The Plow and The Field, Part 2

  • by Danny Maland

(The screenshots used for illustrative purposes in this post were created with GPA 2.49, available here, and Room EQ Wizard 5, available here.)

In Part 1, I spent some time talking about how it can be easy to reach for a tool that only “patches” an issue (as opposed to fixing something outright). While it can certainly be faster and easier to use an equipment-oriented solution to an acoustical problem, that “mitigation of undesirable issues through electronics” is only that. Mitigation. The root cause of an issue isn’t being addressed - rather, the symptoms are being soothed.

It’s all fine and good to say that, but there’s a deeper question involved. Why would the last few sentences be true? Ultimately, the undoing of our tools is that their adjustability to acoustical conditions will fall short in at least one of two areas: Frequency content with respect to time, and frequency content with respect to an observer’s location. Whatever other factors are in play, time invariance and spatial invariance are the key issues surrounding the limitations of electrical and electro-acoustic tools.

So - what would Grandpa Maland say about this? I can just imagine him now, leaning on some agricultural implement while talking with someone from town:

“I’ll tell you what. That boy’s got no sense. No matter where the herd is, he always moves ‘em a mile uphill to graze. Doesn’t matter if there’s hardly a lick of grass where he’s goin’, he just goes there. Winter, summer, pourin’ rain, freezin cold...every day, he moves them cows at seven o’ clock. No sense, I tell ya.”

The cowhand that my Grandpa is (fictitiously) ragging on is just like a vast number of perfectly acceptable audio devices. He always goes the same distance and direction (location invariance), and always goes at the same time (time invariance). In a human, this inability to vary behavior is seen as being not very smart - but in our gear, it’s pretty much the normal state of affairs.

Let’s first consider a very common electro-acoustical device, namely, the loudspeaker. Let’s also consider a common acoustical problem, that of a room that is highly reverberant. What’s quite obvious is that the speaker can not de-reverberate the room - in fact, as an acoustical source it causes reverberation to occur. What may not be so immediately obvious is that the loudspeaker’s output is spatially and temporally invariant.

“Wait a second!” I can hear you exclaim. “The speaker’s output is most definitely variant with respect to location! It has different measured output if you’re at a different angle, and its SPL decays as you get farther from the box.”

What you’re saying is true, but I would respectfully put it to you that what you’re describing is different observed acoustical responses based on different frames of reference. If you move your frame of reference, the coverage pattern of the loudspeaker has not changed. You have merely moved to a different location with respect to the loudspeaker’s coverage pattern. The coverage of the loudspeaker is spatially and temporally invariant, in that the directivity of the loudspeaker for any given input signal remains fixed for all observation locations and times. Further, the acoustical effects of the loudspeaker itself (including resonances, distortion products, and other issues) do not change based on observation location and time (that is, unless the loudspeaker undergoes a significant physical alteration between two observation times).

Wide, Far Coverage
Since we can’t vary the speaker’s coverage based on listener location, and we’re unable to resort to any practical trickery that would cause the speaker to produce a signal that reduces or eliminates the space’s reverb time, we’re basically stuck with having to choose a spatially and temporally static coverage pattern, speaker placement, and overall output that reduces the effects of the reverberation on our listeners. We can probably get pretty good results by using higher directivity speakers producing smaller outputs at shorter distances - but the number of loudspeakers needed goes up as those factors (coverage, output, and distance) are reduced.

Narrow, Close Coverage

Now, if we really want to go “whole hog,” we can just give everybody headphones. Those would effectively eliminate the room from the equation. Of course, we’d have to buy a lot of headphones.

“Ah ha!” you say. “You haven’t talked about EQ. We’ll use EQ to make things sound nice!”

Well, yes, you can do a lot with EQ. EQ is my favorite audio tool by far. However, I would again put it to you (respectfully) that EQ can’t fully fix the issues you’re facing. If your acoustical problem is really nasty, even a whole mountain of EQ can’t stop the issue from ruining your day - it may even bring attention to the problem!


First off, EQ (even more than loudspeakers) is THE poster child for spatial invariance. In fact, the highly talented, well respected, greatly experienced, and just flat-out cool Bob McCarthy has this quote attributed to him:

"Any electrical filter on an acoustical device is a spatially invariant solution to a spatially variant problem. As grownups we have to decide what part of the space to tune the solution to and let the others go."

