  We analyze the spectrum of the exactly duality and gauge invariant
higher-derivative double field theory. While this theory is based on a chiral
CFT and does not correspond to a standard string theory, our analysis
illuminates a number of issues central in string theory. The full quadratic
action is rewritten as a two-derivative theory with additional fields. This
allows for a simple analysis of the spectrum, which contains two massive spin-2
ghosts and massive scalars, in addition to the massless fields. Moreover, in
this formulation, the massless or tensionless limit $\alpha'\rightarrow \infty$
is non-singular and leads to an enhanced gauge symmetry. We show that the
massive modes can be integrated out exactly at the quadratic level, leading to
an infinite series of higher-derivative corrections. Finally, we present a
ghost-free massive extension of linearized double field theory, which employs a
novel mass term for the dilaton and metric.
