Physics of Sound and Music I week 9 - Media Lab...

Physics of Sound and Music I week 9pitch and timbre

Pitch ( perde, aralık) timbre (tını, ses rengi)

if we start with a pure tone, there is a correspondence between the frequency of the sound and our perception of the frequency (pitch).

the pitch depends on the loudness levelon the spectrum (timbre) of the frequencies in the soundon the durationon the attack ( the start of the sound)

pitch attributes of the auditory sensation which in turn maps onto a musical scale

subjectiontwo people listening to the same sound may assign a different position on the pitch or musical scale


Pitch ( perde, aralık) timbre (tını, ses rengi)

e.g.the sound pitch in the right ear can be different from the sensation produced in the left ear (binaural diplacusis - çift işitme)

basic unit of pitch - OCTAVE

the notes just an octave apart are on the frequency ration of 2:1

discussed by Pythagorus in 5th century BC.

Standard Frequency Ratios

Ratio Name 1:1 Unison1:2 Octave1:3 Twelfth2:3 Fifth3:4 Fourth4:5 Major Third3:5 Major Sixth


the correspondence of the physical frequency and the perceived pitch.

the frequency is given in units of Hz, while the perceived pitch is in units of mels

at f = 1000Hz, the critical bandwidth along the basilar membrave is 160Hz this corresponds to 100mels


experiment on OCTAVE

let f = 4000Hzlisten and memorize this patch

reduce the pitch; ask the person to step when the pitch is 1/2 of 4000Hz or 2000Hz

typical result: person chooses a pitch about....

PD exercise


experiment on OCTAVE

let f = 4000Hzlisten and memorize this patch

reduce the pitch; ask the person to step when the pitch is 1/2 of 4000Hz or 2000Hz

typical result: person chooses a pitch about 1000Hz?


Pitch Discrimination ( perde ayırtetme)

ability to distinguish between two notesdefined as jnd = just noticeable difference

jnd is frequency dependentsound level dependentduration of tone dependentsuddenness of frequency change dependent

The difference limen is that difference or change in the stimulus that is at the threshold of detectability

we plot the jnd and critical bandwidth vs frequency

CB is related to the physical stimulation along the basilar membrane in the inner ear

between frequencies f= 1000HZ and f = 4000Hz the jnd is

jnd ≈ 0.5% f = 0.005 f


Pitch Discrimination ( perde ayırtetme)

ex.

f = 1KHzjnd = ?

jnd = 0.005xf= 0.005 x 1000 = 5Hz

for hearing we are sensitive to 10 OCTAVES, which is equivalent to 5000 jnd


Pitch Perception and Sound level

how we perceive different frequency pure tones as we change the sound level

- lower frequencies (f =200)the perception of the pitch decreases as we increase the sound level, The sound level form 40dB to 90dB

- higher frequencies ( f 4000Hz - 6000Hz)the perception of the pitch increases as we increase the sound level


Pitch Perception and Sound level

how we perceive different frequency pure tones as we change the sound level

- middle frequencies (f ≈ 1000Hz)show little change in perception as we increase the sound level

this is somehow small effect and most of the people can not really experience this phenomenon

the change is 1% of the frequencyfor C4 = middle C = 262 Hzpitch change is ≈ 2.6 Hz which in many case it is the jnd

unit cent

previously we talked about an octave which is a frequency ratio of 2:1

if we break up the octave into 12 equal intervals = > the resulting frequency ratio for a single note (called semitone)is 1/12 of an octave which is about 1.059% between noteswe further breakdown the semitone interval into 100 equal parts = cent


Pitch and Duration

how long does a tone need to be heard in order for a person to perceive it as an identifiable pitch?

about 2 - 5 full cycles of the sounddepends on the frequency and the wavelength

if f = 50Hzperiod T = 1/ f = 1/ 50 = 0.02s = 20ms

Time required ≈ 2 times the duration = 40ms

experimentally minimum time required to create musicallyperceptible sound is 3ms

if the time is less then 3 ms, the we hear series of clicks,the transition of the clicks to a tone depends on the sound level


Pitch of Complex tones - Virtual Pitch

if a particular instrument played a tone in which the following frequencies are present600Hz, 800 Hz, 1000Hz, 1200Hz

we would perceive the pitch= ?

demo --” Missing Fundamental”

we percieve the pitch of this complex tone to be f₁ = 200Hz, the lowest common factor of in the complex tone,of 600Hz, 800 Hz, 1000Hz, 1200Hz

PD exercise


Pitch of Complex tones - Virtual Pitch

in this case we play f₃, f₄, f₅, f₆ we hear only the fundamental f₁ = 200Hz

This has been found experimentally that it is the best to have forth and fifth harmonics presentto hear the missing fundamental

our brain supplies the missing fundamental. This is no or very little power in the fundamentalbut we repeat hearing the fundamental


Theories of Pitch

Place vs Periodicity

we have discussed the the place theory previously, Signals from the basilar membrane (place theory)travel to the brain and are interpreted as a specific pitch

the ear performs both frequency and time analysis; the brain does extensive computations in order to determine the pitch

vibrations of different frequencies excite different areas along the basilar membrane => the place theorycochlea converts vibrations in time to vibrations in space along basilar membrane

Helmholtz regarded basilar membrane as a frequency analyzer, different parts are tuned to different frequenciese.g. high frequency excite oval window, low frequency at far end

