The other day I saw this question here:
I got really excited, as this has been bugging me for many years now. I started reading the answers, but they seem to answer a slightly different question than mine, and possibly different to that of the OP. Definitely a different question than I thought OP was asking. But the question was marked as answered, so I decided to write my own question instead of initiating a discussion in the comments.
The answers to @JessicaCunningham 's question make fine job explaining how time signatures like 3/4 and 3/8 are written differently. Some then go on to explain how 3/8 and 3/4 sound different, but they don't explain WHY they are different, except for "that's just the way it is"-type answers.
What I'm dying to know is: Is there some rule (or even a tendency or pattern) that tells you how stuff played in X/2, X/4, X/8 etc sound different, given a positive integer X?
NB: I don't care about the notation. I can read the different signatures, but this question is rather about the music than about the notation.
Following a convention defined on a case-by-case basis works great when playing "normal" music, but it only gets you so far. I know how 6/8, 3/4, 3/8, and even 7/8 sounds, but it would be great to be able to say anything at all about the sound (not the notation!) of 4/2, 3/16, 10/2, 10/4 etc, except for what I'm told by the numerator of the fraction.
I do suspect no such rule or pattern exists, except for higher denominators sometimes indicating faster pace.* I'm just griping for straws. In that case, all the information about the rhythm carried by the denominator could just as well be carried by a non-numerical name, like we do with Greek names of modes, but we just happened to choose numbers for historical reasons.
If this is how it is I'm totally fine with that; I'm not here to complain about tradition. I'm asking just in case there is something there. It would be so nice to actually understand what is happening and not just learn a bunch of cases by heart!
*I've seen What is the difference between 3/2 and 3/4 time signature and Is there any practical difference between 3/4 and 3/8 time? and What makes a composer decide between time signatures 3/4, 3/8, or 3/2?. They suggest larger denominators suggest quicker pace, but in my experience this isn't always the case. Also, we already have separate notation to tell us the number of beats per minute.
I maintain this is not a duplicate, as the kind of answer I'm looking for (what the rule is or a firm "there is no rule", in either case with some motivation) isn't given in any of the questions I've read. As everyone seem happy with the answers, I conclude they answer a different question then mine.