In a way that is related to a half step in music, like when you play the next key on a piano.
This word is used in music and is not very common in everyday talk.
Examples:
She played the notes semitonically.
The music went up semitonically.
He moved his fingers semitonically on the piano.
The cat walked semitonically across the keys.
The sound went semitonically higher and higher.
The music teacher showed us how to play semitonically.