7 and 3 = dorian since a dorian scale has a lowered 7th and 3rd compared with its parallel major.7 = mixolydian because mixolydian has a lowered the 7th.When I see '7,' '7 and 3,' and '7, 3, 6,' etc., particularly in that order, I don't think 'oh, that's the order sharps in scale degrees as applied to the major scales,' I think 'Modes!' Here's why: They don't actually look like they represent sharps, do they? They look like they represent the flats of the modes! Now, if you're like me, then the order of sharps represented in scale degrees stood out to you.

Nothing particularly interesting here, just look it over and keep reading below. It lists 1) the order of sharps in notes, 2) the corresponding major scale, 3) the order of sharps in scale degrees, and 4) the corresponding 'C' scale. Observation: the order of sharps, as scale degrees applied to the major scales, if treated as flats, create the order of flats in modes Either way, I'm pretty sure I took the long route to get there, but I'll explain the path I took, and you tell me what you think. Frankly, I can't tell if this is complicated, or extremely simple.

Band order of flats and sharps