If we take out the sharps and flats, I'm wondering if all scales need to be in alphabetical order in terms of their letters: A,B,C,D,E,F,G where 'A' comes after 'G'.
no repeating notes: A,A#,B,C,D,E, etc.
no skipping notes: A,C,D,E,etc.
no combining flats and sharps: A,B♭,C#,etc.
Therefore the scales are always in alphabetical order and each note is different. (?)
So the scale of C minor:
C, D, E♭, F, G, A♭, B♭
The scale of F# major:
F#, G#, A#, B, C#, D#, and E#
So if we don't look at the flats then the scales satisfy the above conditions. Is this true for all scales/modes in music? I'm guessing this is some kind of agreed upon convention to make things easier to memorize because it's just alphabetical order at that point. So the only thing we have to memorize is how many sharps or flats are in each scale.