@Jingledale
Brian - no stupid questions!
This needs a minor but very important correction.
There are no NOTES / TONES (in western music) between B and C then E and F respectively.
All four of those notes can be natural (B, C, E, F), sharp (B#, C#, E#, F#) or flat (Bb, Cb, Eb, Fb).
B# = C (enharmonic equivalent notes given different names depending on the context).
E# = F (enharmonic equivalent notes given different names depending on the context).
Cb = B (enharmonic equivalent notes given different names depending on the context).
Fb = E (enharmonic equivalent notes given different names depending on the context).
The reason for their existence is …
a] When spelling a major scale all seven letters must be used once and once only.
b] a key with one or more sharps can only contain natural or sharp notes (no flats allowed).
c] A key with one or more flat notes can only contain natural or flat notes (no sharps allowed).
Examples of each.
a]
C major using all seven letters once and once only.
C, D, E, F, G, A, B
b]
A major (using sharps and natural notes only)
A, B, C#, D, E, F#, G#
c]
Eb major (using flats and natural notes only)
Eb, F, G, Ab, Bb, C, D
So far so good I hope and none of those examples use the ‘oddities’ you ask about.
When do the oddities become necessary?
B# (= C) is needed if a major scale has already use the letter C. The letter C being used cannot be the natural note C as, just as we cannot use a letter twice nor can we use the same tone twice. If B# is needed it will be due to the fact that C# appears in the scale. If the letter C has already been used, and B follows along later, it must be that we started at letter C, the position of the 1st scale degree, and the letter B is found at the position of the 7th scale degree. There is only one scale that fits the bill, namely C#.
C#, D#, E#, F#, G#, A#, B#
E# is needed if a major scale has already use the letter F. The letter F being used cannot be the natural note F as, just as we cannot use a letter twice nor can we use the same tone twice. If E# is needed it will be due to the fact that F# appears in the scale. If the letter F has already been used, and E follows along later, it must be that we started at F, the position of the 1st scale degree, and the letter E is found at the position of the 7th scale degree. There is only one scale that fits the bill, namely F#.
F#, G#, A#, B, C#, D#, E#
Cb is needed for the Cb major scale (of course it is).
Cb, Db, Eb, Fb, Gb, Ab, Bb
Fb is needed (as shown directly above) in the Cb major scale and in no other major scale unless you venture into the world of double flats. This matches with the order of flats - the note F is the last of seven to take a flat. See Mr Cato’s trick.