Why EQ Cannot Give an Open Earbud Bass

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For a sealed headphone running comfortably inside its limits, much less than people claim. For anything that does not seal your ear, far more than an equaliser can reach, and the gap is about 110 decibels at 50 hertz rather than a matter of taste.

The reason is that an equaliser and a driver are working in different currencies. An equaliser moves a curve. A driver has to move air, and the way it does that is by moving a distance. How much distance a given loudness costs is decided almost entirely by how the earbud is coupled to your ear, and hardly at all by anything on the specification sheet. So the honest answer to the question is that the headphone barely matters and the seal matters enormously, which is not the answer either side of the argument usually gives.

Start by granting the point, because most of it is true

An equaliser applies a linear filter. If a headphone's deviation from the target is a minimum phase magnitude error, which most of it is, then inverting that error with a filter genuinely removes it, phase and all. That is not a workaround or an approximation. It is the same correction, applied earlier in the chain.

So for two sealed headphones playing at a sensible level, well inside what their drivers can do, a measured equaliser really does collapse most of the audible difference between them. The remaining differences are in things a filter cannot touch, and the question is what those things are and how big they get.

Our own page on why 100 watts is not twice as loud as 50 already names the first one for loudspeakers: output "is limited by cone excursion and cabinet volume long before any amplifier runs out". That sentence is the entire argument of this page, moved from a living room to an ear, where the volumes involved are a few thousand times smaller and the consequences are correspondingly stranger.

What a seal is worth, in decibels

Here is the first equation, and it is the surprising one. A driver sitting on a genuinely closed volume does not radiate sound at all in the usual sense. It compresses the trapped air. The pressure it makes is the adiabatic stiffness of that air, 1.4 times atmospheric or 141,855 pascals, multiplied by the volume it sweeps and divided by the volume it is compressing.

Notice what is missing: there is no frequency anywhere in it. A sealed driver makes the same pressure from the same movement at 20 hertz as at 2,000, which is why a properly sealed in-ear bud has bass that simply continues downward until something else stops it.

Put numbers in. The residual volume between an earbud and an eardrum is about one cubic centimetre. An 11 millimetre driver has a cone area of 95 square millimetres. Reaching 100 decibels in that volume takes 0.21 micrometres of movement, which is about a fifth of a thousandth of a millimetre, and is nothing. Give that driver the 0.3 millimetres of travel a micro driver of its size typically has and the arithmetic says 163 decibels, flat.

Nobody reaches 163 decibels, and the reasons are distortion, the leak that always exists, and the fact that no real suspension stays linear to its mechanical limit. That is the point rather than an objection. A sealed driver has so much bass headroom on paper that it is never the thing that runs out, which is exactly why fit dominates measured bass on the same pair of buds by more than 10 decibels and why everyone who has swapped eartips already knows it.

There is only one listing in our earbud catalogue that describes a seal at all. A set of ultra flat sleep earbuds for side sleepers lists "Soft seal dampens outside noise" among its strengths, and it is a bedtime bud whose own drawbacks say the "Sound is soothing rather than detailed hi-fi". So the single sealed product on the shelf is the one not aiming at sound quality, and every bud that is aiming at it has given the seal away. That is a finding about the catalogue and about the market it reflects.

Take the seal away and the frequency arrives squared

Now the second equation, and it is where the question gets answered. An unsealed bud is not compressing a volume. It is a small source radiating into open air a short distance from your ear canal, and for that the pressure is the air density times the cone area times pi times the square of the frequency times the displacement, divided by the distance.

The frequency is squared. That single exponent is the whole difference between the two designs. Halve the frequency and the same movement makes a quarter of the pressure, which is 12 decibels down per octave. Put the other way round: holding a level as you descend costs four times the travel every octave, and the travel is finite.

