2. infinity-project.org Engineering education for today’s classroom 53 Design Problem - Digital Band Build a digital system that can create music of any style, with any performers, whenever we want to hear it User controls Music source

3. infinity-project.org Engineering education for today’s classroom 54 Outline Music, Sound, and Signals Making Music from Sines and Cosines Improving the Design - Making Different Instruments

4. infinity-project.org Engineering education for today’s classroom 55 2.1 Introduction

5. infinity-project.org Engineering education for today’s classroom 56 Ways to Make Music All systems that make music Have a musical source Have a way to read music information Convert musical information to sound Create sound waves in air The result: A sound signal - but what is it?

6. infinity-project.org Engineering education for today’s classroom 57 Signals are Everywhere Signal: A pattern or variation that contains information

7. infinity-project.org Engineering education for today’s classroom 58 2.2 Music, Sound and Signals

8. infinity-project.org Engineering education for today’s classroom 59 Sound Signals Sound Signal: A pattern or variation in molecules that a sound makes Sound has a speed that is different for different materials

9. infinity-project.org Engineering education for today’s classroom 60 Making Sounds Using Signals Amazing Fact: Any sound can be created, stored, and played using signals! Microphones and loudspeakers enable us to record and play sounds We only need one signal to represent any one sound

10. infinity-project.org Engineering education for today’s classroom 61 Exercise: Plotting Signals Plot the signals s(t) = 2 t + 3 s(t) = 0.3 cos(3 t) s(t) = 6 t 2 - 4 time (sec) Which one of these looks like a musical signal?

11. infinity-project.org Engineering education for today’s classroom 62 Manipulating Signals Three musically-useful ways: 1. Amplitude scaling: Changing its height x(t) = A s(t) 2. Time shifting: Moving left or right y(t) = s(t + d) 3. Time scaling: Stretching or shrinking the time axis z(t) = s(c t)

12. infinity-project.org Engineering education for today’s classroom 63 Plots of Real Instrument Signals

13. infinity-project.org Engineering education for today’s classroom 64 Plots of Notes on a Piano Keyboard

14. infinity-project.org Engineering education for today’s classroom 65 Musical Signals and Period Observation: The simplest musical signals are periodic; they have shapes that repeat Period: The repeating interval T of a periodic signal in units of time (seconds, milliseconds.) For any periodic signal p(t), p(t) = p(t + T). time (sec) p(t) Example: T = 0.0038 sec = 3.8 msec p(t+T)

15. infinity-project.org Engineering education for today’s classroom 66 Pitch and Fundamental Frequency Pitch: how high or low a periodic signal sounds. Can we be more precise? Yes! Use fundamental frequency, given by f = 1/T Units of frequency: cycles per second or Hertz (Hz)

16. infinity-project.org Engineering education for today’s classroom 67 Problem: Fundamental Frequency and Period Determine the fundamental frequencies of the sounds shown timeSinusoidal SignaltimeSaxophone Signal Solution: Both have periods of 0.0038 sec. Therefore, f=1/0.0038 f = 263Hz (middle C)

17. infinity-project.org Engineering education for today’s classroom 68 A Little Musical Notation Each note on a page of sheet music corresponds to a signal with a particular frequency and duration… The x-axis is time The y-axis is frequency

18. infinity-project.org Engineering education for today’s classroom 69 The Key to Reading Music When a musical score is played, each note becomes a signal with a fundamental frequency The type of note determines its duration

19. infinity-project.org Engineering education for today’s classroom 70 Making Musical Sounds Signals that have a pitch are periodic A periodic signal repeats over and over Therefore, to make a single note from a musical instrument, we need to create one period of its sound and play it over and over. p(t)

20. infinity-project.org Engineering education for today’s classroom 71 Our First Digital Band Design Loudspeaker Sound Waves Single period of instrument signal Translate notes to fundamental frequencies and durations

21. infinity-project.org Engineering education for today’s classroom 72 Infinity Project Experiment - 2.1

22. infinity-project.org Engineering education for today’s classroom 73 Plots of Speech

23. infinity-project.org Engineering education for today’s classroom 74 Plots of Speech - Block Diagram

24. infinity-project.org Engineering education for today’s classroom 75 2.3 Making Music from Sines and Cosines

25. infinity-project.org Engineering education for today’s classroom 76 Refining the Design How do we get the musical information to our digital band? How do we specify each instrument’s signal shape? How do we make several instrument sounds and play them simultaneously?

