When playing music that is mostly diatonic, like most folk music, the ear expects to only hear the notes that fall within one major scale. This means that the available chords are limited. In a C major scale, you can have C, Dm, Em, F, G, Am, and Bdim. When the melody goes to, say, an A at the beginning of a measure, the chords that might fit in that location are Dm (D, F, A,) or F (F, A, C) or Am (A, C, E). Thus, if you play a D note by itself while the melody is playing that A, the ear will hear a Dm chord. If you play an E, the ear will hear an Am chord. If you play a C, the ear will hear either an F chord or an Am chord, depending on what else is going on around it. If you want it to be more specified than that you will have to play two notes. Since you are more likely to be playing two or more notes anyway, the chord will usually become obvious when heard along with the melody note.
Or not -- you could play a C and an A along with the A in the melody, and the ear could still hear either an F chord or an Am chord and you would have to play all three notes to be completely obvious. Or not -- the rest of the notes in the measure may well define your chord for you, even if you only play one or two notes. For instance, with the A in the melody on the first beat of the measure, you play an A and an F. This could be either a Dm chord or an F chord. But let's say the third beat of the measure has a C in the melody. Now, between the A and the F you are playing, and the the A and the C in the melody, you have a clearly defined F chord. Or not -- maybe when the third beat comes you change to playing an A and an E. Suddenly you have an Am chord on the third beat, just by changing one note by half a step. You can, of course, start adding sevenths to chords and make it a good deal more complicated. It goes on and on . . .

John Peekstok