Physics 1251 The Science and Technology of Musical Sound Session 43 MWF Summary and Review Session 43 MWF Summary and Review

Physics 1251Physics 1251The Science and The Science and

Technology of Musical Technology of Musical SoundSound

Physics 1251Physics 1251The Science and The Science and

Technology of Musical Technology of Musical SoundSound

Session 43 MWFSession 43 MWF

Summary and ReviewSummary and ReviewSession 43 MWFSession 43 MWF

Summary and ReviewSummary and Review

Physics 1251Physics 1251 Session 43 MWFSession 43 MWF Summary and ReviewSummary and Review

What is MP-3 and how does it do its What is MP-3 and how does it do its “magic?”“magic?”

MP-3 is a three (3) layer compression MP-3 is a three (3) layer compression algorithm that was adopted as a algorithm that was adopted as a standard by the Motion Picture Experts standard by the Motion Picture Experts Group (MPEG).Group (MPEG).

(1)(1)Audio data is transformed to a Audio data is transformed to a frequency spectrum;frequency spectrum;

(2)(2) A masking filter is applied;A masking filter is applied;

(3)(3) The residual data is encoded in a more The residual data is encoded in a more efficient code.efficient code.


MIDI is a control protocol that MIDI is a control protocol that can make the sound card in our can make the sound card in our PC play music.PC play music.

http://www.http://www.rememberjosierememberjosie.org/carols.org/carols

MIDI coded Christmas CarolsMIDI coded Christmas Carols

http://www.rememberjosie.org/carols




11′ Lecture:′ Lecture:• This course contains approximately 275 This course contains approximately 275

essential facts and concepts.essential facts and concepts.• There are 31 significant equations.There are 31 significant equations.• The sensation of sound depends on The sensation of sound depends on

psychoacoustical phenomena as well as psychoacoustical phenomena as well as the frequency spectrum or the the frequency spectrum or the vibration recipe.vibration recipe.

• Musical sound is characterized by a Musical sound is characterized by a harmonic series.harmonic series.

• Strings, pipes, the voice and Strings, pipes, the voice and percussion, all achieve sound according percussion, all achieve sound according to their individual modes of oscillation.to their individual modes of oscillation.


Computer based music exploits Computer based music exploits novel “tonal possibilities.”novel “tonal possibilities.”

www.research.www.research.ibmibm.com/.com/mathscimathsci//cmccmc/do_lamentations1./do_lamentations1.htmhtm

Lamentation for JerusalemLamentation for Jerusalem

For solo Saxophone and DMIXFor solo Saxophone and DMIX

By Daniel V. OppenheimBy Daniel V. Oppenheim

http://www.research.ibm.com/mathsci/cmc/do_lamentations1.htm









What one hears can be What one hears can be objectively characterized by a objectively characterized by a time-dependent “Vibration time-dependent “Vibration Recipe” or the “Frequency Recipe” or the “Frequency Spectrum” (Fourier Spectrum):Spectrum” (Fourier Spectrum):

Log

(Am

plitu

de)

Log

(Am

plitu

de)

dB

dB

Frequency HzFrequency Hz


The acoustic properties of the The acoustic properties of the room affect the time room affect the time dependence of the vibration dependence of the vibration recipe.recipe.

The reverberation time is an The reverberation time is an important property of a room.important property of a room.

Physics 1251Physics 1251 Unit 2 Session 19Unit 2 Session 19ReverberationReverberation

Intensity of Sound in a Room:Intensity of Sound in a Room:

Time (ms)Time (ms)

PressurePressure

AmplitudeAmplitude

I = II = Ioo ‧ ‧ 1010 –6 –6

t / Tt / TRR

~ I~ Ioo

t = t = ⅙ T⅙ TRR

~ ~ 1/101/10 IIoo

t = t = ⅓ T⅓ TRR~ ~ 1/1001/100 I Ioo

http://hybrid.colorado.edu/~phys1240/sounds.html






http://hybrdi.colorado.edu/~phys.1240/sounds.html

http://hybrid.colorado.edu/~phy.1240/sounds.html

Physics 1251Physics 1251 Unit 2 Session 19Unit 2 Session 19ReverberationReverberation

80/2080/20The Sabine Equation:The Sabine Equation:

I = II = Ioo ‧ ‧ 10 10 – 6 (t/T– 6 (t/TRR))

TTRR = 0.16 V/S = 0.16 V/Se e

• V is the volume of the room.V is the volume of the room.• SSee is the “effective surface area” of the is the “effective surface area” of the

walls Swalls S11 , floor S , floor S22 and ceiling S and ceiling S33 (in sabin) (in sabin) etc.etc.

