The essential centre of the mod a diagonalization ideal commutant of an n-tuple of commuting hermitian operators

We show that for a commuting n-tuple of hermitian operators, with perfect spectrum, the essential centre of the algebra of operators commuting with the n-tuple mod a diagonalization ideal arises from the C*-algebra of the n-tuple. This answers a question for normal operators and the Hilbert-Schmidt class connected to K-theory for almost normal operators.