Joe, your mid-sweep is a semi-parametric eq. Fully parametric lets you specify the width of the Q, or the range of the notch that you are boosting or cutting.
I suggest that you look at a 31 band graphic EQ (the kind with the sliders) first because the particular frequencies are all labeled, which makes it much easier to learn what they are. Many parametrics are not labelled so well, so you could end up with the same situation you have now...you hear what sounds good, but you're not really sure what to call it.