How to change clip speed without changing audio pitch?
I need to change the speed of a small video clip without changing the pitch of the audio. How can I do this? Pretty straightforward.
Comments

Drop your clip into a comp. Rightclick and choose "Speed/Duration" and change the speed to what you want. Add the Pitch audio effect, and adjust the Semitone Shift property to return to the original pitch.
Most people don't think in semitones, but it's fairly easy to figure out. There are 12 semitones in an octave. If you double the clip's speed (200%), the pitch goes an octave higher, so set Semitone Shift to 12 to compensate. Only raise the speed to 150%? That's 1.5x faster, and 1.5 octaves higher in pitch, so make up the halfoctave difference by setting Semitone Shift to 6.

Is there an equation I can use to find out how much I need to shift if the speed change is extremely specific (into the hundredths)?

Sure. Just take the portion that's over 100%, turn it into a decimal, multiply it by 12, then make it negative. Examples:
150% > 50% over > 0.5 * 12 = 6 semitones
137.8% > 37.8% over > 0.378 * 12 = 4.536 semitones
214.69% > 114.69% over > 1.1469 * 12 = 13.7628 semitonesEDIT: Fixed the formula. For clips that are sped up, the semitone pitch shift should be negative to compensate.

If it has to be slowed down, would the equation go like this:
82% = 18% lower = 0.18 x 12 = 2.16

Yes. BUT for a LOWER pitch you need a NEGATIVE number, so the final answer is "2.16" semitones.

@Triem23 Actually @Lyrehc is correct. It should be 2.16. Because the video is slowing down, he wants to increase the pitch to compensate so that it sounds "normal."
Which means that my original formula needs an update to make the resulting values negative. To maintain pitch, faster clips should have negative semitone adjustment values, while slower clips should have positive ones. Somehow I missed this when making my original post. Off to fix the post. Sorry for the confusion.

Very useful! Thanks a lot JsBarett!

Actually, the video slow down vs audio transpose equation is wrong.
For example, it's wrong if video slow down to 0.25x => 75% lower => 0.75 * 12 = +8 semitone shift;
instead, while experimenting, I realized 0.25 = 1 divided by 2 and divided by 2 => 2 octaves higher = +24;
So, I've come up with the following equation, should be close enough if incorrect...
1. if new speed is 0.68x, 1 divided by 0.68 = 1.4705882352941176470588235294118;
2. log base 2 (log_{2}) of 1.470588... = 0.5563933485243854
3. 12 * 0.55639... = +6.6767201822926248
4. Semitone shift = around +6.68
viola~
p.s. use a log base 2 calculator like https://www.miniwebtool.com/logbase2calculator/ for sake of easiness;
or you can calculate with the log base transform equation Log_{b} x = Log_{a} x/Log_{a} b
like here, Log_{2} 1.470588 = Log_{10} 1.470588 / Log_{10} 2 = 0.5563933...

For slowed down video, equation to calculate semitone shift is as follow:
(it might not be completely correct as I figured it out myself but the answer should be close enough)For a video slowed down to 0.68x,
1. 1 / 0.68 = 1.470588...
2. Log_{2} 1.470588 = 0.5563933...
3. 12 * 0.5563933 = 6.67672...Viola~ the required semitone shift is around +6.68.
p.s. equation to calculate log base 2:
Log_{b} x = Log_{a} x/Log_{a} b => Log_{2} 1.47 = Log_{10} 1.47 / Log_{10} 2
or you can use a calculator like https://www.miniwebtool.com/logbase2calculator/ 
Actually, speed up and slow down should both apply the same equation.
Let X be new video playback speed, be it 0.68x (68%) or 2.15x (215%).
Semitone shift = 12 * log(1 / X) / log(2)
For 0.68x => 12 * log(1 / 0.68) / log(2) = +6.68
For 2.15x => 12 * log(1 / 2.15) / log(2) = 13.25