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Physics 1251 The Science and Technology of Musical Sound

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

  2. 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). • Audio data is transformed to a frequency spectrum; • A masking filter is applied; • The residual data is encoded in a more efficient code.

  3. 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

  4. 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.

  5. 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

  6. 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): Log(Amplitude) dB Frequency Hz

  7. 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.

  8. Physics 1251 Unit 2 Session 19 Reverberation Intensity of Sound in a Room: ~ Io I = Io‧ 10 –6 t / TR t = ⅙ TR ~ 1/10 Io Pressure Amplitude t = ⅓ TR ~ 1/100 Io Time (ms) http://hybrid.colorado.edu/~phys1240/sounds.html

  9. Physics 1251 Unit 2 Session 19 Reverberation 80/20The Sabine Equation: I = Io‧ 10 – 6 (t/TR) TR = 0.16 V/Se • V is the volume of the room. • Se is the “effective surface area” of the walls S1 , floor S2 and ceiling S3 (in sabin) etc. • α is the absorptivity of the surface (in table) Se = α1 S1 + α2 S2 + α3 S3 + α4 S4 +…

  10. Physics 1251 Session 43 MWF Summary and Review The psychoacoustic response of the human ear is frequency dependent.

  11. Physics 1251 Unit 2 Session 14 Human Perception: Loudness Fletcher- Munson Diagram Fletcher and Munson (1933) J. Acoust. Soc. Am. 5, 82-108 130 120 110 100 90 SIL (dB) 80 70 60 50 40 30 20 10 Loudness (phon) Frequency (Hz)

  12. Physics 1251 Unit 2 Session 14 Human Perception: Loudness The Density of Hair Cells (HC) varies with distance from the stapes. Fewer HC More HC Fewer HC

  13. Physics 1251 Session 43 MWF Summary and Review The character of sound depends on physical acoustical phenomena as well.

  14. 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 I2 = I1 (A1/A2) I2 = I1 (r1 / r2) 2 A = ⅔π r 2 r

  15. Physics 1251 Unit 2 Session 18 Room Acoustics When the surface is smooth we have “specular” (mirror-like) reflection. Reflection Smooth Surface Roughness ≲ λ

  16. Physics 1251 Unit 2 Session 18 Room Acoustics Refraction occurs when a wave “enters” a medium that has a different velocity? Refraction V1 < V2

  17. Physics 1251 Unit 2 Session 18 Room Acoustics Diffraction What happens when a wave “is partially obstructed?

  18. Physics 1251 Unit 2 Session 18 Room Acoustics Doppler Shift: Moving source Lower f Higher f fobserver = fsource [v + vobserver] / [v – vsource]

  19. Physics 1251 Unit 2 Session 18 Room Acoustics Beats f1 f2 In phase Out of phase fmean fbeat

  20. Physics 1251 Unit 2 Session 18 Room Acoustics Interference Constructive Destructive Softer Louder

  21. Or pipers pipe? Or Drummers drum Or Fiddlers fiddle, too? Physics 1251 Session 43 MWF Summary and Review But why do Jingle Bells jingle, anyway?

  22. Physics 1251 Session 43 MWF Summary and Review The Normal Modes of Oscillation determine the frequencies present in the radiated sound.

  23. L = 2/₄ λ1 Physics 1251 Unit 2 Session 22 Strings: Guitar, Harp, Piano & Harpsichord A Standing Wave results from interference of counter-reflecting waves. Fundamental Mode f1 = vstring / λ1 = vstring / 2L Node Node Antinode λ1 /4 λ1 /4

  24. L = 4/₄ λ2 Physics 1251 Unit 2 Session 22 Strings: Guitar, Harp, Piano & Harpsichord 80/20The distance between neighboring nodes & antinodes is ¼ λ. [ “N-A d = ¼ λ” ] Second Harmonic f2 = vstring / λ2 = vstring / L Node Node Node Antinode Antinode λ2 /4 λ2 /4 λ2 /4 λ2 /4

