  General Relativity (GR) is shown to be a complete theory with respect to the
isochrony of the pendulum. This guarantees that time can be measured with a
mechanical clock within the theory itself as a matter of principle. The proper
and coordinate oscillation frequencies of a simple pendulum are computed as a
function of 3 coordinate parameters: the distance of the fulcrum to the gravity
source, its length and the Schwarzschild radius. Novel GR effects appear in the
Schwarzschild coordinates as divergences, zeroes and other instabilities of the
oscillation frequencies that are absent in Newtonian gravity. The anomalies in
the proper and coordinate frequencies occur under extreme conditions: either
the fulcrum or the pendulum mass or both remain inside the Event Horizon.
