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Chapter 21

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MUSICAL SOUNDS

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This lecture will help you understand:

  • Noise and Music
  • Musical Sounds
  • Pitch
  • Sound Intensity and Loudness
  • Quality
  • Musical Instruments
  • Fourier Analysis
  • Digital Versatile Discs (DVDs)

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Noise

  • Noise corresponds to an irregular vibration of the eardrum produced by some irregular vibration in our surroundings, a jumble of wavelengths and amplitudes.
    • White noise is a mixture of a variety of frequencies of sound. This is similar to white light being composed of all the colors in the visible spectrum.

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Music

  • Music is the art of sound and has a different character.
  • Musical sounds have periodic tones–or musical notes.
  • The line that separates music and noise can be thin and subjective.

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Musical Sounds

Musical tone

  • Three characteristics:
    • Pitch
      • determined by frequency of sound waves as received by the ear
      • determined by fundamental frequency, lowest frequency
    • Intensity
      • determines the perceived loudness of sound

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Musical Sounds

Musical tone

  • Three characteristics (continued):
    • Quality
      • determined by prominence of the harmonics
      • determined by presence and relative intensity of the various partials

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Pitch

  • Music is organized on many different levels. Most noticeable are musical notes.

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  • Each note has its own pitch. We can describe pitch by frequency.
    • Rapid vibrations of the sound source (high frequency) produce sound of a high pitch.
    • Slow vibrations (low frequency) produce a low pitch.

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Pitch

  • Musicians give different pitches different letter names: A, B, C, D, E, F, G.
    • Notes A through G are all notes within one octave.
    • Multiply the frequency on any note by 2, and you have the same note at a higher pitch in the next octave.
    • A piano keyboard covers a little more than seven octaves.

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A Note by Any Other Name...

Source: http://en.wikipedia.org/wiki/C_%28musical_note%29

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Pitch

  • Different musical notes are obtained by changing the frequency of the vibrating sound source.
  • This is usually done by altering the size, the tightness, or the mass of the vibrating object.

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Pitch

  • High-pitched sounds used in music are most often less than 4000 Hz, but the average human ear can hear sounds with frequencies up to 18,000 Hz.
    • Some people and most dogs can hear tones of higher pitch than this.
    • The upper limit of hearing in people gets lower as they grow older.
    • A high-pitched sound is often inaudible to an older person and yet may be clearly heard by a younger one.

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Sound Intensity and Loudness

  • The intensity of sound depends on the amplitude of pressure variations within the sound wave.
  • The human ear responds to intensities covering the enormous range from 10–12 W/m2 (the threshold of hearing) to more than 1 W/m2 (the threshold of pain).

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Sound Intensity and Loudness

  • Because the range is so great, intensities are scaled by factors of 10, with the barely audible 10–12 W/m2 as a reference intensity called 0 bel (a unit named after Alexander Bell).
  • A sound 10 times more intense has an intensity of 1 bel (10–11 W/m2) or 10 decibels (dB)

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Sound Intensity and Loudness

  • Sound intensity is a purely objective and physical attribute of a sound wave, and it can be measured by various acoustical instruments.

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  • Loudness is a physiological sensation.
    • The ear senses some frequencies much better than others.
    • A 3500-Hz sound at 80 decibels sounds about twice as loud to most people as a 125-Hz sound at 80 decibels.
    • Humans are more sensitive to the 3500-Hz range of frequencies.

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The Threshold of Hearing

The decibel scale

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The Decibel Scale

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Quality

  • We have no trouble distinguishing between the tone from a piano and a tone of the same pitch from a clarinet.
  • Each of these tones has a characteristic sound that differs in quality, the “color” of a tone —timbre.
  • Timbre describes all of the aspects of a musical sound other than pitch, loudness, or length of tone.

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Quality

  • Most musical sounds are composed of a superposition of many tones differing in frequency.

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  • The various tones are called partial tones, or simply partials. The lowest frequency, called the fundamental frequency, determines the pitch of the note.

