Yes, but only with pitch bends. For example the Great Highland Bagpipe is tuned to a just intonation scale, which commonly approximates A Mixolydian (neither a major nor minor scale). (It's actually 3 pentatonic scales overlaid, but let's not get into that...)

Some info: http://publish.uwo.ca/~emacphe3/pipes/acoustics/pipescale.ht...

Getting that to sound right in MIDI requires the use of pitch bends, since MIDI only understands 12 tone equal temperament.