Time signatures are about writing and reading music. A beat being in 3 or 6 is independent from the time signature, which is whatever the transcriber thought best (you can always count a song in 6 in 3.) A piece in 4 might have pervasive use of triplets, so it would make it more readable to notate in 12/8 rather than 4/4, but there is no triplet-pervasiveness threshold for when to prefer one over the other. Likewise, it would be foolish to have the stress in a waltz occur on the 1st and 4th, then 3rd, then 2nd beat of the bar (this happens if you notate one in 4), but any enterprising composer would be able to thwart any rules you cared to come up with to codify that without much effort.So: the time signature just describes how many times to count within a bar/measure, and what subdivision (that corresponds to a certain notation) you are counting. For communicating to another musician the rhythm of a song you'd just drop the subdivision part, because it's only relevant to notation.

 > you can always count a song in 6 in 3.You would lose something by doing so; when a song is written in 6 it's because (unless someone is playing silly buggers) it has some kind of 1-2 pattern. For a lot of songs in 6, if you want to count something smaller you're better off counting it in 2s (with some level of triplet-pervasiveness).
 As someone who casually plays the guitar and piano and understands the basics of time signatures, your explanation left me more confused and almost forgot what I already know. You seem like a very knowledgeable person, but don't seem to realize that what is common knowledge to you is meaningless technical jargon to everyone else.
 That’s fair, but my assumption was that someone reading my reply would also have read the others, and I didn’t want to repeat what has already been said.

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