Halve the hi-hat and the backbeat grows. Exercise 1 is the basic backbeat you built in the foundations with one change: a quarter-note hi-hat, four hat notes per bar instead of eight, all of them closed, kick still on 1 and 3, snare still on 2 and 4. The snare reads louder even though you are playing it exactly as hard, because there is no longer a stream of cymbal notes crowding it. Classic rock, mid-tempo rootsy rock and a lot of songwriter material live in this texture, and it is every bit as canonical as the 8th-note version.
Keeping time with half the hi-hat
Cutting the cymbal in half cuts your reference points in half too. Four hat notes a bar means the 8ths in between now come from you rather than from the cymbal, and Ex 1 and Ex 2 both run at ♩ = 104, well above the ♩ = 80 where you first built this groove. At that tempo the click lands on the same grid as the hat, so run it and try to make the two one sound. If you can still pick the hat out of the click, the quarters are not placed yet, and playing it faster will not place them.
The thin texture also exposes your hands. Every backbeat in this lesson is a hi-hat and a snare struck together, one attack out of two limbs, with no other voice sounding at that instant to hide a mismatch. Loop Ex 1 slowly enough to hear whether 2 and 4 arrive as a single event or as a small flam, and fix that before you push the tempo. You never need to muscle the snare to be heard here; the empty space is doing that work for you.
Taking a note out, then putting one back
Ex 2 is Ex 1 with exactly one note removed. The snare on 2 is gone, so the bar reads as three beats of setup and an arrival on 4. Two things go wrong. The first is filling the hole on 2 with something, anything, because the gap feels like a mistake. The second is subtler: shift the whole bar two beats and the kick pattern looks identical, with the snare now falling on 2, so nothing inside the bar rules out that reading and the time can quietly turn around on you. Count 1 2 3 4 out loud and let the metronome check you: on 4/4 it accents beat 1, so your kick should land on the accented click. Then run Ex 1 and Ex 2 back to back without stopping; they share a tempo and a kick pattern, and the switch between them is one note appearing and disappearing.
Ex 3 puts a note back where it costs something. The kick doubles at the top of the bar, on 1 and the & immediately after, which makes that second stroke the only note in the lesson that does not share an attack with a hi-hat quarter. It has to sit exactly halfway between the hat on 1 and the hat on 2, and the usual miss is late, dragging toward beat 2 until the figure sounds like a stumble instead of a shove into the bar. Ex 3 runs at ♩ = 100 rather than 104, and the extra room goes into placing that second kick. Keep the hat hand indifferent to the foot: if the cymbal flinches or swells when the kick doubles, split the limbs apart and rebuild the bar from the feet up.