• α is the absorptivity of the surface (in table) α is the absorptivity of the surface (in table)

SSee = α = α11 S S11 + α + α22 S S22 + α + α33 S S33 + α + α44 S S4 4 +…+…


The psychoacoustic response of the The psychoacoustic response of the human ear is frequency dependent.human ear is frequency dependent.

Physics 1251Physics 1251 Unit 2 Session 14Unit 2 Session 14Human Perception: LoudnessHuman Perception: Loudness

Fletcher- Munson DiagramFletcher- Munson Diagram

Fletcher and Munson (1933) Fletcher and Munson (1933) J. Acoust. Soc. Am. J. Acoust. Soc. Am. 55, 82-108, 82-108Frequency (Hz)Frequency (Hz)

SIL SIL (dB)(dB)

101020203030404050506060707080809090

100100110110120120130130

Loudness Loudness (phon)(phon)

Physics 1251Physics 1251 Unit 2 Session 14Unit 2 Session 14Human Perception: LoudnessHuman Perception: Loudness

The Density The Density of Hair Cof Hair Cells (HC)ells (HC)

varies with distancevaries with distance

from the stapes.from the stapes.

Fewer Fewer HCHC

Fewer HCFewer HC

More HCMore HC


The character of sound depends on The character of sound depends on physical acoustical phenomena as physical acoustical phenomena as well.well.

Physics 1251Physics 1251 Unit 2 Session 16Unit 2 Session 16Wave Properties: PropagationWave Properties: Propagation

Intensity is Power per Unit Area Intensity is Power per Unit Area Why 1/r Why 1/r 22??

Area = 2/3Area = 2/3π π ‧ ‧ r r 22 I = Power/AreaI = Power/Area

II22 = I = I11 (A (A11/A/A22))

II22 = I = I11 (r (r1 1 / r/ r22) ) 22

rrA = A = ⅔⅔π r π r 22

Physics 1251Physics 1251 Unit 2 Session 18Unit 2 Session 18Room AcousticsRoom Acoustics

When the surface is smooth we have When the surface is smooth we have “specular” (mirror-like) reflection.“specular” (mirror-like) reflection.

ReflectionReflection

Smooth SurfaceSmooth Surface

Roughness Roughness ≲ ≲ λλ


RefractionRefraction occurs when a wave occurs when a wave “enters” a medium that has a “enters” a medium that has a different velocity?different velocity?

RefractionRefraction

VV11 < V < V22


What happens when a wave “is What happens when a wave “is partially obstructed?partially obstructed?

DiffractionDiffraction

Doppler Shift:Doppler Shift: Moving sourceMoving source


ffobserverobserver = f = fsourcesource [v + v [v + vobserverobserver] / [v – v] / [v – vsourcesource] ]

Higher fHigher fLower fLower f

BeatsBeats

ff11

ff22


In phaseIn phase Out of phaseOut of phase

ffmeanmean ffbeatbeat

InterferenceInterference


ConstructiveConstructive

DestructiveDestructive

LouderLouder

SofterSofter


But why do Jingle Bells jingle, But why do Jingle Bells jingle, anyway?anyway?

Or pipers pipe?Or pipers pipe?

Or Drummers drumOr Drummers drum

Or Fiddlers fiddle, Or Fiddlers fiddle, too?too?


The Normal Modes of Oscillation The Normal Modes of Oscillation determine the frequencies determine the frequencies present in the radiated sound.present in the radiated sound.

Physics 1251Physics 1251 Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & Harpsichord

A Standing Wave results from interference A Standing Wave results from interference of counter-reflecting waves. of counter-reflecting waves.

L = L = 22/₄/₄ λλ11

λλ1 1 /4/4 λλ1 1 /4/4

Fundamental ModeFundamental Mode ff11 = v = vstringstring / λ / λ1 1 = v= vstringstring / / 2L 2L

NodeNode NodeNode

AntinodeAntinode

Physics 1251Physics 1251 Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & Harpsichord

80/2080/20The distance between neighboring The distance between neighboring nodes & antinodes is ¼ λ. [ “N-A d = ¼ nodes & antinodes is ¼ λ. [ “N-A d = ¼ λ” ]λ” ]

NodeNode NodeNode NodeNode

AntinodeAntinode AntinodeAntinode

λλ2 2 /4/4 λλ2 2 /4/4 λλ2 2 /4/4 λλ2 2 /4/4

L = L = 44/₄/₄ λλ22

Second Second HarmonicHarmonic

ff22 = v = vstringstring / λ / λ2 2 = v= vstringstring / / L L

Physics 1251Physics 1251 Unit 3 Session 30Unit 3 Session 30 The Timbre of Wind The Timbre of Wind

