1. Harmonic Series and Spectrograms
By Jordan Kearns (W&L ‘14)
& Jon Erickson (still here )

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

3. Waveform
Piano
Guitar
Sine Wave

4. 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 (1st Harmonic): 220Hz
1st Overtone (2nd Harmonic): 440Hz
2nd Overtone (3rd Harmonic): 660Hz
Video produced by Brandon Pletsch
Univ. of Georgia Medical School
URL:

5. Frequency Spectrum
Piano
Guitar

6. Modes of Vibration: Standing Waves

7. Harmonic Motion in Guitar

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

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

10. Composite Wave I

11. Composite Wave II

12. Waveform
Piano
Guitar
Sine Wave

13. Spectrogram: Piano

14. Piano: Component Sine Waves
Microphone Signal Amplitude
Time

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

16. Fourier Series and Superposition
Any wave (sound) can be mathematically represented as some combination of sine waves.
Wave= SineWave1 + SineWave2 + SineWave3+…
𝑓 𝑡 = 𝑎 1 sin 2𝜋∗𝑓∗𝑡 + 𝑎 2 sin 2𝜋∗2𝑓∗𝑡 + 𝑎 3 sin 2𝜋∗3𝑓∗𝑡 +…
Fourier Series = Frequency Spectrum lets us see the component frequencies that make up the unique sound!

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

18. Piano C chord (2nd inversion)
C major chord
G4 (388)
E5 (657) C5
1171
G5 (775)
1314
1564

19. Frequency Spectra for Different Instruments
Same pitch played, but
TIMBRE
is entirely unique