  The increase in glacial cycle length from approximately $41$ to on average
$100$ thousand years around $1$ million years ago, called the Middle
Pleistocene Transition (MPT), lacks a conclusive explanation. We describe a
dynamical mechanism which we call Ramping with Frequency Locking (RFL), that
explains the transition by an interaction between the internal period of a
self-sustained oscillator and forcing that contains periodic components. This
mechanism naturally explains the abrupt increase in cycle length from
approximately $40$ to $80$ thousand years observed in proxy data, unlike some
previously proposed mechanisms for the MPT. A rapid increase in durations can
be produced by a rapid change in an external parameter, but this assumes rather
than explains the abruptness. In contrast, models relying on frequency locking
can produce a rapid change in durations assuming only a slow change in an
external parameter. We propose a scheme for detecting RFL in complex,
computationally expensive models, and motivate the search for climate variables
that can gradually increase the internal period of the glacial cycles.
