Imagine if you will, a chromatic harmonica that can change keys.
So, you have a standard C/C# harmonica, that has seven secondary buttons somewhere that changes every note by a semitone. You might press the B button, and drop the B on the C scale to a Bb, thus changing that deck to F major, but it also changes the B# (enharmonic C) to B natural, thus changing the C# to a .... whatever that works out as. My theory knowledge doesn't extend that far.
And here's where (and why) I need your help.
I have a string instrument on the way to me, which pretty much works this way. Imagine it like a concert harp but with two sets of strings which cross over. One string juts out so you can pluck it at the top, but falls behind the other strings at the bottom, and the next is prominent at the bottom so you can pluck it, and ducks behind the others at the top. So if you pluck them or strum a glissando at the bottom of the instrument, you'd get the diatonic "slide out" scale on a corresponding harmonica. Pluck the strings or strum a glissando at the top of the instrument, you get the opposing diatonic "slide out" scale on a harmonica. There are seven levers, all of which change A, B, C, D, E, F, and G by a semitone on both sets of strings (the levers are actually arranged by circle of fifths).
I have so far gleaned that with all levers "open", the lower scale strings should be tuned to Eb. As you close each lever in turn, one note on each string set goes up a semitone, and that lower scale first becomes Bb Major (by sharpening all the As), then F Major (by sharpening all the Es), then C Major (by sharpening all the Bs), and so on. Where my limited theory fails me, is what the OTHER strings should be tuned to, so that the upper scale always gives the opposing scale for all the accidentals, no matter what the lower scale is set to. Note that when all the As on the lower scale are sharpened, to go from Eb major to Bb major, all the As on the upper scale are sharpened too.
I'm asking about this here on SlideMeisters, as the instrument in question is actually Ukranian, and I can't find what I need to know in any English language reference site, and the chromatic harmonica is the only other instrument I know of which has this upper deck/lower deck complimenting diatonic arrangement to give a full chromatic scale. If there's a table somewhere of keyed chromatic harmonicas, which shows all the various pairings I might be able to figure it out from that.
Apologies if I made anyone's brain hurt, but of all the instrument forums I'm on, I figured you lot would be the best folks to ask.