If you were jamming with someone and they asked you "what key?", then you would say "G# minor" to get them in the ballpark. If we think on the A chord as the outside chord, as Wurlitzer suggested above, then this tune is G# aeolian (scale of B major) and G# phrygian (scale of E major) for a bar when the chord is A.
To be "in a minor key" though it would have a D#7 - G#m cadence which uses the harmonic or melodic minor. Without that it's modal and uses modes of major scales.
House of The Rising Sun is in a minor key and has a real minor sound because it uses the natural, harmonic and melodic minors :
Am C (natural) D (melodic) F Am C (natural) E E (harmonic) Am
There's also a well used progression :
Am G F (natural) E (harmonic) Am
If that was
Am G F Em Am
It would be modal.
For a real theory-fest if the A chord in Frank's tune was A7 it would be more like a minor key because A7 is a tritone substitution for D#7. In A7 the third is C# and the seventh is G. In D#7 the seventh is C# and the third is F## (=G). A7 is D#7b5b9 which works in a minor key. A7 brings in a G (F##) note (the major seventh of G#) from the harmonic minor.
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Chords progression of one of my songs - phrygian mode?
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