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For Students · Harmonic Series

Harmonic Series for a room echo

Built for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition. Simulate a room echo live below — adjust the inputs and watch it respond, right in your browser.

Harmonic SeriesLive

overtones & timbre

Controls

Presets

Fundamental f₀ (Hz)

Number of harmonics

Rolloff (brightness)

Every musical note is a stack of harmonics — integer multiples of the fundamental. Their relative strengths (the rolloff) define timbre: why a violin and a flute playing the same pitch sound different. The intervals between harmonics also spell out the octave, fifth, and major third that ground Western harmony.

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Data Inspector

Fundamental110 Hz

2nd harmonic220 Hz (octave)

3rd harmonic330 Hz (fifth)

Harmonics8

Governing equation

f_{n} = n f_{0} = n \times 110 Hz, n = 1 \dots 8

Reading this result: Stacking 8 harmonics on 110 Hz — each an integer multiple (220 Hz, 330 Hz, …). Their relative strengths (rolloff 1) define the timbre: how a violin and a flute at the same pitch differ.

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Frequently asked questions

Is this good for students?: Yes — this version of "Harmonic Series for a room echo" is framed for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.