  I discuss the range of validity of Detweiler's formula for the resonant
frequencies of rapidly rotating Kerr black holes. While his formula is correct
for extremal black holes, it has also been commonly accepted that it describes
very well the resonant frequencies of near extremal black holes, and that
therefore there is a large number of modes clustering on the real axis as the
black hole becomes extremal. I will show that this last statement is not only
incorrect, but that it also does not follow from Detweiler's formula, provided
it is handled with due care. It turns out that only the first n <<
-log{(r_+-r_-)/r_+} modes are well described by that formula, which translates,
for any astrophysical black hole, into one or two modes only. All existing
numerical data gives further support to this claim. I also discuss some
implications of this result for recent investigations on the late-time dynamics
of rapidly rotating black holes.