  25. 6fO 5f1 6f1 5f1 5fO 5f1 4f1 4fO 4f1 3f1 3fO 3f1 3f1 2f1 2fO 2f1 fO f1 f1 f1 f1 Physics 1251 Unit 3 Session 30 The Timbre of Wind Instruments Comparison of Wind Instruments f Pedal Tone fo = (1+ξ)v/4(L+c) L f1 = v/2L f1 = v/4L f1 = v/2(L+c) Other Woodwinds Flute Clarinet Brass c

  26. Physics 1251 Unit 3 Session 30 The Timbre of Wind Instruments Open Cylinder Np – Np fn = nf1 f1 = v/2L Stopped Cylinder Ap – Np f2n-1 = (2n-1)f1 f1= v/4L Stopped Cone Ap – Np fn = nf1 f1= v/2(L+c) Stopped Combination Ap – Np fn = nf0f0= (1+ξ)v/4(L+c) Comparison of Wind Instruments (cont’d.) fo = (1+ξ)v/4(L+c) L f1 = v/2L f1 = v/4L f1 = v/2(L+c) Other Woodwinds Flute Clarinet Brass c

  27. Physics 1251 Unit 3 Session 32 The Singing Voice Anatomy of the Human Voice 80/20The vocal folds comprise muscle, lamina propria and epithelium. Cover Body Epithelium Lamina Propria (3 layers) Thyroarytenoid Muscle

  28. Physics 1251 Unit 3 Session 32 The Singing Voice Harmonics align with Formants Singers’ Formant Formants and Singing • Vowel modification shifts formats. •Alignment of formants with harmonics intensifies pitch. •Dilation of vocal tract causes Singer’s Formant.

  29. Surface density σ Surface Tension S Physics 1251 Unit 3 Session 33 Percussion The Modes of Oscillation of an (Ideal) Clamped Membrane Mode: (0,1) f0 1 = x0 1 /(π d) ‧ √(S/ σ) x0 1 = 2.405 Mode: (1,1) Mode: (2,1) f1 1 = (x1 1 / x0 1) f0 1 x1 1 / x0 1 = 1.594 f2 1 = (x2 1 / x0 1) f0 1 x2 1 / x0 1 = 2.136

  30. Physics 1251 Unit 3 Session 33 Percussion The Modes of Oscillation of a Clamped Membrane Mode: (0,1) xn m / x0 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

  31. Physics 1251 Unit 3 Session 33 Percussion 80/20The timbre of an instrument’s sounds depends on its vibration recipe. fn = n f1 Pitched Amplitude f1 2f1 3f1 4f1 fn m = xn m f1 Unpitched Amplitude f01 Frequency

  32. fn = n f1 Pitched Amplitude f1 2f1 3f1 4f1 fn m = xn m f10 Unpitched Amplitude f01 Physics 1251 Unit 3 Session 34 Percussion with Pitch 80/20The task of producing pitch in a percussion instrument is an exercise in manipulating the overtones into a harmonic series. Frequency

  33. Physics 1251 Unit 3 Session 34 Percussion with Pitch Free Ends Bending Modes in Bars: f1= 1.133 fo f2= 3.125 fo f3=6.125 fo fo∝ h/L2 .224 L

  34. Physics 1251 Session 43 MWF Summary and Review What is musical sound? Harmonics are the key.

  35. 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 Do Re Mi Fa So La Ti Do C-major G-major Guido d’Arezzo: “gamma ut→gamut” • Solfeggio G is “Do” in the G-scale

  36. ♩ ♩ 440 Hz ♩ ♩ ♩ ♩ A4 G3 C3 F3 B2 E3 A2 D3 Physics 1251 Unit 2 Session 20 Musical Scales ♩ Musical Notation ♩ ♩ ♩ ♩ ♩ ♩ ♩ ♩ ♩ ♩ G4 D5 A5 C6 G5 F4 C5 F5 ♩ B4 B5 E4 ♩ D4 A4 E5 ♩ ♩ ♩ ♩ ♩ ♩ ♩ ♩ ♩ ♩ C4 F2 B3 E2 A4 D2 G2 C2

  37. Physics 1251 Unit 2 Session 20 Musical Scales Harmonics! The harmonics must be “in tune” to avoid beats. Why does this work? 3 rd 5 th Octave Unison Frequency

  38. 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

  39. 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.

  40. 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