Formula to slow down audio with pitch correction

Special Interest Groups Audio Processing
1

Hello - I need to slow down audio by 25% and want to verify the math, after reading the wiki article, I was hoping you someone could validate that I am doing it correctly: http://wiki.audacityteam.org/wiki/Change_Speed

( ((original length) - (target length)) / (target length) ) * 100 = Percent Change

I want to reduce the speed by 25%, and therefore I will start with a length of 100 minutes.

(100 minutes - 75 minutes )/75 minutes * 100 = 33.3333333…%

That means I need to increase the speed by 33.3333% in order to slow down audio by 25% and have the pitch stay the same correct?

Thanks
Ron

2

If the original duration is 100 minutes and the “target” (final) length is 75 minutes, then it must be playing faster!

This is the tricky part. “Percent” does not mean anything unless you say what it is a percentage of.
If I say that I want 25% of the money in your pocket, that is (probably) very different to saying that I want 25% of the money in Bill Gates’ bank account.

If I have a recording and say that it is “slowed 25%”, that is ambiguous because I have not specified whether the “25%” is “25% of the original” or 25% of the new track.

The way that it works in Audacity (and I don’t think that this is very intuitive) is that it is 25% of the new track.

If your original file 100 minutes duration, and you slow it down by 25% in the Audacity “Change Speed” effect, (Percent Change = -25), then the equation is:

( ((original length) - (target length)) / (target length) ) * 100 = Percent Change
( (100 - (target length)) / (target length) ) * 100 = -25

which can be rearranged as:

( (100 - (target-length)) /  (target length) ) = -25/100
(100 -  (target length) ) = (-25 *  (target length) ) / 100
100 = ( (-25 *  (target length) ) / 100 ) +  (target length)
100 = ( (-25 *  (target length) ) / 100 ) +  (100 * (target length)) / 100)
100 = (75 * (target length) ) / 100
(100 * 100) = (75 + (target length) )
((100 * 100) / 75) = (target length)
(target length) = 133.333333333

or to put it more simply… (I bet you’re glad I said that :wink:)

((original length) * 100) / (100 + (Percent Change)) = New length
3

Thank you! So good to have someone review. Ok so to make sure I have it correct, slowing down the video:

100 second song original length
125 second target length

( ((original length) - (target length)) / (target length) ) * 100 = Percent Change
( ((100) - (125)) / (target length) ) * 100 = -20

So therefore decreasing the speed by 25% means an increase in pitch by 20% if I want the pitch to maintain.

Correct?

Ron

4

There’s that “tricky part” again. “Percent” does not mean anything unless you say what it is a percentage of.

If the original length is 100 seconds and the final length is 125 seconds,
then the final length is ( ((125 -100) / 100) * 100) = 25 percent longer than the original
which is also ( ((125 -100) / 125) * 100) = 20 percent of the final length.

The same goes for tempo and frequency.
As it speeds up, the pitch goes up and the duration becomes less.
As it slows down, the pitch goes down and it goes on longer.