  Our purpose is to give an account of the $r$-tuple problem on the increasing
sequence of reduced fractions having denominators bounded by a certain size and
belonging to a fixed real interval. We show that when the size grows to
infinity, the proportion of the $r$-tuples of consecutive denominators with
components in certain apriori fixed arithmetic progressions with the same ratio
approaches a limit, which is independent on the interval. The limit is given
explicitly and it is completely described in a few particular instances.
