00:01
When we have two frequencies where one frequency is twice the value of the other, we call the distance between those frequencies an octave.
00:10
And this effect is additive, of course.
00:13
So if we have a third frequency that is four times the value of the first frequency, then that's a separation of two octaves because four is two times two.
00:27
Now more generally, if we have two frequencies, f1 and f2, and we want to know how many octaves separate them.
00:40
What we're really asking then is how many times n do we have to double the first frequency in order for us to reach the second.
00:52
So in order to solve for n here, we can just do a little bit of rearranging of this equation.
00:58
And we can first divide by f1 to give us 2 to the n equals f2 over f1.
01:04
And then to get n alone, we can take the base 2 logarithm...