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II.1 Physical Reality II.1.1 (W Sept 15) Sound Anatomy

II.1 Physical Reality II.1.1 (W Sept 15) Sound Anatomy air waves 343 m/s auditory cortex ear room acoustics instrument (sound source) musician The overall picture f = sound wave frequency pitch( f ) = 1200/log 10 (2) . log 10 ( f ) + const. [Ct] (Cent)

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II.1 Physical Reality II.1.1 (W Sept 15) Sound Anatomy

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  1. II.1 Physical Reality II.1.1 (W Sept 15) Sound Anatomy

  2. air waves 343 m/s auditory cortex ear room acoustics instrument(sound source) musician The overall picture f = sound wave frequencypitch( f ) = 1200/log10(2) . log10( f ) + const. [Ct] (Cent) A = sound wave pressure amplitudeloudness(A ) = 20. log10(A/A0 ) + const. [dB] (Dezibel)A0 = 2.10-5 N/m2 (threshold) Weber-Fechner

  3. 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

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

  5. 2nd partial = 2nd overtone amplitudelength of arrow wave w phase (angle) fundamental= 1st partial = 1st overtone Sound anatomy Classical Joseph Fourier (partials/overtones) ~ 1800 every periodic function!!! w(t) = Ac + A1 sin(2.ft+Ph1) + A2 sin(2.2ft+Ph2) + A3 sin(2.3ft+Ph3) +...

  6. Yamaha DX7 modulator carrier Sound anatomy Classical Joseph Fourier (partials/overtones) ~ 1800 Frequency modulation (FM) John Chowning ~ 1970 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

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

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

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