Traditionally in rock/blues/pop music, the kick/snare drum pattern will match what the bass player is doing, with the snare playing a relatively simple backbeat on 2 & 4 and the kick pedal playing the more complicated stuff. Hi- hat/ride will then play single notes, half notes or quarter notes (in a 4/4 pattern), depending how fast the song is and how good the drummer’s co-ordination is. E.g 1 2 3 4, 1 & 2 & 3 & 4 &, 1 a & a 2 a & a 3 a & a 4 a & a
Fast 1/2 or 1/4 note patterns on the hi-hat will typically be played using both left and right hands on the hi-hat and pull the right hand (right handed drummer) onto the snare on the 2 and 4
Example – https://www.reverbnation.com/chasingglass4/song/23943001-be-my-step-behind
I’m not the best drummer in the world but you can hear in the verse part what I mean about the bass drum and snare matching what the bass player is doing. Or is he matching what I’m doing?
Slower blues or rock songs can go for Triplets on the hi-hat and will sometime miss out the middle note of each triplet to give a shuffle feel. E.g 1 & a 2 & a 3 & a 4 & a… becoming 1 _ a 2 _ a 3 _ a 4 _ a. Again, the kick pedal will typically do the complicated stuff while the snare keeps the rest of the band in time
When I write patterns on a drum machine I personally tend to stick to what I’d do if playing it live
Drum n bass is, by contrast, really busy in the snare/hi-hat/kick combination, usually at very high bpm.