundamental for the purpose of
pitch determination
500 Hz + 750 Hz together, followed by the 250 Hz fundamental
900 Hz + 1200 Hz together, followed by the 300 Hz fundamental
700 Hz + 1050 Hz together, followed by the 350 Hz fundamental
500 Hz + 750 Hz
has the same pitch as
250 Hz
an octave above (x 2)
BUT
750 Hz + 1000 Hz has the same pitch as
an octave and a fifth above (x 3)
250 Hz
note D
note D minus fundamental
note D minus fundamental and 2nd
harmonic
Aural harmonics
sin(2p 50 t)
sin(2p 50 t)+ 0.2 sin(2p 100
t) +0.1 sin(2p 150 t) +…
extra frequencies
“aural harmonics”
400Hz, 400Hz+802Hz, 400Hz+1202Hz
f  n f1  m f 2 , n, m  0,1, 2,...
300Hz+400Hz,
300Hz+400Hz=700Hz, 702Hz,
300Hz+2 400Hz=1100Hz, 1102Hz
f  2 f1  f 2
rising
fixed
lowering
Shepard tones
Sound localization
How do we know where the sound is coming from ?
• interaural level differences (ILD)
• interaural time differences (ITD)
• head-related transfer function (HRTF)
http://www.aip.org/pt/nov99/locsound.html
Interaural level difference:
one ear will be on the shadow cast by the head
we can
detect even
0.5 dB in
ILD
diffraction makes it
ineffective at low
frequencies
300 Hz:
2000 Hz:
Interaural time difference: peaks and through will
arrive at ears at different times
t ~ L/v ~ (0.15 m)/(340m/s) ~ 0.0005 s
difference in
arrival time
distance
between ears
much shorter than
synaptic delays !
Phase ambiguity:
l/2=10 cm, f=340 m/s /0.2 m = 1700 Hz
distance between ears
Artificial sounds and recording including ILD and
ITD give a sense of localization but with the source
inside the head
Head-related transfer function: includes the reflection,
refraction and diffraction from ears, chest, head, …
Recordings using the hrtf give the sensation of a
source outside the head
This really should be heard on earphones but …
Aside: since we are talking about auditory illusions
Tritone paradox:
Are the tones going up
or down ?
What are they saying ?
Precedence effect
The source appears to be entirely on the direction
of the first (direct or reflected) sound to arrive
sound appears to
come entirely
from the blue
speaker