2. Square wave Fourier Analysis

3. + + =

4. Adding sines with multiple frequencies we can reproduce ANY shape

5. Joseph Fourier (1768-1830)

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

7. A i and f i wave shape timbre

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

9. A i timbre A i timbre but not  i

10. Fourier spectrum same information (except the phases) f A

11. Examples of Fourier spectra

13. Clarinet now

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

15. Roughly … Amplitude Loudness Frequency Pitch Wave shape Timbre

16. 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

17. Roughly … Amplitude Loudness Frequency Pitch Wave shape Timbre

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

19. Attack and decay transients

20. Spectrum decay

21. Inharmonicities higher harmonics slightly off the integer x f value

22. Vibrato Tremolo oscillation in frequency oscillation in amplitude

23. Formants

24. Chorus effect [let us all sing together]

25. Some real examples but first, spectrographs