I'm assuming that each tube is set up as a normal (-ish!) clarinet, fully chromatic over its range, and that the two tubes are tuned a quarter of a tone from each other.
MusicalPanda – quarter-tones are half semitones – so, for instance, midway between C and C# you'd find C-quarter-sharp. Midway between C# and D you'd find C-three-quarters-sharp (or D-quarter-flat).
Here's some further reading (and the infamous clarinet pic):
So if they played a chromatic scale it'd sound more like a glissando then anything? I can't imagine all that much music has quarter tones written into it. Hmm very interesting. I once read somewhere about a piano with like 16th tones... I can't imagine the notes sound too much different xD.
The Sydney trad community has (or, until very recently, had) Albert, Oehler and Hammerschmidt (same as Oehler??) players ... not to mention the occasional appearance of the saxello and tarogato. But the Romero instrument beats that lot hands down! Looks like you'd need hands and toes ...