Transcript Physics 1251 The Science and Technology of Musical Sound
Physics 1251 The Science and Technology of Musical Sound
Session 43 MWF Summary and Review
Physics 1251 Session 43 MWF
Summary and Review What is MP-3 and how does it do its “magic?” MP-3 is a three (3) layer compression algorithm that was adopted as a standard by the Motion Picture Experts Group (MPEG).
(1) Audio data is transformed to a frequency spectrum; (2) A masking filter is applied; (3) The residual data is encoded in a more efficient code.
Physics 1251 Session 43 MWF
Summary and Review MIDI is a control protocol that can make the sound card in our PC play music.
http://www.rememberjosie.org/carols MIDI coded Christmas Carols
Physics 1251 Session 43 MWF
Summary and Review • • • • •
1′ Lecture:
This course contains approximately 275 essential facts and concepts.
There are 31 significant equations.
The sensation of sound depends on psychoacoustical phenomena as well as the frequency spectrum or the vibration recipe.
Musical sound is characterized by a harmonic series.
Strings, pipes, the voice and percussion, all achieve sound according to their individual modes of oscillation.
Physics 1251 Session 43 MWF
Summary and Review Computer based music exploits novel “tonal possibilities.” www.research.ibm.com/mathsci/cmc/do_lamentations1.htm
Lamentation for Jerusalem For solo Saxophone and DMIX By Daniel V. Oppenheim
Physics 1251 Session 43 MWF
Summary and Review What one hears can be objectively characterized by a time-dependent “Vibration Recipe” or the “Frequency Spectrum” (Fourier Spectrum): Frequency Hz
Physics 1251 Session 43 MWF
Summary and Review The acoustic properties of the room affect the time dependence of the vibration recipe.
The reverberation time is an important property of a room.
Physics 1251 Unit 2 Session 19 Reverberation
Intensity of Sound in a Room: ~ I o Pressure Amplitude I = I o ‧ 10 –6 t / T R t = ⅙ T R ~ 1/10 I o t = ⅓ T ~ 1/100 I o R Time (ms) http://hybrid.colorado.edu/~phys1240/sounds.html
Physics 1251 Unit 2 Session 19 Reverberation
80/20 The Sabine Equation: • • • I = I o ‧ 10 – 6 (t/T R ) T R = 0.16 V/S e V is the volume of the room.
S e S 1 is the “effective surface area” of the walls , floor S 2 and ceiling S 3 (in sabin) etc.
α is the absorptivity of the surface (in table) S e = α 1 S 1 + α 2 S 2 + α 3 S 3 + α 4 S 4 +…
Physics 1251 Session 43 MWF
Summary and Review The psychoacoustic response of the human ear is frequency dependent.
Physics 1251 Unit 2 Session 14 Human Perception: Loudness
Fletcher- Munson Diagram SIL (dB) 30 10 Loudness (phon) Frequency (Hz) Fletcher and Munson (1933) J. Acoust. Soc. Am. 5, 82-108
Physics 1251 Unit 2 Session 14 Human Perception: Loudness
The Density of Hair C ells (HC) varies with distance from the stapes.
Fewer HC More HC Fewer HC
Physics 1251 Session 43 MWF
Summary and Review The character of sound depends on physical acoustical phenomena as well.
Physics 1251 Unit 2 Session 16 Wave Properties: Propagation
Intensity is Power per Unit Area Why 1/r 2 ?
Area = 2/3π ‧ r 2 I = Power/Area A = ⅔π r 2 r I 2 I 2 = I 1 = I 1 (A 1 /A 2 ) (r 1 / r 2 ) 2
Physics 1251 Unit 2 Session 18 Room Acoustics
When the surface is smooth we have “specular” (mirror-like) reflection.
Reflection Smooth Surface Roughness ≲ λ
Physics 1251 Unit 2 Session 18 Room Acoustics
Refraction occurs when a wave “enters” a medium that has a different velocity?
Refraction
V 1 < V 2
Physics 1251 Unit 2 Session 18 Room Acoustics
What happens when a wave “is partially obstructed?
Diffraction
Physics 1251 Unit 2 Session 18
Doppler Shift:
Room Acoustics
Moving source Lower f Higher f f observer = f source [v + v observer ] / [v – v source ]
Physics 1251
Beats f 1 In phase
Unit 2 Session 18 Room Acoustics
Out of phase f 2 f mean f beat
Physics 1251
Interference
Unit 2 Session 18 Room Acoustics
Constructive Destructive Softer Louder
Physics 1251 Session 43 MWF
Summary and Review But why do Jingle Bells jingle, anyway?
Or pipers pipe?
Or Drummers drum Or Fiddlers fiddle, too?
Physics 1251 Session 43 MWF
Summary and Review The Normal Modes of Oscillation determine the frequencies present in the radiated sound.
