The relation between Hodge theory of a smooth subcanonical \(n\)-dimensional projective variety \(X \subset \mathbb P_{\mathbb C}^N\) (i.e. \(\omega_X = \mathcal O_X(m)\) for some \(m\in \mathbb Z\)) and the deformation theory of the affine cone \(A_X\) over \(X\) is investigated. It is proved that there is a canonical isomorphism \[ (T_{A_X}^0)_m =H_{prim}^{n,0}(X) . \] If \(H^1(X,\mathcal O_X(k))=0\) for all \(k \in \mathbb Z\) then there is a canonical isomorphism \[ (T_{A_X}^1)_m =H_{prim}^{n-1,1}(X) . \] If also \(H^2(X,\mathcal O_X(k))=0\) for all \(k \in \mathbb Z\) then there is a canonical isomorphism \[ (T_{A_X}^2)_m =H_{prim}^{n-2,1}(X) . \] Moreover the whole primitive cohomology of \(X\) can be identified as a distinguished graded component of the Hochschild cohomology module of the punctured affine cone over \(X\). The results are used to compute Hodge numbers of smooth subcanonical projective varieties. The corresponding Singular code is given.