In the last week, I finally discovered the reason that my serpentine belt on my Taurus would squeal embarrassingly, even tough it was a relatively new belt.
I say relatively new, because it was a couple years old and had been replaced by a new belt with the head gaskets.
A week or more ago, I pulled both the old belt (a Gates) and the new (USA, brand illegible) alongside each other and found that the newer belt was longer than the older Gates belt.
I did this because when I tried to apply more tension on it, nothing tightened.
So I put the Gates back on (after cleaning it thoroughly) and it stopped squealing, for a few days.
Then it started again.
With the engine running, I put a wrench on the tensioner and put more tension on the belt.
(Note: I am an idiot. Kids don't try this at home.)
Putting more tension on the belt only caused it to squeal more!
Taking tension off quieted it and as it got quieter I observed that it ran "truer".
So I did what anyone would do.
I removed the tensioner, put it on a steel plate and measured the difference in height from the table of four positions (compass points) on the pulley.
So it was forty thousandths of an inch out of alignment!
I found that hard to believe, but I went out to get a Gates tensioner ($55!) and when I measured it, it had five thousandths.
So I installed it, and the squeal is gone.
Today, my air compressor threw a belt.
Of all things, the motor has twisted over the years to be out of line with the pump.
Nothing a torch and a hammer couldn't fix.
Cheaper than the car.