Xurtio

The full C major scale is [C D E F G A B]. As the lyrics are said here are the chords played:

C "Well it goes like this"
F "The fourth"
G 'The fifth, the"
Am "minor fall and the"
F "major lift"

So the tonic (I) is played first, then the F, which is the fourth (notice it's the fourth letter in the scale, and same with G). Then they go to an A minor chord: the B falls back to an A and a G falls back to an E on open chords on the guitar, then they go up to an F chord (a major chords as well as the fourth) in which E->F, A->C.

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