Download - Physics and Neurophysiology of Hearing
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Physics and Neurophysiology of Hearing
H.G. Dosch, Inst. Theor. Phys. Heidelberg
I Signal and Percept
II The Physics of the Ear
III From the Ear to the Cortex
IV Electrophysiology
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Part I: Signal and Percept
1)The time scales in hearing2)Relation between Physics and Sensation (Psychophysics) a) Propagation and Production of Sound b) The principal relations and caveats c) A Byte of Signal processing (mainly Fourier etc) d) Application to acoustics: Ohms Law e) Theory of Musical Consonance f) Fusion of Harmonics and Fundamental Tracking
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Sound pressure curve of the sentence:
Typical time scale of variation 0.1 s and larger
sound-pressure-example.wav in praat1.collection
each acoustical signal can be mapped unto a sound pressure curve
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selection of the previous sentence: mapped
Typical time scale of variation: 10 ms
sound-pressure-selection.wav in praat1.collection
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101praat:sinfreqmod10.wavsinfreqmod100.wav
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Time scales in auditive processes
Time scales in visual processes
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Original collage by Helmholtz to illustrate the optical and acoustical spectrum.The red has faded away
The reception of sound waves in the ear is achieved by mechanical means on the basilar membrane,the reception of light by chemical processes in the retina.
In the following only concerned on the time variations in the ms range.
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time reolution for angular resolution of 10 degrees
101praatgap01-005.wav in 1praat
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2Relation between Physics and Sensation Signal-Percept
Psychophysics
Principal perceived properties of sound:
Loudeness (volume)
Pitch
Timbre
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2a
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2 4 6 8 10 12 14
-1
-0.5
0.5
1
tx xt
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0.5 1 1.5 2 2.5 3
-1
-0.5
0.5
1
101praat sin440
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2b Relation between acoustical signal (sound pressure) and perception(to be refined later)
Amplitude of sp Loudeness
101praat: chain leise-mittel-laut
Relation Energy-loudeness not so simple
101praat: karm1,harm3,harm7
,
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Periodicity pitch of the tone
101praat: tief-hoch.wav
again: real life is a bit more complicated
101praat: sound-440_3-5, 366_4_6
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A2 A1 A a a' a'' a''' a''''
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101praat: sound440- sound 13_75c (pitch-range.collection)
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Most complicated sensation: timbre
not (approximately) 1 dimensional like volume and pitchbut many properties:
full, thin, soft, harsh .............
general relation:
form of the SP curve timbre
A very important distinction is the different timbre of different vowels
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The human vocal tract
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The vowels sound very different, though the sp curves look similar:
101praat: e_reg - u_reg
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The sound pressure curves look different, but the sounds are practically indistinguishable
101prat: schroederplus10, sin10,cos10
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Fourier and wavelet transforms
Fourier transform:
magic formula
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Convolution:
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Signalpower spectrum
T 2 T 1/T 2/T 3/T
fundamental higher harmonics partial tones
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Fourier transform
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Fourier transform
b=0.5 b=2
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c=0 b=0.5 b=2
+
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spectral function power spectrum
db
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Windowed Fourier Analysis, Wavelet analysis
Fourier analysis over a time window, g(t) :
possible time windows rectangular
Gaussian window
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Representaion windowed Fourier transform by Spectrogramm:
time as x-Axes, frequency as y axis and intensity as gray value
sin(2*pi*100*x-4*cos(2*pi*3*x))Example: tone with modulated frequency: modulation frequency 3 Hz
Spectrogram D=0.05 s Spectrum
102praat: frequency-modulated.wav
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Spectrogram and spectrum of ``Each acoustical signal can be mapped onto a sound pressure curve''
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Spectrogram and spectrum taken at 2.1 s with gaussian window 0.05 s
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h(u) is called a ``note'' :
102praat note.wav
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In acoustics the gamma-tone is a particularly popular wavelet
signal and spectrum of gamma-tone witht=4b = 150 Hz =1000 Hz
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Vowels, spectra and signals102praatvokale-hgdrauschen fuer rauschvokale
a 1000 1400e 500 2300i 320 3200o 500 1000u 320 800
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App. of Helmholtz to produce artificially vowelssponsored by Ludwig II von Bayern
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The sound pressure curves look different, but the sounds are practically indistinguishable
102
but the power spectra are up to a scale identical
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First refinement:
Timbre determined by the power spectrum
General features: No structure in sp curve and in spectrum : Noise
102praat cymbal.wav, noise.wav
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Few spectral lines (few harmonics) soft tonemany harmonics sharp tone
102praat flute.wav spinett.wavi-reg.wav cymbal.wavnoise.wav click.wav
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Ohm's Law of Acoustics:Ohm 1841, Helmholtz 1863
1) Ear performs a (windowed) Fourier analysis
2) Phases play no role.
