  We prove an inequality for the number of periods in a word x in terms of the
length of x and its initial critical exponent. Next, we characterize all
periods of the length-n prefix of a characteristic Sturmian word in terms of
the lazy Ostrowski representation of n, and use this result to show that our
inequality is tight for infinitely many words x. We propose two related
measures of periodicity for infinite words. Finally, we also consider special
cases where x is overlap-free or squarefree.
