  We study the spectrum of fermions hopping on a chain with a weak
incommensuration close to dimerization; both q, the deviation of the wave
number from pi, and delta, the strength of the incommensuration, are small. For
free fermions, we use a continuum Dirac theory to show that there are an
infinite number of bands which meet at zero energy as q approaches zero. In the
limit that the ratio q/delta ---> 0, the number of states lying inside the q =
0 gap is nonzero and equal to 2 delta / pi^2. Thus the limit q ---> 0 differs
from q = 0; this can be seen clearly in the behavior of the specific heat at
low temperature. For interacting fermions or the XXZ spin-1/2 chain, we use
bosonization to argue that similar results hold.
