What is Q in EQ?

Q in plain English

Every bell on a parametric EQ has three controls. Frequency says where the band sits, gain says how far it boosts or cuts, and Q says how many of the neighbouring frequencies come along with it. Turn the Q down and the band spreads into a broad, gentle hill. Turn it up and the hill gets thinner until it's a spike that touches a single note.

The letter stands for quality factor, a term from electronics, where it describes how sharply a circuit responds at one frequency. You don't need the electronics to use it. A higher number is narrower, and that's the part to remember, because it runs the opposite way to bandwidth, the other name you'll see for the same control.

The EQ lesson covers all the controls together. This page stays on width: how Q is worked out, what wide and narrow bands sound like, which values suit which jobs, and why the same number can look different from one EQ to the next.

Reading the lab

The lab starts on pink noise, a hiss with the same amount of energy in every octave. The big screen tilts its spectrum so pink noise reads as a roughly level line, which means anything you do with the EQ shows up in the teal shape as the shape of the curve itself. It's the clearest way to see width, and the easiest sound to hear it on.

Band 1 is a bell, the orange point numbered 1, and the pink line is the EQ curve it draws. Drag the point sideways to move it and up or down to boost or cut, and use the Q control under the screen to change its width. Turn the Q and the Right now panel reads out the width in octaves and as a range of frequencies. Band 2 is a high-pass filter, switched off until the last step.

Press Listen to this band and the lab plays only the slice of the sound your bell covers. Turn the Q while it's on and you hear the slice grow and shrink, down to about a third of an octave, which is as narrow as the listening filter goes. A/B switches the EQ off and matches the level, so a boost doesn't win just by being louder. Once you've heard the noise, move on to the full mix or the vocal; from step 5 the lesson does that for you.

How is Q calculated?

Q is the centre frequency divided by the width of the band in hertz:

Q = centre frequency ÷ bandwidth in Hz

Take a 9 dB bell at 1 kHz with a Q of 1.41. Its width is measured between the two points where the boost has reached half its height, so at +4.5 dB, and those points are at about 707 Hz and 1,414 Hz. That's 707 Hz apart, and 1,000 ÷ 707 is 1.41. Each edge is the centre multiplied or divided by the same amount, about 1.41 here, which is why the band looks symmetrical on an EQ screen even though it reaches further above the centre in hertz than below it.

Because Q is a ratio, the same setting gives the same musical width anywhere on the spectrum. A Q of 1.41 at 100 Hz is only 71 Hz wide, from 71 Hz to 141 Hz, and at 10 kHz it's 7.1 kHz wide, from 7.1 kHz to 14.1 kHz. Both are one octave, and your ears hear them as the same size of slice. That's the reason most EQs use Q instead of a width in hertz: you can move a band from the bass to the treble and its character stays the same.

A Q of 10 is about a seventh of an octave wherever you put it, a little less than the gap between two notes a whole tone apart. At 50 Hz that's just 5 Hz, and at 5 kHz it's 500 Hz.

Converting Q to bandwidth in octaves

Some EQs show bandwidth in octaves instead of Q, and older hardware sometimes just says wide and narrow. To go from one to the other, use Q = √(2^N) ÷ (2^N − 1), where N is the width in octaves. You'll rarely need the formula, because a handful of values covers nearly everything you'll do.

Watch the direction when you switch between them. If one EQ says 1 octave and another says a Q of 1.41, they mean the same width, and raising the bandwidth widens the band while raising the Q narrows it.

What wide and narrow bands sound like

A wide band changes the tone of a sound without drawing attention to itself. Boost two octaves around 1 kHz and the sound gets more forward and a bit nasal across the whole middle, much as turning up the mid knob on a guitar amp does. Nothing sticks out, because the change is spread over many notes and overtones at once.

As the band narrows, you start to hear its frequency as a pitch. At a third of an octave there's a faint tone in the pink noise, and by a Q of 10 it's a clear whistle. A narrow band is close to the width of a single note, so a big boost pulls a near-pure tone at that frequency out of anything that has energy there.

Narrow bands also ring. A filter that picks out a thin slice keeps sounding for a moment after the sound feeding it stops, like a bell struck once, and the narrower the band and the lower its frequency, the longer the ring lasts. On drums that turns a tight hit into one with a tonal tail. It's the same effect that makes a synth filter whistle when you turn its resonance up.

Why you cut narrow and boost wide

Put the narrow boost on music and anything that happens to land near its frequency jumps out, which on a full mix means a random note or overtone ringing above everything else. Flip the same band to a cut and the change almost disappears. Only a thin slice has gone, and ears are much less sensitive to a narrow dip than to a narrow peak of the same depth.

That difference is the whole reason for the rule of thumb. A narrow cut can take out one bad frequency, like the hollow ring of a snare or a boxy room tone on a vocal, and leave the rest of the sound untouched. A narrow boost does the opposite of what you want, because it creates a resonance where there wasn't one. When something needs more of a range, a wide, gentle boost of 1 to 3 dB brings it out without any one frequency poking through.

Wide cuts have their place too. When a whole range is too thick, as the low mids of stacked guitars and keys often are, a cut of 2 to 4 dB at a Q around 1 thins it out evenly. Step 7 in the lab does this at 300 Hz.

Which Q to use

These are starting points. Set the band, then turn the Q slowly while you listen, and stop at the widest setting that still does the job. Wider bands sound more natural, so only go narrow when you have to.

Gain and Q work together. A deep cut at a low Q takes a lot out of the sound, so when you widen a band you'll usually want less gain for the same effect. It works the other way round too: a narrow cut can need 6 dB or more before you notice it on a full mix.

