You Shall Not (All) Pass?

Last summer, I designed a system for a festival main stage for which horizontal uniformity was a design goal. Usually it’s the front to back variance that gets the lion’s share of attention when it comes to uniformity, especially in many festival situations, in which systems must overcome very high range ratios (closest listeners are very close, farthest listeners are very far), often with the restriction of the relatively low trim height offered by a mobile stage.

Horizontal uniformity is often dictated almost completely by the polar behavior of the loudspeakers in use for the application. We start on-axis to the array, and as we move off-axis, HF begins to roll off until we reach the -6 dB point and the edge of the horn, at which point it’s time to call in reinforcements. Our options if we don’t find this behavior suitable are quite limited and typically require using a different product. Some array products allow the user to adjust the horizontal dispersion of the HF, such as with L-Acoustics’ PANFLEX adjustable waveguide, offering a choice of 70°, 90° or 110° horizontal dispersion per box. The PK Sound Trinity Black offers remotely adjustable HF dispersion from 60° - 120° per module in 5° increments. d&b audiotechnik’s SL-Series produces a cardioid dispersion.

This particular festival was deploying the Meyer Sound PANTHER as mains, whose HF horn exhibits a somewhat unique behavior: rather than a smooth, gradual HF rolloff between Onax and Offax, the PANTHER horn maintains more consistent HF over more of its horizontal polar, rather than starting its rolloff immediately, and then ends more quickly. Imagine your listening experience as you walk along the path of the red arrow in the graphics below.

LEFT: An example of typical HF lateral behavior (Meyer Sound LYON @ 4 kHz).

RIGHT: The more flat-fronted lateral behavior of the PANTHER (4 kHz).

In this context, this means that we need to make sure our sub array always maintains some manner of horizontal consistency, otherwise when we move laterally, the sub array will begin to roll off faster than the HF from the mains, creating an undesirably bright listening experience for audience members towards the edges of the audience plane.

The vendor had provided 16 dual-18 subwoofers, which we deployed in carts of two as a broadside gradient array across the front of the stage. Left to its own devices, this array exhibits substantial beam narrowing in the horizontal plane, making it a poor fit for the coverage shape created by the mains HF.

The HF extends uniformly to the edges of the listening area, while the subs have lost over 15 dB by the time they reach the outer edge. With some delay tapering, we can widen the dispersion (see Part 1 of my beam steering series for more). The center four stacks ride together at 0ms, then 2ms, then 4ms on the outer stacks, a technique I’ve taken to calling the Pauley Array. Keeping the center 4 together helps decrease the audible smearing of the array’s IR at mix position, a natural consequence of beam spreading that some FOH (including this array’s namesake) can find objectionable.

Sub array delay taper of 0ms, 0ms, 2ms, 4ms.

This roughly doubles the dispersion of the subwoofer array and brings it more into line with the HF coverage dispersion. This solution worked pretty well and seemed to be well received by all the mix engineers involved with the festival. However, as I am not one to content myself with “worked pretty well,” I set upon improving the design for this year’s festival.

These older-model double-18’s have been reallocated to the B stage, replaced by 12 single-21” units. They are higher output, so we are not worried about an SPL loss, and it means we can pack that power into a smaller line length (6 carts instead of 8) which array theory tells us will give us a wider dispersion mechanically (before we start steering it).

As readers will recall from Steer Me Right, Part 1, delay is of limited effectiveness as a steering tool because it causes different phase offsets at different frequencies, and thus the perfect amount of steering at 63 Hz is not enough at 32 Hz, and too much at 100 Hz. Perhaps we can quantify this.

The left of the image below shows the magnitude response of the array as measured at FOH, about 85’ feet from the stage (red) vs the response at the same depth but 55’ off center towards the edge of the coverage area. The chart on the right lists the level offset (in dB) between the two curves, or in other words, quantifies the variance between mix position and the edge. Overall the array is about 6 dB down on the edge compared to FOH, and tilted more towards the top end of the bandwidth.

LEFT: Response @ FOH (red) vs 55’ off center (blue), at 85’ depth.

RIGHT: dB offsets per frequency between the two curves

My goals for this year were to increase horizontal consistency in two ways - both by making the subwoofer coverage shape an even better match for the horizontally consistent HF dispersion, and also by making the subwoofer coverage shape hold more consistently throughout the frequency range. Those goals could be quantified as making the FOH and EDGE curves on the above chart closer together, and more similar in shape. The new model subwoofers have better extension so we now need to be more conscious of our polar down at 31 Hz - we can’t leave it as an afterthought when the rig is putting out real energy down there. The wider bandwidth means that delay is a less satisfactory steering mechanism, as the right amount of delay at 50 Hz is not enough at 31 Hz and too much at 80 Hz. We need to get frequency-dependent.

