What is a filter slope?

Filter slopes in plain English

A high-pass or low-pass filter has two settings that decide what it removes. The cutoff says where the cut starts. The slope says how hard it cuts from there on, and it's the difference between a filter that fades the low end out gradually and one that stops it dead.

Slopes are written in decibels per octave. An octave is a doubling of frequency, from 50 Hz to 100 Hz or from 4 kHz to 8 kHz, so a slope of 12 dB per octave means every halving of frequency below a high-pass cutoff takes off another 12 dB. Bigger numbers are steeper. Six decibels per octave is about as gentle as a filter gets, and 48 dB per octave is close to a wall.

The EQ lesson covers filters alongside bells and shelves, and the high-pass and low-pass filters lesson covers where to put the cutoff on each instrument. This page stays on the slope: what the numbers mean, where they come from, how gentle and steep filters sound and which one to pick.

Reading the lab

The lab starts on pink noise, a hiss with equal energy in every octave. The big screen tilts its spectrum so pink noise reads as a flat line, which means the teal shape takes on the shape of the filter itself. It's the easiest way to see a slope, and the noise is a good sound to hear one on, because there's something at every frequency for the filter to remove.

Band 1 is a high-pass filter and band 2 is a low-pass, switched off until step 6. Select a band and turn the Slope control under the screen to move between 12, 24, 36 and 48 dB per octave. Drag a band's point sideways, or use the Freq control, to move its cutoff. Q is locked on this page so the filters keep their plain, bump-free shape; the resonance lesson is where that control comes in.

The Right now panel reads the curve one octave past the cutoff and tells you how far down the sound is there, along with how much of the loop's energy sat in the part being removed. Listen to this band plays only the stretch the selected filter works on, so on a high-pass you hear the low end it's taking away. A/B switches the filters off and matches the level, which counts for a lot here, because a high-pass that removes a big chunk of bass also makes the loop quieter.

What does dB per octave mean?

It's a rate. Past the cutoff, the filter takes away the same number of decibels for every octave you move. Put a high-pass at 200 Hz with a slope of 12 dB per octave and you get roughly this:

• 200 Hz, the cutoff: 3 dB down
• 100 Hz, one octave below: 12 dB down
• 50 Hz, two octaves below: 24 dB down
• 25 Hz, three octaves below: 36 dB down

Change the slope to 24 dB per octave and the cutoff stays put while each of those numbers doubles: 100 Hz is now 24 dB down and 50 Hz is 48 dB down. At 48 dB per octave, 100 Hz has already lost 48 dB. For a sense of scale, 6 dB down is the wave at half its height, 20 dB is a tenth, and 40 dB is a hundredth, which on most sounds is too quiet to hear under everything else.

A low-pass works the same way in the other direction. A 12 dB per octave low-pass at 4 kHz is 12 dB down at 8 kHz and 24 dB down at 16 kHz. In a digital EQ a low-pass up there cuts a little faster than that, because a standard digital filter falls all the way to silence at half the sample rate, so the lab's 4 kHz low-pass is about 14 dB down at 8 kHz.

The figure shows something else about the cutoff. All four filters are 3 dB down at the cutoff frequency whatever their slope, because that's how the cutoff of a standard filter is defined. The slope decides how quickly the level falls once you're past it, and how much of the sound just inside the cutoff gets touched. Half an octave above a 200 Hz high-pass, at about 280 Hz, the 12 dB filter is still taking off about 1 dB, while the 48 dB filter has let the sound back up to full level.

The common slopes

Filters come in steps of 6 dB per octave. These are the ones you'll see most, with the cut measured on a Butterworth filter, the flat, bump-free design that most EQs use for their high-pass and low-pass bands.

Look at the 6 dB row. One octave past the cutoff it's 7 dB down, more than its slope, because the curve is still bending into its full rate there. The dB per octave figure is the rate a filter settles into once it's well past the cutoff; close to the cutoff, every filter is still turning the corner.

