Let $\mathbf{ T}_{ d, N}: \Omega \to \mathbb{ R}^{ N^d}$ be a random real symmetric Wigner-type tensor. For unit vectors $(u_N^{ (i, j)})_{ i \in I, j \in [d-2]} \subset \mathbb{ S}^{ N-1}$, we study the contracted tensor ensemble \[ \left(\frac{ 1}{ \sqrt{ N}}\mathbf{ T}_{ d, N}\left[u_N^{ (i, 1)} \otimes \cdots \otimes u_N^{ (i, d-2)}\right]\right)_{ i \in I}. \] For large $N$, we show that the joint spectral distribution of this ensemble is well-approximated by a semicircular family $(s_i)_{ i \in I}$ whose covariance $(\mathbf{ K}_{ i, i'}^{ (N)})_{ i, i'\in I}$ is given by the rescaled overlaps of the corresponding symmetrized contractions \[ \mathbf{ K}_{ i, i'}^{ (N)} = \frac{ 1}{ d(d-1)}\langle u_N^{ (i, 1)} \odot \cdots \odot u_N^{ (i, d-2)}, u_N^{ (i', 1)} \odot \cdots \odot u_N^{ (i', d-2)} \rangle, \] which is the true covariance of the ensemble up to a $O_d(N^{ -1})$ correction. We further characterize the extreme cases of the variance $\mathbf{ K}_{ i, i}^{ (N)} \in [\frac{ 1}{ d!}, \frac{ 1}{ d(d-1)}]$. Our analysis relies on a tensorial extension of the usual graphical calculus for moment method calculations in random matrix theory, allowing us to access the independence in our random tensor ensemble.
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