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Collatz · 3n + 1 · sonified
Every whole number sings a hailstone melody. Halve an even number and the tune falls; triple an odd one and add one, and it leaps. Every sequence anyone has ever tested comes to rest on 1 — the tonic.
One step per sixteenth note
Reverb and echo
Space play/pause · ↑↓ next number
How far the melody can travel
Needs two or more numbers
Click any number to play from there
An even number is halved. In Contour the melody steps down the scale; in Harmonic series it drops exactly one octave, because halving a frequency is an octave.
An odd number is tripled, plus one: the leap. Tripling a frequency lands an octave and a perfect fifth higher; the +1 nudges it a hair sharp.
1 is the tonic, so every piece ends at home. From 1 the rule loops 4 → 2 → 1 forever. Computers have checked every starting number past 1021; nobody has proved they all land.
Enter several numbers. Converge lines them up to finish together: once two paths meet they share every later note, so the voices fold into unison. Canon starts them together, so shared stretches return as echoes.