Why do we need note names like B♭, D♭ etc.? Why not use only A♯, C♯ and so on?

Question

The very same sharp/flat tones can be written in two ways:

• C♯ is the same as D♭
• D♯ is the same as E♭
• …and so on

This is so confusing. What is the reason for it? Wouldn't it be easier to use only X♯ or only X♭?

Answer 1

The equivalences you mention---C♯/D♭, D♯/E♭, etc.---aren't actually the same note. They're called enharmonically equivalent pairs, but only in Equal Temperament are they tuned to the same frequency. See this question for more information on why they're not the same note.

As for why we need flatted notes at all, let's look at the how major scales are put together. We need to agree on these things:

• Every major scale has seven notes. They all start on a root note and proceed to go up in the following pattern: Whole Step, Whole Step, Half Step, Whole Step, Whole Step, Whole Step, and then a final Half Step returns to the root note (an octave above where we started).
• A major scale names each of its seven notes using the letters A, B, C, D, E, F, and G exactly once. It's important not to use the same letter twice because otherwise notation would be really inconvenient. Imagine if your major scale had both an F and an F♯ in it. Then every time you wrote a note in the first space of the treble clef, you'd also have to explicitly tag it with an accidental, either natural or sharp. What a pain, both for the composer and the reader. Key signatures avoid this problem, but they only work if we agree on this no-using-the-same-letter-twice rule.

With these two principles in mind, let's build an F Major scale:

We start with F. A whole note up and we get to G. Another whole note, and we have A. Now the first half-step. What is this note? It can't be an A♯, because we've already used A. It can't be a B♮, because B is a whole step up from A. It has to be some kind of B, but a half-step lower than B♮. And so: B♭.

Now that we've invented B♭, let's create the B♭ Major scale: B♭, C, D,... uh-oh. Guess we need an E♭. And when we create the E♭ Major scale, we'll have to create an A♭, etc. etc.

Of course this same idea justifies the existence of sharped notes as well. Create the G Major scale, and when you get to the seventh note you find that you've used up all the letters except F, yet you need a note a whole step up from E (or, if you like, a half step down from G). And so you're forced to create F♯.

One could ask why it is that the interval from E to F need be a half step. If E to F were a whole step and F to G a half step, then we wouldn't need an F♯ to make the G Major scale. This is true, but it's also robbing Peter to pay Paul: then the D Major scale would still require a C♯, while the C Major scale would now require an F♭.

Answer 2

C# is not the same as Db any more than the English word "hear" is the same word as "here".

Understanding why there is a difference is an important foundation to Western melody and harmony. It's important to understand the following:

• 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)
• each letter name is only used once amongst the diatonic notes
• 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 A major. The diatonic notes are: A B C♯ D E F♯ G♯. What does C♯ mean? It means the third note of the scale. What does D♭ mean? It means you've taken the fourth note of the scale and lowered it it.

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 A major scale, you can only write it C♯ and not D♭. C♯ means something completely different.

In non-12-et tunings, they won't even sound the same.

Answer 3

The flats and sharps came about separately as modulations toward the subdominant and the dominant, respectively. The subdominant is more important in older western music and church music. The dominant modulation was a more recent development.

So going from C to F is a modulation toward the subdominant. To modify the lydian mode (C scale starting on F, w-w-w-h-w-w-h) into the Ionian mode (F scale starting on F, w-w-h-w-w-w-h) means the fourth (B) has to be flattened (B♭).

To go from C to G is a modulation toward the dominant. To modify the myxolydian mode (C scale starting on G, w-w-h-w-w-h-w) into the Ionian mode (G scale starting on G, w-w-h-w-w-w-h) means the seventh (F) has to be raised (F♯).

Additional sharps and flats in the key signature represent further deviations from the C-Major scale; but always they are patching the fours and sevens to realign the modes.

Answer 4

Because they are not really the same, only in equal temperament tuning they are. Look here: http://en.wikipedia.org/wiki/Enharmonic.