I hope that I'm understanding your question correctly.
When working with a metronome, you can set it so that it clicks the
downbeats or
pulses of the time signature you are playing in. With the drum tab that you wrote out in the post, it seems that you would set the metronome to
click with the HiHat, as you stated,
120 bpm, which would be two clicks every second. The
120 beats per minute (bpm) would be set to the quarter note.
In 4/4 or Common Time, which is what this drum tab is in, you would count
1 2 3 4, coinciding with the HiHat. To allow your counting to line-up with the Snare part, you would count eighth-notes (as you already stated):
1 & 2 & 3 & 4 &
or
1 te 2 te 3 te 4 te
To count so that all the parts are included (HiHat, Snare and Kick drum) you would count sixteenth-notes:
1 e & u 2 e & u 3 e & u 4 e & u
or
1 ta te ta 2 ta te ta 3 ta te ta 4 ta te ta
The
bold show where the metronome click would be. Some metronomes provide a way to add eighth-notes and/or sixteenth-notes to the clicks ... so that it would click on every subdivision ... not just the pulse or downbeats. If you metronome does not do this, you would then have to do what you already mentioned which is to speed the metronome up to twice the tempo marking (240 bpm) to cover the eighth-notes which are played by the Snare drum. To have enough clicks to also cover the Kick drum, you would have to double the tempo again so that it's now at 480 bpm. Metronomes typically do NOT go this high. So, the only thing left for you to do is SLOW the entire groove down ... which you should be doing anyway when it's a new beat.
Try playing the groove so that the HiHat (quarter-note) is at
60 bpm. This would mean that you could set it to 120 bpm for the Snare, or 240 bpm for the Kick.
Just remember to work it out
slowly and be able to count and/or sing what it is you are wanting to play. Once you get the groove down, you can speed it back up 120 bpm ... or whatever tempo you are wanting.
