Here's the problem. The third of the chord. Some Appachian tunes vascilate between major and minor. So the third of the chord is deliberately left out.
With the autoharp, you have two choices.
1. Eliminate the third of the chords you are playing.
2. Find out which mode the tune is in and then select the appropriate chords.
IE: Most of the modes you will use will be Myxolydian, Aeolian or Dorian.
Let's take the key of C. Dorian mode is built on the second degree of the scale. The right chords would be D minor, G major and seconarilly, C major. The Myxolydian mode is built on the fifth degree of the scale. The right chords would be G major, F major or D min (as F major and D minor contain two of the same notes). Aolian: A minor, G Major or E minor (as G contains two of the same notes as E minor).
You can break the mode by adding different chords if you want but to emphasize the modal characteristics of the tune, you have to employ some of the essential modal chords.
One of the reasons that the mountain modal tuning was used was to keep the purity of the mode in the tune without clashing in the accompaniment using the third (major or minor third) in the chords. The substitution of the fourth for the third of the chord accomplishes this. It lets the tune breathe without being associated with major or minor tonality.