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There are 7 white notes, and 5 black notes on the piano, so all together you have 12 different notes, and therefore, 12 different sounding major scales.
If we include the three enharmonic ones - that makes fifteen key signatures and, therefore, fifteen major scales in total.

They are, from the flattest key (the one with the most amount of flats) to the sharpest key, in order: Cb, Gb, Db, Ab, Eb, Bb, F, C, G, D, A, E, B, F# and C#. These are all the "real keys".


Now, if you want to get theory crazy - you can look at the "imaginary scales" as well - which are scales you can figure out theoretically, but you wouldn't use them for practical reasons. This would include keys like D# Major (9 sharps) and Gbb Major (13 flats), in which case there would be an additional 20 major scales (one for every note and its enharmonic equivalent) as well, making a total of 35 scales (for the 15 real key signatures and the 20 imaginary keys).



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