wow.. 7/8 over 4/4 haven't tried that one for sure...haha
the common ones you encounter are 2 against 3 and 3 against 4. you can flip em over so you get 4 combinations.
it takes time to settle so don't rush it.
once you get the hang of it, try "stacking" patterns. the stacking is kind of my way of understanding and making use of it.
for example, using 2 against 3,
2 plays snare-tom,
3 plays bell-ride-ride
this one's quite safe.
you can experiment and have fun many ways.
i like the 4 against 3 - 2 bar pattern
with the 4, play snare-tom-snare-tom or snare-tom1-tom2-tom1
with the 3, play bell-ride-bell, then ride-bell-ride (oh man if only this forum has built in scoring)
there's a lot of room for creativity for building up your polyrhythm chops so don't be afraid to just go out there and go nuts. you'll find the ones that stick over time are those you can use in the music repertoire you play.
you may also find that you simplify and find more ways to play just one or two of them when you get busier and have less time for just going nuts on the drums. for you younger guys, just play everything to death. it'll pay off real well later....
while at it, polyrhythms are 'intentional' by nature, meaning we write it down and set out to play 2 or more patterns that resolve over time.
i also tend to not want to refer to 2 - 3 as 2 "against" 3 . this is because the nature of using the word "against" makes me feel like its a conflicting (unless i want to introduce tension in the music). i like it that the 2 or more patterns are playing in "harmony"
if i'd write a book, i'd sure to refer to it as 2 "harmony" 3 ... lol!
do check out glenn kotche (wilco) ... in MD interview he mentioned he was intrigued by "accidental" rhythm, ie. the sound of water droplets falling during rain, although there is no premediated pattern (ie. polyrythm) the sound is beautiful. he was encouraged by his lecturer in uni to pursue it. check it up on youtube or something. i love glenn
cheers