  We derive a new class of correlation Bell-type inequalities. The inequalities
are valid for any number of outcomes of two observables per each of n parties,
including continuous and unbounded observables. We show that there are no
first-moment correlation Bell inequalities for that scenario, but such
inequalities can be found if one considers at least second moments. The
derivation stems from a simple variance inequality by setting local commutators
to zero. We show that above a constant detector efficiency threshold, the
continuous variable Bell violation can survive even in the macroscopic limit of
large n. This method can be used to derive other well-known Bell inequalities,
shedding new light on the importance of non-commutativity for violations of
local realism.
