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To understand the relevance of the graphic equalizer, first we need to delve back into audio history...
Back in the 1970s console equalizers were not anywhere near as sophisticated as even the standard EQ plug-in of your digital audio workstation software. You might get fixed-frequency HF and LF sections, a couple of mid sections with switched frequency and no Q control, and possibly a fixed-frequency on/off high-pass filter. And that's on a high-grade console.
It should be said that it is possible to achieve amazing things with these limited resources, but even then it was clear that a more flexible method of equalization might be desirable.
So enter the graphic equalizer. This has, in its archetypal professional version, 30 frequency bands, each cuttable or boostable by 12 dB. A classic example is the Klark Teknik DN360, pictured above, which you can still buy today.
The difference between the graphic equalizer and typical console EQs was that with the graphic it seemed that you could set any EQ curve, without limitation. This isn't quite true because of the way the bands interact with each other. It also isn't true that the positions of the knobs show the EQ curve precisely - they approximate it, but it isn't an exact depiction of the frequency response set.
Still, although the graphic equalizer didn't work in quite the way it seemed to, it offered an interesting and useful alternative method of EQ back in the day.
These days we have incredibly flexible parametric EQ implemented in software. Having seven bands, each with frequency, gain and Q controls is commonplace. It's hard to imagine an EQ curve that you wouldn't be able to achieve if you wanted to. Against this scope and power, the graphic simply can't compete.
The graphic has another issue to consider too - Whenever you EQ a signal you change the phase relationships of the various frequencies. It is commonly thought that it is best to keep phase shifts to as little as possible. Putting a signal through 30 bands of EQ however is far from being the way to do it. Having said that, if a signal is in need of EQ, then it is likely to sound better when EQed tastefully by any method, regardless of phase issues.
Technically therefore it is likely that a digital EQ plug-in will be a better option than a graphic. But the graphic has a certain advantage that a parametric EQ doesn't...
The presentation of the graphic EQ in the form of 30 frequency bands provides an extremely intuitive method of operation. Quick too. Graphic equalizers are used in live sound between the output of the mixing console and the crossover feeding the power amplifiers. The object is to optimize the sound according to the requirements of the auditorium, correcting as much as possible for frequency response anomalies in the sound of the room. This can be done with modern parametric EQ, but the graphic was the more flexible tool in the days when modern PA as we know it today was being developed. The graphic can maintain its place in this role through this historical reason.
Live sound engineers also have to deal with feedback (howlround). As you raise the faders, feedback will occur first at a certain frequency. But if you lower the band on the graphic EQ that contains that frequency, you can achieve an extra few, but useful, decibels of level before feedback occurs at another frequency. Kill that too and you can achieve a little more level, or a little more headroom between your working level and the danger zone. You can iterate this procedure a couple more times, but there comes a point where you are messing too much with the actual sound that you are amplifying and more EQ becomes counter-productive.
Experienced live sound engineers also like the graphic because if feedback occurs unexpectedly they can kill it quickly by reaching out and lowering the problem band. An experienced live sound engineer will over time develop an instinct that allows them to get the right frequency band first time. Well that's the aim at least.
It's worth saying also that many venues have fixed sound installations for day-to-day use. Here a graphic might be put in during the installation process, ideal settings found, then the panel covered over so it can't easily be changed.
Now that we have the background, when considering how to set the graphic equalizer the first decision is a little philosophical - should you set smoothly changing curves or do you consider that it's OK if the positions of the knobs are 'lumpy'?
The thought behind this is that if you use smoothly changing curves then you are being 'gentle and considerate' with the signal. If you use lumpy settings then you are hacking it around. Ultimately, what you want is something that sounds good, so it doesn't matter. But operationally you would make the choice whether to grab the bands in handfuls and skew them smoothly, or tweak individual bands separately.
In live sound, then a good way of working is to play some known audio through the system. Use your iPod if you like, but it's best for the source to be a .wav file, not a .mp3 or .m4a. If you have a selection of tracks that you know really well and have heard in many other rooms, then you should quickly be able to tune the graphic EQ to get close to the best sound that the auditorium is capable of.
Once you have achieved the optimum sound from your test tracks you have a base to start working from to get the best sound from the band using the controls of the console and your other outboard. As the sound check progresses then you will find any problem feedback frequencies and turn again to the graphic for corrections.
In the studio, well to be honest there isn't really any reason to use a graphic. All the tools you need are there inside your DAW already. But often it is useful to have a different way of working. Different methods can lead to different results, and it can make a pleasant change to do things in a novel way, rather than endless pursuing the same routes towards that elusive, hoped-for perfection.
In summary, the graphic equalizer is a useful tool in live sound and fixed installations. You don't need one in the studio, but it can be a fun tool to have around.