#1
I was doing some finger picking before and came up with a progression I like, but I can't figure out what key it is. Well, maybe it's not exactly a 'progression', it's just two chords, but I'm still not sure.

The first chords is just the simple first-position C, so I thought it would be in C major, but the second chord is an F/A#, played like so:

e |--x
B |--1
G |--2
D |--3
A |--1
E |--x

I've tried to go back and make it fit by playing the A string open but it doesn't sound nearly as good to me, but I don't know what key would fit having both an A and an A# while still being almost exactly like C. Can anyone help me out?
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#2
the A# is a Bb so you have a C going to F4. Dominant to tonic in the key of F.
#3
Sounds to me like a chromatic alteration in C major.

It does look a lot like a V I in F major, but that Bb destabilizes the F chord a lot, thus making me believe that C is the tonic.
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