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

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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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slide1

II.1 Physical Reality

II.1.1 (W Sept 15) Sound Anatomy

slide2

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

slide4

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

slide5

envelope H

+

=

wave w

w. H

support

Sound anatomy

Classical Joseph Fourier (partials/overtones) ~ 1800

shift and squeeze

slide6

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) +...

slide7

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

slide8

Sound anatomy

Classical Joseph Fourier (partials/overtones) ~ 1800

Frequency Modulation (FM) John Chowning ~ 1970

Wavelets (Jean Morlet et al.) ~ 1984

slide9

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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