Chords come in all combinations. People have scoffed at the idea of two note chords saying that they aren’t chords. The dry definition of a chord is any combination of at least two different notes played together. The fact that current western music prefers three note chords as a minimum is neither here nor there in the context of traditions from around the world, including those of afro roots. I have been playing two note chords on my harmonium since yonks. I find them more evocative and open than the clamping 3 noters. Two note chords can invite greater melodic freedom and innovation.
I would say two notes and only just those two notes played together, separate from any other context, are an interval.
Those two notes played together in the context of music imply a chord; in fact, the ear will often “hear” (or actually, the brain will provide) the missing third note. This is what allows us to recognize a harmonic progression in a duet, for instance.
Guitar players also sometimes refer to the interval of a perfect fifth as a “power chord,” but that’s a special case and usually is referred to in the context of rock music.
This is a very minor point, however; in general usage, you are correct that two notes played together function as a chord.
we play two note (we refer to them as "partial) chords on mountain dulcimer all the time. Since it’s a diatonically fretted instrument, we don’t have (unless we retune) all there notes of a chord, but we have one or two. If I’m playing backup, especially, I’ll “fit” with what others are doing on chromatic instruments (like guitar), even though I’m not carrying the chord itself.
Since a dulcimer has only three strings (in most cases) I also have to make a “choice” when it comes to sevenths, etc. Depending on the song, I’ll just play the root chord - or I may drop one the 3rd or 5th to add the 7th. But, of course, I’m not playing a “full” 7th.
Playing “partial” chords also allows a dulcimer to keep a drone going - which in many cases is what MAKES the sound of the dulcimer.
They don’t call it a “power chord”, but lots of modern Bluegrass players commonly omit the third from the root chord. Back in about 1997 or so, there was a big flamewar on the Bluegrass-L mail list that might’ve started when Sonny Osborne made some disparaging remarks about this practice–and its practitioners.
One reason that I recall being given for omitting the third is that improvised melody lines can move more readily between major and minor without clashing with the backup.
[quote=“talasiga”] Two note chords can invite greater melodic freedom and innovation.
… it depends entirely on the genre of music involved. Jazz routinely
employs very complex, discordant harmonies involving multi-note chords
which in no way restricts the melodic freedom and innovation of the
player. Indeed, improvisation, freedom and innovation are the very
essence of that music form, however, clearly a basic tonic-dominant
drone style harmony can be an appropriate and fertile foundation for
the typical modal folk melody.