Harmonic Series and Spectrograms

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Presentation transcript:

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

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

Waveform Piano Guitar Sine Wave

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: https://www.youtube.com/watch?v=PeTriGTENoc

Frequency Spectrum Piano Guitar

Modes of Vibration: Standing Waves

Harmonic Motion in Guitar

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

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

Composite Wave I

Composite Wave II

Waveform Piano Guitar Sine Wave

Spectrogram: Piano

Piano: Component Sine Waves Microphone Signal Amplitude Time

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

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!

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

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

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