What's on offer depends on the EQ. Ableton Live's EQ Eight gives its high-pass and low-pass bands a choice of 12 or 48 dB per octave. FabFilter Pro-Q 3 runs from 6 up to 96 dB per octave and adds a brickwall setting, a near-vertical cut. This lab covers 12 to 48 in steps of 12.

Poles, order and where the numbers come from

The simplest filter there is, one resistor and one capacitor, has a slope of 6 dB per octave. Well below its cutoff, a high-pass built that way lets through half as much signal every time the frequency halves, and a wave at half its height is 6 dB quieter. Engineers call that a first-order or one-pole filter.

To get a steeper slope, you chain more of these stages together, and each one adds another 6 dB per octave. Two poles make 12 dB per octave, four make 24 and eight make 48. That's why synth makers talk about 2-pole and 4-pole filters, and why soft synths often label their filters LP12 and LP24: the number is the slope, and dividing it by 6 gives the number of poles. Digital EQs usually build their filters from two-pole sections called biquads, so this lab's 48 dB per octave filter is four of them in a row.

You'll sometimes see slopes in decibels per decade instead, mostly in electronics. A decade is a tenfold change in frequency, and 6 dB per octave works out at 20 dB per decade.

Stacking two filters

Putting two identical 12 dB per octave filters in a row does give you 24 dB per octave far from the cutoff. Near the cutoff the two 3 dB losses add up, so the pair is 6 dB down at the cutoff and starts bending earlier than a single 24 dB filter would. That pairing has its own name, a Linkwitz-Riley filter. A Linkwitz-Riley low-pass and high-pass at the same frequency add back up to a flat line, which is why many multiband compressors and speaker crossovers use them. If an EQ's filter is further down at the cutoff than you expect, it may be one of these.

Gentle and steep slopes on real sounds

A gentle slope sounds like a change of tone. A 12 dB per octave high-pass under a bass turns the lowest notes down without removing them, so the bass gets lighter and some of its weight is still there. The cut is spread across a couple of octaves, which makes it hard to hear exactly where it starts.

A steep slope sounds like a line has been drawn. At 48 dB per octave and 80 Hz, the same bass keeps every note above about 110 Hz at full level and loses 20 dB or more of everything below 60 Hz, so a low E at 41 Hz drops by 46 dB and stops being part of the sound. When the cutoff lands in the middle of what an instrument is playing, a steep filter leaves some notes full and others hollow, and you can hear the join.

Low-pass filters follow the same pattern. A gentle low-pass at 4 kHz darkens a mix gradually, much as distance does, because the top end fades out instead of stopping. A steep one at the same cutoff keeps everything below 3 kHz as it was and wipes out the cymbals above, which sounds much more like an effect.

There's a trade-off in those examples. With a gentle slope, you have to set the cutoff further from the sound you want to keep, or the filter starts eating into it. A steep slope lets you put the cutoff right next to the lowest note and still remove what's below, so steep filters are the tool for taking rumble or hum out from under a part without changing the part itself.

Steep slopes and phase

Every ordinary filter, analogue or digital, also shifts the phase of the frequencies around its cutoff, which means it delays some frequencies a little more than others. The steeper the slope, the bigger the shift. At the cutoff of a Butterworth filter it's 45 degrees for every pole: 90 degrees for a 12 dB filter, 180 for a 24 dB filter and a full 360 for a 48 dB filter.

On a single sound played on its own you won't hear that as a delay. It shows up when the filtered sound is mixed with another copy of itself. High-pass one of two microphones on a kick drum, or one copy of a bass on a parallel bus, and the phase shift near the cutoff changes how the two add up, so the low end can get thinner or fuller in ways the curve on the screen doesn't show.

Steep filters also ring. A filter with a sharp corner keeps sounding at its cutoff frequency for a moment after a sudden sound, so a 48 dB per octave high-pass can give a kick a faint tonal tail right at the cutoff. Gentle slopes ring much less. Linear-phase EQs avoid the phase shift altogether, at the cost of a short pre-echo before each hit and extra latency, and the linear-phase EQ lesson covers when that's worth it.

