Since I predicted a war I may as well take part.

Richard, your very informative notes (above) include, under "There were seven Greek Modes (The white notes on a piano)." the following:

"lonian (our major modeNodus lascivus)       C to C"

which is correct, and:

"Mixolydian       C to C"

which is not.

Of course, one can play a Mixolydian scale from C to C, but not on the white notes.