Mass · Stability · Harmony

The no-fly zone

Two worlds orbiting a star can only sit so close before gravity throws them out. That limit, written as a musical interval, is the tightest harmony their mass allows. Drag the mass — watch the forbidden region sweep across the fretboard, blocking off the intervals too tight to survive. Click a fret to hear it.

mass each: Earth m/M = 3.0e-6 tightest interval allowed: minor 2nd
no-fly zone
gravity forbids
unisonoctave2 octaves
MoonMarsEarthNeptuneJupiterbrown dwarfred dwarf

The blue dots are real resonant pairs — Io:Europa, Neptune:Pluto, Titan:Hyperion. Notice they always sit to the right of the no-fly line for their mass: nature never parks a pair inside the forbidden zone, because anything that did was ejected long ago. Slide up to Jupiter mass and watch the line march past the perfect fourth and fifth — giant planets simply cannot hold a close interval. Slide down to Moon mass and almost the whole board opens up: light bodies can crowd into near-unison.

click a fret or the board to enable sound