  It is well known that because of the axial anomaly in QCD, mesons with $J^P =
0^-$ are close to $SU(3)_{\mathrm{V}}$ eigenstates: the $eta^\prime(958)$ meson
is largely a singlet, and the $\eta$ meson an octet. In contrast, states with
$J^P = 1^-$ are flavor diagonal: \textit{e.g.}, the $\phi(1020)$ is almost pure
$\bar{s} s$. Using effective Lagrangians, we show how this generalizes to
states with higher spin, assuming that they can be classified according to the
unbroken chiral symmetry of $G_{\mathrm{fl}} = SU(3)_{\mathrm{L}} \times
SU(3)_{\mathrm{R}}$. We construct effective Lagrangians from terms invariant
under $G_{\mathrm{fl}}$, and introduce the concept of \textit{hetero-} and
\textit{homo}chiral multiplets. Because of the axial anomaly, only terms
invariant under the $Z(3)_{\mathrm{A}}$ subgroup of the axial
$U(1)_{\mathrm{A}}$ enter. For heterochiral multiplets, which begin with that
including the $\eta$ and $\eta^\prime(958)$, there are $Z(3)_{\mathrm{A}}$
invariant terms with low mass dimension which cause states to mix according to
$SU(3)_{\mathrm{V}}$ flavor. For homochiral multiplets, which begin with that
including the $\phi(1020)$, there are no $Z(3)_{\mathrm{A}}$ invariant terms
with low mass dimension, and so states are diagonal in flavor. In this way we
predict the flavor mixing for the heterochiral multiplet with spin one, as well
as for hetero- and homochiral multiplets with spin two and spin three.
