Hey Matt...this may have been written in F# for no better reason than that was the first chord.

When the original demo was made none of these people played well enough and Sly Stone had to play all the instruments. Grace Slick did teach Jefferson Airplane how to play the song. She was married to the drummer.

The half step up or down is pretty common in any key. F# to G in this case. It is easy to hear and recognize.

The A C D A by it could be in the key of A but there is no C major in the key of A.

This song became very popular for a number of reasons, not the least of which was the fact that the singer/songwriter was a very good looking fashion model. Looking back it was a prototypical vision for the Haight Ashbury LSD drug culture.

It is still being used in 2020 in TV commercials and film.

Billy
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Sears, Roebuck and Co guitar, Black Diamond Strings, RCA Victor Radio