piano scale
A♯ major
The seven-note scale everything else is measured against: two whole steps, a half, three whole steps, a half.
The same sounds spelled from the other side are B♭ major.
Written out
Every accidental is written in, rather than left to a key signature, so the letters can be read one at a time.
The step pattern
What is true of it
A♯ major is A♯, B♯, C𝄪, D♯, E♯, F𝄪 and G𝄪, and back to A♯.
Its steps are W – W – H – W – W – W – H, where W is a whole step and H a half.
Written correctly it needs 10 alterations, C𝄪, F𝄪 and G𝄪 among them. That is what the letters force, and it is also why nobody writes music in this key: the same notes spelled from the other side are easier to read.
On the same tonic, A♯ melodic minor differs from it by exactly one note.
It cannot be written as a key signature at all, because a signature has no room for a double accidental.
Chords made only of these notes
Found by testing every chord in the catalogue against these 7 sounds, not chosen.