The Physics of Sound

1. 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

2. Simple Harmonic Motion • Harmonic oscillations, or sinusoid (sine) curves

3. Simple Harmonic Motion, con’t • 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)

4. Simple Harmonic Motion, con’t • Decay of harmonic motion

5. Additivity and Superposition of Sine Waves

6. Additivity and Superposition of Sine Waves, con’t

7. Fourier Decomposition or Fourier Analysis

8. Fourier Decomposition, con’t Systems for Naming Frequency Components Freq.Harmonics Overtones Partials f0Fundamental Fundamental 1st Partial 2f02nd Harmonic 1st Overtone 2nd Partial 3f03nd Harmonic 2st Overtone 3nd Partial 4f04nd Harmonic 3st Overtone 4nd Partial

9. Fourier Decomposition, con’t

10. The Perception of Pitch The physiology of the ear

11. The Perception of Pitch, con’t • The place theory of pitch perception • The basilar membrane as a set of independently tuned resonators • Tone of single frequency causes corresponding place on basilar membrane to vibrate

12. The Perception of Pitch, con’t • The frequency theory of pitch perception • 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

13. The Perception of Pitch, con’t • The psychophysics of frequency • The Mel Scale: Perceived pitch as a function of frequency • Non-linear relation between frequency and pitch

14. The Perception of Pitch, con’t • The Cognitive-Structural approach • Octave equivalence • Tones in a 2:1 frequency ratio have a special relation • Evidence for octave equivalence: • The harmonic series • The musical pitch set

15. The Perception of Pitch, con’t • The Cognitive-Structural approach • Psychological evidence for octave equivalence • Deutsch (1973) • Standard Intervening Sequence Comparison

16. The Perception of Pitch, con’t • The Cognitive-Structural approach • Psychological evidence for octave equivalence • Octave-scramble nursery rhymes

17. The Perception of Pitch, con’t • A bi-dimensional approach • 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

18. The Perception of Pitch, con’t • A bi-dimensional approach • Shepard / Circular tones • Single tones: • Continuous glide: • Tritone paradox:

19. The Perception of Loudness • The psychophysics of loudness • Audibility curves

20. The Perception of Loudness, con’t • The psychological scale of loudness • Sones scale

21. The Perception of Timbre • The steady state component approach • Components that remain the same over time • Problems with the steady state view of timbre

22. The Perception of Timbre, con’t • The importance of transient components • 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

23. The Perception of Timbre, con’t • The perceptual similarity of musical timbre • John Grey’s studies of musical timbre