A sound.
A shape.

01 / Start with a repeating movement

A sine wave is a smooth repetition. For a pure tone, frequency is the number of cycles per second, measured in hertz (Hz). Our starting frequency is 220 Hz. Press Listen to hear the synthesised tone; no microphone or upload is needed.

Choose one harmonic. The small graph shows one complete cycle from left to right. The orange dot traces the matching outline slowly so you can inspect it. Its five-second circuit is an explanatory guide, not the speed of the audible vibration.

02 / Mix a little tone colour

A harmonic is a sine wave at a whole-number multiple of the base frequency. This study uses odd harmonics: 1, 3, 5, 7 and 9. Each has a weight of 1 / k, where k is that multiple. At 220 Hz, four terms play at 220, 660, 1100 and 1540 Hz.

Add harmonics while keeping the pitch fixed. The wave becomes less rounded and the tone becomes richer. We divide by the sum of the weights to bound the signal, rather than promising equal perceived loudness. Tone colour and loudness perception are more complex than one slider.

03 / Wrap the wave around a circle

Let θ travel once around a circle, from 0 to 2π. Evaluate the same mixture at θ, then use that value to move the edge in or out. R is the resting radius and A is the level slider. Positive values push outward; negative values pull inward.

w(θ) = Σ sin(kθ)/k ÷ Σ 1/k
r(θ) = R × [1 + A × w(θ)]
x = r cos θ;  y = r sin θ
s(t) = 0.18 × A × w(2πf₀t)
k = 1, 3, …, 2N − 1

The thirteen nested contours repeat this rule at different resting radii. They are an illustration of the mapping, not measurements of pressure in space. Rotate the drawing under Composition to change its orientation without changing the sound.

04 / Separate pitch from shape

Keep harmonics and level fixed, then move the pitch slider from 220 to 440 Hz. Every audio frequency doubles. The outline stays the same because it represents one normalised cycle, not a fixed duration of sound.

A different artist could map pitch to height, spectral brightness to colour, or amplitude to size. The rule determines what the image reveals. There is no single correct picture of a sound, and this is not a physical cymatics simulation.

05 / Make a three-shape study

Save one shape with one harmonic, one with four, and one with four at twice the pitch. Keep level at 0.65. Which pair has the same outline? Which pair sounds different? Try level zero: the tone falls silent and every contour becomes a circle.

The second and third images match even though their pitches differ. The first and second use different harmonic mixtures. Changing one variable at a time makes the relationship easier to understand.

Keep the experiment

Download this lesson with its working sound and drawing controls in one editable HTML file. Everything runs locally. Save a clean PNG for a post, square or story, or keep an SVG to edit the lines. These exports are still images.