Mode formulas made simple

First we divide the modes according to whether they are major or minor.
Then we compare the major modes to the major scale and the minor modes to the natural minor scale.

Major modes (by definition modes with a natural 3rd)

Mode 1 = IONIAN = same as major scale
Mode 4 = LYDIAN = major scale with #4
Mode 5 = MIXOLYDIAN = major scale with b7

Minor modes (modes with flatted 3rds)

Compared to Natural Minor Scale (b3,b6,b7)

Mode 2 = DORIAN = natural minor scale with natural 6th
Mode 3 = PHRYGIAN = natural minor scale with b2
Mode 6 = AEOLIAN = same as natural minor scale
Mode 7 =  LOCRIAN = natural minor scale with b2 and b5