OK, so each fifth of a scale moving clockwise adds a sharp to that scale and each fourth (counter-clockwise) adds a flat to that particular scale.

When we find ourselves at F# or Gb we have six sharps or six flats respectively.

If F# (F#-G#-A#-B-C#-D#-E#-octave), the 7th degree would be the 6th sharp - E#. E#? This is F. Right?

If Gb (Gb-Ab-Bb-Cb-Db-Eb-F-octave), the 7th here is indeed F, but the 4th would have to be Cb - which is B?

What is the reason for noting it that way?

If F# (F#-G#-A#-B-C#-D#-E#-octave), the 7th degree would be the 6th sharp - E#. E#? This is F. Right?

No, E# is not F. Ok, so the pitch is the same. E# and F are the same pitch. They sound the same. But from a theory standpoint they are different notes. the F# major scale has no F natural in. Only an E# and an F#.

If Gb (Gb-Ab-Bb-Cb-Db-Eb-F-octave), the 7th here is indeed F, but the 4th would have to be Cb - which is B?

No again, same reason. Cb and B are the same pitch, but are different notes.

If you're asking why the same pitches are notated in different ways (e.g. it's called E# in one and F in the other) - that's how the system works. See, in a major or minor scale, there is always one of each note name, and every note name is used. So, every scale has an A (flat/sharp/natural), then a B (flat/sharp/natural) then a C (flat/sharp/natural) etc. etc. Regardless of what note it starts on.

So, any kind of F scale, must have the following note names: F G A B C D E F. If it was F major, it'd be F G A Bb C D E F. If it were F# major, it'd be F# G# A# B C# D# E# F#. F# major couldn't have an F natural in, because then it'd be F# G# A# B C# D# F F#. That'd break the rules - you see, it has no E note in it, and 2 consecutive F notes. It would also be a bitch to read in a piece of music, because you'd have to keep having accidentals to naturalise the F, then re-sharpen it etc, it'd be madness, really confusing.

Likewise, and G scale must have the note names G A B C D E F G. To be G major it would have to have G A B C D E F# G. To be Gb major it would have to be Gb Ab Bb Cb Db Eb F Gb. If it were Gb Ab Bb B Db Eb F Gb - it would break the rules - it would have two B notes and no C note... you see?

Does that make things clearer?

http://www.talkbass.com/forum/showthread.php?s=&threadid=11675&highlight=circle+of+fifths

hope that helps a bit too.

Damn the circle of fifths!!! DAMN IT TO HELL!!!!!!!