One octave has 12 sounds and 21 letter symbols: 7 natural, 7 flat (b) and 7 sharp (#). And with these 21 letter symbols we can spell 15 major scales in 15 major keys.
Now, here’s a simple question: aren’t there really 21 major scales? The answer is yes, but to spell them we need 14 more letter symbols: 7 double flat and 7 double sharp.
For example, to spell the Fb major scale, we need B double flat (Bbb): Fb Gb Ab Bbb Cb Db Eb, and to spell the G# major scale, we need F double sharp (F##): G# A# B# C# D# E# F##.
Remember, the reason why there are only 15 traditional major scales is because only 15 major scales can be spelled with 21 letter symbols. To spell any other major scale not shown above we would need to use double flat or double sharp letter symbols.
Here is something important. Even though each major scale has a different letter spelling, they all have the same tone number (scale degree) spelling: 1 2 3 4 5 6 7!
The different letter spellings are the result of applying the major scale interval pattern (whole step, whole step, half step, whole step, whole step, whole step, half step,), to each of the 15 major scale key letters. On the guitar and bass fretboard, a half step is one fret and a whole step is two frets.
’til next time, have some fun playing 15 major scales with 12 sounds, and spelling 15 major key signatures with 21 symbols… I’ll be listening!