====== Speaker Directivity and Room EQ ======

How do you EQ an exponential horn? That's what this entry is about, although it could apply to any speaker or speaker driver that exhibits increasing directivity at higher frequencies.

Back around 2017 I completed a pair of large corner horn speakers. These incorporated an exponential midrange horn with an exponential tweeter horn mounted coaxially. The reason for this choice was a goal of maximal efficiency and minimal speaker membrane motion, which was taken to be the ultimate cause of poor audio quality. The mid-horn was intended to operate from 200 Hz up to 2000 Hz, with the tweeter horn operating from 2000 Hz on up. This was a loud and powerful combination that could produce enrapturing sound at times. But it could also annoy the ears, and I assumed a number of causes, not the least being it's poor off axis response. The mid horn would beam at 2 kHz, and then the tweeter above that would have much wider dispersion before again beaming up above 4 kHz or so. 

After much frustration with this horn assembly I decided around 2020 to retire the coaxial tweeter horn and employ a large constant directivity waveguide for the tweeter instead. To match directivity to the mid horn required a much lower crossover for the tweeter - about 600 Hz, which left the mid-horn running a single octave from 300 to 600 Hz. This solved much of the tonal irritation I was perceiving but not without some loss of ultimate impact and especially efficiency. Getting the tweeter down to 600 Hz took a lot of EQ. This setup also ruined the look of the speaker because placing the big waveguide above the mid-horn was mechanically awkward.

Recently a thought occurred to me about how to target the room curve for a speaker. I decided to measure the output from the mid horn at the listening position with a long IR window to see its native cumulative in-room response. To my surprise, this turned out to be a remarkably straight line response from about 300 Hz up to 6000 Hz with a roughly 3 dB / octave slope. That's a lot of slope for a room curve, but I decided to play some music with just the mid operating by itself full range, and to my surprise it sounded remarkably natural and quite easy on the ear. That was encouraging, so I decided to match the tweeter and woofers with crossovers at 300 and 6000 Hz, their levels adjusted to match the midrange nicely so that the rather steep 3 dB/ octave slope was extended at the listening position. This was  bass heavy, but not as bad as I expected. I decided to EQ the bass response below 300 flat, so zero slope below 300 Hz and 3 dB/octave above that. Now I had some remarkably nice sound, and the big constant directivity tweeter horn wasn't really doing much anymore. 

Encouraged and inspired further, I decided to re-activate the coaxial tweeter horn. After listening and making some adjustments I settled on a crossover to the tweeter at 3500 Hz. Some room EQ that's always required between 100 and 400 Hz was then applied by ear, and then I heard some great sound from this crazy mid-horn / coaxial tweeter arrangement that I had thought was a write off! So what's going on here?

I decided to look again at the nearfield measurement of the mid-horn to see what the curve looked like. It is also sloped downward with rising frequency, but at a much greater 6 dB/ octave. What I used to do with this horn was EQ it flat nearfield and then try to adjust from there. But what does that do at the listening position? It gives a 3 dB/ octave rise at the listening position. Now that isn't likely to sound good. I've never seen a room curve recommendation with a rising slope in any frequency band. Obviously EQing that horn flat nearfield was not a good approach.

The frequency response slope decreases with distance on an exponential horn, which means we can't eq the exponential horn flat up close. It needs to have a slope that won't be reversed at the listening position. But why does the slope decrease with distance? This is a simple fall-off rate issue. Sound that is more directional falls off at a slower rate. So as you move away from the horn, the less directional lower frequencies fall off faster than the higher frequencies. But isn't total energy in the room still the same? Yes, to some degree. The bass spreads out over the room more quickly and eventually bounces back to the listening position, adding to the cumulative total. Some of the reflected energy gets absorbed before it makes it back to the listening position, so in my case at least, the direct sound fall-off rate is overwhelming the later reflections addition to the cumulative sound level at the listening position. The early reflections are largely redirected away from the listening position by the corner placement of the speakers. 

In summary, I've found a way to return my speakers to their original design configuration and have them sound very pleasing by NOT equalizing the output of the mid-horn flat at nearfield. I will continue to listen and perhaps tweak the equalization of the mid horn to result in a more gentle slope at the listening position and find out if that's better or worse. I've got a lot of questions remaining. Why doesn't it perceptually sound unnaturally dull when listening off-axis, or in another room? The upper frequencies being so narrow should be adding less total energy to the room. Somehow I'm not perceiving it as at all unnaturally "dark" sounding anywhere in the room or in adjacent rooms. It's really nice and easy on the ears. It also can get a //lot// louder because the EQ requirements are greatly minimized, and the tweeter isn't being asked to go so low.

Update December 22, 2025

I tried to adjust the room slope at the listening position to 0.5 dB/octave. This sounds too bright. I've also tried to model the fall-off rates for narrow vs wide dispersion drivers and the results are not showing a consistent brightening. This may be a specific problem with my room and the specific characteristics of the speaker I'm using. Fall-off rate is not intrinsically about directivity. It's more about the curvature of the wave front. It's possible to have a narrower pattern that is still made by a curved wave front, which means it will have the same fall off rate as a wider dispersion pattern that has the same wave front curvature at any given distance. As we move away from a small plane source we see that it's wave front curvature becomes very close to the same as the curvature of a point source at the same location. It's only up very close that this fall off rate differs a lot. This may be why 2 meters is considered sufficient for on-axis measurements. The anechoic on-axis response shouldn't change much with distance after that for most any "normal" speaker. 
My simulations did suggest that room acoustics can have some surprising effects, with diffusion being typically more effective on high frequencies than lower, this could mean diffusive elements can beam more high frequency energy back to the listener. If the walls are bass leaky, this could result in a brighter than expected response at distance, although the same would hold true with a speaker that was not beamy up top.
I'm starting to suspect that the reason my speakers need a fairly steep room curve is due to the fact that for the anechoic response to be flat on axis at the listening position, the off axis energy in the lower frequencies is actually quite a bit higher. My problem may be that I don't have any way to get the anechoic on-axis response at 2 meters because of room reflections, so I'm really shooting in the dark and getting confused by the reflections creeping in. I had better luck by starting with an no-EQ result and then working backwards from there. I suspect now that if I could figure out how to get the on-axis anechoic response for the speaker what I like the sound of would actually look pretty flat.

Update January 2, 2026

It turns out that I can't seem to get a sound I really like that makes much sense in terms of ancehoic on axis response being prefectly flat for each driver. I'm not sure why, but it always seems best if I don't EQ the speaker drivers, but only set the crossovers and adjust their levels by ear. The end result in this room is a fairly steep room curve as noted earlier, but with some specific frequency cut backs as a room treatment. 

Update January 20, 2026

Somehow I now am EQing the drivers flat fairly nearfield and I am liking the sound. I should never be a speaker reviewer. I don't know if it's my perception that changed or what but now I'm liking the sound with the coaxial tweeter EQ'd flat on-axis measured at 2 meters and crossed over all the way down at 600 Hz to the mid-horn, which is also EQ'd flat from it's 600 Hz crossover down to about 130 Hz. I don't understand what changed, but now at least this makes some sense. It actually sounded prettty good with a large overlap between the mid and tweeter, covering from about 1000 Hz to 5000 Hz working together. It was a little crunchy sounding at times but very present and lively and not strident or overly sibilent. Not perfectly neutral but very easy on the ears and worked well for me with everything I listened to. With the 600 Hz crossover I avoid dips in the off-axis response. Instead the off-axis starts sloping down at about 700 Hz or so in a straight line. This also sounds good. Not quite as punchy and intense but seemingly smoother, less colored.