26. infinity-project.org Engineering education for today’s classroom 77 Specifying the Musical Score Traditionally, music has been written on paper Portable and easy for humans to read Destructible and a little hard for digital devices to read Is there a more convenient format for our musical information?

27. infinity-project.org Engineering education for today’s classroom 78 Musical Instrument Digital Interface (MIDI) MIDI specifies (a) note on/off time stamps and (b) note frequencies Convenient digital format A standard in widespread use Translate notes to fundamental frequencies and time stamps

28. infinity-project.org Engineering education for today’s classroom 79 Specifying the Shape of the Musical Instrument Sound Most musical instrument signals have complicated shapes We shall start with simple periodic signals - the sine and cosine functions

29. infinity-project.org Engineering education for today’s classroom 80 Turning a Sine or Cosine into a Sinusoid To make a sound from a sine or cosine function, make the angle a function of time s(t) = A cos(2 π t / T) [angle units: radians] A = {Amplitude}, T = {Period} Can show: s(t) = s(t + T) is periodic Example: A = 3.1 T = 2.5 msec People can’t hear the difference between sines and cosines!

30. infinity-project.org Engineering education for today’s classroom 81 Making Simple Melodies time (sec) Saxophone Sinusoid

31. infinity-project.org Engineering education for today’s classroom 82 Our Second Digital Band Design Translate notes to fundamental frequencies and time stamps Cosine generator This system allows us to play simple single-note melodies with a simple (sinusoidal) instrument sound. How do we extend this system to play (a)Different instruments? (b) Multiple notes simultaneously?

32. infinity-project.org Engineering education for today’s classroom 83 Making More than One Note at a Time To play two notes simultaneously, add their signals together MIDI Information: Translate notes to period values and time stamps Cosine generator Block Diagram:

33. infinity-project.org Engineering education for today’s classroom 84 Example Problem: Adding Two Signals Together time (sec)

34. infinity-project.org Engineering education for today’s classroom 85 Example Problem: Solution

35. infinity-project.org Engineering education for today’s classroom 86 Example: Adding Two Sinusoids Together This problem is hard to do by hand… …but easy to do digitally!

36. infinity-project.org Engineering education for today’s classroom 87 Reverse-Engineering the Musical Score Spectrum: A plot of a signal’s frequency content over a specified window “Spikes” in the spectrum correspond to sinusoids Spectrum Analysis: A procedure for computing the spectrum Spectrum Analysis is also easy to do digitally!

37. infinity-project.org Engineering education for today’s classroom 88 Spectrogram

38. infinity-project.org Engineering education for today’s classroom 89 Infinity Project Experiment - 2.2

39. infinity-project.org Engineering education for today’s classroom 90 Generating Sine and Cosine Signals

40. infinity-project.org Engineering education for today’s classroom 91 Generating Sine and Cosine Signals

41. infinity-project.org Engineering education for today’s classroom 92 Infinity Project Experiment-2.3

42. infinity-project.org Engineering education for today’s classroom 93 Listening to Sines and Cosines

43. infinity-project.org Engineering education for today’s classroom 94 Listening to Sines and Cosines

44. infinity-project.org Engineering education for today’s classroom 95 Infinity Project Experiment-2.4

45. infinity-project.org Engineering education for today’s classroom 96 Measuring a Tuning Fork

46. infinity-project.org Engineering education for today’s classroom 97 Measuring a Tuning Fork

47. infinity-project.org Engineering education for today’s classroom 98 Infinity Project Experiment - 2.5

48. infinity-project.org Engineering education for today’s classroom 99 Building the Sinusoidal MIDI Player

49. infinity-project.org Engineering education for today’s classroom 100 Building the Sinusoidal MIDI Player

50. infinity-project.org Engineering education for today’s classroom 101 Infinity Project Experiment - 2.6

51. infinity-project.org Engineering education for today’s classroom 102 The Spectrogram File Read

52. infinity-project.org Engineering education for today’s classroom 103 The Spectrogram File Read

