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I was wondering why B and E don't have a sharp?

Yes, they have. They are called B sharp (a.k.a. "C") and E sharp (a.k.a. "F"). The reason why they are not so commonly called like that is because there's a distance of two semitones between each grade of the diatonic scale, with the exception of III-IV and VII-I, which are separated by just one semitone. That's why there are no black keys between those notes on a piano keyboard. More info here.

Hope this helps.
 
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Yes technically they do but we all know what the OP meant... Why don't they have a sharp that isn't also a natural note. And as far as I know it's just how the frequencies were arbitrarily named. But what I wonder is why is the major scale the way it is? Why does that specific order of whole and half steps sound "right" to us? Why not six whole steps? I know a lot of world music uses other scales that may sound weird to our ears but I think it's still enough to make one wonder why those seemingly random half steps stuck arbitrarily in the major scale sound so right...?

Brian
 
Sorry if this comes across as "smart-mouthing", but:

In most cases B# does NOT equal C, or E# equal F. If you're only listening to the notes on a piano, yes. But if you look at them from a functionality aspect theres quite a difference.

For example, a G# major chord consists of the notes G#, B# and D#. Calling the third "C" would not be correct since "C" is the diminshed fourth...lowered from "C#". Same as you can't call the third of a Ab major chord "B#". And you probably wouldn't either....

Of course you all know this and I'm only stating the obvious. And being a smart-*ss. So, sorry.
 
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There is a difference between a C# and a Db... Pianists, bass and guitar players don't have this 'problem', but violin or saxophone players, to name two, do have this 'problem' because they have to intonate correctly, which can be very difficult.

The problem is that each whole tone is actually divided in 9 comma's (http://en.wikipedia.org/wiki/Comma_(music)). With 9 comma's, the semitone in between that whole tone can't be perfectly in the middle 'cause there are 9 comma's and you 'can't' split them in two. So this makes that a C# is actually one comma higher-pitched than a Db as C# lays 5 comma's above C and Db lays 4 comma's below D.

This is also the reason that some piano's are tuned different than others. A common tuning is 'a tad too low in the lows and a tad too high in the highs'. Our ears have accustomed to this. It would sound rather odd if we'd tune our piano's the old way (before J.S. Bach's introduction of the equal temperament). If you'd start on the lowest A, the C on the high end of the piano would be considerably 'too high' to our ears.
 
In response to the OP, I think it's partly because the layout of the piano keybaord predates the naming system. The intervals in a major scale are whole step, whole step, half step, whole step, whole step, whole step, half step. The two half-step intervals create places where there isn't another note bewteen the consecutive notes of the major scale. Piano keyboards are set up so that one particular major scale has all of its notes on white keys, with the remaining five notes on black keys. That scale is called C, and the half step intervals occur between the third and fourth notes (E and F) and the seventh and eighth (B and C). Why is that particular scale called C, and not A? Because the lowest note on the keyboard was arbitrarily called A, and the rest of the white keys just went up the alphabet from there.

So it's partly for a musical reason, and partly just a historical accident. We could probably come up with a better system, but the one we have works and has been around for centuries, so we're kind of stuck with it.
 
... But what I wonder is why is the major scale the way it is? Why does that specific order of whole and half steps sound "right" to us?
That's a good question. It's partly because those notes are close to the harmonic overtones of a vibrating string, so they sound "consonant" (although I seem to recall reading that the notes of the lydian dominant scale are actually closer). The rest of the reason is cultural: we're so used to hearing that series of notes associated with happy lyrics and upbeat music, that we think of it as the "happy" scale.
 
I'm just guessing. I'm quite limited in my early music history. But wasn't early (gregorian chant) music just modal, not chromatic? Let me explain better:

It's my (perhaps false) understanding that early musicians just used different modes within the same key to change tonality, so their entire scale would be all natural, or the C major and all of its related modes. So there wouldn't be a need for sharps or flats would there?

Now when "keys" started developing, people had to obviously name semitones in between the established CDEFGABC scale, and so they placed the sharps where they fit, and therefore leaving E and F without a semitone in between, and B and C. Does that make any sense? It's just kind of a theory I have... Don't flame too bad!!
 
True. It was J.S. Bach who introduced the equal temperament. Remember his 'das wohltemperierte Klavier' (http://en.wikipedia.org/wiki/Well_temperament)?

Indeed, the reason behind why the major scale sounds good is to find in the overtones. Actually, the lydian scale is the most stable, then follows the ionian (= major) scale. The stability of a scale depends on where the half steps are. This also influences the atmosphere / color of the scale. The more in front the half steps lay, the darker / more unstable a scale becomes. From bright to dark, stable to unstable: lydian, ionian, mixolydian, dorian, aeolian, phrygian, locrian.

Anyway, the lydian scale is the most stable 'cause: if you take all the overtones of C, you get:

C, D, E, F#, G, A, B

Of course not in this order, but if you re-order them, you'll get this. George Russell wrote a book about this: "Lydian Chromatic Concept of Tonal Organisation".