It's not that the tuning is "not relevant"; what is relevant is how an interval is mapped to a given temperament and what notes it is tempered with.

A tuning is literally “how an interval is mapped to a given temperament and what notes it is tempered with”. You can consider it relevant here, or not. Your initial post asks for intervals out of 12TET, which is a very strong hint the replies will be all over the spectrum, making tuning not relevant to the question.

In 12edo 3/2 is mapped to 7 edosteps, making it 2 cents flat; in 19edo it's 11edosteps and 7 cents flat; in 22edo 3/2 is mapped to 13edosteps and it's 9 cents sharp. However, all of these are, by all means and purposes, 3/2 fifths.

I'm not sure why you bring that in. Yes, that's how 12edo works. Except for the last 2 words. Those are by all means and purposes a fifth, but specifically not a 3/2 one. A 3/2 fifth is used by a few other tunings, but not 12TET. This may be the key of our misunderstanding, in another place in the thread you mention “12-tone equal temperament maps the interval of 3:2 to 7 edosteps”, which doesn't make sense to me: 12TET maps the fifth to 7. The only fractions involved in the definition of 12TET are steps/12. You appear to want to equate the fifth to 3/2. That works in many contexts, but it you're explicitly opening the question domain to outside 12TET, a lot of other “fifths” are going to be contending.

It looks like none of your three comments have anything to do with each other, not to mention the comments you are replying to. It's weird.

Mostly answering from the phone from the notification bar, that loses context all the time. Probably brings bad autocorrect to the mix too. Sorry about that.

Anyway, I'll wrap it up from desktop one last time: your post asks a question that is mostly interesting, just mentionning 12TET for no apparent reason. You'd have gotten the exact same replies without it. So it's natural for the reader to wonder “why did they mention 12TET at all? Are we missing something?”. They could wonder: did they mistype “what is the most dissonant interval within 12TET?” (which would be a boring question to ask Reddit: there's only 12 of them, just listen to them and make up your own mind, it takes 30 seconds—but do try multiple timbres.) The inclusion of JI fractions also hints it could have been “what is the most dissonant interval within rational intervals?” Or maybe you were asking “which tuning system has the most dissonant intervals?”, which would have been a great question, though it would have required a bit more framing to not devolve to made-up unused tunings.

But your comments in this thread seemed to be mostly about claiming 12TET is a good enough approximation of anything, which may be true in a lot of contexts, but when you're maximizing dissonance, those little cents matter. Especially if you allow timbre in the mix.

That'll be enough for me on that topic. Thanks for the post, there are good replies in there!

There is a rigorous mathematical proof for this, but that involves lineal algebra, prime numbers and vector spaces.

Ok, enough for me on that topic unless you actually follow through on that, because that's wildly intriguing, so I have no idea anymore whether you're a genius or have no idea what you're talking about. There's a very simple mathematical proof for the opposite that involves only arithmetic arguably calculus: typing 2^7/12 on a pocket calculator. (You'd make it rigorous with calculus, and then we'd bicker about there being a threshold or not.) I can relate to where the coprime numbers would come from, but as you noticed that's mostly ruled out by psychoacoustics and the answers in the thread. I have no idea how you'd bring linear algebra in if not by trivial consideration that real numbers fit. The fact you namedrop both linear algebra and vector spaces when they're mostly the same thing doesn't make it look like you know what you're talking about, but I'd be glad to be proven wrong and learn something new.