Peter -

Don hits some good points.

From the original posting:

"Obviously it varies according to context, but how few notes do you need in order to signify a chord?"

If we discern that you asked how to "signify a chord" as opposed to how to "play a chord," then the answer may be a little different than we have seen thus far.

"I ask this because of thinking about various instruments where you can only get two out of the three note for a chord, ..."

Okay - so you're playing a mandolin???

(It's the lesser evil of the possibilities, since I try to play one myself - which makes it the most obviously beautiful instrument there is. The other possibilities are fiddle, banjo(?) - in standard tunings, mountain dulcimer, and hammered dulcimer - if you only use two hammers.)

If you are attempting a solo piece, you play what you can - and try to make it sound nice. The standard mountain dulcimists mantra of "find a pleasant tone" is the governing rule here. If it sounds right, it is right.

As has been indicated above, the tonic and third notes "define" a chord; so if that's what you play, it should be fairly obvious "to the listening ear."

If you play the tonic and fifth, either a major or minor chord could fit - and the listener may perceive either. The context of the surrounding music will generally "drive" the listener to perceive whichever one "fits" the piece.

If you play the third and fifth, there is the possibility that a listener might hear it as a III-minor chord, but most likely they will fill in what they expect to hear and will get it "right," because of the surrounding structure of the tune.

If it is absolutely necessary that your instrument alone must project the full chord unambiguously, then you probably need to "roll" or "arpegiate" accross the chord, or play alternates, like "walking" a chord on a string bass. You could, perhaps, play either the tonic or 1,3 notes on the "on beat" with 1,5 or 3,5 on the off beats.

Fiddlers tend to think of "doubles" as "augmenting the melody" rather than as an attempt to produce chords. Mandolinists have fallen into referring to what they do as "chording," but it is an abominable corruption of the music to do so. The most common incentive to "chord" a mandolin is in bluegrass "backbeat chops." If this is your concern, note that you are not playing "the music" - you are "simulating a snare drum" - (Bill Monroe's description.)

The chord that can be produced on a mando in full 3 note form are the proof (IMNSHO) that inversions do matter, and generally do not support the stucture of most tunes as well as if you used only the dyads.

In general, as long as both of the two notes you can play are contained in the appropriate chord (or in the chord and immediately adjacent melody) you won't produce any dissonance and you won't detract from the tune.

If you are playing in a group - or even a duet - then, between members, you can produce the three notes needed for a full chord if you agree on an "arrangement" with your partners.

John