53. infinity-project.org Engineering education for today’s classroom 104 The Spectrogram Microphone

54. infinity-project.org Engineering education for today’s classroom 105 The Spectrogram Microphone

55. infinity-project.org Engineering education for today’s classroom 106 2.4 Improving the Design— Making Different Instruments

56. infinity-project.org Engineering education for today’s classroom 107 Improving the Design - Making Better Instrument Sounds Synthesis: The creation of useful and interesting sounds from more basic signals Three types: Waveform Synthesis Additive Synthesis (Physical Modeling Synthesis)

57. infinity-project.org Engineering education for today’s classroom 108 Waveform Synthesis Method: Using a single period from a real instrument sound, make period signals at different frequencies Procedure: Copy, Time Warp, and Repeat T

58. infinity-project.org Engineering education for today’s classroom 109 Time Warping Goal: “Stretch” or “squeeze” a periodic signal to change its period Formula:p new (t) = p((T new / T) t) p new (t) = p((f / f new ) t) Result: p new (t) = p new (t + T new )

59. infinity-project.org Engineering education for today’s classroom 110 Example Problem: Time Warping Original SignalTime Warped Signal #1 Time Warped Signal #2 What are the fundamental frequencies of these signals?

60. infinity-project.org Engineering education for today’s classroom 111 Additive Synthesis Fact: Any signal can be approximated to arbitrary accuracy by adding the right sinusoids together. Example: Saxophone sound

61. infinity-project.org Engineering education for today’s classroom 112 Giving a Sound its Character: The Envelope Most musical sounds don’t have a constant volume Piano and guitar: Decay away Flute and trumpet: Always changing Envelope: The (changing) amplitude of a sound over time, denoted as e(t). Example: Piano e(t)

62. infinity-project.org Engineering education for today’s classroom 113 Using the Envelope for Sound Synthesis Formula: s(t) = e(t) x p(t) Can use with p(t) from either waveform or additive synthesis e(t) x p(t) = s(t)

63. infinity-project.org Engineering education for today’s classroom 114 Making Music Using Envelope and Periodic Signals

64. infinity-project.org Engineering education for today’s classroom 115 Plots of Clarinet Note

65. infinity-project.org Engineering education for today’s classroom 116 Infinity Project Experiment - 2.7

66. infinity-project.org Engineering education for today’s classroom 117 SketchWave with MIDI

67. infinity-project.org Engineering education for today’s classroom 118 SketchWave with MIDI

68. infinity-project.org Engineering education for today’s classroom 119 Infinity Project Experiment - 2.8

69. infinity-project.org Engineering education for today’s classroom 120 SketchWave with Envelope Functions

70. infinity-project.org Engineering education for today’s classroom 121 Sketch-Wave with Envelope Functions

71. infinity-project.org Engineering education for today’s classroom 122 Infinity Project Experiment - 2.9

72. infinity-project.org Engineering education for today’s classroom 123 Echo Generator

73. infinity-project.org Engineering education for today’s classroom 124 Echo Generator

74. infinity-project.org Engineering education for today’s classroom 125 Interesting Application - 2.10

75. infinity-project.org Engineering education for today’s classroom 126 Sound Effects: Reverberation

76. infinity-project.org Engineering education for today’s classroom 127 Sound Effects: Reverberation

77. infinity-project.org Engineering education for today’s classroom 128 Sound Effects -Flanging

78. infinity-project.org Engineering education for today’s classroom 129 Sound Effects Flanging

79. infinity-project.org Engineering education for today’s classroom 130 Master Design Problem

80. infinity-project.org Engineering education for today’s classroom 131 Master Design Problem: Ultimate Karaoke Machine Design a system that would make any singer sound like a music superstar! Goals Pitch correction - “Fix” any wrong notes while the singer is singing? Music creation - Background tracks? Special effects - An “Elvis” preset? Practice - Can it teach the singer to sing better?

81. infinity-project.org Engineering education for today’s classroom 132 Steps in the Design Constraints Low cost, portable, wireless…? Research and Gather Information Has this been done before? Create and Analyze Block diagram? Functions of each block? Choose, Build, and Test How well does it work?

82. infinity-project.org Engineering education for today’s classroom 133 End of Chapter 2