A grandfather clock (with a pendulum) keeps perfect time on earth. if you were to transport this clock to the moon, would its period of oscillation increase, decrease, or stay the same?

The period of a pendulum is inversely proportional to the square root of the gravitational acceleration in the place where the pendulum is pendulating.

In other words, the stronger gravity is, the faster the pendulum swings, and the weaker gravity is, the slower it swings.

Your pendulum clock that's perfectly accurate on Earth will run slow on the Moon. You'll need to tinker around, making the pendulum quite a bit shorter, to make it keep accurate time there. You'll burn up valuable mission time messing with the grandfather clock, where a $1.50 Mickey Mouse quartz watch would have done the job.

It would increase due to gravity being decreased on the surface of the moon