Why is B flat and not a sharp?

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♯.

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 does A D+ chord mean?

The D augmented chord (D+) is a D Major chord, with a raised 5th. It contains the notes D, F# and A#. Each note of the D augmented chord is separated by an interval of a Major 3rd.

onlineguitarbooks.com - D Augmented Chord on the Guitar (D+) - Diagrams, Finger Positions ...

The D augmented chord (D+) is a D Major chord, with a raised 5th. It contains the notes D, F# and A#. Each note of the D augmented chord is separated by an interval of a Major 3rd. Because every interval inside the D augmented chord is identical, it is known as a symmetrical chord. Another way of looking at this is as follows – If you play an augmented chord starting from any of the notes inside the D+ chord, the new chord will contain the same notes as the D augmented chord:

The D augmented chord contains the notes D, F#, A#

The F# augmented chord contains the notes F#, A#, Cx (that’s C double sharp, which is the same as D) The A# augmented chord contains the notes A#, Cx (same as D), Ex (that’s E double sharp, which is the same as F#)

Some Quick D+ Chord Theory

The D augmented chord contains the notes D, F# and A#.

The D+ chord is produced by playing the 1st (root), 3rd and sharp 5th note of the D Major scale. The D augmented chord (just like all augmented chords) contains the following intervals (from the root note): Major 3rd, Major 3rd, Major 3rd (back to the root note).