How do eighth note triplets work in 9/8 or 6/8 time? I know in 4/4 they take up the space of two eighth notes but haven't been able to figure out how they work in 8.
Lee is right, but there is a simpler way to think of triplets. Typically we break notes up into sets of 2 (or duples). For example, two half notes make a whole note, two quarter notes make a half notes, two eighth notes make a quarter note etc.
All a triplet is is putting 3 notes where 2 normally go. So 3 eighth note triplets will always equal a quarter note or two normal eighth notes. In 9/8, you only have 4 pairs of eighth notes and 1 unpaired so you cannot have a whole measure of eighth note triples. You can have up to 13 eighth note triples, then you need something to take up the last 1/3 of an eighth note (aka a sixteenth note triplet).
I think triplets are always 2/3 of the duration of the 3 notes regardless of the meter indicated by the time signature.
So a triplet of quarter notes will take up the space of a half note (or two quarter notes).
A triplet of eighth notes will take up the space of a quarter note (or two eighth notes).
...and so on.
I pulled up some useful links in discussion, for further information:
The question has already been answered correctly by Lee and Dom, but I would like to add some pictures as clarification...
I don't have an example right now from an actual piece, though I'm quite sure I've seen something similar. Anyway, it's not hard to come up with your own examples, so here's one which shouldn't even sound that odd:
This should at least show that it is completely possible to have 8th note triplets (top staff) in 9/8 which are different from the triples (bottom staff) of 8th notes associated to the time signature.
You can also see how it works. As has been said, you just cram 3 8th notes where two would go. The following way of writing might make it easier to see:
In the first beat you play three against two as usual for the first two eight notes, and then play one more eight note.
Of course, you can also cross beats like this:
This might be quite rare in general (and if the pattern continues, I would probably write the time signature for the top staff (or both staves) as (3/4)+(3/8)). It is certainly not exotic compared to a lot of contemporary classical music, though.
I suspect that there might be some confusion in the question. As I see things, 6/8 is a way of notating a 2/4 rhythm whilst showing that there is a triplet beat; 9/8 is a way of notating 3/4. I came to this backwards, hearing songs which I considered to be in 12/8 then discovering that they were notated in 4/4.
One can count songs both ways as the rhythm can be discerned on two levels: the 'outer' level having four beats to a bar, and the 'inner' level in which each beat is further subdivided into three beats (triplets). 4/4 is the 'outer' rhythm and 12/8 in the 'inner' rhythm.
I would be curious as to see a real life example as to why this would happen. Time signatures at there core tell you how many beats there is in a bar and also what each beat consists of. When you take 3/4 time. It tells you in essence that we have three beats of crotchets.
If you would take this and make a compound time signature you would basically put a dot next to the groups of crotchets giving you three groups of dotted crotchets or 9/8 time.
If you take 3/4 and make a full bar of triplets you in essence also have nine notes but they are played slightly differently. You would have three notes played in the time of two, played three times in the bar.
This is slightly different to 9/8 where you just have 9 quavers in each bar.
They should be approached slightly differently although the playing has only a slight difference between the two.