  The spectrum of Harper's equation is determined by the discriminant, which is
a certain polynomial of degree Q if the commensurability parameter of Harper's
equation is P/Q, where P, Q are coprime positive integers. A simple expression
is indicated for the derivative of the discriminant at zero energy for odd Q.
Three dominant terms of the asymptotics of this derivative are calculated for
the case of an arbitrary P as Q increases. The result gives a lower bound on
the width of the centermost band of Harper's equation and shows the effects of
band clustering.
  It is noticed that the Hausdorff dimension of the spectrum is zero for the
case P=1, Q infinitely large.
