  We have calculated the low-lying elementary excitations of three-dimensional
few-vortex arrays in trapped Bose-Einstein condensates. The number of different
Kelvin-Tkachenko vortex wave branches matches the number of vortices in the
condensate. The lowest odd-parity modes exhibit superfluid gyroscopic vortex
motion. Experimentally, these modes could be excited and observed individually
or in connection with the formation and decay of quantum turbulence.