Which filter slope to use

Start at 12 dB per octave and only go steeper when the job needs it. A gentle slope sounds more natural and adds less phase shift, so it's the right default for almost all clean-up and tone shaping. Reach for 24 dB per octave or more when you need everything past a point gone and the sound right next to it untouched.

The telephone voice in the last step of the lab uses both filters at 24 dB per octave, with the high-pass at 300 Hz and the low-pass at 3.4 kHz. Those cutoffs come from the old landline telephone band. Turn both slopes down to 12 dB per octave at the same cutoffs and the voice sounds thinner and duller but much less like a phone.

How to set a high-pass filter's slope

This works for most clean-up filters on individual tracks. Do it with the rest of the mix playing, because a filter that sounds like too much on its own is often right in context.

1. Start at 12 dB per octave with the cutoff lowPut the cutoff well below the lowest note of the part, around 30 Hz for most sounds, so the filter starts out doing almost nothing.
2. Raise the cutoff slowlyStop when the part starts to sound thinner, then back off a little. That's the most you can take off with this slope without touching the sound itself.
3. Check what's still below the cutoffLook at the spectrum, or use a band solo like this lab's Listen to this band. If there's still rumble or hum under the part, the slope is too gentle for this job.
4. Steepen the slope instead of raising the cutoffGo to 24 dB per octave and listen again. A steeper slope clears more from below without reaching further up into the part.
5. Compare at matched levelSwitch the filter in and out. If the low end of the part sounds hollow, or the kick and bass change when it's in, go back to a gentler slope or move the cutoff down.

Slopes on synth filters

On a synth the filter is part of the sound, and the slope changes its character. A 12 dB per octave low-pass lets more of an oscillator's upper harmonics through above the cutoff, so a saw wave stays brighter and buzzier as you close it down; the Oberheim SEM's filter is a 12 dB per octave design. A 24 dB per octave low-pass, like the four-pole ladder filter Moog used on the Minimoog, removes the harmonics past the cutoff faster, so the same saw sounds rounder and the sweep from closed to open sounds more dramatic.

Neither one is better. Many soft synths let you switch between the two on the same filter, and it's worth trying both on any patch where the filter moves, especially one driven by a filter envelope. Synth filters also add resonance, a peak at the cutoff, which you'll rarely want on a mixing filter.

Common filter slope mistakes

Using the steepest slope on everything

A 48 dB per octave high-pass on every track looks tidy on the screen, but each one adds phase shift and a sharp edge at the cutoff, and across a whole mix that can leave the low end sounding hollow. Save steep filters for the jobs that need them.

Thinking a gentle slope has removed the rumble

A 12 dB per octave high-pass at 30 Hz leaves 15 Hz only 12 dB down. If the point of the filter is to stop sub rumble eating headroom, that may not be enough; a 24 or 48 dB slope at the same cutoff takes 15 Hz down by 24 or 48 dB.

Raising the cutoff when the slope is the problem

If there's still low end you don't want under a part, pushing the cutoff up removes it but also starts thinning the part. Try a steeper slope at the same cutoff first.

Judging filters at different levels

A high-pass that removes a lot of bass makes the sound quieter, and quieter tends to sound worse at first. Compare at matched level, as the A/B in the lab does, before you decide a filter has taken too much.

Trusting the number over the curve

Two EQs can show the same cutoff and slope and draw different curves, because some put the cutoff at the −3 dB point and some at −6 dB. Look at the curve on the screen and listen.

Training your ears to hear slopes

The quiz under the lab puts a high-pass filter with a 400 Hz cutoff on the sound and asks whether its slope is 12, 24 or 48 dB per octave, with the screens covered and the level matched. Pink noise is the easiest sound to start on: a gentle slope sounds like the low end fading out, and a steep one like it stopping. Once that is reliable, switch to the bass loop and listen to what happens to the lowest notes. Your best score out of eight is saved in your browser.

Questions people ask

Keep going