How to figure out time signature of complex type

Here according to me the left side time signature is 9/8 and the right side is 4/4. Am I going down the right path or are my thoughts wrong ?

• One important point: You can't necessarily determine a time signature just by looking at the music. You can rule many out, and you can make common-sense guesses (these examples let you do both pretty conclusively). But material in 4/4 and in "cut time" (2/2) would look the same; the difference would be in what is thought of as the beat. Nov 3 '21 at 19:37
• @AndyBonner while it's true that there will be some pieces, or at least some measures, that could be written identically in 4/4 and 2/2, many will be identifiable as one or the other from internal clues. For example, it's pretty clear that the second excerpt here is 4/4, as I suspect you will agree. Nov 5 '21 at 15:10
• @phoog There's a "high probability" that it is (if for no other reason, simply because common time is, well, more common, and there's no particular reason to suspect 2/2). I just wanted to make the point, though, since this came along as one of a rash of questions starting from the assumption that one can accurately reverse-engineer a time signature by looking at the notes (and confusing time signature with meter). Nov 5 '21 at 15:17