Question about music theory?

Question

I was looking into major scales, and I came across this.

C maj – 0 sharps

G maj – 1 sharp – F♯

D maj – 2 sharps – F♯, C♯

A maj – 3 sharps – F♯, C♯, G♯

E maj – 4 sharps – F♯, C♯, G♯, D♯

B maj – 5 sharps – F♯, C♯, G♯, D♯, A♯

F♯ maj – 6 sharps – F♯, C♯, G♯, D♯, A♯, E♯

C♯ maj – 7 sharps – F♯, C♯, G♯, D♯, A♯, E♯, B♯

What I want to know is, why are they saying E♯ instead of F, and B♯ instead of C? Or am I confused already?

Answer 1

Why is there an E# in F# and C# major and a B# in C# major? Because those scales already have an F (namely, F#) and C (that is, C#) and the major scale must use each of the seven letters in the musical alphabet. Adding the sharps in the sequence shown preserves the proper intervals within a major scale (W-W-H-W-W-W-H).

Answer 2

yes, exactly.  E# and F are the same note - one half-step up from E; B# and C are the same note, one half step up from B.

This is known as the "Circle of Fifths", meaning that the interval between C and G is a perfect fifth; the same between G and D, and so forth.  Each fifth adds one sharp to the scale.

There is also the "Circle of Fourths", btw, which adds a flat - the C major scale has no flats - move up a fourth to an F major scale and add B-flat, move up a fourth to B-flat and add an E-flat, and so forth.