Quantum Hall effect (QHE) has been theoretically predicted in 4-dimensions and higher. In hypothetical $2n$-dimensions, the topological characters of both the bulk and the boundary are manifested as quantized non-linear transport coefficients that relate to higher Chern numbers of the bulk gap projection and winding numbers of the Weyl spectral singularities on the $(2n-1)$-dimensional boundaries. Here, we introduce the concept of phason engineering in metamaterials and use it to access QHE in arbitrary dimensions. We fabricate a re-configurable 2-dimensional aperiodic acoustic crystal displaying the 4D QHE and we supply a direct experimental confirmation that the topological boundary spectrum assembles in a Weyl singularity when mapped as function of the quasi-momenta. We also demonstrate novel topological wave steering enabled by this Weyl singularity.
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