In other words, any “tuning” that you do with an equalizer can only be 100 percent “correct” at one point in a room. Don’t get me wrong! The tuning might be 99 percent correct at every other possible listening position, but you still have to accept that the filtering you’ve applied simply can’t change based on a listener’s physical positioning. True, you can always add more discrete channels of reproduction, each with discrete filters and discrete loudspeakers so as to get solutions that are more correct at more locations - but there are always practical limits to how much gear you can throw at a problem.

Here’s a graphical depiction of what I’m talking about. The three different traces show the measured response of a loudspeaker in a room, under three different conditions. One condition is with no EQ, and a relatively close observation point. (I’m pretty sure that big notch at around 1k was being caused by a number of electrical and acoustical factors, because even a huge amount of corrective EQ couldn’t fully fix it. Hey - there’s an object example, eh?) Another condition is with corrective EQ for the original observation point, and the final condition is that same EQ being applied with an observation point much farther from the loudspeaker.

Frequency Response Traces Under Different Conditions
The problem should become apparent fairly quickly. If we use EQ to get the frequency response “just so” for one observation position, it doesn’t guarantee that any other observation position will get the same results. If we extrapolated the situation in Figure 3 to a more severe situation, we might have to be very mindful that getting the frequency response to be really balanced for the folks in the back might submerge the closer listeners in a sea of low frequency material, while slicing their heads off with high frequency content. (Again - if we have enough money, time, and space in the room we could have different speakers with discrete EQ for folks in different areas.)

The final major point to make in all of this is that EQ is also time invariant. For simple filters, this is easy to understand. A filter with a given frequency, bandwidth, and gain is set and left. It is always operational with those settings, at all times (unless removed or altered by an operator). One might choose to mention that there are such things as dynamic equalizers, which alter filter characteristics in real time, based on inputs or feedback methods. However, I think a strong argument can be made that even though a dynamic EQ changes a filter over time, it does not actually change a filter with respect to time experienced by an outside observer. The filter is changed with respect to some detected signal level, and this probably involves detection of how long a signal level is greater or lesser than a given threshold - but, the change over time is incidental. The time that a signal spends at any point in relation to the threshold is essentially ignored. Further, signal being detected is usually an input to the device, and not a measurement of total acoustic response in the actual room. (Please notice that I said “usually.” There are some devices that can do dynamic EQ by measuring the “in room output” in some way. However, the spatial invariance problem still exists in that you can only have so many measurement devices, and you ultimately have to pick one average that you can live with.)

Figure 4 is a graphical depiction of why time invariance matters for acoustical problems. It shows the RT60 (reverb time) and waterfall plots for my final measurement from Figure 3. What is apparent rather immediately is that all the frequencies present do not decay at the same rate. The lower frequencies tend to “hang around” a bit. The problem, then, is that the corrective EQ I’m using does not change over time. If those resonant frequencies in the room reverberation are causing me a problem (such as the masking of sounds), then I have to simply reduce their output level. I have no way of reducing their reverberation time without modifying the room. Even a dynamic EQ can’t reduce reverberation time - it can only reduce a frequency that is being judged to be getting beyond a certain level.

Now, here’s why this situation can actually make EQ draw attention to an acoustical problem. In a highly reverberant space, especially where, say, low frequencies dominate the reverb, you may end up in a situation where the only way to tame the problem is to severely cut the problem areas. What you can end up with is a PA system that very obviously has a huge “hole” in its low frequency response. You ultimately are forced to make sounds that have almost no low frequency content in them to avoid a low frequency reverberation problem. The reverberation can’t fill in content that isn’t there, of course, so you can end up with the “gorgeous room, but why does the sound system remind me of my old clock radio?” effect.

With all this virtual ink having been spilt, I hope I’ve made a convincing case for why we can’t really and truly fix acoustical problems with electronic and electro-acoustic tools. I’m definitely not saying that we shouldn’t use our tools to their full potential when dealing with acoustical issues - what I am saying is that it helps to be cognizant of what the limitations are, and why those limitations are present.