Why is A sharp and the same as B flat?

Answer 1

On a keyboard, there is no semi-tone between these two notes.

They are not the same note, though. The difference is theoretical, but that's the topic here, isn't it? It comes down to what is known as spelling.

For example, if we were talking about english words, you might ask why is c the same as k? Kake (cake), kat (cat), cing (king), and cnocc (knock) are all misspelled words despite a sonic similarity.

The question is where is that note likely to go. D-flat is more likely to lead to C or E-flat, whereas C-sharp is more likely to head for D or B. Like much of life, it's all a matter of context.

Actually, before 12-tone standard A440 equal tempered tuning, C♯ and D♭ we're two different notes! These two notes we're in the places of our modern-day black keys but we're split so the note at the the top would play C♯ and the bottom note would play D♭, these we're called "split sharps" but nowadays C♯ and D♭ are played on the same key due to the so called "wolf" intervals (e.g in that tuning system from G♯ to E♭). The sharps and flats in those days we're two awful sounding pitches and back the C♯ was a bit flatter than the modern C♯/D♭ and the D♭ was a bit sharper that the modern D♭/C♯. In those scales the notes would have went C, C♯, Db, D, D♯, E♭, E, F, F♯, G♭, G, G♯, A♭, A, A♯, B♭, B and C - totalling 17 notes.

Answer 2

The note A is one tone lower than the note B. Western music is divided into semitones (or half tones) so there is only space for one note between A and B.

So, A sharp (one semitone HIGHER than A) and B flat (one semitone LOWER than B) must be the same note.

Answer 3

D# is not the same note as Db. D# is Eb