I have been asked several times since publishing Part 2 about the efficacy of using All Pass filtering (APF) for beam spreading of subwoofer arrays. The short answer is, it can be done, but - as with any beamsteering method - it is not without drawbacks. As an example, let’s explore a variation of the approach to see what improvements we can bring to this year’s array design - and at what costs.

After considering a number of physical deployment variations and some of the logistical limitations surrounding the stage structure, I settled on 6 carts of 2 subwoofers, with the bottom element in each stack reversed, spaced about 18” forward of the downstage edge (to give the gradient array room to work) and with one foot of space between carts (closer spacing begins to impede the wraparound paths that enable the rear cancellation and can change the necessary timings for the gradient array). Yes, this does depart from the ideal 2:1 front:back ratio for optimal rear cancellation, but optimal rear cancellation is not the number one goal here. We’ll take what we get while making the desired coverage shape (i.e. a wide, even arc) out front.

I started by adjusting the delay arc until I created my desired pattern at the top of the sub range around 80 Hz. I made note of those values, and then increased the delay taper until I was happy with the dispersion at the bottom of the sub range at 31 Hz. I then input the original (80 Hz) delay values into the prediction, and subtracted these values from the 31 Hz values. The twist is to convert the excess delay to degrees of phase at 31 Hz, and use staggered all-pass to create that additional offset between the carts at 31 Hz without disturbing the top of the sub range. For example, if 4 ms on the outer stack makes a nice shape at 80 Hz, and 9 ms makes the same nice shape at 31 Hz, we’ll put 4 ms into the DSP, and the 5ms difference translates into 5 ms x (31 Hz / 1000 ms) x 360° = 56°. We would then insert the DSP’s all pass filters on each sub cart, tuned to higher f in the center of the array and lower f at the ends, such that the difference in phase between the middle and the end at 31 Hz amounts to 56°. Yes, this is just a by-hand version of the Low-Mid Beam Control “Beam Spread” algorithm, done with a bit of trial and error and a little help from our friend Excel.

My array ended up with the inner carts at 0ms (time zero reference), the middle carts at 1ms, and the outer carts at 4ms, with 2nd order APF Q=0.6 tuned to 20 Hz on the inners, 17.3 Hz on the middles, and 16.5 Hz on the outers. Intuition might lead us to think that such small differences in center frequency would produce a negligible effect, however once we deployed the array, the FOH mixer and I did extensive listening with this arrangement vs a more traditional delay-only taper and found that the delay+APF version was significantly more consistent horizontally. I used the decorrelation EQ filters mentioned in previous posts to further smooth out some of the combing between stacks, and after another round of listening we found the result to be quite successful.

The first question to answer is: does it work? The short answer is “yes.” Thanks to the aspect ratio of the image you’ll have to do some scrolling though. I never claimed to be a graphic designer.

1/3 oct polars

Our horizontal coverage pattern is much more consistent between middle and edge - a much better fit for the high frequency shape we’re trying to match. If we return to our earlier “horizontal consistency” metric of comparing the dB loss between center and 55 feet off center at 85 foot depth for each third octave band, we can see we have a substantial improvement (red line) over last year’s design (blue).

The caveats: all beam steering costs a penalty in impulse response smearing, but APF steering + delay steering costs you a double penalty. The delay pushes the stacks of subs apart from each other in time, and the APF pushes the frequencies in the sub range apart from each other as well, giving you in essence IR smearing in ‘two dimensions.’ Whether or not this is acceptable tradeoff sonically is highly situation dependent, and should be carefully evaluated before making a decision.

Note also the higher level of precision required to achieve the desired results - physical positioning, delay times, and filter frequencies need to be carefully checked in order to make our real-life array look like it did in the prediction. If production needs us to move a sub cart a few feet later on to accommodate a concrete ballast block, our array may respond in highly unpredictable ways. Also, every subwoofer in the array ends up with a unique combination of DSP settings, so patching must be carefully checked.

Polarity, timing and gain settings for the left half of the array.

The result of the APF and EQ decorrelation filters for one half of the array.

I was quite satisfied with the end result, and it seems to be well received by the guest mix engineers (although this may be one of those “don’t show them what you did to it” situations, and if any of them are reading this now after having mixed on it, I suppose the cat’s out of the bag). I found the IR of the array at FOH to be well acceptable as a trade off for the wide, smooth coverage dispersion, especially given that a large portion of the audience attending the headline set was listening from the far edges of the audience area. However, given a different day, different artist, different mix engineer, different environment, etc, the tradeoff may not be the right one, and as the Bard of Avon tells us: ay, there’s the rub.

The array as deployed.