Here's a great process to keep in mind when you're deciding whether to EQ or compress first.
1. Repair First
If there are obvious frequency problems in your signal that you want to get rid of then put an EQ before the compressor.
If there's low rumble you filter it out.
If there's obvious muddiness then you cut that in the 200ish Hz area.
If you're mixing a kick drum and it sounds like it's inside a cardboard box then set your attenuators to stun around 300 - 600 Hz.
The reason you don't want to put a compressor before is because you don't want the compressor to accent those annoying frequencies you're going to EQ out anyway. It's unnecessary work on the compressor's part.
2. Compress When Ready
Once you've taken out all the frequencies you don't want on the track you can slap on a compressor and dial in the compression setting of your choice.
Giving the compressor a "prettier" signal to deal with makes for a more enjoyable experience.
However, the compressor will be compressing the frequencies that you left intact in the repair phase.
At that point, you might need to bring them back out in the mix. The relative difference between the frequencies you cut and the frequencies that are being compressed are now closer together so you need a second EQ to bring those frequencies back out in the mix.
3. Flatter Your Frequencies
Adding a second EQ after your compressor allows you to add boosts to the frequencies that you want to bring out in the mix without the compressor fighting them.
If you had also boosted during the "repair" phase then the compressor would have pushed down those frequencies even harder because an EQ boost is essentially just a frequency-specific volume boost.
With a louder volume in those frequencies and the compression threshold staying the same, the compressor would react even harder to compress those boosts.
Make sense?
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