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  • A partial tone whose frequency is a whole-number multiple of the fundamental frequency is called a harmonic.

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Quality

  • A composite vibration of the fundamental mode and the third harmonic is shown in the figure.

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Quality

  • The quality of a tone is determined by the presence and relative intensity of the various partials.
  • The sound produced by a certain tone from the piano and a clarinet of the same pitch have different qualities that the ear can recognize because their partials are different.
  • A pair of tones of the same pitch with different qualities have either different partials or a difference in the relative intensity of the partials.

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Musical Instruments

Vibrating strings

    • Vibration of stringed instruments is transferred to a sounding board and then to the air.

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Vibrating air columns

    • Brass instruments.
    • Woodwinds—stream of air produced by musician sets a reed vibrating.
    • Fifes, flutes, piccolos—musician blows air against the edge of a hole to produce a fluttering stream.

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Musical Instruments

Percussion

    • Striking a 2-dimensional membrane.
    • Tone produced depends on geometry, elasticity, and tension in the vibrating surface.
    • Pitch produced by changes in tension.

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Musical Instruments

Electronic musical instrument

  • differs from conventional musical instruments
  • uses electrons to generate the signals that make up musical sounds
  • modifies sound from an acoustic instrument
  • demands the composer and player demonstrate an expertise beyond the knowledge of musicology

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Fourier Analysis

  • The sound of an oboe displayed on the screen of an oscilloscope looks like this.
  • The sound of an clarinet displayed on the screen of an oscilloscope looks like this.
  • The two together look like this.

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Fourier Analysis

  • Fourier discovered a mathematical regularity to the component parts of periodic wave motion.
  • He found that even the most complex periodic wave motion can be disassembled into simple sine waves that add together.
  • Fourier found that all periodic waves may be broken down into constituent sine waves of different amplitudes and frequencies.
  • The mathematical operation for performing this is called Fourier analysis.

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Fourier Analysis

  • When these pure tones are sounded together, they combine to give the tone of the violin.
  • The lowest-frequency sine wave is the fundamental and determines the pitch.

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  • The higher-frequency sine waves are the partials that determine the quality.
  • Thus, the waveform of any musical sound is no more than a sum of simple sine waves.

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Wave Components in Frequency Space

Fourier Analysis

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Musical Instruments

Frequency Components

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Violin Trumpet Clarinet

Musical Instrument Waveforms

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Frequency Component Structure

Violin

Clarinet

Organ Pipes

Piano

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Typical Musical Overtone Structures

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Fourier Analysis Tool

http://www.austincc.edu/mmcgraw/physics_simulations.htm

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Standing Wave Patterns

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Ringing Bell - Resonant Modes

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Guitar - Resonant Modes

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Digital Versatile Discs (DVDs)

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Digital Versatile Discs (DVDs)

  • The signal below is the output of a phonograph.

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  • This type of continuous waveform is called an analog signal.
  • The analog signal can be changed to a digital signal by measuring the numerical value of its amplitude during each split second.

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Digital Versatile Discs (DVDs)

  • Microscopic pits about one-thirtieth the diameter of a strand of human hair are imbedded in the CD or DVD
    • The short pits corresponding to 0.
    • The long pits corresponding to 1.

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Digital Versatile Discs (DVDs)

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  • When the beam falls on a short pit, it is reflected directly into the player’s optical system and registers a 0.
  • When the beam is incident upon a passing longer pit, the optical sensor registers a 1.
  • Hence the beam reads the 1 and 0 digits of the binary code.

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DVD vs Blu-Ray

Single layer storage comparison

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DVD vs Blu-Ray

DVD

λ = 650nm

Blu-Ray

λ = 405nm

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Summary

  • Noise and Music
  • Musical Sounds
  • Pitch
  • Sound Intensity and Loudness
  • Quality
  • Musical Instruments
  • Fourier Analysis
  • Digital Versatile Discs (DVDs)

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