The following beat explanation and adjustment procedure has been borrowed from another clockmaker who didn’t attach his/her name to it, and I can’t remember what decade it was that I first copied the file:

As each escape-wheel tooth slides off the pallet, it gives the pallet a little push, or impulse. That impulse travels down the crutch to the pendulum. The little push in each direction is what keeps the pendulum swinging instead of running down.

THIS PART IS IMPORTANT — PAY ATTENTION:  In order for it to work, the pushes have to happen at exactly the right moment in the pendulum's swing, in order to assist it instead of interfering with it. That moment is when the pendulum is about to change directions.  If the push is before the change of direction, it will be pushing one way while the pendulum is traveling in the other, slowing the pendulum instead of helping it. If the push is after the change of direction, the pendulum has moved away and the push misses its target. When the pushes, or impulses, occur at the wrong time, the clock is "out of beat" and the pendulum will eventually stop swinging. When it's out of beat, the push in one direction is too early and in the other direction it's too late.

Each impulse is accompanied by either a "tick" or a "tock". So when the clock is out of beat, one will be too early and the other too late in the pendulum's travel. Their sounds will be uneven.

The crutch is the part that delivers the impulse to the pendulum, so the crutch is what determines when the impulses will be given. Putting the clock in beat is therefore a matter of adjusting the crutch. Let's talk about that.

Imagine a line that extends along the pendulum rod at the moment when the pendulum is exactly halfway between tick and tock. I call that line the "beat-center". The pendulum passes back and forth across the beat-center in its progression from tick to tock and back. The clock is in beat when the beat-center is perfectly vertical: tick and tock are equal distances from the vertical line.  Vertical is determined by gravity. Imagine it as a line from the suspension post to the center of the earth: straight down.

Beat-center is determined by the angle of the crutch relative to the escapement (the pallets up there, interacting with the escape wheel).

There are two ways to align the beat-center to the vertical. One way is to rotate the clock, by lifting one side or the other.  The other way is to adjust the angle of the crutch relative to the escapement.

Imagine that the beat-center is deflected to the right. That is, the line runs somewhere between the vertical and the lower righthand pillar nut. (If it were a hand, and you were looking at the dial, it would be pointing at 5.) Now imagine how you would have to rotate the clock to bring the numeral 5 to the bottom, so the hand is pointing straight down. Correct-o. You would rotate it clockwise, by lifting the lefthand side, until the hand (the beat-center) is vertical.  Imagine again that the beat-center is deflected to the right. You want to move it to the left, so it will be on top of the vertical line. Since the crutch loop determines the location of the beat-center, adjust the crutch to the left until the two lines coincide. 

 "Tilt her 'till she ticks with pride, then adjust the crutch to the high side."

If the crutch is a wire, adjust it by bending it in the desired direction. If it's not a wire, it's attached to the verge arbor with a friction clutch. Adjust it by holding the verge steady and pushing the crutch in the desired direction.

You can usually tell which way the crutch needs to be adjusted, without tilting the clock, by manually moving the crutch one way until an escape tooth releases; note how far its line is from the vertical. Move it the other way until an escape tooth releases; note how far its line is from the vertical. If one distance is larger than the other, shrink it by adjusting the crutch in that direction, until the two distances are equal.

Finally, to determine when the beat-center is vertical, listen to the tick and the tock. When a clock is in beat, it produces a rhythmic, even, steady: 

tick...tock...tick...tock

When it is out of beat, it produces an uneven, "galloping":

TICK...tockTICK...tockTICK...,or

tickTOCK...tickTOCK...tickTOCK...

If it is badly out of beat, the uneven rhythm is quite obvious. But as it gets closer to in-beat, it gets closer to even, and you may have to listen carefully, for a while, to decide whether it's really even or just close.

When a clock is out of beat, the "tilting test" can clearly reveal the difference. Tilt it one way. If it gets worse and quits,

tilt it the other way. As you gradually raise one side, you can hear the beat even out, until at a certain point it really is just:

tick...tock...tick...tock...

That's the sound you want to recapture when you make the clock level, and adjust the crutch to "the high side".

When they are perfectly even, you've got it: the pushes are synchronized. And now you know what's going on, and why.