LONG and TECHNICAL
IANAPMT (I am not a professional music theorist) but
as far as I can remember from my long ago theory days, a lot of the difference comes from the relative stress upon the subdivisions of the bar, and the groupings of those subdivisions within a greater rhythmic pattern. Okay, that’s a little obtuse, let’s see if I can clarify it:
In 4/4 or other examples of duple time, there is inherently a downbeat and upbeat - certain styles of music stress one or the other, but they’re always there. The stress can be 1 2 3 4 or 1 2 3 4, but you’re always feeling the duple nature of the beat
In 3/4 time (and 6/8, 9/8, 6/4 and other types of triple time) however, the beat structure breaks down thusly:
1 2 3 | 1 2 3 |1 2 3
Now you can of course stress other beats in triple time, I’m just trying to delineate the difference between duple and triple (and yes there are other types, such as 5/4, 7/4 etc but I was always taught that while yes, there are specific and distinct feels to 5/4, 7/4 etc. the easiest and commonest way to feel them, play them and analyze them is as multiples of 3 and 3 (5/4 = a “bar” of 2/4 and a bar of 3/4, or vice versa)
So…(and I apologize for the above diversion, just trying to forestall the inevitable cry of ‘but what about x?’ where x is irrelevant to my point)…
3/4 or 3/8 is going to be one grouping of 1 2 3
6/8 is going to generally be two groupings:
1 2 3 |1 2 3 written as 1 2 3 4 5 6
with a superimposed stress on one of the subgroups, either in whole or only on the first beat. (Italics indicate a greater stress than just bold)
So you can see that the subgroups are still triple in nature, but the overall bar is duple - 2 groups of 3
9/8 is the same principle - but a triple superimposed beat, so every bar stays triple:
1 2 3 | 1 2 3 |1 2 3 written as
1 2 3 4 5 67 8 9
and played as
1 2 3 4 5 67 8 9
12/8 keeps moving on along, although the superimposed group carries the feel of 4/4 rather than 2/4
And so on…although stress can be put on any beat at any time by the performer or composer, these are the most common, and would tend to be the “default” feels.
Please note that I did NOT discuss triplet feel, swing etc and so no inference should be made about those rhythmic feels.