Musical Instruments
Virtual guitar, flute, drum. Builds on Standing Waves & Harmonics.
A violinist and a flutist both play concert A (440 Hz). Both instruments produce exactly the same fundamental frequency.
Why do they sound so obviously different?
It’s the overtones! When any instrument plays 440 Hz, it also produces harmonics: 880, 1320, 1760 Hz, and so on. The relative strengths of these harmonics are different for each instrument — this is called timbre. A violin has strong, rich overtones. A flute is nearly a pure sine wave. Same note, completely different harmonic fingerprint.
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Listen to different instruments playing the same note. Watch the waveform and frequency spectrum change. Notice the violin has many tall harmonic bars while the flute is dominated by the fundamental.
f(t) = Σ Aₙ sin(nωt + φₙ)
Timbre is the ‘recipe’ of harmonic amplitudes Aₙ. Each instrument has a unique recipe. Your brain does an unconscious Fourier analysis to decode it!
Bowing near the bridge (sul ponticello) emphasizes high harmonics for a glassy, metallic tone. Bowing near the fingerboard (sul tasto) suppresses overtones for a softer, flute-like sound. Same string, different timbre.
The saxophone has a conical bore, which is why it produces all harmonics despite being a reed (closed-end) instrument. A clarinet’s cylindrical bore gives it only odd harmonics, creating its distinctive hollow sound.
A drumhead’s overtone frequencies are NOT integer multiples of the fundamental (they’re Bessel function zeros). This inharmonic spectrum is why most drums sound ‘noisy’ rather than ‘musical.’ Timpani are specially shaped to make overtones more harmonic.
Synthesizers create any timbre by mixing sine waves with controllable amplitudes. ‘Subtractive synthesis’ starts with a harmonically rich wave and filters out overtones. It’s Fourier analysis made into a musical instrument.
“Pitch tells you the note. Timbre tells you the instrument. One is the fundamental; the other is the recipe of overtones riding on top.”
Instrument Lab
Build sounds from harmonics. Compare waveforms and spectra of different virtual instruments. Adjust individual harmonic amplitudes to morph one instrument’s sound into another.
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Start with a pure sine wave (only the fundamental). Gradually add the 2nd, 3rd, and 4th harmonics — hear how the sound gets richer. Try the violin preset and look at its harmonic spectrum. Now try the clarinet — notice the missing even harmonics! Switch to ‘drum’ mode to hear inharmonic overtones and compare the messy waveform.
Every instrument’s unique sound is just a specific recipe of harmonics. Fourier showed that ANY periodic waveform can be decomposed into sine waves — your ear does this decomposition naturally.