Given an irrational number α and a positive integer m, the distinct fractional parts of α, 2α, ..., mα determine a partition of the interval [0,1]. Defining d_α(m) and d'_α(m) to be the maximum and minimum lengths, respectively, of the subintervals of the partition corresponding to the integer m, it is shown that the sequence (d_α(m)/d'_α(m))_m=1^∞ is bounded if and only if α is of constant type. (The proof of this assertion is based on the continued fraction expansion of irrational numbers.)