The spin dynamics of high-aspect-ratio nickel nanorings in a longitudinal magnetic field have been investigated by Brillouin spectroscopy and the results are compared with a macroscopic theory and three-dimensional micromagnetic simulations. Good agreement is found between the measured and calculated magnetic field dependence of the spin wave frequency. Simulations show that as the field decreases from saturation, the rings switch from a "bamboo" to a novel "twisted bamboo" state at a certain critical field, and predict a corresponding dip in the dependence of the spin wave frequency on the magnetic field.