physics 1251 the science and technology of musical sound session 43 mwf summary and review session...
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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.
Physics 1251Physics 1251 Session 43 MWFSession 43 MWF Summary and ReviewSummary and Review
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
Physics 1251Physics 1251 Session 43 MWFSession 43 MWF Summary and ReviewSummary and Review
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.
Physics 1251Physics 1251 Session 43 MWFSession 43 MWF Summary and ReviewSummary and Review
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
Physics 1251Physics 1251 Session 43 MWFSession 43 MWF Summary and ReviewSummary and Review
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
Physics 1251Physics 1251 Session 43 MWFSession 43 MWF Summary and ReviewSummary and Review
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
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 +…+…
Physics 1251Physics 1251 Session 43 MWFSession 43 MWF Summary and ReviewSummary and Review
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
Physics 1251Physics 1251 Session 43 MWFSession 43 MWF Summary and ReviewSummary and Review
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
Physics 1251Physics 1251 Unit 2 Session 18Unit 2 Session 18Room AcousticsRoom Acoustics
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
Physics 1251Physics 1251 Unit 2 Session 18Unit 2 Session 18Room AcousticsRoom Acoustics
What happens when a wave “is What happens when a wave “is partially obstructed?partially obstructed?
DiffractionDiffraction
Doppler Shift:Doppler Shift: Moving sourceMoving source
Physics 1251Physics 1251 Unit 2 Session 18Unit 2 Session 18Room AcousticsRoom Acoustics
ffobserverobserver = f = fsourcesource [v + v [v + vobserverobserver] / [v – v] / [v – vsourcesource] ]
Higher fHigher fLower fLower f
BeatsBeats
ff11
ff22
Physics 1251Physics 1251 Unit 2 Session 18Unit 2 Session 18Room AcousticsRoom Acoustics
In phaseIn phase Out of phaseOut of phase
ffmeanmean ffbeatbeat
InterferenceInterference
Physics 1251Physics 1251 Unit 2 Session 18Unit 2 Session 18Room AcousticsRoom Acoustics
ConstructiveConstructive
DestructiveDestructive
LouderLouder
SofterSofter
Physics 1251Physics 1251 Session 43 MWFSession 43 MWF Summary and ReviewSummary and Review
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?
Physics 1251Physics 1251 Session 43 MWFSession 43 MWF Summary and ReviewSummary and Review
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
Physics 1251Physics 1251 Unit 3 Session 33Unit 3 Session 33 PercussionPercussion
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
Physics 1251Physics 1251 Unit 3 Session 33Unit 3 Session 33 PercussionPercussion
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
Physics 1251Physics 1251 Session 43 MWFSession 43 MWF Summary and ReviewSummary and Review
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
Physics 1251Physics 1251 Session 43 MWFSession 43 MWF Summary and ReviewSummary and Review
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