Oscilloscope music

An oscilloscope in XY mode moves its dot right as the left channel rises and up as the right channel rises. So to draw a shape with sound, walk once around it at a steady pace and send the x coordinate to the left speaker and the y coordinate to the right one. Repeat the walk 110 times a second and the dot traces the shape so fast it looks solid, and you hear a buzzing chord at 110 Hz.

Each channel is one repeating wave, so it is a sum of harmonics: whole multiples of the base frequency. The page works out those harmonics (the same Fourier series that Fourier epicycles draws with circles) and gives each ear its own wave, with both oscillators locked to the same clock. The scope here is not drawn from the maths: it reads the sound itself, from an analyser on each channel.

Sound is sampled, at 44,100 or 48,000 numbers a second. A harmonic above half that rate (the Nyquist limit) cannot be stored and would fold back as a false tone, so it is dropped. Sharp corners need many harmonics, which is why a star at a high note goes round at the tips. Spin detunes x by a few hertz, so the phase between the ears drifts and the figure turns.

Maths or seed turns text into a shape, like Maths art, using the same safe parser (it builds a tree of operations, so nothing typed is ever run as code). x = …; y = … is a parametric curve and r = … (in t or θ) a polar one; the page finds how many turns of 2π it takes to repeat and walks it once per period, or closes it with a straight line if it never repeats. Any other text, a word, a number or a date, is hashed into a seed that grows a closed curve: spinning harmonics with a symmetry, a rose, a spirograph or a twisted Lissajous. The same text always gives the same curve, and the link keeps it.

a picture and a chord are the same numbers: your ears hear the shape's harmonics, the scope sees the shape.