Hi John!
I'm not sure what your question is but I'll give it a try.
You ask if you can use either F or F# as a key.
If that's right, my answer is neither.
The key is the comfort zone of a song. The tonal center.
If a melody starts with the note G there are, and I'm not overstating,
about a hundred chords (if you count all twelve keys(though math
is not my strong side)) you can harmonize to that G. So a single note
is not a ground for choosing or determining the key.
The rest that I write is about pop/country music. Not classical or jazz.
Chords are harmonization. Turning a melody into chords is not as straight
forward as it could appear. Most of us, I assume, play what sounds right/nice/
interesting/fresh when we choose chords. But theory can always, for better or worse,
be applied. So how does it work?
Well If a song starts on the note G then goes to A then E then C what chord should we use?
There are two obvious chords C(6) or Am(7). Why? Because most(all) of those notes are
within those chords. And as a bonus a tonal center is presented. And since the keys
C and Am are using the same notes there is no conflict between them in the aspect
of harmonization. They use the same chords C Dm Em F G Am Bdim(almost the same as G7).
If as you described, not use the notes F or F# you use the chords C Em G Am?
I might bee mistaken but the give a good example.
Those chords give the notes C D E G A B. So what key?
The short answer is that the first chord you use establishes the key.
Possible keys are C major E minor G major A minor. If the key is C you lack
the very common chord F(substitute Am), if its Em you lack B(m) the very useful dominant chord.
And so forth. So looking at the chords are not the way to go.
We need to go back to the melody.
Let the melody tell you the chords. Unless you know how to write notation or have prefect
pitch it's difficult but you can take out the melody on your instrument.
You then add up the notes, for an example the first bar, and look at how the melody flows.
Is the melody climbing eg C E F A and then needs to go 'back' to G. I'd harmonize it
with the chords C then F then home to C. (But Am Dm C would be an option).
So as a conclusion to this huge post. Most of it is up to you but don't hesitate to flirt with
the Minor or Major parallel-key. I'm sure I've been too easygoing with music theory
at some places so feel free to correct me. And please ask if you need further clarification.
Best regards,
- Martin