EQ Slope Question

Any sort of hard cut will introduce distortion; a gentle (or not so gentle) slope will prevent this from happening.
 
It would be very difficult to implement a brickwall cut of this nature in the analog domain, I imagine it would be easy enough with digital, but the same caveat about distortion still applies.

The target frequency is the mathematical center of the slope based on a simulated analog curve.  Not the beginning or the end.  A steeper filter will narrow range of both high and low frequencies affected.  

There are times when you use a very steep slope and other times you might use a much more relaxed slope. eg 6 db/oct slope is gentle. This type of slope is good when you have got quite a lot of excess low end energy on a track. You might set it up reasonably high eg 200 Hz. At 100 Hz you are only 6 db down and at 50 Hz 12 dB down.. This type of slope will sound good and it will just clean up excess low end without changing the sound too much.
 
There are other times when you want all the bass energy to stay right in up to a point and then everything below that point you want to remove. This is when you might select a steeper slope eg 48 db/oct. And set this to say 40 Hz. Now everything will remain intact right down to 40 Hz but below that everything is removed fast. This is good for removing rumble or very low end (rumble) in a track without changing its low end content hardly at all. Sometimes this is needed on a track or in mastering too.
 
You just have to listen to the material and decide what needs to be done. That will determine the slope required. Steeper slopes leave the sound basically alone and clean up sharply below the cutoff frequency. Gentle slopes do effect the sound in a nice way and are good for just thinning out a sound that is a little bass heavy. With gentle slopes you have to move the cutoff freq higher so you can hear the effect of them more so. The position of the cutoff freq with a gentle slope will determine how much low end is removed. It is a nice way to tame excess low end without effecting the sound too much.
 
The same applies to the high end except you tend to use more gentle slopes up the high end to perform more subtle rolling off of high frequencies.

different software eq's are written different ways.
 
one size does not fit all.
 
that's why people pay big bucks for well written software EQ's, and argue endlessly about which ones sound the best.
 
math is math, right?
 
not always
 
there's a thing called 'fuzzy math', beauty is in the eye of the beholder.

Cutoff frequency for LPF and HPF is usually defined as the point at which there is 3dB reduction.  So if you set your cutoff on a HPF to 30Hz, the signal will start being attenuated at a somewhat higher frequency.