1. Guerino Mazzola (Fall 2015 © ): Honors Seminar II.1Physical Reality II.1.1 (F Sept 11) Sound Anatomy

2. Guerino Mazzola (Fall 2015 © ): Honors Seminar air waves 343 m/s The overall picture instrument (sound source) musician auditory cortex f = sound wave frequency pitch( f ) = 1200/log 10 (2). log 10 ( f ) + const. [Ct] (Cent) A = sound wave pressure amplitude loudness(A ) = 20. log 10 (A/A 0 ) + const. [dB] (Dezibel) A 0 = 2.10 -5 N/m 2 (threshold) ear room acoustics Weber-Fechner

3. Guerino Mazzola (Fall 2015 © ): Honors Seminar

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

5. Guerino Mazzola (Fall 2015 © ): Honors Seminar Sound anatomy A.Classical Joseph Fourier (partials/overtones) ~ 1800 wave w shift and squeeze support envelope H + w. H =

6. Guerino Mazzola (Fall 2015 © ): Honors Seminar Sound anatomy A.Classical Joseph Fourier (partials/overtones) ~ 1800 wave w w(t) = A c + A 1 sin(2 .ft+Ph 1 ) + A 2 sin(2 .2ft+Ph 2 ) + A 3 sin(2 .3ft+Ph 3 ) +... fundamental = 1st partial = 1st overtone 2nd partial = 2nd overtone amplitude length of arrow phase (angle) every periodic function!!!

7. Guerino Mazzola (Fall 2015 © ): Honors Seminar Sound anatomy Amplitude spectrum w(t) = A c + A 1 sin(2 .ft+Ph 1 ) + A 2 sin(2 .2ft+Ph 2 ) + A 3 sin(2 .3ft+Ph 3 ) +...

8. Guerino Mazzola (Fall 2015 © ): Honors Seminar Sound anatomy A.Classical Joseph Fourier (partials/overtones) ~ 1800 B.Frequency modulation (FM) John Chowning ~ 1970 W(t) = A c + A 1 sin(2 .ft+Ph 1 + A 2 sin(2 .2ft+Ph 2 + A 3 sin(2 .3ft+Ph 3 ))) carriermodulatormodulator Yamaha DX7 carrier modulator w(t) = A c + A 1 sin(2 .ft+Ph 1 ) + A 2 sin(2 .2ft+Ph 2 ) + A 3 sin(2 .3ft+Ph 3 ) +...

9. Guerino Mazzola (Fall 2015 © ): Honors Seminar Sound anatomy A.Classical Joseph Fourier (partials/overtones) ~ 1800 B.Frequency Modulation (FM) John Chowning ~ 1970 C.Wavelets (Jean Morlet et al.) ~ 1984

10. Guerino Mazzola (Fall 2015 © ): Honors Seminar Sound anatomy A.Classical Joseph Fourier (partials/overtones) ~ 1800 B.Frequency Modulation (FM) John Chowning ~ 1970 C.Wavelets (Jean Morlet et al.) ~ 1984 D.Physical Modeling (Claude Cadoz et al.) ~ 1989 http://www.cs.princeton.edu/%7eprc/SingingSynth.html Singer Synthesis: Perry Cook