Answer: Scales are patterns of steps, not specific pitches. A major scale, for example, consists of these steps: whole, whole, half, whole, whole, whole. If you begin on C it's a "C major scale" and you're in the "key of C." Depending on the pitch you choose to start the pattern with, any pitch is a possible member of the scale. But people are often curious about pitches like B# and E# (and Cb and Fb) because the only way to play them on the piano is to use a white key: C for B# and so on. So the question arises: why do we bother with pitches like that anyway?

Most familiar melodies are based on the pattern of whole and half steps found in the major scale. That pattern is represented by the white keys of the piano and also by the natural notes on the staff. If you start on the right pitch you can play many melodies on the white keys only: start on E to play the famous choral theme from Beethoven's 9th Symphony, or on C to play the Beatles' "She loves you," or on G for "Home on the Range." (If you're learning to improvise tunes, try playing just on the white keys for a start).

The pattern formed by those seven notes C, D, E, F, G, A, B is the major scale: whole step, whole step, half step, whole step, whole step, whole step. Start on A and you get the natural minor pattern, A, B, C, D, E, F, G. But suppose you want to play something using that same pattern of steps but starting higher or lower? If that's what you want, you'll need to add some in-between notes, which are represented by the black keys. To play the major pattern starting on F, for example, you'll need to add a Bb, a lower form of B, between the A and the B. To play it starting on G you'll need to use a higher F, F#. This is the origin of the black keys, which are now found between every pair of white keys that is separated by a whole step.

Between B and C and between E and F there is just a half step - no room there for a black key. But there is a reason to have a "B#" and an "E#." For just one example, if you have written a G# in your music and want to make it the root of a major harmony you'll need a major third above it. A third brings you to the third letter, B, but to be major (4 half steps wide) it has to be a raised B: B#. You can't write C as a substitute because that wouldn't be a major harmony; it would confuse the band. C would be a diminished fourth above G# and would have different musical implications.

Since there's no black key between B and C you'll be playing that B# on the same piano key used for C, but that's part of the compromise that makes the piano workable. There was a time when musicians tried making keyboards with separate keys for B# and C, Fb and E, F# and Gb, and all the others, each tuned slightly different - but such keyboards were expensive to make and difficult to use - some had 53 keys to the octave. Musicians compromised by tuning just 12 keys in such a way that C could pass for B#, and so on.

To sum up: B# and E# can indeed be part of a scale, depending on the tonic (starting note) of the scale.