  Seismology of the gas giants holds the potential to resolve long-standing
questions about their internal structure and rotation state. We construct a
family of Saturn interior models constrained by the gravity field and compute
their adiabatic mode eigenfrequencies and corresponding Lindblad and vertical
resonances in Saturn's C ring, where more than twenty waves with pattern speeds
faster than the ring mean motion have been detected and characterized using
high-resolution Cassini Visual and Infrared Mapping Spectrometer (VIMS) stellar
occultation data. We present identifications of the fundamental modes of Saturn
that appear to be the origin of these observed ring waves, and use their
observed pattern speeds and azimuthal wavenumbers to estimate the bulk rotation
period of Saturn's interior to be $10{\rm h}\, 33{\rm m}\, 38{\rm s}^{+1{\rm
m}\, 52{\rm s}}_{-1{\rm m}\, 19{\rm s}}$ (median and 5%/95% quantiles),
significantly faster than Voyager and Cassini measurements of periods in
Saturn's kilometric radiation, the traditional proxy for Saturn's bulk rotation
period. The global fit does not exhibit any clear systematics indicating strong
differential rotation in Saturn's outer envelope.