How to find and remove a resonance

A resonance is one frequency that rings louder than the rest, from the shell of a drum, the body of an acoustic guitar or the walls of a small room. The narrow end of the Q range is built for this job.

1. Set up a narrow boostA bell with a Q of 6 to 10 and a boost of 8 to 10 dB. Turn your monitors down a little first, because the sweep can get loud and harsh.
2. Sweep it slowly through the range you suspectMove the frequency while the sound plays. Most of the way it'll sound like a whistle passing through; at the problem frequency the ringing jumps out much louder than anywhere else.
3. Flip the boost into a cutLeave the frequency where it is and turn the gain down to about −3 to −6 dB.
4. Widen it until it sounds naturalLower the Q a little at a time. Stop as soon as the ring has gone and the sound around it still feels whole.
5. Check it in the mix at matched levelSwitch the band in and out with the rest of the track playing. If you can't hear what improved, take some of the cut back out.

Use the sweep only when you can already hear a problem. Sweep through any sound with a 10 dB boost and every frequency will sound wrong, which leads to a curve full of small cuts that each took away a bit of the tone. In the lab, Listen to this band does a gentler version of the same search: it plays only the band's slice, so you can hear what's in it without boosting anything.

Q on filters, shelves and notches

High-pass and low-pass filters

A high-pass or low-pass filter keeps cutting all the way to the end of the spectrum, so there's no width for Q to set. On a filter, Q sets resonance, the shape of the curve right at the cutoff. At a Q of about 0.71 the filter stays as flat as it can up to the cutoff and is 3 dB down there. At 0.5 the roll-off starts earlier and the cutoff is 6 dB down. Above 0.71 a bump grows: on a 12 dB per octave filter, a Q of 2 puts the cutoff about 6 dB above the flat level.

Mixing filters are usually left at about 0.71 so they don't add a bump. Synth filters use resonance on purpose, and the filter resonance lesson covers that side of it.

Shelves

Many plug-in EQs give shelves a Q control too. Turned up past about 0.7, it makes the shelf steeper and adds a small bump on the boosted side of the corner with a dip on the other side, so a boosting low shelf picks up a small cut just above it. That shape is close to the curve behind the Pultec low-end trick. The shelves in this lab have no Q, because Web Audio's shelving filters ignore it; the shelving EQ lesson covers what they do have.

Notches

A notch is a cut so deep that a frequency is almost entirely removed, and its Q is measured between the points 3 dB down from the flat level. At 50 Hz a notch with a Q of 10 is 5 Hz wide, and at a Q of 30 it's under 2 Hz wide, narrow enough to take out mains hum and leave the bass notes around it alone. The notch filter lesson goes further.

Why the same Q looks different on different EQs

There's no single agreed way to measure the width of a bell. This lab, like Web Audio's filters and Robert Bristow-Johnson's Audio EQ Cookbook that they're based on, measures between the points where the boost reaches half its height in decibels. Other designs measure 3 dB below the peak, which gives a different width for the same curve and doesn't work at all for boosts smaller than 3 dB. So a Q of 2 in one plug-in can draw a wider or narrower bell than a Q of 2 in another.

Some EQs also change the width as you change the gain. On a proportional-Q design, such as the API 550A, small boosts are wide and big boosts get narrower, so gentle moves stay smooth and bigger ones sound focused. Other EQs have no Q control at all: the mid band of a Neve 1073 has a fixed width, and the Pultec EQP-1A has a bandwidth knob running from sharp to broad that only applies to its high boost.

Digital EQs have one more quirk near the top of the spectrum. A basic digital bell gets squeezed as it nears half the sample rate, so a wide boost at 15 kHz in a 44.1 kHz session can come out narrower and lopsided compared with the same settings at 1 kHz. Many modern EQs correct for this, often by running at a higher sample rate inside, which is another reason two EQs with the same numbers can sound different on a wide high boost.

Common Q mistakes

Big, narrow boosts

A 9 dB boost at a Q of 10 picks out one frequency and makes it whistle, which is step 5 in the lab. If you want more of something, widen the band and use less gain. A boost that only works when it's narrow and huge is usually trying to add something the sound doesn't have.

Reading the Q backwards

Because bandwidth and Q run in opposite directions, moving from an EQ that shows octaves to one that shows Q can catch you out. When in doubt, look at the shape on the screen: a thin spike is a high Q.

Notching everything you hear in a sweep

A narrow boost makes every frequency sound suspicious. Five or six narrow cuts on one track can each be inaudible and still add up to a sound that's lost its body. Cut only what you could hear as a problem before you started sweeping.

Using narrow cuts for broad problems

If a whole range sounds too heavy, a narrow notch inside it won't fix it. Mud spread across 200 to 500 Hz needs a wide cut at a Q of 1 or 2; a Q of 8 just takes a sliver out of the middle.

Forgetting that a filter's Q is resonance

Turning up the Q of a high-pass to make it feel tighter adds a bump right where the low end of the sound is, which often makes a bass or kick boomier at the cutoff. Leave mixing filters near 0.71 unless you want that bump.

Training your ears to hear width

The quiz under the lab puts a 9 dB boost in the sound and asks how wide it is: wide (a Q of 0.7), medium (2) or narrow (8). The screens are covered and the level is matched. The centre frequency changes from round to round, so only the width gives it away. Pink noise is the easiest sound to start on. On the vocal and the full mix, listen for the point where a change of tone turns into a pitch. Your best score out of eight is saved in your browser.

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