the Moyal space with usual Dirac operator is a spectral triple, the corresponding spectral action was computed in [@nc-S], with the result that it is the usual not renormalizable action on Moyal plane. In [@8-dim] H.Grosse and R.Wulkenhaar, in order to obtain a gauge theory with an oscillator potential via the spectral action principle, used a Dirac operator constructed using the statement $ \mathcal{D}^2= H$ where the four dimensional Laplacian is substituted by the four dimensional oscillator Hamiltonian $H = -\Delta+\Omega^2 ||x||^2$. The idea behind is that the spectral dimension is defined through the Dirac operator so the spectral dimension defined by such Dirac operator is related to the harmonic oscillator phase space dimension. It turns out that to write down an Dirac operator, so that its square equals the 4D harmonic oscillator Hamiltonian, is an easy task using eight dimension Clifford algebra. In addition, can be shown that using this Dirac operator on 4D-Moyal space, is possible define an eight-dimensional spectral triple. After defined the Dirac operator with the desired spectrum it is considered the total spectral triple as the tensor product of the “oscillating” spectral triple $(\mathcal{A}_4, \mathcal{H}_4, \mathcal{D}_4 )$ with an almost-commutative triple and then is perform 