key: C lydian
mode: C D E F# G A B
melody: D R M f (r) l (t)
form: verse-chorus
meter: duple
English function names: tonic supertonic
Tagg (modified): home counterpoise (away)
Riemann: T ???
Scale degrees: I II
Chords: C D
C D
|:/ / / / |/ / / / :| loop
How sure are we that this is I-II in lydian and not VII-I in mixolydian? Or something else? The melody doesn't help much, because it doesn't lead us to either C or D. It spends most of the time starting on G, which would be the relative major/ionian mode of this pitch set. G, however, is a member of the C chord, and would emphasize its supremacy over the D chord for the choice of tonic. Yet, even though the phrases start on G, they end on A, because the D chord in play for the second half of the loop. So which is the tonic?
This is the same conundrum that the far more famous Fleetwood Mac song "Dreams" presents. The chords shuttle between F and G in that song, but the melody of the chorus most definitely cadences on C.1 Rick Beato feels that the song is in C and that the chord functions are subdominant to dominant and that it's the greatest two-chord song ever written because of the inherent complexity of both following (melodically) and not following (harmonically) common practice rules. If you've been following along, you can probably guess how I feel about that.2
In Traditional Classical Music Theory® thinking, you can't really have a song that never has the tonic chord. But we are open to suggestions here in two-chord land. Riemann can't help us here, because he just didn't have this situation in mind when he came up with his theory. In classical music, you actually don't find a whole lot of songs in lydian. Same with European folk music. There are absolutely examples, but it's distinctly less common, which is why it doesn't show up in the theory.3
This is where we turn to our old friend Philip Tagg. In Tagg's view (ears? what's the equivalent?), two-chord songs are often tonicless, instead presenting two harmonic poles of their own, which occupy equal air time. The point is not creating a sense of direction toward a harmonic goal, but more of a state of being. Flux, perhaps? Instability? "You haven't cooled down," as the lyrics in our song example here say. Having a melody that also does not reinforce either root of either chord on top of these fluctuating harmonies helps support this preference for a state of being over a sense of direction.
Unfortunately, that's the alternative — no definitive answer. There is no tonic, just a diatonic pitch set in which no one pitch is emphasized enough to create a sense of gravity around it. Unlike "Dreams," where the melody is clearly in C so we can argue, as Beato asserts, the chords have to be subdominant and dominant, here the melody isn't clearly in G or A or C, and neither are the chords. What one hears may be entirely dependent on prior listening habits.
The internet may tell you A minor, I'm guessing because the verses start on A, but I'm going to veto that.
But if you can't guess, here goes: He doesn't actually say that in his video about "the greatest" two-chord songs, because he doesn't give any explanation whatsoever about why these three are the greatest. But I find the implication of much of his shpil is Harmonic Complexity is God. For me, this explains why he is incapable of thinking of any "good" songs with just tonic and subdominant off the top of his head. His worship of harmonic complexity deafens him to some of the very obviously fine songs with only two chords, that I'm sure he's heard, but has dismissed from the get-go. Not to mention that there is more to a great piece of music than the choice of harmonies.
Overtone flutes, common in the Carpathians and the Tatras among other places, play a lydian scale, due to their lack of fingerholes. One is strictly bound to the harmonic series when you just have an open pipe: