Having a graphic eq is not "totally worthless" in the studio like Blue Bear suggests. If you need an analog eq for some particular reason, it could fill the role quite well.
The difference between a graphic eq and a parametric eq are this:
Graphic eq have fixed frequency points.
Graphic eq's have a fixed bandwidth for each frequency point (10 band are a 1 octave, 15 bands are 2/3 octave, 31 bands are 1/3 octave) Bandwidth is the "width" of frequencies that are effected by adjust the frequency point. On a 1/3 octave eq, supposedly only 1/3 of a full octave are effected by adjusting one of the bands.
There are two types of parametric eq's normally. Full parametric and semi-parametric (or quazi parametric). The only difference between the two is that Full Parametric has bandwidth control, and quazi parametric has a fixed bandwidth.
Parametric eq's have an adjustable bandwidth, which is primarily how they differ from graphic eq's.
Parametric eq's generally have less "bands" of eq you can cut/boost at the same time.
Full Parametric eq's generally can have down to a 1/10 octave bandwidth, which means that they can carve out a much smaller amount of frequency than a 1/3 octave graphic band can.
Those are the differences for the most part. Both parametric and graphic eq's use a "bell curve" type of equalization, so there is no difference there.
Which eq you use depends upon what your needs are.
Graphic eq's are normally used in live sound applications to help correct the outputted audio to make up for bad room acoustics, of a PA system that is not balanced the way you want it to be. In this application, you may have a need for several eq points to be cut and/or boosted. In the case of a 31 band 1/3 octave eq, you have 31 individual bands that can be cut/boost at once. In this application, having a bandwidth of 1/3 octave is considered perfectly acceptable. In live sound, we generally don't need as surgical of cut/boost in an eq band as we might want in the studio.
Full Parametric eq's offer less "bands" of frequencies that can be cut/boosted at the same time, but they do offer a greater ability of control over the band that you are working on. The "bandwidth" , or "Q" control is central to this increased control.
Let's say that you need to do a VERY sugical cut of a frequency to keep it from exciting a ringy filter elsewhere (or maybe your eq circuit is ringy itself!?!?!?!?!?). With a graphic eq, you can only affect the audio range in as little as 1/3 of an octave. This may be too big of an area for your tastes. This is where a full parametric eq would offer the better solution! You can zero in on the frequency with 1/10 of an octave accuracy and cut/boost it. The graphic eq just can't do this.
Let's say though that you need to effect a 2 octave region of the audio. Let's say that 1KHz needs to be cut, but you want everything up to 2KHz and down to 500Hz to be effected too. On a graphic eq, you would need to adjust 6 bands to create this eq curve. In addition, you would have to carefully do this to assimulate the "bell curve" over 2 octaves (yes each band has a bell curve in it's circuit, but when you start adjusting bands that are next to each other, there is a bit of overlap, or the "crossover point" between the bands...equally adjusting two bands next to each other the same amount on a graphic eq would produce an outputted eq curve that is not a bell curve in nature...). Thus, it is harder to get the familiar bell curve sound on a graphic eq over anything over 1/3 of an octave (if it is a 1/3 octave eq) because of a number of things. The full parametric eq in this case wins out again! You can pick your 1KHz center frequency and adjust the "Q" to be 2 octaves, and now you have a bell shaped curve centered at 1KHz with a 2 octave bandwidth. It is just much easier to do on a parametric.
Let's say though that you need to cut/boost several bands at once. On something like a poorly recorded bass guitar track, having up to 10 bands of eq is NOT totally out of the question (I know folks, in this case, I would just rather retrack the part rather than apply that much eq, but retracking is not always an option!). Most parametric eq's don't have any more than 5 bands that can be cut/boost at the same time! Yikes! What do you do? Well, a graphic eq would be much better suited in this case.
So, the above examples aside, each of these eq's has a strength and a weakness. You have to be able to access what your needs are before determining which eq is best suited to meet that need. If a lot of bands of eq at once are needed, and tight bandwidth control, or at least control tighter than 1/3 of an octave, than the graphic eq is your box! If you don't have a need for more than say a couple of bands of eq, maybe up to 4 bands, but you need bandwidth control of all those bands that is both wider and narrower than 1/3 of an octave, then the full parametric eq is your box!
In the studio, I have only a few times over the years where a two band full parametric eq with a low and high shelf filter was needed. In those cases, I usually just insert another parametric eq in the circuit.
Hope this clears things up a little bit. Blue Bear COULD HAVE spent all this fucking time writing this just as clearly as I have, but he seldomly does and just likes to impress upon you that you are a dipshit for asking the question. Well, okay, he doesn't mean to come across that way, but he does, and it is usually his laziness to explain things that causes him to post crap like he did. (sorry BB, it HAD to be said...you post like this far too often...
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I didn't go into high and low pass filters and high and low shelf eq's in this. Neither a graphic or a parametric eq offer true pass filters or shelf filters. pass and shelf filters have key rolls in audio too. If you do a search here you could probably find a post I made about a year ago concerning all the eq types.
Ed