kingpatzer wrote:I'm not talking about roots (there are 15 by the way, not 12).
15? Please, go on! It is very interesting!
Sure, if you take the 7 base tones (A B C D E F G) and consider each along with it's sharp and flat (Ab A A#, Bb B B# etc) you get 21 notes. Of course some are enharmonic.
If you look at a circle of fifths, you'll find 12 "boxes" the following key signatures:
(going in fifths)
C, F, Bb, Eb, Ab, Db, Gb, B, E, A, D, G
You'll notice though that Db is also written as C#, Gb is also written as F#, and B is also written as Cb. That is 15 common key signatures, three of which have enharmonic spellings. Each key signature has it's corresponding major scale, giving you 15 common tonics. These can be broken down into three groups. The first group consists just of C, it is the scale without any sharps or flats. The second group consists of G, D, A, E, B, F#, and C#. Those are the seven key signatures that can be written with sharpened notes. The third group consists of F, Bb, Eb, Ab, Db, Gb, and Cb. Those are the seven key signatures that can be written with flattened notes.
So why 15 and not 21? Because by convention we don't consider key signatures that require double flats or double sharps. That means you'll never see D#, E#, Fb, G#, A# or B# in practice because those six create double sharps or double flats in the key signatures. So out of the 21 note names, there are 15 practical, common major scales.
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