13.3Why are they called 9, 11, and 13?

Because chord notation assumes stacked thirds.

Start:

1 = root

3 = third

5 = fifth

7 = seventh

then continue:

9

11

13

If we reduce them into the same octave:

9 → 2

11 → 4

13 → 6

So in C:

9 = D

11 = F

13 = A

But calling D the 9th tells us:

This note is functioning as a chord extension above a seventh chord.