1.4Exercise: stop naming keys for a minute

Sit at the piano.

Pick any C.

Now count every physical key upward:

C = 0

C♯ = 1

D = 2

D♯ = 3

E = 4

F = 5

F♯ = 6

G = 7

G♯ = 8

A = 9

A♯ = 10

B = 11

C = 12

That 12 matters.

Twelve semitones = one octave.

So you can think of an octave as a circular system:

0 → 1 → 2 → ... → 11 → back to 0

This is why harmony can be transposed mathematically.