  Using the ``glueball dominance'' picture of the mixing between q\bar{q}
mesons of different hidden flavors, we establish new glueball-meson mass
relations which serve as a basis for glueball spectral systematics. For the
tensor glueball mass 2.3\pm 0.1 GeV used as an input parameter, these relations
predict the following glueball masses: M(0^{++})\simeq 1.65\pm 0.05 GeV,
M(1^{--})\simeq 3.2\pm 0.2 GeV, M(2^{-+})\simeq 2.95\pm 0.15 GeV,
M(3^{--})\simeq 2.8\pm 0.15 GeV. We briefly discuss the failure of such
relations for the pseudoscalar sector. Our results are consistent with
(quasi)-linear Regge trajectories for glueballs with slope \simeq 0.3\pm 0.1
GeV^{-2}.