InstrumentsInstruments

Comparison of Wind InstrumentsComparison of Wind Instruments

BrassBrass

ffPedaPedal l ToneTone

Other Other Woodwinds Woodwinds ClarinetClarinetFluteFlute

ff11

2f2f11

3f3f11

4f4f11

5f5f11

ff11

3f3f11

5f5f11 5f5f11

ff11

2f2f11

3f3f11

4f4f11

6f6f11

ff11 = v/2L = v/2L ff11 = v/4L = v/4L ff11 = = v/2(L+c)v/2(L+c)

LL

cc

ffoo = = (1+(1+ξξ)v/)v/4(L+c)4(L+c)

ff11

ffOO

2f2f

OO

3f3f

OO

4f4f

OO

5f5f

OO

6f6f

OO

Physics 1251Physics 1251 Unit 3 Session 30Unit 3 Session 30 The Timbre of Wind The Timbre of Wind

InstrumentsInstruments

Comparison of Wind Instruments Comparison of Wind Instruments (cont’d.)(cont’d.)

BrassBrassOther Other Woodwinds Woodwinds ClarinetClarinetFluteFlute

ff11 = v/2L = v/2L ff11 = v/4L = v/4L ff11 = = v/2(L+c)v/2(L+c)

LL

cc

ffoo = = (1+(1+ξξ)v/)v/4(L+c)4(L+c)

Open Open

CylindCylind

er Ner Npp – –

NNpp

ffnn = = nfnf1 1

ff11 = = v/2Lv/2L

Stopped Stopped

Cylinder Cylinder

A App – N – Npp

f f2n-12n-1 = =

(2n-1)f(2n-1)f11 f f11= =

v/4Lv/4L

Stopped Stopped

Cone Cone

AApp – N – Np p

f fnn = nf = nf11

f f11= =

v/2(L+c)v/2(L+c)

Stopped Stopped

CombinatiCombinati

on on

AApp – N – Np p

f fnn = nf = nf00

ff00= =

(1+(1+ξ)ξ)v/4(L+cv/4(L+c

))

Physics 1251Physics 1251 Unit 3 Session 32Unit 3 Session 32 The Singing VoiceThe Singing Voice

Anatomy of the Human VoiceAnatomy of the Human Voice80/2080/20The vocal folds comprise muscle, lamina The vocal folds comprise muscle, lamina

propria and epithelium.propria and epithelium.

EpitheliumEpithelium

Lamina Propria Lamina Propria (3 layers)(3 layers)

ThyroarytenThyroarytenoid Muscleoid Muscle

CoverCoverBodyBody

Physics 1251Physics 1251 Unit 3 Session 32Unit 3 Session 32 The Singing VoiceThe Singing Voice

Formants and SingingFormants and Singing

•Vowel modification shifts formats. Vowel modification shifts formats. ••Alignment of formants with Alignment of formants with harmonics harmonics intensifies pitch. intensifies pitch. ••Dilation of vocal Dilation of vocal tract causes Singer’s Formant.tract causes Singer’s Formant.

Harmonics Harmonics align with align with FormantsFormants

Singers’ Singers’ FormantFormant

Physics 1251Physics 1251 Unit 3 Session 33Unit 3 Session 33 PercussionPercussion

The Modes of Oscillation The Modes of Oscillation of an (Ideal) of an (Ideal) Clamped MembraneClamped MembraneMode: Mode:

(0,1)(0,1)ff0 10 1 = = xx0 10 1 /( /(π d) π d) ‧ √(S/ ‧ √(S/ σ)σ)

xx0 1 0 1 = 2.405= 2.405Mode: Mode: (1,1)(1,1)ff1 11 1 = ( = (xx1 11 1 / / xx0 10 1) f) f0 10 1

xx1 11 1 / / xx0 10 1 = 1.594 = 1.594

Mode: Mode: (2,1)(2,1)ff2 12 1 = ( = (xx2 12 1 / / xx0 10 1) f) f0 10 1

xx2 12 1 / / xx0 10 1 = 2.136 = 2.136

Surface Surface Tension STension S

Surface density Surface density σσ


The Modes of Oscillation The Modes of Oscillation of a Clamped of a Clamped MembraneMembrane

Mode: Mode: (0,1) (0,1) xxn m n m / /

xx0 1 0 1 : 1: 1

(1,1(1,1))1.51.59494

(2,1(2,1))2.12.13636

(0,2(0,2))2.22.29696

(3,1(3,1))2.62.65353

(1,2(1,2))2.92.91818

(4,1(4,1))3.13.15656

(2,2(2,2))3.53.50101

(0,3(0,3))3.63.60000

(5,1(5,1))3.63.65252


80/2080/20The timbre of an instrument’s The timbre of an instrument’s sounds depends on its vibration sounds depends on its vibration recipe.recipe.

