What property of a pendulum did Galileo study in the early 1600s?

Galileo studied the isochronism of a pendulum—the near independence of its period from the width of a small swing.

According to accounts of his experiments beginning around 1602, Galileo investigated how a pendulum’s length, bob, and swing affected its timing. He recognized that small oscillations take approximately equal amounts of time even as the swing gradually becomes narrower. That regularity made pendulums promising for measuring time and comparing durations.

The result is only approximately true. For larger amplitudes, a pendulum’s period increases slightly, so broad swings are not perfectly isochronous. Christiaan Huygens later analyzed this limitation and developed the pendulum clock, publishing his major treatment in 1673.

A common mix-up is confusing isochronism with independence from mass. Galileo also investigated that a pendulum’s period is essentially independent of the bob’s mass, but the defining property highlighted in this question is isochronism: equal timing for swings of different small amplitudes.