I dunno, if you ever played a brass instrument, then you're playing on an (approximately?) just-tempered scale -- each valve combination is a harmonic series starting from the 2nd harmonic. Whether it's just-tempered over the entire scale depends on the way the valves are tuned, I guess, and it's likely that the tuning reference is equal-tempered most of the time, so it's kind of a hodgepodge. It probably has a name.
I play brass (trumpet) and was always warned on assuming the tuning was accurate; even with the perfect player using the perfect compensation on the relevant valves the lower notes are definitely iffy (they tend towards flat and the compensation slides can't push them sharp).
That perfect player is improbable though. On the lower notes I can bend them by in the order of a quarter tone without touching the valves. If I pick up the instrument on a cold day without first warming it, not just me, up then it will be probably a quarter tone or so flat for the first few minutes. If you leave it on your chair and come back to find someone's turned the heater on while you were away (happened to me before), it can easily be a semitone sharp, IF it's cool enough to hold in the first place!
I love my trumpet but it's one of the last instruments I'd use to illustrate really precise tuning.
> This is used to lower the pitch of the 1-3 and 1-2-3 valve combinations.
In other words, the tuning slides described in that section of the article are solving a different problem (which is described in a bit more detail in the previous section). As a1k0n said, a given valve combination is a harmonic series. If you play a major third on a trumpet without moving your hands, the distance between the notes will be 386 cents, not 400. Of course, a good player will do whatever they need to do to sound in tune with whoever they're playing with. My understanding is that the lips are the main thing used to get harmonics of a particular valve combination in tune with each other.
