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

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Presentation transcript:

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

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 = 2.10-5 N/m2 (threshold) room acoustics air waves 343 m/s auditory cortex ear instrument (sound source) musician Weber-Fechner

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

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

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

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

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

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

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 http://www.cs.princeton.edu/%7eprc/SingingSynth.html