We are used to thinking of gravitational waves as messengers from catastrophes in space, the ringing of spacetime after black holes collide for example. But our own Galaxy hums with a fainter, steadier signal, a chorus of millions of unseen binary stars. A new study has found that this hum carries a hidden fingerprint of the Milky Way's spin, and that if a future space mission ignores it, our picture of the Galaxy itself could come out subtly wrong.