  Previous studies of incommensurate systems concluded that critical scaling in
such systems is sensitively dependent on the irrational, $\alpha$, which
determines the incommensuration. Contrary to this belief, in the canonical
Harper-Hofstadter model, we show there is universal $\alpha$-independent
scaling for almost all $\alpha$. This critical scaling is characterized by
non-power law time-length scaling $t \sim r^{\zeta \log \log r}$. We
demonstrate this in the superfluid fraction of a Bose gas, and the heat
capacity of a Fermi gas. We argue that this scaling is generic of a broad class
of incommensurate models.
