I have see this also from modes perspective, but some doubts came up.
Considering only the triads and modes formulas, and because I have only 3 chords (I, VII and IV), it could be G Dorian, G Phrygian, G Aeolian or G Locrian. I made a direct relation between scales degrees and chords, i.e., using modes formulas, we would have the characteristic chords:
Dorian: 1 2 b3 4 5 6 b7 => Bb and F chords
Phrygian: 1 b2 b3 4 5 b6 b7 => Ab, Bb, Eb and Fchords
Lydian: 1 2 3 #4 5 6 7 => C# chord
Mixolydian: 1 2 3 4 5 6 b7 => F chord
Aeolian: 1 2 b3 4 5 b6 b7 => Bb, Eb and F chords
Locrian: 1 b2 b3 4 b5 b6 b7 => Ab, Bb, Db, Eb and F chords
But it makes no sense to see things from this perspective because scales formulas apply to scales degrees. Even if we don't have all chords defined, they are implicitly defined because the 3 chords available contain all the scales notes.
So, it's Mixolydian.
And the F chord can't be considered a borrowed chord from a minor scale because if that was true, it would be borrowed from the A natural minor (but we "need" something in G minor).
Or applying minor scales formulas to the key of G we will get different notes from those we have in the chords.
Harmonic Minor Scale: 1 - 2 - b3 - 4 - 5 - b6 - 7 - 8 (G A Bb C D Eb F#)
Natural or Relative Minor Scale: 1 - 2 - b3 - 4 - 5 - b6 - b7 - 8 (G A Bb C D EB F)
Melodic Minor Scale: 1 - 2 - b3 - 4 - 5 - 6 - 7 - 8 (G A Bb C D E F#)
I believe I'm thinking correctly.


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- that's not what it's for! It's just a system of classification of sounds. (The latin names we give diseases don't explain the disease...)
Please clarify.