# Harmonic Series and Spectrograms 220 Hz (A3) Why do they sound different? Instrument 1 Instrument 2Sine Wave.

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Harmonic Series and Spectrograms

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

Waveform Piano Guitar Sine Wave

Overtones 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

PianoGuitar Spectrogram

Modes of Vibration: Standing Waves

Harmonic Motion

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

Waveform Piano Guitar Sine Wave

Spectrogram: Piano

Piano: Component Sine Waves

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

Fourier Series

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

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