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Part I$ Signal and Percept
%&The tie scales in hearing'&(elation bet)een Physics and Sensation*Psychophysics& a& Propagation and Production of Sound
b& The principal relations and ca+eats c& -yte of Signal processing *ainly Fourier etc& d& pplication to acoustics$ hs /a) e& Theory of 0usical !onsonance
f& Fusion of Haronics and Fundaental Trac1ing
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Sound pressure cur+e of the sentence$
Typical tie scale of +ariation 2.% s and larger
sound3pressure3e"aple.)a+ in praat%.collection
each acoustical signal can be mapped unto a sound pressure curve
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selection of the pre+ious sentence$ apped
Typical tie scale of +ariation$ %2 s
sound3pressure3selection.)a+ in praat%.collection
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%2%praat$sinfre4od%2.)a+sinfre4od%22.)a+
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Tie scales in auditi+e processes
Tie scales in +isual processes
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riginal collage by Helholt5 to illustrate the optical and acousticalspectru.
The red has faded a)ay
The reception of sound )a+es in the ear is achie+ed by echanical eanson the basilar ebrane,the reception of light by cheical processes in the retina.
In the follo)ing only concerned on the tie +ariations in the srange.
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tie reolution for angular resolution of %2 degrees
%2%praatgap2%3226.)a+ in %praat
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'(elation bet)een Physics and Sensation Signal3Percept
Psychophysics
Principal percei+ed properties of sound$
/oudeness *+olue&
Pitch
Tibre
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'a
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2 4 6 8 10 12 14
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-0.5
0.5
1
t" "
t
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0.5 1 1.5 2 2.5 3
-1
-0.5
0.5
1
%2%praat sin772
'b ( l ti b t ti l i l * d & d ti
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'b (elation bet)een acoustical signal *sound pressure& and perception*to be refined later&
plitude of sp /oudeness
%2%praat$ chain leise3ittel3laut
(elation Energy3loudenessnot so siple
%2%praat$1ar%,har8,har9
,
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Periodicity pitch of the tone
%2%praat$ tief3hoch.)a+
again$ real life is a bit ore coplicated
%2%praat$ sound3772:836, 8;;:7:;
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' % a a< a
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%2%praat$ sound7723 sound %8:96c *pitch3range.collection&
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0ost coplicated sensation$ tibre
not *appro"iately& % diensional li1e +olue and pitchbut any properties$
full, thin, soft, harsh .............
general relation$
for of the SP cur+e tibre
+ery iportant distinction is the different tibre of different +o)els
The huan +ocal tract
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The huan +ocal tract
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The +o)els sound +ery different, though the sp cur+es loo1 siilar$
%2%praat$ e:reg 3 u:reg
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The soundpressure cur+esloo1 different, butthe sounds arepractically
indistinguishable
%2%prat$schroederplus%2,
sin%2,cos%2
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Fourier and )a+elet transfors
Fourier transfor$
agicforula
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!on+olution$
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Signalpo)er spectru
T ' T %=T '=T 8=T
fundaental higher haronics
partial tones
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Fourier transfor
Fourier transfor
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Fourier transfor
b>2.6 b>'
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c>2 b>2.6 b>'
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spectral function po)er spectru
db
@indo)ed Fourier nalysis, @a+elet analysis
Fourier analysis o+er a tie )indo) g(t) :
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Fourier analysis o+er a tie )indo), g(t) :
possible tie )indo)s rectangular
Gaussian )indo)
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(epresentaion )indo)ed Fourier transfor by Spectrogra$
tie as "3"es, fre4uency as y a"is and intensity as gray +alue
sin(2*pi*100*x-4*cos(2*pi*3*x))
E"aple$ tone )ith odulated fre4uency$ odulation fre4uency 8 H5
Spectrogra D=0.05 s Spectru
%2'praat$ fre4uency3odulated.)a+
Spectrogra and spectru of
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Spectrogra and spectru ofAAEach acoustical signal can be apped onto a sound pressure cur+e
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Spectrogra and spectru ta1en at '.% s )ith gaussian )indo) 2.26 s
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h(u)is called a AAnote
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In acoustics the gaa tone is aparticularly popular )a+elet
signal and spectru ofgaa3tone )itht>7b > %62 H5 >%222 H5
#o)els, spectra and signals
%2'praat1 l h d
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+o1ale3hgdrauschen fuerrausch+o1ale
a 1000%722e 622 2300i 8'2 3200
o 500 %222u 320 B22
pp. of
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ppHelholt5to produceartificially+o)els
sponsored by/ud)ig II +on
-ayern
The sound
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pressure cur+esloo1 different, butthe sounds arepractically
indistinguishable
%2'
but the po)erspectra are up toa scale identical
First refineent$
Tibre deterined by the power spectrum
%2'praat cybal.)a+, noise.)a+
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Tibre deterined by the power spectrum
General features$ No structure in sp cur+e and in spectru $ Noise
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Fe) spectral lines *fe)haronics& soft toneany haronics sharptone
%2'praatflute.)a+ spinett.)a+i3reg.)a+ cybal.)a+noise.)a+ clic1.)a+
h
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h %B7%, Helholt5 %B;8
%& Ear perfors a *)indo)ed& Fourier analysis
'& Phases play no role.
