The Physics of Sound
• Sound begins with a vibration of an
object
• Vibrating object transfers energy
to air medium
• All complex vibration patterns
seen as a combination of many
simple vibration patterns
• Simple harmonic motion
• Elastic restoring force
• Move object from equilibrium point,
force returns it to equilibrium point
• Force is proportion to distance from
equilibrium – Displacement
Simple Harmonic Motion
• Harmonic oscillations, or sinusoid
(sine) curves
Simple Harmonic Motion, con’t
1
0.5
0
-0.5
-1
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Amplitude: Maximum displacement from one
extreme to resting position
Periodic vibration: Wave repeats itself
• Frequency (F): Number of cycles per sec (Hz)
• Period (T): Time (sec) to complete one cycle
• F=1/T
Phase: Progression of wave through one cycle
(measured in degrees)
Simple Harmonic Motion, con’t
• Decay of harmonic motion
Additivity and Superposition of
Sine Waves
Additivity and Superposition of
Sine Waves, con’t
Fourier Decomposition or
Fourier Analysis
Fourier Decomposition, con’t
Systems for Naming Frequency
Components
Freq.
Harmonics
Overtones
Partials
f0
Fundamental
Fundamental
1st Partial
2f0
2nd Harmonic
1st Overtone
2nd Partial
3f0
3nd Harmonic
2st Overtone
3nd Partial
4f0
4nd Harmonic
3st Overtone
4nd Partial
Fourier Decomposition, con’t
The Perception of Pitch
The physiology of the ear
The Perception of Pitch, con’t
The place theory of pitch perception
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The basilar membrane as a set of
independently tuned resonators
Tone of single frequency causes
corresponding place on basilar
membrane to vibrate
The Perception of Pitch, con’t
The frequency theory of pitch perception
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Basilar membrane vibrates to match frequency
Because of refractory period, nerve fibers cannot
encode high frequency
Volley principle: nerve fibers working together can
encode high frequencies
The Perception of Pitch, con’t
The psychophysics of frequency
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The Mel Scale: Perceived pitch as a
function of frequency
Non-linear relation between frequency
and pitch
The Perception of Pitch, con’t
The Cognitive-Structural approach
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Octave equivalence
• Tones in a 2:1 frequency ratio have a
special relation
Evidence for octave equivalence:
• The harmonic series
• The musical pitch set
The Perception of Pitch, con’t
The Cognitive-Structural approach
•
Psychological evidence for octave
equivalence
• Deutsch (1973)
Standard
Intervening Sequence
Comparison
The Perception of Pitch, con’t
The Cognitive-Structural approach
•
Psychological evidence for octave
equivalence
• Octave-scramble nursery rhymes
The Perception of Pitch, con’t
A bi-dimensional approach
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Tone / Pitch Height: A continuous
dimension that increases with frequency
Tone / Pitch Chroma: Circular component
representing tones with 2:1 freq. ratio
The pitch helix
The Perception of Pitch, con’t
A bi-dimensional approach
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Shepard / Circular tones
Single tones:
Continuous glide:
Tritone paradox:
The Perception of Loudness
The psychophysics of loudness
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Audibility curves
The Perception of Loudness, con’t
The psychological scale of loudness
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Sones scale
The Perception of Timbre
The steady state component approach
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Components that remain the same over
time
Problems with the steady state view of
timbre
The Perception of Timbre, con’t
The importance of transient
components
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Onset rapidity: Rate of onset of the tone
Noise bursts: Amount/type of noise in
beginning of tone
Spectral energy shift: Changes in relative
intensity of harmonics over time
The Perception of Timbre, con’t
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The perceptual similarity of musical
timbre
John Grey’s studies of musical timbre