A Baseus Bowie MC2 Air clip on open ear earbud is the right product to run that on, because it publishes the one acoustic figure the arithmetic needs: "11mm custom dynamic drivers with titanium-coated diaphragms". At 0.3 millimetres of travel and 20 millimetres from the canal, an 11 millimetre driver tops out at 105.6 decibels at a thousand hertz, 77.6 at two hundred, 65.6 at one hundred, and 53.5 at fifty.

Compare that with the 163 flat decibels of the sealed case and the gap at 50 hertz is 109.6 decibels, which is a factor of about 302,000 in pressure. Nothing an equaliser does is within six orders of magnitude of that.

The record states the conclusion correctly and without the magnitude. Its drawbacks say "Bass will not match sealed in-ear buds" and its performance text says "bass will never hit as hard as a sealed tip delivers", and then adds the sentence that matters most: "The main points come from the open-ear design itself, not this particular pair." That is exactly right, and 110 decibels is what "not this particular pair" is worth. The record also credits a "SuperBass 2.0 mode" for a fuller low end, and on this arithmetic such a mode can only be an equaliser boost, which means it is spending travel the driver does not have and will reach its limit before the boost does.

So what does the hardware buy? Diameter, squared, and about half an octave

Area goes as the square of diameter, and area is the only term in the open equation that a buyer gets to choose. Our catalogue happens to publish three driver sizes, which makes this unusually concrete.

A Defunc True LITE II open fit wireless earbud publishes "a 13mm dynamic driver, relatively large for an earbud". Thirteen over eleven, squared, is 1.397, so it is 2.90 decibels louder than the 11 millimetre bud everywhere: 56.4 decibels at fifty hertz instead of 53.5.

A pair of JabNecter open ear headphones publishes 16 millimetre drivers and 25 grams. Sixteen over eleven, squared, is 2.116, so it is 6.52 decibels louder: 60.0 decibels at fifty hertz.

Convert those into the currency that means something. At a 12 decibel per octave slope, 2.90 decibels is 0.242 of an octave and 6.52 decibels is 0.543. So the 13 millimetre bud reaches the 11 millimetre bud's fifty hertz ceiling at 42.3 hertz, and the 16 millimetre bud reaches it at 34.3. Five millimetres of extra diameter is worth a little over half an octave of extension.

That is a real gain and it is a small one, and it is the honest size of the "does the hardware matter" question for this class of product. Half an octave. Against which the seal is worth 109.6 decibels, or 9.1 octaves at the same slope, which is more than the entire audible range.

The JabNecter record also contains the single best sentence in the category on this subject. It says the lack of isolation and deep bass "is the physics of an open design, not a fault", and then flags the tension in its own marketing: "The maker highlights bold sound and bass, yet open-ear audio is inherently less isolated and less bass-heavy than sealed options." A record that notices its own product's claim pulling against its own product's physics is doing the job properly.

One bud on the shelf whose ceiling cannot be worked out at all

A set of Defunc True Basic wireless earbuds uses a "patented MultiTip semi-in-ear shape with soft silicone ear wings" that "sits securely without pushing into the ear canal", and its drawbacks say "Open fit means lighter bass". Both true. But the listing publishes no driver diameter, and without a diameter there is no area, and without an area the open equation has nothing to work on.

So of four unsealed listings, three publish the number this arithmetic needs and one does not, and none of the four publishes the other number it needs, which is the travel. Not one earbud we carry states an excursion, a sensitivity in decibels per milliwatt, or a frequency response. The diameter is published because it is easy to measure and sounds impressive. It is also the smaller half of the product that decides the answer, since area scales as the square of a quantity that varies by 45 percent across the catalogue while travel is unstated and varies by rather more.

The other thing an equaliser cannot do is subtract

This is where the second question comes in, the one about wearing open headphones near an air conditioner, and it is the same arithmetic read from the other end.

An equaliser can add music. It cannot remove noise, because the noise does not pass through it. An open coupling provides essentially zero decibels of passive attenuation by design, so whatever is in the room arrives at full strength and the only lever you have is to put the music above it, band by band.

