  We prove estimates on the H\"older exponent of the density of states measure
for discrete Schr\"odinger operators with potential of the form $V(n) =
\lambda(\lfloor(n+1)\beta\rfloor - \lfloor n\beta\rfloor)$, with $\lambda$
large enough, and conclude that for almost all values of $\beta$, the density
of states measure is not H\"older continuous.
