Square wave Fourier Analysis + + = Adding sines with multiple frequencies we can reproduce ANY shape.

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Presentation transcript:

Square wave Fourier Analysis

+ + =

Adding sines with multiple frequencies we can reproduce ANY shape

Joseph Fourier ( )

ANY periodic function fundamental 1 st harmonic 2 nd harmonic integer multiples of fundamental frequency

A i and f i wave shape timbre

Ohm’s law We ( pretty much ) can’t hear the phases

A i timbre A i timbre but not  i

Fourier spectrum same information (except the phases) f A

Examples of Fourier spectra

Clarinet now

It is now a great time to read chapter 4 of Berg & Stork

Roughly … Amplitude Loudness Frequency Pitch Wave shape Timbre

But … Tone quality other things contributing to timbre besides the waveform of the steady tone other things contributing to timbre besides the waveform of the steady tone

Roughly … Amplitude Loudness Frequency Pitch Wave shape Timbre

It is the wave shape of the whole sound that matters, not only of the “steady state” Regarding timbre …

Attack and decay transients

Spectrum decay

Inharmonicities higher harmonics slightly off the integer x f value

Vibrato Tremolo oscillation in frequency oscillation in amplitude

Formants

Chorus effect [let us all sing together]

Some real examples but first, spectrographs

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