It may be just out of habit, what with the 12-edo temperament all around us, but anyway: I find the dominant-seventh rendition 20:25:30:36 sounds extremely harsh. In particular, the tritone from the third to the seventh is so wide that it raises suspicions about being just an extremely detuned perfect fifth. Sure, the chord is meant to be dissonant, but like that?
The alternative with a Pythagorean minor seventh 16:9, on the other hand (though requiring higher ratio numbers 36:45:54:64), comes out less jarring. Its tritone is closer to the √2 : 2 we know from 12-edo, which at least makes it much more suitable for tritone-subtitution techniques. Those were after all used a lot in music – not just in Jazz!
What arguments (historical, musical, practical or otherwise) are there, in favour of either of these possibilities? I'd figure there are a lot of considerations about the leading tones etc..
While there are no answers, I tried my best (which isn't very much I'm afraid... overall intonation does not exactly deserve the name "just", but I hope it's good enough to make the issue clear. Anyway...) to contrast the different possibilities.
Here's a simple cadence for string quartet, played six times in a row. Each iteration is identical, except for the V7 chord, which has each time a different ratio of frequencies. It's all the possible ways to do it in random order, with both just and Pythagorean and, for fun, even harmonic seventh (7:4). Each of these was combined both with a just third 5:4, and also with a Pythagorean third 81:64, to make it complete.
Well, for me that has settled the question of what I like best: (Hover cursor to see)
Surprise, surprise! The all-just intonation wins, after all. Within a proper context, it doesn't sound harsh at all but rather "sparkling" and adds the right amount of tension the dominant needs.
The harmonic seventh, as I expected, is right out: it completely undermines the leading melody. The Pythagorean seventh sounds quite ok actually (albeit only together with a just third, otherwise it's much too low in comparison), but it's rather dull compared to the all-just chord 20:25:30:36.
Can you spot which one it is, in the audio file?
Pythagorean third, just seventh.
Pythagorean third, Pythagorean seventh.
3. Just third, Pythagorean seventh.
Pythagorean third, harmonic seventh.
5. Just third, just seventh.
Just third, harmonic seventh.
...Of course, that doesn't answer the question though, it's just a personal impression. What I'd like to know is if that's really the generally accepted way to do it.