  We report a precise match between the high temperature $(D+2)$-dimensional
Tangherlini-AdS black hole and the low temperature quantum phonon gas in
$D$-dimensional nonmetallic crystals residing in $(D+1)$-dimensional flat
spacetime. The match is realized by use of the recently proposed restricted
phase space formalism for black hole thermodynamics, and the result can be
viewed as a novel contribution to the AdS/CMT correspondence on a quantitative
level.
