| Summary: | Working on closed Riemannian manifolds the first author and Schueth gave a list of curvature properties which cannot be determined by the eigenvalue spectrum of the Laplace−Beltrami operator. Following Kac, it is said that such properties are inaudible. Here, we add to that list the dimension of the manifold minus three new properties namely <i>k</i>-D’Atri for <inline-formula> <math display="inline"> <semantics> <mrow> <mi>k</mi> <mo>=</mo> <mn>3</mn> <mo>,</mo> <mo>…</mo> <mo>,</mo> <mo form="prefix">dim</mo> <mi>M</mi> <mo>−</mo> <mn>1</mn> </mrow> </semantics> </math> </inline-formula>.
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