  Given a constant magnetic field on Euclidean space ${\mathbb R}^p$ determined
by a skew-symmetric $(p\times p)$ matrix $\Theta$, and a ${\mathbb
Z}^p$-invariant probability measure $\mu$ on the disorder set $\Sigma$ which is
by hypothesis a Cantor set, where the action is assumed to be minimal, the
corresponding Integrated Density of States of any self-adjoint operator
affiliated to the twisted crossed product algebra $C(\Sigma) \rtimes_\sigma
{\mathbb Z}^p$, where $\sigma$ is the multiplier on ${\mathbb Z}^p$ associated
to $\Theta$, takes on values on spectral gaps in the magnetic gap-labelling
group. The magnetic frequency group is defined as an explicit countable
subgroup of $\mathbb R$ involving Pfaffians of $\Theta$ and its sub-matrices.
We conjecture that the magnetic gap labelling group is a subgroup of the
magnetic frequency group. We give evidence for the validity of our conjecture
in 2D, 3D, the Jordan block diagonal case and the periodic case in all
dimensions.
