> I'm in a song in C major and I often see Emaj and Amaj appearing.
My question is where are Emaj and Amaj borrowed from?

These are really E7 and A7 chords, meaning that there is a flatted 7th. You don’t have to play that, but it would be wrong to play something like EMaj7 ar AMaj7, at least very few songs would ever do that, and it might be considered out of the key of C if you did it.
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Here is the theory behind it.

In the key of C, in addition to the chords in C, the dominant 7th approaches to each of the chords are allowed, and seen often. This brings in all these chords, G7,A7,B7,C7,D7,E7,F#7. Of those chords these ones are used very commonly C7, D7, A7, E7, G7
G7 -> C
A7 -> Dm
B7-> Em
C7 -> F
D7-> G
E7-> Am
F#7-> Bdim
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It is important to realize this, because the Emaj is really an E7. And the AMaj is really an A7. Of course it is fjne to play just an E or A chord, but if you need to okay the 7th of the chord, it would be the flatted 7th, or if you need to solo over the chord, you should be thinking of E7 (not EMajor scale, which doesn’t have a flatted 7th).

The chord builder in BiaB is a good place to see what chords belong in the key of C (or any key you set it to.
Because each row brings in new chords.
Row 1 are the diatonic chords
Additional rows bring chords like
- the dominant 7ths above
- chords from the key of Cm, which brings in nice chords like Fm and Bb7 to they key of C
- Cdim7 and related Ebdim7, F#dim7

Inside the chird buikder, you can just click on those chords and see how they sound. If you stick to row 1 (diatonic), you’re sure to get a “normal, nice” chord progression, it would be hard to come up with something bad, and then start experimenting with the lower rows.

Here is a pic of the chord builder. Note that you need to press “show more” to see all this.

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Have Fun!
Peter Gannon
PG Music Inc.