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"What's the black key next to G on the piano?" Haha! You might be surprised how many people ask that question! And it's understandable when learning the notes on the piano. The black keys on the piano form two "groups" or "sets" - a "set of two" and a "set of three." Well, that black key next to G is...
An F#? A Gb? ...
Or is it a G# or an Ab?
It's all of these! Naturally, it depends what direction you are going on the keyboard. When you go to the left of a white key on the piano by a half step to a black key, the key you land on is referred to as a "b" or "flat." So the black key to the left of G is a Gb. However, if you think of this black key as being a half step higher than F, then it's an F#, since when you go right from a white key on the piano by a half step to a black key, the key you land on is referred to as a "#" or "sharp."
Regarding that black key to the right of G... well, the same rule applies. If you think of that key as being a half step higher than G, then it's a G#. If you think about it as being a half step lower than the A (white key next to the G), it's an Ab.
So, yes, both black keys have two names... and this is commonly referred to in music as enharmonic spelling.