David W. answered 05/07/19
Music Theory Professor and Composer with 5+ Years Teaching Experience
If you're eliminating modes, then you're asking about just major and minor, right? In the major scale, the supertonic triad is minor; in the minor scale, the supertonic triad is diminished.
Both Phrygian and Lydian modes, as well as the much less frequently used Locrian, have major chords built on the 2nd scale degree. But you said you weren't considering modes.