2. Harmonic Series and Spectrograms BY JORDAN KEARNS (W&L ‘14) & JON ERICKSON (STILL HERE )

3. 220 Hz (A3) Why do they sound different? Instrument 1 Instrument 2Sine Wave

4. Waveform Piano Guitar Sine Wave

5. Overtones and Music Perception Overtones occur at integer multiples of the fundamental frequency when an object vibrates. The addition of these tones at regular intervals is musical to the human ear. Example: Fundamental (1 st Harmonic): 220Hz 1 st Overtone (2 nd Harmonic): 440Hz 2 nd Overtone (3 rd Harmonic): 660Hz Video produced by Brandon Pletsch Univ. of Georgia Medical School URL: https://www.youtube.com/watch?v=PeTriGTENoc

6. PianoGuitar Frequency Spectrum

7. Modes of Vibration: Standing Waves

8. Harmonic Motion in Guitar

9. Frequency Decomposition: Pure Sine Wave T = 2ms f = 1/T f = 500Hz

10. Frequency Decomposition: Pure Sine Wave T = 1ms f = 1/T f = 1000Hz

11. Composite Wave I

12. Composite Wave II

13. Waveform Piano Guitar Sine Wave

14. Spectrogram: Piano

15. Piano: Component Sine Waves Time Microphone Signal Amplitude

16. Piano: Component Sine Waves Composite Wave (From Previous Slide) Original Piano Wave Look how close with only three sine waves!!!

17. Fourier Series and Superposition

18. Why you should change strings A quick experiment with a spectrogram Old New