Follow up for my own troubleshooting of the issue. Thanks to users like K1mac and penguinnss I've also isolated the ringing to fan #3. I found out I was using an incompatible version of Precision X1 because I was using the version provided by Steam which is 1.0.7. For 30 series cards you need 1.1.0 either for Windows Gamebar or as a stand alone from EVGA's website. With the correct version of Precision X1 I was able to control all three fans via software and one by one turned each off until the ringing stopped. I tested all three twice and have successfully silenced ringing with the card by shutting off fan 3. I will also be submitting a support ticket with my findings and post back with results.

Working as intended. It's a ceremonial whine programmed in by EVGA on behalf of the 99.9% who didn't get a card. It's saying "never forget" over and over again in a dolphin like fashion. It typically goes away after the GPU reaches 70 C. So keep it running hot in Battlefield 4 on high settings or your other favorite title to keep it content.
 
You could purchase the upgraded fan for $299 to fix it but guess what - it's Out of Stock.

I'm assuming the first part of that is a joke? But does it really go away after a while?

I am also having this issue, and also submitted a ticket. 

I was also able to isloate this to the fan below the two 8 pin connectors.

If I have to RMA it, I will. This fan noise is crazy loud; right as it spins up beeeeeeeeeeeeeeep.... Ill disable for the time being i guess. 

I'm trying to isolate mine but setting a custom fan curve to 0 in X1 doesn't seem to do anything.

Tunatron
I'm trying to isolate mine but setting a custom fan curve to 0 in X1 doesn't seem to do anything.

You tested and made sure that you enabled the custom curve right? :) 

Are you using the new 30 series PX1? I can't slide my fan curve below 30% even with "enable custom curve" checked?

You need to go over to the other side to move it to 0%