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Why is B flat not a sharp?

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.

jtauber.com - Why A-Sharp is Not B-Flat - James Tauber

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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♯.

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What is the a below middle C called?

This is an issue of what we call octave designation. There is actually an international standard here: called International Pitch Notation (IPN), it labels Middle C as C4. An octave above Middle C is C5, an octave below Middle C is C3, etc.

music.stackexchange.com - How do you refer to a note that is more than one octave above or below ...

This is an issue of what we call octave designation.

There is actually an international standard here: called International Pitch Notation (IPN), it labels Middle C as C4. An octave above Middle C is C5, an octave below Middle C is C3, etc. In short, the C's octave range is in play until the next C changes the octave register. In other words, from C3 to B3 is all X3; it's not until C4 that pitches enter the X4 octave. The G below Middle C, for instance, is G3, because it's within the C3 to B3 range. The G at the top of the treble clef will be G5. Lastly, sometimes accidentals can be a little tricky. Imagine the B♯ that's enharmonic to Middle C. It's raised from B3, but it's enharmonic to C4. In this case, we focus on the note name. Since it's a chromatic alteration of B3, it's B♯3, even if it's enharmonic to C4. I should also mention another system, that of Helmholtz notation, which uses a mixture of capital/lowercase letters and sub/superscript slashes: It functions in a very similar way that the above IPN does, it's just a different labeling system.

In my experience, C4 as Middle C is very much the standard.

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