(I'd like to clarify that this is the first time that I'm approaching scales and modes)
I was searching for the key of this song when I've found that it's in G major, but if it's from G major where the F chord came from? Thanks!
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I think most of the song is in G Maj (G Ionian mode), but the chorus is in F Maj (F Ionian):
The verse, including the vocals and guitar solo, all include the F# from the G Maj scale. This is cleary in G Maj (ionian).
Before reaching the first F (on the line "Momma's gonna make all of you nightmares come true"), the F is approached from C, which is the fifth in F Major (ionian) scale, so this seems to be a typical modulation into a new key, using the dominant of the new key (V --> I , C --> F).
The chorus not only includes the FMaj chord, but the vocals also hit a Bb, further supporting the new F Major (Ionian) feel.
I guess I must make clear as well, as it is pretty common in this site, that songs do not need to include only diatonic chords. In this case there is a clear modulation into a new key for a section of the song, but there are plenty of cases where a song just includes one chord that does not fit in the key, so expect to encounter this in the future!
You are right that F is a chord that can be built from the G mixolydian scale but like @hirschme’s answer says this song is simply in the key of G major with a 1-4-5 or G C D progression (FYI the V chord built on a mixolydian scale would actually be a D minor chord). Usually modes don’t represent keys but rather are scales that offer different colors as an alternative to regular major and minor scales.
I am not saying that @hirschme’s answer is right or wrong because in analysis more than one thing can be right but to me it sounds like the second section is in C major, a modulation to the IV of G and the F chord serves as a IV chord in the key of C. My reasoning is the melody, phrasing and lyrics seem to resolve to the C chord in this section that goes back and forth from F to C. The primary melody note on the F chord is an A and on the C chord is G to C which makes the C sound like the tonic. At the end of this section it goes from C to G which sounds like a IV-I modulation back to G.
This song has a complexity within it’s simplicity. The great thing about analysis is that people can have different interpretations and justify them in different ways. The beauty is the music and the creativity comes first and then we all say: “Wow, that’s great, what was that?” and then try and figure it out.