One number. An entire instrument.
The starting point
A mathematical sequence can be more than a list of numbers. Hailstone explores how its rises, falls and patterns can become something you hear, see and play.
What I built
Start with a positive integer. Odd numbers are tripled and increased by one; even numbers are halved. Hailstone turns those operations into a musical sequence and a moving visual path.
The sequence shapes both the notes and a custom oscillator waveform. Odd and even steps have contrasting voices, with controls for FM, tone, decay, reverb and delay. Presets offer starting points; a touch field and keyboard pads let you play the sound yourself.
Choose a key, scale, tempo and pitch mapping, then take the result elsewhere. Stereo WAV exports include the synth and effects; multitrack MIDI carries musical events for another instrument. Patches can be saved and loaded, and the last settings stay in the browser.
The instrument lives in one self-contained HTML file. It generates sound locally with Web Audio, starts audio after a tap and has no external libraries, microphone input or upload service.
The arithmetic uses exact integers. A trajectory stops at one, a repeated value or a fixed step limit; an unresolved result is shown as a limit, rather than treated as evidence that it diverges.