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# Parametric EQ

A Guide to Parametric Equalisers in Live Sound

## EQ Parameters

Parametric EQ is so-called because it has controls to adjust all the parameters of tone-shaping. These are:

### Frequency

The central frequency of the envelope in which the signal is boosted or cut.

### Bandwidth

Q* (see below) is a relation of Bandwidth. The number of octaves (or fractions of an octave) over which the signal is affected by boosting or cutting.

In EQ circuits bandwidth and Q describe the same thing, but use different (and inverse) scales: the higher the Q, the lower the bandwidth, and vice versa. The range of possible adjustment can run from about 1/60 octave (Q ≈ 90) to about 3 octaves (Q ≈ 0.4).

Bandwidth is derived from the points on the EQ curve that are 3dB above or below the amount by which the central frequency has been cut or boosted. The centre frequency is at the midpoint (in octaves) between the lower and upper frequencies: if the bandwidth is 2 octaves, the centre frequency is one octave above the lower frequency, and one octave below the upper frequency (e.g. 1kHz lower, 2kHz centre, 4kHz upper).

*Q refers to the Quality of a frequency filter, in the sense that a narrow filter is of higher quality than a broader filter.

### Gain

The amount by which the signal is boosted or cut.

For the budding mathematicians among you...

### To Calculate Bandwidth

• Divide the upper frequency by the lower frequency

F2/F1

• Find the logarithm (base 10) of the result

Log10(F2/F1)

• Divide the logarithm by 0.301

Log10(F2/F1)/0.301

### To Calculate Q

• Subtract the lower frequency from the upper frequency

F2 − F1

• Divide the centre frequency by the result.

F3/(F2 − F1)

### To Convert Bandwidth to Q

• Raise 2 to the power of the bandwidth

2^bandwidth

• Find the square root of the result [solution A]

sqrt(2^bandwidth)

[A]

• Raise 2 to the power of the bandwidth

2^bandwidth

• Subtract 1 from the result [solution B]

(2^bandwidth) − 1

[B]

• Divide solution A by solution B

(sqrt(2^bandwidth))/((2^bandwidth) − 1)

[A]/[B]

...and if you really have nothing better to do....

### To Convert Q to Bandwidth

• Take a deep breath...

(INHALE...............!)

• Square Q [Solution A]

Q^2

[A]

• Double the result [Solution B]

2x(Q^2)

[B]

2x(Q^2)+1

[C]

• Divide solution C by solution B [Solution D]

(2x(Q^2)+1)/(2x(Q^2))

[C]/[B] = [D]

• Divide solution C by solution A

(2x(Q^2)+1)/(Q^2)

[C]/[A]

• Square the result

((2x(Q^2)+1)/(Q^2))^2

([C]/[A])^2

• Divide the result by 4

((((2x(Q^2)+1)/(Q^2))^2)/4

(([C]/[A])^2)/4

• Subtract 1

(((((2x(Q^2)+1)/(Q^2))^2)/4)-1

((([C]/[A])^2)/4)-1

• Find the square root of the result [solution E]

sqrt(((((2x(Q^2)+1)/(Q^2))^2)/4)-1)

[E]

• Add solution D to solution E  [solution F]

(2x(Q^2)+1)/(2x(Q^2))+sqrt(((((2x(Q^2)+1)/(Q^2))^2)/4)-1)

[D]+[E] = [F]

• Find the logarithm (base 10) of the result

Log10((2x(Q^2)+1)/(2x(Q^2))+sqrt(((((2x(Q^2)+1)/(Q^2))^2)/4)-1))

Log(10)[F]

• ...and finally...

...sigh...

• Divide the result by 0.301

(Log10((2x(Q^2)+1)/(2x(Q^2))+sqrt(((((2x(Q^2)+1)/(Q^2))^2)/4)-1)))/0.301

(Log(10)[F])/0.301

## What it is

A parametric EQ is an equaliser which has controls for Frequency, Bandwidth or Q, and Gain.

Some desks have one or more parametric EQ sections on each channel. However, single- or multi-channel parametric EQs (with a varying number of bands) are available as rack-mountable units.

