  After black holes collide, the remnant settles to a stationary state by
emitting gravitational waves. Once non-linearities subside, these ringdown
waves are dominated by exponentially-damped sinusoids, or quasinormal modes. We
develop a general method using perturbative spectral expansions to calculate
the quasinormal-mode frequencies and damping times in a wide class of modified
gravity theories for black holes with any subextremal spin. We apply this
method to scalar-Gauss-Bonnet gravity to show its accuracy, thus enabling
robust ringdown tests with gravitational wave data.