8& The different Haronics of a periodic tone are fused
7& Pitch of a sound deterined by lo)est haronic,
roughly$long tie scales *C2.% s& processed as teporalproperties,short tie scales * 2.% s& as po)er spectral
properties
Independence of phases$
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Independence of phases$
schroederplus%2, sin%2
pparatus of helholt5 to test the independence on phases *Tonepf.&
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but$ spectra o+er finite tieinter+al loo1 also differentFourier transfor should only differ in phase, i.e. identical po)er spectru
%2'praat$ sin3coherent.)a+ sin3rando,)a+
ur ear perfors a )indo)ed Fourier analysis, since )e can percei+e directlytie +ariations of ca 2 % s this should be the a"ial )idth of the )indo)
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tie +ariations of ca 2.% s, this should be the a"ial )idth of the )indo).
E"aple beats and roughness.
%2'praatbeats3third.)a+beats3%2.)a+
beats3rough.)a+
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Theory of harmony Pythagoras - Helmholt
c*682& 682 %2;2 %62 '%'2 ';62 8%B2 89%2 7'72
d*62& 62 %%B2 %992 '8;2 '62 8672 7%82 79'2
g*92& 92 %6B2 '892 8%;2 862
h*%222& %222 '222 8222 7222
c*%2;2& %2;2 '%'2 8%B2 7'72
based on pysiology of the ear
$B
8$'
%6$B
'$%
li+e3usic
!alculationsof Helholt5for the degreeof roughness
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of roughnessfor a +iolin
Helholt5,
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,%B;8
aeo1a,uriyaga)a,%;
dissonan5
consonan5
Inter+al od roughness larger at lo) fre4uencies$
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inor third inor third
fifth fifthDosch and Specht, %B;a+erage of B subects
!hopin, Scher5o
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-eet+o+en, ppasionata
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-ut one can also hear the coponents, soe people better, soe)orse.
%2'praatsin3%, sin36,
Fusion of tones
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tone )ith se+eral haronics$ is it a single tone or a collection of tones
both$
Helholt5$)e percei+e synthetically *per5ipieren& the )hole tone)e can percei+e analytically *apper5ipieren& the coponents of the tone.
%2'praatsin3%.)a+sin36.)a+chain3haronic3insert.)a+
The issing fundaental@e no) ta1e off coponents fro belo)
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@e ta1e subse4uently one haronic tone out of the cople" tone
ca g
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%28praat 8'62H53a73real3stein)ay
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E"planation until ca %72 $ Difference tones
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For a haronic tone
the difference ton is the fundaental tone
%28praat dif3tone3laut, leise %222,%''2H5
lo) le+el high le+el
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lo) le+el high le+el
Spectrogra of the rcorded tone, consisting of t)o coponents at %222and %''2 H5. t the high le+el the nonlinear distortions are clearly +isible.
Schouten$
The periodicity of the tone is essential for the pitch of the AAresidue
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The periodicity of the tone is essential for the pitch of the residue , that isthe percei+ed, but not present fundaental tone.
Indeed sp cur+es sho) this periodicity$
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sp for theharonic tones%39, '39,839,739,639,939,9
The difference tone )as e"cluded by +an Schouten by a series of ingeniouse"perients. particular siple one is the shifted haonic tone.
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The difference tone )as e"cluded by +an Schouten by a series of ingeniouse"perients. particular siple one is the shifted haonic tone.
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onehears
%28praat har3'22 '22?72
The difference tone )as e"cluded by +an Schouten by a series of ingeniouse"perients. particular siple one is the shifted haonic tone )ith issingfundaental.
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onehears '273har
The fact that the shifted tone has a ditincly different pitch is a sure sign thatthe difference tone is not reponsible for fundaental trac1ing, since the
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The 4uestion )hat deterines the pitch of a cople" tone is stillcontro+ersial. @e shall coe bac1 to it after loo1ing closer into the physics ofthe ear and the auditory path)ay.
difference tone is unaffected by the shift
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