1. II.1 Physical Reality
II.1.1 (F Sept 08) Sound Anatomy

2. Weber-Fechner The overall picture
f = sound wave frequency pitch( f ) = 1200/log10(2) . log10( f ) + const. [Ct] (Cent)
A = sound wave pressure amplitude loudness(A ) = 20. log10(A/A0 ) + const. [dB] (Dezibel) A0 = N/m2 (threshold)
room acoustics
air waves 343 m/s
auditory cortex
ear
instrument (sound source)
musician
Weber-Fechner

4. Sound anatomy
Classical Joseph Fourier (partials/overtones) ~ 1800
Frequency Modulation (FM) John Chowning ~ 1970
Wavelets (Jean Morlet et al.) ~ 1984
Physical Modeling (Claude Cadoz et al.) ~ 1989

5. + = Sound anatomy Classical Joseph Fourier (partials/overtones) ~ 1800
wave w
envelope H +
w. H =
shift and squeeze
support

6. Sound anatomy
Classical Joseph Fourier (partials/overtones) ~ 1800
wave w
every periodic function!!!
2nd partial
= 2nd overtone
amplitude length of arrow
fundamental = 1st partial
= 1st overtone
w(t) = Ac + A1 sin(2.ft+Ph1) + A2 sin(2.2ft+Ph2) + A3 sin(2.3ft+Ph3) +...
phase (angle)
time

7. Sound anatomy
Amplitude spectrum
w(t) = Ac + A1 sin(2.ft+Ph1) + A2 sin(2.2ft+Ph2) + A3 sin(2.3ft+Ph3) +...

8. Sound anatomy
Classical Joseph Fourier (partials/overtones) ~ 1800
Frequency modulation (FM) John Chowning ~ 1970
Yamaha DX7
modulator
carrier
w(t) = Ac + A1 sin(2.ft+Ph1) + A2 sin(2.2ft+Ph2) + A3 sin(2.3ft+Ph3) +...
W(t) = Ac + A1 sin(2.ft+Ph1 + A2 sin(2.2ft+Ph2 + A3 sin(2.3ft+Ph3)))
carrier
modulator
modulator

9. Sound anatomy
Classical Joseph Fourier (partials/overtones) ~ 1800
Frequency Modulation (FM) John Chowning ~ 1970
Wavelets (Jean Morlet et al.) ~ 1984

10. Singer Synthesis: Perry Cook
Sound anatomy
Classical Joseph Fourier (partials/overtones) ~ 1800
Frequency Modulation (FM) John Chowning ~ 1970
Wavelets (Jean Morlet et al.) ~ 1984
Physical Modeling (Claude Cadoz et al.) ~ 1989
Singer Synthesis: Perry Cook