The orbit
the cell's (x, y) its size at the strikeThe cell's own state, every other sub-step, straight from the engine's ring: a pure tone is a circle. The shear pushes x by a function of y each step — the orbit bends, and the bend is the harmonics you hear.
Spectrum
the note's harmonics- Note
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- ε a sub-step
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- The orbit's size
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The orbit's size over time
x² + y² − εxy over whole turns, the quantity the leapfrog keeps exactly, in dB from the strikePlay
the engine loads with the soundLab mode — the red controls
The leapfrog keeps the orbit's size exactly. The naive update — x and y moved together from the same old values — multiplies the orbit's area by 1 + ε² every sub-step: at A3 that is twenty-thousandfold a second. The engine ships the leapfrog; this switch shows why. The lab mutes the sound and restarts the engine when it blows up.
The glide's retune: the shipped form re-bases the orbit as the pitch moves; the plain recurrence stepped once a block ripples the level — glide and watch the size.
Click a key to hold the note. Keys also on the keyboard: A W S E D F T G Y H U J K.