How Many Notes Are There In a Musical Scale? Start with a Chromatic Scale

How many notes are there in a musical scale, at least in theory?

Start with a chromatic scale.

With a chromatic scale of 5 equally-spaced notes, A, B, C, D, and A, the number of possible scales you could create would be seven:

Next, try a chromatic scale of 6 notes, A, B, C, D, E, and A. The number of possible scales more than doubles, to 15:

And so it goes:

Chromatic scale of 7 notes = 31 possible scales

Chromatic scale of 8 notes = 63 possible scales

. . .

Chromatic scale of 13 notes = 2,047 possible scales