Being a motherboard repairer, and a big Gigabyte fan, I thought I'd offer some insight. The squealing and whistling people are hearing is harmonic distortion, or crosstalk. It's the CPU VRM (Voltage Regulator Modules) making the noise. The VRM's are made up of capacitors, ferrite chokes, and other components, all the amazing circuitry you see around the CPU socket, and the noises means they're running out of frequency because they're either:
A) Faulty
If they're faulty this would explain the noise. Remember the big faulty capacitor headlines when a Taiwanese capacitor firm stole an incomplete electrolyte formula? I'm still replacing these nearly ten years later. They were electrolytic, not solid state like most GB boards today, but faults still happen and get missed in batches.
or
B) Recieving too much or not enough power
This can be down to the PSU as some have reported. Taking voltages down in the BIOS cures it in some cases. Harmonic distortion happens normally too. I repair TV's and all sorts of consumer equipment, and I have TV's whose PSU's whistle faintly while the TV is off, when switched on the whistling disappears. My 16" TV for the Xbox 360 does it, when the room is quiet and the TV in Standby it gets annoying. It's just the way high frequency voltage supplies work, and not necessarily a fault. VRM's are a critical part of a motherboard, the power has to be filtered and smoothed so it is perfect. The PSU is the first step to this, as here's what it does:
* Voltage conversion – changing the 115/230 VAC line voltage into one or more other voltages as determined by application.
* Rectification – turning the AC into DC.
* Filtering – smoothing the ripple of the rectified voltage(s).
* Regulation – making the output voltage(s) independent of line and load variations.
* Isolation – separating the supply outputs from any direct connection to the AC line.
The CPU VRM's do a lot of smoothing, the capacitors and chokes are responsible, it also converts the 12v into the 1-5v a CPU needs, and distributes the rest around the system. They still should NOT hum, whistle or buzz, as they're DC-DC converters. I think Gigabyte are being ignorant, and I'm disappointed, I thought your QA guys tackled things head on!! I read just 5 pages of this thread!
This doesn't give a definitive answer, but I hope it's given the less tech savvy people an insight to just how important VRM's and PSU's are. I use a EX58-UD3R, and have no problems. My PSU whistles and hums while off, but I turn the mains off!
It won't be the CPU, otherwise Intel will have noticed faults in the batches and put out a recall, or possibly kept quiet because they don't want their rep damaging. A faulty CPU could cause hum, but the machine would crash a lot more.