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An instrument for curious ears
Inside
a note.
A single note can hold
a whole world of waves.
Change the ingredients.
Hear what happens.
Fixed note names: C = Do · D = Re · E = Mi · F = Fa · G = Sol · A = La · B = Si. Numbers indicate octaves.
One pitch. Many ingredients.
Eight harmonics, with amplitudes 1/n. Their frequencies fit together as whole-number multiples of the fundamental.
8 HARMONICS · ZERO INITIAL PHASE
Behind the instrument
A sound has
an inner life.
What am I changing?
The sliders change the strengths of eight sine waves. Their frequencies are 1, 2, 3… times the fundamental. Adding them creates a complex periodic wave. This distribution of components is its spectrum.
The graph shows two periods. In Components, the individual waves are enlarged for inspection. Overlay puts every wave and the sum on the same scale. Animation slows the waves down; it does not depict their real speed.
Why can a missing frequency still suggest a pitch?
A group of higher harmonics can preserve the spacing and repeating pattern associated with the fundamental. The auditory system can perceive that pitch even when the fundamental component is absent. Try Bright, start the sound, then remove and restore the fundamental.
This is a demonstration, not a hearing test. The effect varies with the chosen spectrum, playback equipment, and listener.
What does this model leave out?
Real instruments have attacks, decays, noise, and sometimes inharmonic components. Those also shape timbre. These recipes are mathematical examples, not recordings or faithful instrument imitations. Eight harmonics only approximate richer waveforms.
Audio and the summed curve use the same amplitudes, scaled together to keep the signal bounded. Loudness is not equalized between recipes. All components start with zero relative phase.
Sources & method
Scientific grounding: Joe Wolfe and colleagues, UNSW Music Acoustics.
y(t) = Σ aₙ sin(2πnft), n = 1…8
Pure: a₁ = 1, others 0. Round: aₙ = 1/n². Hollow: odd n → 1/n, even n → 0. Bright: aₙ = 1/n. The common gain is 1 / max(1, Σ|aₙ|).