Sorry if my first reply seemed a bit flippant. I guess it was but there was also an important point I wanted to make: When we compose polytonal or atonal music it's easy to end up with the process becoming more important than the result. That's good if it's only intended as an exercise in composition techinques but not really if the purpose is to write a piece of music that's actually meant to be performed.
tony wrote:With this approach, esp. with contrary motion, lines will cross. Hindemith and Fux have specific rules about this. I dont know if these same rules apply here.
They may but not necessarily. I think it's important to realise that the purpose of the classical choral harmonisation and polyphony rules is to create the fullest possible sound with a relatively limited number of voices within a relatively limited harmonic framework.
In bitonal music the challenge usually is to achieve clarity, not fullness.
tony wrote:Lets say I'm using the key of C (main key) against the key of Gb. There is a 2 measure passage on the G7 chord. Lines cross and F simultaneously comes together with Gb (F#). So you have a b7 and a MA7 on the Dominant chord (on a strong beat/downbeat).
The key word in such a situation is separation. It has to be clear to the listener that the Gb belongs to the Gb major element while the F belongs to the C major element. You can achieve this by placing the two keys with two different instrument groups (if you're wiritng for an ensemble) or in different ranges (if you write for a solo instrument).
tony wrote: I wouldnt expect normalcy as it would have an atonal character to it, more or less.
Do not confuse bitonality with atonality, they are two completely different ideas. In bitonal music we want to establish and maintain two different tonal centers at the same time. Atonal music has the opposite aim, to avoid any tonal centers completely.