Békésy experimented with the same result as well


Theories of Pitch


problems with the theory - fine frequency determination

to respond to changes in frequency = > damping (sönük)damping decreases selectivity - can not distinguish small changes in frequency

complex tone sound heard or perceived as one pitch rather than many


Theories of Pitch


Periodicity theory

ear perform time analyses

time distributes on auditory nerve to brain decoded by central nerves system

1930 Schauten experimentmissing fundamental experiment600Hz, 800 Hz, 1000Hz, 1200Hz = f fundamental is 200Hz

if we play complex tone frequencies together with 206Hz tone, 206 should beat with 200Hz, but it doesnt,because processing happens inside the brain, this is where the interpretation takes place

Schauten pitch shift phenomena is due to the synchronous firing of auditory nerve


Theories of Pitch


Periodicity theory

Repetition

pitch changes with time delay

T = time delay = L / v

L= distancev = velocity

perceived pitch = f = 1/ T

= v / L 1-7ms to distinguish

blind persons make use of this phenomenon to locate abstractions by interaction of direct + reflected sounds

repetition pitch is due to interference between noise and its delayed repetition


Theories of Pitch

The ability to recognize and define pitch of a tone without a reference

compare with color perception ability to recognize green without a comparison spectrum

%98 of people can do this task%2 color blind can not do this task

1 in 10000 people have absolute pitch

absolute pitch vs relative pitch

we can tell if one tone is higher or lower than another

ex 1000Hz -- go up one octave --- 2000hz actually it can be 2046 or 2035


Theories of Pitch

absolute pitch theories

Heredity theorypeople learn pitch names like color names in early life , but is born with the ability

Learning theoryanyone with practice (constant) can learn

Unlearning theoryability is universal, but it is trained out of people - emphasis of relative pitch

Imprinting theoryrapid irreversible learning that takes place at a specific development state


Theories of Pitch

people with absolute pitch recognition often make 1 octave errors in identifying tones

also it can vary with age

person with perfect pitch age 52 --> C --> C# age 71 --> C --> D


speech in tone language

speech sound can take on several meanings depending on the tonetypically have absolute pitch ( or close to it)

Chinese ( Mandarin ) on Vietnamese language

the sound of “ma”

Pitch standarts

note “A” = f = 374Hz - 567Hz pipe organs

1619 Praetorians = > 424 Hz defined as “A”

Händel’s tuning fork = 422.5Hz

1859 = > French government = 435 Hz

scientific pitch ( powers of 2) 126, 256, 512 - for C’s => A = 431Hz

1939 440Hz in International Conference in London

pitch raising

ex 442 to 444 some instrument designed to be played at certain pitch, and it sounds terrible if tuned differentlyclarinet

greatenes


pitch raising

singers usually sing about a semitone above pitch where they were written

old violins strengthened as to play at higher pitch

tuning forks are used as standards

short wave radio station in US - 440Hz tone broadcast

string instruments pitch falls as temperature risesstring expends = tension lowered

wooden instrumentsvelocity of sound increases for 0.6m/s for each Celsius Degrees, so the pitch of a wind instrument raises about 3 cents ( 3/100 semitones) per degree of temperature raise-


timber or tone quality

timber french word is used for tone quality or tone color

definitionTimber is that attribute of auditory sensation in terms of which a listener can judge two sounds similarly presented and having the same loudness and pitch as dissimilar.

alternateTimber is that attribute of auditory sensation whereby a listener can judge two sounds dissimilar using any criteria other than pitch, loudness or duration.

dull ---- brilliantcold --- warmpure ---- richdull --sharpfull -- emptycolorful --- colorless


Helmholtz - 1877 - series of Harmonics

-- simple tonestuning forkssoft, pleasant, free of roughness, but dull at low frequency

-- musical tonesmoderately loud series of harmonics up to 6th (piano, human voice)richer

-- Tone consisting of only odd harmonics (clarinet) sound hollow (içi boş), and if many harmonics are present then, nasal (geniz sesi)

--Complex tones harmonics above 6th and 7through and cutting


Fourier Analysis of Complex tones

the determination of the harmonic components of a periodic waveform is called Fourier analysis

math theoremany periodic vibration, however complicated, can be built up from a series of simple vibrations, whose frequencies areharmonics of fundamental frequency, by choosing the proper amplitudes and phases of these harmonics.

constructing a complex tone from its harmonics (the oposite of Fourier analysis) is called Fourier synthesis.

A specification of the strengths of the various harmonics (usually in the form of graph) is called a spectrum.A sound spectrum is a representation of a sound - usually a short sample of a sound - in terms of the amount of vibration at each individual frequency.



square wave only made up of odd harmonics

f₁ f₃ f₅ f₇A₁ 1/3A₁ 1/5A₁ 1/7A₁

triangle wave 1amp ∝ ———

n²

n= harmonic number

f₁ f₃ f₅ f₇ A₁ A₁ A₁ A₁ ––– ––– ––– 9 25 49



sawtooth wave 1amp ∝ ———

n

n= harmonic number

f₁ f₂ f₃ f₄ f₅ A₁ A₁ A₁ A₁ A₁ ––– ––– ––– ––– 2 3 4 5



Digital spectrum analysisbegins with sampling one period of the wave at regular intervals, then computer calculates the amplitudeand phase of each harmonic

analog spectrum analysisuse filters or other electronic circuits to isolate the harmonics one after anotherif this is done in a few milliseconds, then it is called real-time spectrum analysis.


Timber and dynamic effects

attack

extremely importantduring attack, the various partials of a musical sound may develop at different rate.attack is important because of these partial in terms of timber characteristics


Vibrato

vibrato is the family of tonal effects in music and depend on periodic variations of one or more characteristics of sound wave

frequency vibratoamplitude vibratophase vibrato

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