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We report the discovery of both intermediate-order gravity mode and low-order pressure mode pulsation in the same star, HD 209295. It is therefore both a gamma Doradus and a delta Scuti star, which makes it the first confirmed member of two classes of pulsating star. This object is located in a close binary system with an unknown, but likely degenerate companion in an eccentric orbit, and some of the gamma Doradus pulsation frequencies are exact integer multiples of the orbital frequency. We suggest that these pulsations are tidally excited. HD 209295 may be the progenitor of an intermediate-mass X-Ray binary.

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