Why A-Sharp is Not B-Flat

I've talked before about note naming but because I was recently IMing with a friend about why A♯ != B♭ I've been thinking about a simpler way to explain it. It also explains why you can have double flats and double sharps (leading to 35 possible note names for 12 different pitches). Here goes...

• the vast majority of western music involves 12 notes in an octave
• the vast majority of western music is based around a scale consisting of 7 of those notes specific to the choice of key (the notes are called the diatonic notes for that key)
• a particular note in a piece is functioning either as a diatonic note or as a note a semitone higher or lower than a diatonic note
• when expressing a note that is functioning as a raised or lowered note, you use the same letter name as the diatonic note you are raising or lowering. e.g. a raised G is G♯ and a lowered G is G♭.
• if the diatonic note is already written with a sharp, the raised note has a double sharp and the lowered note has a natural symbol
• if the diatonic note is already written with a flat, the raised note has a natural and the lowered note has a double flat
• but in all cases, the letter part of the note name stays the same

So, imagine you're in the key of Gm. The diatonic notes are: G A B♭ C D E♭ F. What does A♯ mean? It means you've taken the second note of the scale and raised it. What does B♭ mean? It means the third note of the scale.

In 12-tone equal temperament, they may sound the same; you may play them the same on the piano or the guitar. But if the function of the note at a particular point in the piece is as the third note in the Gm scale, you can only write it B♭ and not A♯. A♯ means something completely different.

It's the musical equivalent of "hear" versus "here". Just because they are homophonic doesn't mean they are the same word. Similarly, in western tonal music B♭ doesn't mean the same as A♯.