Work that against the ceilings. A room with a unit running in it sits somewhere around 60 decibels, and most of that energy is low frequency. At a hundred hertz the 11 millimetre bud's ceiling is 65.6 decibels, which is 5.6 decibels over the noise, and 5.6 decibels of margin is audible as a change in tone and not as bass. At fifty hertz its ceiling is 53.5, which is 6.5 decibels under the noise. Below the noise is below the noise. There is no equaliser curve, no bass boost mode and no fit adjustment that recovers a signal you are not generating.

Which means the answer to "how do people handle it" is that they stop trying to win that band. Raise the whole level and the midrange and treble come clear of the noise long before the bass does, because the noise falls with frequency and the bud's ceiling rises with it. The two curves pull apart, and content that lives above a few hundred hertz, speech, podcasts, most vocal music, works fine. Bass heavy material does not, and no amount of processing changes that.

A Poly Blackwire 3325 stereo USB headset is the opposite case and the only product here with cushions on both ears. Its record says "Stereo with cushions on both ears gives passive isolation and makes the headset usable for more than voice", which is the correct mechanism named in the correct order: the isolation comes first and the usefulness follows from it. Its drawbacks then say "Stereo covers both ears, so no room awareness", which is the same fact counted as a cost, and both entries are right because it is a trade and not a feature.

That record also deserves crediting for something it does not do. It states plainly that there is "no frequency response, driver size or microphone pickup pattern anywhere on the listing" and that "We have reported that absence rather than filling it with plausible-sounding figures." That is the correct response to a missing specification and it is rarer than it should be. It also means this is the one headphone on the shelf whose behaviour cannot be estimated even roughly, because a cushioned over ear cup is somewhere between the sealed and open equations and which end it sits nearer is decided by the pad seal, which nobody measures and everybody's head changes.

What I deliberately did not calculate

Distortion. It belongs in this argument and I have left it out on purpose.

An equaliser is linear and a driver near its travel limit is not. The region where a bass boost is asking for most of the available excursion is exactly the region where the suspension stiffens, the motor leaves its uniform field and harmonic distortion climbs steeply. So a boost that flattens the response on a measurement sweep can manufacture audible distortion at the same time, and the two effects are invisible to each other on a frequency response plot.

I cannot put a number on it from what our records contain. Not one listing publishes a total harmonic distortion figure at any level or frequency, which means any estimate would be a guess dressed as arithmetic. What I can say is the direction, and the direction is that the equaliser setting which looks most successful on paper is the one most likely to sound worst, which is the opposite of how people usually report their results.

The honest limit

Three of the inputs above are published and the rest are not. The 11, 13 and 16 millimetre diameters are published. The 15 degree, 25 gram and 4.9 gram figures are published and irrelevant to this. Everything else is representative: 0.3 millimetres of peak travel is typical for micro drivers of this size and no listing states it, the 20 millimetre radiating distance stands in for a bud's offset from the canal entrance and varies with ear shape, the one cubic centimetre residual volume is the conventional figure for a sealed bud, and the 60 decibel room and 75 to 85 decibel listening band are ordinary conditions rather than anyone's specification.

What none of those assumptions can move is the structure. The 12 decibels per octave is an exponent, not a measurement. The 2.90 and 6.52 decibel gaps between the three buds come from the diameters alone and are exact. The 0.242 and 0.543 octaves those gaps buy follow from the exponent. And the sealed case has no frequency term in it at all, which is why the seal wins by a margin no choice of driver can approach.

So the answer. If you are comparing two sealed headphones at a reasonable volume, an equaliser gets you most of the way and the hardware matters much less than the hobby believes. If one of them does not seal, the equaliser is being asked to supply displacement rather than gain, and it will fail silently by clipping the driver instead of the signal. Our page on open ear versus sealed headphones puts it in words already, that sealed designs "deliver sound open-ear physically cannot match", and the only thing this page adds is how much of a mismatch "cannot" is. It is 110 decibels at fifty hertz, and the choice of driver inside the open design is worth half an octave of it.