Sweepable midrange EQ which has only frequency and gain controls (found on the channel section of some budget and most mid-priced desks) is sometimes incorrectly described as ‘parametric’. However, the term ‘semi-parametric’ is more often used for this type of EQ. To distinguish it from this, the channel EQ on more expensive desks - which include a bandwidth or Q control - is often described as ‘fully parametric’.

## What it does

It allows very precisely tailored EQ to be applied.

## How it works

It works as a normal peaking midrange EQ control, but the frequency and bandwidth are also adjustable.

## How do you use it?

If all else fails, read the manual!

The main use of a parametric EQ in live systems is for tone shaping or correcting anomalies in the sound of individual instruments or voices (occasionally also in the overall sound). It can also be used (with more accuracy than a graphic EQ) to control feedback.

As a corrective measure, cutting dominant frequencies is generally more effective - and sounds more natural - than boosting weaker frequencies. There are several technical reasons for this, but a simple thing to bear in mind is that peaks stand out, and reducing them will have more effect (and can be achieved more easily and with greater accuracy) than trying to raise the troughs. Also - broadly speaking - if you've already got it you probably don't need to boost it, but no amount of boosting will put back what wasn't there to begin with.

The descriptions below assume that you are using one band of parametric EQ, and that it is inserted in the channel path using the channel insert point.

For tonal correction:

1. Set the gain control at the 0dB - no cut or boost - position (typically this will be 12 o'clock).
2. Set the bandwidth or Q control at a position mid-way through its range (typically this will also be 12 o'clock).
3. Set the frequency control at the lower extreme of its range.

While the sound you wish to change is playing, increase the gain (around 6dB to 10dB of boost). If this causes feedback, reduce the channel level slightly. Sweep the frequency control slowly through its range. When you have found the frequency that sounds worst (or is most resonant, or most prone to feedback), move the gain control to apply a modest amount (from 3dB to 6dB) of cut. Finally try reducing the bandwidth a little. If this makes the feedback return or the sound worse, try increasing it a little.

For feedback control:

1. Set the bandwidth or Q control at a low bandwidth (or high Q) - typically counter-clockwise, at around 8 or 9 o'clock.
2. Set the frequency control at the lower extreme of its range.
3. Apply a moderate amount (around 6dB to 10dB) of cut.

With the channel you wish to correct open, raise the channel's output until it is beginning to feed back. Sweep the frequency control slowly through its range. The feedback should stop when you have found the correct frequency. If it doesn't, increase the amount of cut and/or the bandwidth slightly, and sweep the frequency control slowly through its range again. When you have found the correct frequency, reduce the bandwidth and the amount of cut as much as you can without feedback occurring.

## Do you need one?

If your mixer has one or more sweepable midrange controls, a parametric EQ is something of an indulgence, and if you have a modern digital mixer it probably includes fully parametric EQ on all channels anyway. However, you might reconsider the importance of getting one if you frequently experience problems with feedback (either on your front-of-house or monitor system as a whole, or on individual instruments).

Many system controllers include programmable parametric EQ functions, allowing a system's overall frequency response to be tailored to specific loudspeaker combinations.

## What sort do you need?

You need enough bands to cover most of the usable frequency range (from around 100Hz to 10kHz). Frequencies below 100Hz or above 10kHz can usually be dealt with effectively by shelving (high-pass and low-pass) filters, and feedback above 10kHz is unlikely to be a problem unless you're Doing Something Unadvisable with microphone and loudspeaker positions.

If feedback is a problem at a lot of different frequencies then you are at the limit of your system's capabilities, and a parametric won't help matters much.

These factors combine to mean that you are unlikely to need more than a few bands of parametric EQ.

While very narrow (1/60 octave) and very broad (3+ octave) bandwidths are possible, you are unlikely to need anything much less than 1/30 octave or much more than 2 octaves. If the range is given in Q values, this will be between 0.7 (about 2 octaves) and 45 (about 1/30 octave). Similarly if you need more than 10dB of cut or boost, you should consider getting new pickups, mics or loudspeakers (depending on the cause of the problem).

Apart from this, every EQ has its own ‘sound’, so - if you can - listen before you hire or buy.