FrequencyFrequency

Am

plitu

de

Am

plitu

de

Am

plitu

de

Am

plitu

de

ff11 2f2f11 3f3f11 4f4f11

ff00

11

ffnn = n f = n f11

ffn mn m = = xxn mn m ff11

PitchedPitched

UnpitchedUnpitched

Physics 1251Physics 1251 Unit 3 Session 34Unit 3 Session 34 Percussion with PitchPercussion with Pitch

80/2080/20The task of producing pitch in a The task of producing pitch in a percussion instrument is an percussion instrument is an exercise in manipulating the exercise in manipulating the overtones into a harmonic series.overtones into a harmonic series.

FrequencyFrequency

Am

plitu

de

Am

plitu

de

ff00

11

ffn mn m = = xxn mn m ff1010

UnpitchedUnpitched

Am

plitu

de

Am

plitu

de

ff11 2f2f11 3f3f11 4f4f11

ffnn = n f = n f11 PitchedPitched

Physics 1251Physics 1251 Unit 3 Session 34Unit 3 Session 34 Percussion with PitchPercussion with Pitch

Bending Modes in Bars:Bending Modes in Bars:

ff11= 1.133 = 1.133 ffoo

ff22= 3.125 = 3.125 ffoo

ff33=6.125 =6.125 ffoo

ffoo ∝ ∝ h/Lh/L22

.224 L.224 L

Free EndsFree Ends


What is What is musical musical sound?sound?

Harmonics are the key.Harmonics are the key.

Physics 1251Physics 1251 Unit 2 Session 21Unit 2 Session 21Scales and StringsScales and Strings

What is a scale?What is a scale?• ““Gamut” {Note “G-Clef”}Gamut” {Note “G-Clef”}

♩♩♩♩♩♩♩♩♩♩♩♩♩♩♩♩

Do Re Mi Fa So La Ti Do Re Mi Fa So La Ti Do Do

♯♯♩♩♩♩♩♩♩♩♩♩♩♩♩♩♩♩

Do Re Mi Fa So La Ti Do Do Re Mi Fa So La Ti Do C-C-major major

G-G-major major

Guido d’Arezzo: “gamma utGuido d’Arezzo: “gamma ut→gamut” • →gamut” • SolfeggioSolfeggio

G is “Do” in the G-scaleG is “Do” in the G-scale

Musical NotationMusical Notation

Physics 1251Physics 1251 Unit 2 Session 20Unit 2 Session 20Musical ScalesMusical Scales

♩♩♩♩♩♩♩♩♩♩♩♩♩♩

♩♩♩♩♩♩♩♩♩♩ ♩♩♩♩ ♩♩

♩♩♩♩♩♩♩♩♩♩♩♩♩♩♩♩♩♩ ♩♩♩♩♩♩♩♩

GG55BB44CC55

EE55

DD55

FF55

AA55

BB55

CC66

DD44EE44

FF44GG44

BB22

CC33AA22

GG33EE33DD33

FF33 BB33

CC44

DD22EE22

FF22

GG22CC22

♩♩AA44

AA44

440 Hz440 Hz

♩♩

AA44

Physics 1251Physics 1251 Unit 2 Session 20Unit 2 Session 20Musical ScalesMusical Scales

Why does this work?Why does this work?Harmonics!Harmonics!The harmonics must be “in tune” to avoid The harmonics must be “in tune” to avoid beats.beats.

OctaveOctave

UnisonUnison

5 5 thth

33 rd rd

FrequencyFrequency


What is special about the What is special about the harmonics used in standard harmonics used in standard music?music?

Microtonalists say Microtonalists say “nothing!”“nothing!”

http://www.io.com/~hmiller/music/warped-canon.html






Physics 1251Physics 1251 Unit 4 Session 41Unit 4 Session 41 Computer MusicComputer Music

Summary:Summary:• Read the vibration recipe.Read the vibration recipe.• The vibration recipe happens because The vibration recipe happens because

of the normal modes of the source.of the normal modes of the source.• The normal modes of oscillation result The normal modes of oscillation result

from standing waves in the instrument.from standing waves in the instrument.• Sound is a longitudinal Sound is a longitudinal

displacement/pressure wave that can displacement/pressure wave that can be reflected, refracted, diffracted, be reflected, refracted, diffracted, interfered with, beat and Doppler interfered with, beat and Doppler shifted.shifted.

Physics 1251Physics 1251 Unit 4 Session 41Unit 4 Session 41 Computer MusicComputer Music

Review Quiz:Review Quiz:• Extra credit: 1-2 points added to test Extra credit: 1-2 points added to test

average.average.• Keep test and pick up key.Keep test and pick up key.• Evaluate performance and develop Evaluate performance and develop

review strategyreview strategy• Good luck!Good luck!• Final Exam Friday December 14, 2001Final Exam Friday December 14, 2001

8:00 – 10:00 am Room 1028:00 – 10:00 am Room 102

Documents

Physics 1251 The Science and Technology of Musical Sound Session 43 MWF Summary and Review Session 43 MWF Summary and Review