Using F major chord on a song in the key of G
So I was looking at the chords of a simple song in G major scale. The only 3 chords it's using are G, C and F, all major.
i don't understand from where you get the Fmaj? if it was F#min, that makes sense to me. Is this as a result of mixing G and F scales together?
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This is simply called borrowing. In this example, it is most likely borrowing from the key of C major (C, F and G are very commonly used chords in this key) as C is the 4th of G.
One could also consider the use of F major as a way to bring in the dominant 7th of G - dominant 7th of G is F whereas the major 7th is F#.
“Key of G” means only in the simplest sense that all your notes come from the G Ionian scale. The F note is borrowed from the nearby Mixolydian mode. This is very common in blues, pop and many folk styles.
The song has a tonal base of G major. This is not the same as 'using only the G major scale'. As you have discovered! No need for any special justification. Just know that the bVII chord (In the key of G, that's F major) is frequently used to add a bit of colour.
Often this sort of thing is explained with parallel keys. Songs in G major can use the notes, therefore the chords, from G minor. In Gm (natural) there are F A and C, producing the F chord. So it's sort of in the family. That apart, in the key of C, the three prominent chords just happen to be C, F and G. The difference here is that most songs in G will have the F# note (usually accompanied by a D chord, sometimes Bm or F#o). Using an F note in the melody sometimes has G7 under it, but the F chord fits sonically, if not in the basic theory.
If you want to look at it from a different perspective, think modally. G Mixolydian contains the same notes as C major, so the F chord could be construed to come from that.
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