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

2. Physics 1251Session 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.

3. Physics 1251Session 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 1251Session 43 MWF Summary and Review 1′ Lecture: This course contains approximately 275 essential facts and concepts. This course contains approximately 275 essential facts and concepts. There are 31 significant equations. There are 31 significant equations. The sensation of sound depends on psychoacoustical phenomena as well as the frequency spectrum or the vibration recipe. 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. Musical sound is characterized by a harmonic series. Strings, pipes, the voice and percussion, all achieve sound according to their individual modes of oscillation. Strings, pipes, the voice and percussion, all achieve sound according to their individual modes of oscillation.

5. Physics 1251Session 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 1251Session 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 1251Session 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 1251Unit 2 Session 19 Reverberation Intensity of Sound in a Room: Time (ms) PressureAmplitude I = I o ‧ 10 –6 t / T R ~ I o t = ⅙ T R ~ 1/10 I o t = ⅓ T R ~ 1/100 I o http://hybrid.colorado.edu/~phys1240/sounds.html

9. Physics 1251Unit 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. V is the volume of the room. S e is the “effective surface area” of the walls S 1, floor S 2 and ceiling S 3 (in sabin) etc. S e is the “effective surface area” of the walls S 1, floor S 2 and ceiling S 3 (in sabin) etc. α is the absorptivity of the surface (in table) 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 +…

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

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

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

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

14. Physics 1251Unit 2 Session 16 Wave Properties: Propagation Intensity is Power per Unit Area Why 1/r 2 ? Area = 2/3π ‧ r 2 I = Power/Area I 2 = I 1 (A 1 /A 2 ) I 2 = I 1 (r 1 / r 2 ) 2 r A = ⅔π r 2

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

16. Physics 1251Unit 2 Session 18 Room Acoustics Refraction occurs when a wave “enters” a medium that has a different velocity? Refraction V 1 < V 2

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

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

19. Beats f 1 f 2 Physics 1251Unit 2 Session 18 Room Acoustics In phase Out of phase f mean f beat

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

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

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

23. Physics 1251Unit 2 Session 22 Strings: Guitar, Harp, Piano & Harpsichord A Standing Wave results from interference of counter-reflecting waves. L = 2 /₄ λ 1 λ 1 /4 Fundamental Mode f 1 = v string / λ 1 = v string / 2L NodeNode Antinode

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

25. Physics 1251Unit 3 Session 30 The Timbre of Wind Instruments Comparison of Wind Instruments Brass f Pedal Tone Other Woodwinds ClarinetFlute f1f1f1f1 2f 1 3f 1 4f 1 5f 1 f1f1f1f1 3f 1 5f 1 f1f1f1f1 2f 1 3f 1 4f 1 6f 1 f 1 = v/2L f 1 = v/4L f 1 = v/2(L+c) L c f o = f o = (1+ξ)v/4(L+c) f1f1f1f1 fOfOfOfO 2f O 3f O 4f O 5f O 6f O

26. Physics 1251Unit 3 Session 30 The Timbre of Wind Instruments Comparison of Wind Instruments (cont’d.) Brass Other Woodwinds ClarinetFlute f 1 = v/2L f 1 = v/4L f 1 = v/2(L+c) L c f o = f o = (1+ξ)v/4(L+c) Open Cylinder N p – N p f n = nf 1 f 1 = v/2L Stopped Cylinder A p – N p f 2n-1 = (2n-1)f 1 f 1 = v/4L Stopped Cone A p – N p f n = nf 1 f 1 = v/2(L+c) Stopped Combination A p – N p f n = nf 0 f 0 = (1+ξ)v/4(L+c)

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

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

29. Physics 1251Unit 3 Session 33 Percussion The Modes of Oscillation of an (Ideal) Clamped Membrane Mode: (0,1) 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 Surface Tension S Surface density σ

30. Physics 1251Unit 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

31. Physics 1251Unit 3 Session 33 Percussion 80/20 The timbre of an instrument’s sounds depends on its vibration recipe. Frequency Amplitude Amplitude f1f1f1f1 2f 1 3f 1 4f 1 f 01 f n = n f 1 f n m = x n m f 1 Pitched Unpitched

32. Physics 1251Unit 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. Frequency Amplitude f 01 f n m = x n m f 10 Unpitched Amplitude f1f1f1f1 2f 1 3f 1 4f 1 f n = n f 1 Pitched

33. Physics 1251Unit 3 Session 34 Percussion with Pitch Bending Modes in Bars: f 1 = 1.133 f o f 2 = 3.125 f o f 3 =6.125 f o f o ∝ h/L 2.224 L Free Ends

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

35. Physics 1251Unit 2 Session 21 Scales and Strings What is a scale? “Gamut” {Note “G-Clef”} “Gamut” {Note “G-Clef”} ♩ ♩ ♩ ♩ ♩ ♩♩♩ Do Re Mi Fa So La Ti Do ♯♩♯♩♯♩♯♩ ♩ ♩ ♩ ♩ ♩ ♩ ♩ C-majorG-major Guido d’Arezzo: “gamma ut→gamut” Solfeggio G is “Do” in the G-scale

36. Musical Notation Physics 1251Unit 2 Session 20 Musical Scales ♩ ♩ ♩ ♩ ♩ ♩♩♩ ♩ ♩ ♩ ♩♩ ♩ ♩♩ ♩ ♩ ♩ ♩ ♩ ♩ ♩♩♩ ♩ ♩♩ G5G5G5G5 B4B4B4B4 C5C5C5C5 E5E5E5E5 D5D5D5D5 F5F5F5F5 A5A5A5A5 B5B5B5B5 C6C6C6C6 D4D4D4D4 E4E4E4E4 F4F4F4F4 G4G4G4G4 B2B2B2B2 C3C3C3C3 A2A2A2A2 G3G3G3G3 E3E3E3E3 D3D3D3D3 F3F3F3F3 B3B3B3B3 C4C4C4C4 D2D2D2D2 E2E2E2E2 F2F2F2F2 G2G2G2G2 C2C2C2C2 ♩ A4A4A4A4 A4A4A4A4 440 Hz ♩ A4A4A4A4

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

38. Physics 1251Session 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 1251Unit 4 Session 41 Computer Music Summary: Read the vibration recipe. Read the vibration recipe. The vibration recipe happens because of the normal modes of the source. The vibration recipe happens because of the normal modes of the source. The normal modes of oscillation result from standing waves in the instrument. 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. Sound is a longitudinal displacement/pressure wave that can be reflected, refracted, diffracted, interfered with, beat and Doppler shifted.

40. Physics 1251Unit 4 Session 41 Computer Music Review Quiz: Extra credit: 1-2 points added to test average. Extra credit: 1-2 points added to test average. Keep test and pick up key. Keep test and pick up key. Evaluate performance and develop review strategy Evaluate performance and develop review strategy Good luck! Good luck! Final Exam Friday December 14, 2001 Final Exam Friday December 14, 2001 8:00 – 10:00 am Room 102