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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

-1

-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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