Music and Harmonics

Fourier Analysis · Axiom Academy

REAL WORLD Music and Harmonics How Fourier analysis explains musical timbre and instrument sounds Imagine a piano and a violin both playing the note A4 (440 Hz). They're playing the exact same frequency, yet they sound completely different. You can instantly tell which is which, even without seeing the instruments. Why? If they're both producing 440 Hz vibrations, why don't they sound identical? Click the buttons above to see the waveforms of different instruments playing the same note. Notice how different they look! Each instrument's sound wave looks completely different, even though they're all centered around 440 Hz. The shape of these waveforms determines what we call timbre (pronounced "TAM-ber") - the unique "color" or quality of a sound. What do you think creates these different waveform shapes? Each instrument produces not just the fundamental frequency (440 Hz), but also overtones - integer multiples of that fundamental frequency. These are called harmonics . The Harmonic Series for A4 (440 Hz) 1st Harmonic (Fundamental): 440 Hz 2nd Harmonic: 880 Hz (2 × 440) 3rd Harmonic: 1320 Hz (3 × 440) 4th Harmonic: 1760 Hz (4 × 440) 5th Harmonic: 2200 Hz (5 × 440) Each instrument has a unique "recipe" - different relative amplitudes of these harmonics! Instead of looking at the waveform over time, we can use Fourier analysis to see which frequencies are present and how strong they are. This is called a frequency spectrum or spectrum analysis .

This is the written version of the interactive lesson above. See the full Fourier Analysis course.