  We initiate the analysis of the Kaluza--Klein mass spectrum of massive IIA
supergravity on the warped AdS$_6 \times_w S^4$ background, by deriving the
linearised equations of motion of bosonic and fermionic fluctuations, and
determining the mass spectrum of those of spin-2. The spin-2 modes are given in
terms of hypergeometric functions and a careful analysis of their boundary
conditions uncovers the existence of two branches of mass spectra, bounded from
below. The modes that saturate the bounds belong to short multiplets which we
identify in the representation theory of the $\mathfrak{f}(4)$ symmetry
superalgebra of the AdS$_6 \times_w S^4$ solution.
