The treble clef 𝄞, its four contours joined by thin bridges and sampled at 4096 points, is a sum of circles: z(t) = ∑ cₖ eⁱᵏᵗ.
With the N largest circles the widest gap to the outline falls from 35.7 % of its height at N = 1 to 0.37 % at 256. The tip's distance |z(t)| is played as pitch, floored to C major.
One circle keeps |z| fixed: one note. With 64 the tip plays the outline's own note 93 % of the lap; with 256, 98 %.
Each coordinate of a closed outline has its own real Fourier series: x(t) = ∑ (aₖ cos kt + bₖ sin kt), and the same for y.
A cosine and sine of frequency k make one arm of length √(aₖ² + bₖ²) turning k times per lap. One chain sets x, one sets y, and the pen sits where their guides cross. With N harmonics per axis the knight is off by 30.2 % of its height at N = 1, 0.70 % at N = 50.
At N = 1 both coordinates are pure sinusoids: an ellipse.
@funkdeniz In the early days of crypto, some people used to show gold coin chocolate wrappers labeled with a B and say it was their bitcoin; now, woe unto the beginners in AI and machine learning.