  Context. Many well-known bright stars have been observed by the ongoing
Transiting Exoplanet Survey Satellite (TESS) space mission. For several of
them, these new data reveal previously unobserved variability, such as tidally
perturbed pulsations in close binary stars. Aims. Using newly detected
gravity-mode (g-mode) pulsations in V456 Cyg, we aim to determine the global
stellar properties of this short-period eclipsing binary and evaluate the
interaction between these pulsations and the tides. Methods. We model the
binary orbit and determine the physical properties of the component stars using
the TESS photometry and published spectroscopy. We then measure the pulsation
frequencies from the residuals of the light curve fit using iterative
prewhitening, and analyse them to determine the global asteroseismic stellar
parameters. We evaluate the pulsation parameters as a function of the orbital
phase. Results. We find that the pulsations belong to the secondary component
of V456 Cyg and that this star likely has a uniform radial rotation profile,
synchronous ($\nu_{\rm rot} = 1.113(14) \rm d^{-1}$) with the binary orbit
($\nu_{\rm orb} = 1.122091(8) \rm d^{-1}$). The observed g modes are amplified
by almost a factor three in the stellar hemisphere facing the primary. We
present evidence that this is caused by tidal perturbation of the pulsations,
with the mode coupling being strongly affected. Conclusions. V456 Cyg is only
the second object for which tidally perturbed high-order g-mode pulsations are
identified, after $\pi^5$ Ori. This opens up new opportunities for tidal g-mode
asteroseismology, as it demonstrates another avenue in which g modes and tides
can interact with each other.
