Peter T., I think I now understand one of your earlier questions. Maybe you've worked out the answer yourself by now, but anyhow:

If you want to generate a mixolydian scale by lowering the 7th of a major scale on the same tonic, then, yes, you do "take into account" the sharps or flats of the major scale. If you want to generate X-mixolydian from X-major, and X-major has Z at the 7th, then you change Z to Z-flat. If X-major has Z-flat at the 7th, then (assuming 12-equal temperament) you lower Z-flat to (Z-1)-natural. If X-major has Z-sharp at the 7th, you lower to Z-natural.

If you want to generate X-dorian by taking X-minor and raising the 6th, and X-minor has Y at the 6th, then you create X-dorian by raising Y to Y-sharp. If X-minor has Y-flat at the sixth, you create X-dorian by raising to Y-natural. If X-minor has Y-sharp at the sixth, you create X-dorian (assuming 12-equal temperament) by raising Y-sharp to (Y+1)-natural.

To answer another question, yes, the X-dorian created by raising the 6th of X-minor is the same X-dorian that you get by a cyclic permutation of (X-1)-major. The X-mixolydian you get by lowering the 7th of X-major is the same X-mixolydian you get by a cyclic permutation of (X+3)-major.

T.