A tritone interval by itself (only 2 notes sounding) sounds quite dissonant to me.

But in the context of the dominant 7th chord, the only note dissonant with the bass is the 7th. The tritone itself is not so prominent since it occurs between two non-bass notes.

In some musical cultures it's also totally acceptable and featured all the time, without being considered dissonant.

Yes, this understanding would mean the 12-bar blues and blues music in general are an extremely dissonant form as they use the dominant seven chords as tonics.

How many people consider the blues dissonant?

It reminds me of my first counterpoint assignment. "Fourths aren't dissonant" I said, and it came back covered in red marks

I assume most people would find a dominant dissonant. A V7 is difficult to figure out. A V9 sounds better.

To say blues doesnt sound dissonant sounds more like only adding the relative minor b5. Or British blues rock.

V7 are bog standard in blues and rock, and nowhere near hard to figure out or sounding dissonant.

And other cultures like tritones just fine, featuring them even more prominently.

There's no inherent "tritones are dissonant" human universal, it's a common practice harmony prejudice.

7 chords are dissonant. That’s why a (ii-)V7-I works. Dominant creates tension that gets resolved, or not.

But the chord function is only one third of the picture. Dominant chords can have greater or lesser tension depending on which extensions are used. A closed voicing will sound more dissonant than an open one.

I understand dissonance to be how big the numbers are when you express an interval as a reduced frequency ratio. By that metric it's pretty dissonant. How can it be considered moderately dissonant?

Yes, a tritone is dissonant because it isn’t close to any simple ratio of frequencies. It has a spiciness that makes the music sound interesting without it being overly unpleasant.

Avoiding dissonance entirely can also be unpleasant. e.g. barbershop harmony can sound saccharine because the human voice can hit those simple ratios much closer than 12TET can. 12TET gives us some dissonance for free, which people have learned to appreciate. Like spice tolerance, dissonance tolerance is learned not inate.

A minor second is very dissonant, you can hear pronounced beating between the tones: https://en.wikipedia.org/wiki/Beat_(acoustics). This makes it stick out more than a tritone, so it has to be balanced more carefully.

For me, I don't think it's meaningful to think of two notes in a vacuum as anything. The logical part of me wants to think about it with math like you're suggesting, but 2 notes lack any context to give them meaning. Add another two to the chord or add other notes around it temporally, and now they don't sound bad at all. The idea of consonance and dissonance only makes sense to me within the framework of tension and release.

> now they don't sound bad at all

I didn't mean to suggest that dissonance has any correlation with good/bad.