Physics 1251 Unit 2 Session 22 Strings: Guitar, Harp, Piano & Harpsichord
A Standing Wave results from interference of counter-reflecting waves. Fundamental Mode f 1 = v string L = 2 /₄ λ 1 Node / λ 1 = v string / 2L Node Antinode λ 1 /4 λ 1 /4
Physics 1251 Unit 2 Session 22 Strings: Guitar, Harp, Piano & Harpsichord
80/20 The distance between neighboring nodes & antinodes is ¼ λ. [ “N-A d = ¼ λ” ] Second Harmonic f 2 = v string / λ 2 = v string / L Node L = 4 /₄ λ 2 Node Node Antinode Antinode λ 2 /4 λ 2 /4 λ 2 /4 λ 2 /4
Physics 1251 Unit 3 Session 30
The Timbre of Wind Instruments Comparison of Wind Instruments f 5f 1 4f 1 3f 1 2f 1 f 1 5f 1 3f 1 f 1 6f 1 5f 1 4f 1 3f 1 2f 1 f 1 6f O 5f O 4f O 3f O 2f O f O f 1 Pedal Tone L f 1 = v/2L Flute f 1 = v/4L Clarinet f 1 = v/2(L+c) Other Woodwinds c f o = (1+ξ)v/4(L+c) Brass
Physics 1251 Unit 3 Session 30
The Timbre of Wind Instruments Comparison of Wind Instruments (cont’d.) Open Cylinder N p – N p f n f 1 = nf 1 = v/2L Stopped Cylinder A p f 2n-1 – N p = (2n-1)f 1 f 1 = v/4L Stopped Cone A p f n – N = nf 1 p f 1 = v/2(L+c) Stopped Combination A p – N p f n = nf 0 f 0 = (1+ξ)v/4(L+c) L f 1 = v/2L Flute f 1 = v/4L Clarinet f 1 = v/2(L+c) Other Woodwinds c f o = (1+ξ)v/4(L+c) Brass
Physics 1251 Unit 3 Session 32
The Singing Voice Anatomy of the Human Voice 80/20 The vocal folds comprise muscle, lamina propria and epithelium.
Cover Body Epithelium Lamina Propria (3 layers) Thyroarytenoid Muscle
Physics 1251 Unit 3 Session 32
The Singing Voice Formants and Singing Harmonics align with Formants Singers’ Formant • • Vowel modification shifts formats. Alignment of formants with harmonics intensifies pitch. • Dilation of vocal tract causes Singer’s Formant.
Physics 1251 Unit 3 Session 33
Percussion The Modes of Oscillation of an (Ideal) Clamped Membrane Surface density σ Mode: (0,1) Surface Tension S f 0 1 =
x
0 1 /(π d) ‧ √(S/ σ)
x
0 1 = 2.405
Mode: (1,1) f 1 1 = (
x
1 1 /
x
0 1 ) f 0 1
x
1 1 /
x
0 1 = 1.594
Mode: (2,1) f 2 1 = (
x
2 1 /
x
0 1 ) f 0 1
x
2 1 /
x
0 1 = 2.136
Physics 1251 Unit 3 Session 33
Percussion The Modes of Oscillation of a Clamped Membrane Mode: (0,1)
x
n m /
x
0 1 : 1 (1,1) 1.594
(2,1) 2.136
(0,2) 2.296
(3,1) 2.653
(1,2) 2.918
(4,1) 3.156
(2,2) 3.501
(0,3) 3.600
(5,1) 3.652
Physics 1251 Unit 3 Session 33
Percussion 80/20 The timbre of an instrument’s sounds depends on its vibration recipe.
f 1 2f 1 f n = n f 1 3f 1 Pitched 4f 1 f n m =
x
n m f 1 Unpitched f 01 Frequency
Physics 1251 Unit 3 Session 34
Percussion with Pitch 80/20 The task of producing pitch in a percussion instrument is an exercise in manipulating the overtones into a harmonic series.
f n m =
x
n m f 10 Unpitched f 01 f 1 2f 1 f n = n f 1 3f 1 Frequency Pitched 4f 1
Physics 1251 Unit 3 Session 34
Percussion with Pitch Bending Modes in Bars: Free Ends f 1 = 1.133 f o f 2 = 3.125 f o .224 L f 3 =6.125 f o f o ∝ h/L 2
Physics 1251 Session 43 MWF
Summary and Review What is musical sound?
Harmonics are the key.
Physics 1251 Unit 2 Session 21 Scales and Strings
• What is a scale?
“Gamut” {Note “G-Clef”} ♩ ♩ ♩ ♩ ♩ ♩ ♩ ♩ Do Re Mi Fa So La Ti Do C-major ♩ ♩ ♩ ♩ ♩ ♩ ♯ ♩ ♩ Do Re Mi Fa So La Ti Do G-major Guido d’Arezzo: “gamma ut→gamut” • Solfeggio G is “Do” in the G-scale
Physics 1251 Unit 2 Session 20 Musical Scales
Musical Notation ♩ ♩ C 2 D 2 ♩ ♩ ♩ ♩ ♩ ♩ ♩ ♩ ♩ E 2 F 2 G 2 A 2 B 2 C 3 D 3 E 3 F 3 G 3 A 4 B 3 C 4 ♩ ♩ ♩ 440 Hz ♩ ♩ ♩ ♩ ♩ ♩ D 4 E 4 F 4 G 4 A 4 B 4 C 5 D 5 E 5 F 5 G 5 A 5 B 5 C 6
Physics 1251 Unit 2 Session 20 Musical Scales
Why does this work?
Harmonics!
The harmonics must be “in tune” to avoid beats.
3 rd 5 th Octave Unison Frequency
Physics 1251 Session 43 MWF
Summary and Review What is special about the harmonics used in standard music?
Microtonalists say “nothing!” http://www.io.com/~hmiller/music/warped-canon.html
Physics 1251 Unit 4 Session 41
Computer Music • • • •
Summary:
Read the vibration recipe.
The vibration recipe happens because of the normal modes of the source.
The normal modes of oscillation result from standing waves in the instrument.
Sound is a longitudinal displacement/pressure wave that can be reflected, refracted, diffracted, interfered with, beat and Doppler shifted.
Physics 1251 Unit 4 Session 41
Computer Music • • • • •
Review Quiz:
Extra credit: 1-2 points added to test average.
Keep test and pick up key.
Evaluate performance and develop review strategy Good luck!
Final Exam Friday December 14, 2001 8:00 – 10:00 am Room 102