We study the most general deformations of Fourier-Mukai transforms on families of complex tori. We investigate the relationship between Fourier-Mukai duality and the representation theory of motives and use this to motivate the necessity of considering noncommutative deformations. We prove that the formal gerby deformations of a torus are Fourier-Mukai dual to formal non-commutative deformations of the dual torus, thus verifying on the formal level a conjecture of Kapustin and Orlov.