3) The different Harmonics of a periodic tone are fused
4) Pitch of a sound determined by lowest harmonic,
roughly:long time scales (>0.1 s) processed as temporal properties,short time scales ( < 0.1 s) as power spectral properties
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Independence of phases:
schroederplus10, sin10
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Apparatus of helmholtz to test the independence on phases (Tonempf.)
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but: spectra over finite time interval look also differentFourier transform should only differ in phase, i.e. identical power spectrum
102praat: sin-coherent.wav sin-random,wav
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Our ear performs a windowed Fourier analysis, since we can perceive directly time variations of ca 0.1 s, this should be the maximal width of the window.
Example beats and roughness.
102praatbeats-third.wavbeats-10.wavbeats-rough.wav
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Theory of harmony Pythagoras - Helmholtz
c(530) 530 1060 1590 2120 2650 3180 3710 4240
d(590) 590 1180 1770 2360 2950 3540 4130 4720
g(790) 790 1580 2370 3160 3950
h(1000) 1000 2000 3000 4000
c(1060) 1060 2120 3180 4240
based on pysiology of the ear
9:8
3:2
15:8
2:1
live-music
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Calculations of Helmholtz for the degree of roughness for a violin
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Helmholtz, 1863
Kameoka,Kuriyagawa,1969
dissonanz
consonanz
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Interval od roughness larger at low frequencies:
minor third minor third
fifth fifth Dosch and Specht, 1986average of 89 subjects
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Chopin, Scherzo
Beetvoven, Appasionata
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But one can also hear the components, some people better, someworse.
102praatsin-1, sin-5,
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Fusion of tones
A tone with several harmonics: is it a single tone or a collection of tones?
both:Helmholtz: we perceive synthetically (perzipieren) the whole tonewe can perceive analytically (apperzipieren) the components of the tone.
102praatsin-1.wavsin-5.wavchain-harmonic-insert.wav
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The missing fundamentalWe now take off components from below
We take subsequently one harmonic tone out of the complex tone
ca g'''e'''cis'''a''e''a'a
102praat chain-fundamental-tracking.collection
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This happens also in musical instruments103praat 27_5Hz_A2_real_steinway.wav 110Hz-A_real
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103praat 3250Hz-a4-real-steinway
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Explanation until ca 1940 : Difference tones
For a harmonic tone
the difference ton is the fundamental tone
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103praat dif-tone-laut, leise 1000,1220 Hz
low level high level
Spectrogram of the rcorded tone, consisting of two components at 1000 and 1220 Hz. At the high level the nonlinear distortions are clearly visible.
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Schouten:
The periodicity of the tone is essential for the pitch of the ``residue'', that is the perceived, but not present fundamental tone.
Indeed sp curves show this periodicity:
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sp for the harmonic tones 1-7, 2-7,3-7,4-7,5-7,7-7,7
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The difference tone was excluded by van Schouten by a series of ingenious experiments. A particular simple one is the shifted hamonic tone.
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The difference tone was excluded by van Schouten by a series of ingenious experiments. A particular simple one is the shifted hamonic tone.
one hears
103praat harm-200 200+40
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The difference tone was excluded by van Schouten by a series of ingenious experiments. A particular simple one is the shifted hamonic tone with missing fundamental.
one hears 204-harm
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The question what determines the pitch of a complex tone is still controversial. We shall come back to it after looking closer into the physics of the ear and the auditory pathway.
The fact that the shifted tone has a ditincly different pitch is a sure sign that the difference tone is not reponsible for fundamental tracking, since the difference tone is unaffected by the shift
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