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Applying the Scientific Method to Audio

By Dr. Floyd Toole

As history has it, in 1991 I moved from the National Research Council and our Canadian home, to southern California to join Harman International as Corporate Vice President of Engineering. We hated to leave the beautiful house and property, but  . . . new opportunities beckoned.

In addition to my mainstream duties with the many companies under the corporate umbrella, I set up a small research group, aimed at pushing the envelope of knowledge - there was no product development, but only ideas that might benefit products. Papers were to be published, the information shared, not kept as corporate “knowhow”, unlike several other corporations. Thank you Harman!  I am now retired, but under the guidance of Dr. Sean Olive, the group continues to ask and answer questions using the scientific method.

I never forgot the neat acoustical solutions just described, but in thinking about it further I reckoned that in small rooms there are only a small number of modes in the subwoofer frequency range - maybe there could be a more generalized solution that could benefit multiple listeners. After I hired Todd Welti we had the means to explore this using his expertise with Matlab. It was not long before he had the first multi-sub solutions (AES preprint 5602 (2002). After exploring what was possible with up to 5000 subs (aka. acoustic wallpaper) it was found that in practice no more than four subs were needed, and two could do a reasonable job - but only in simple rectangular rooms and only for seats in the middle of the room. Figure 13.17 shows some results. This is not what many people think: more subs "filling in" holes or scrambling the sound field. It is pure room mode manipulation, discouraging some modes and encouraging others. By reducing the number of active modes in the room to the second-order length, width and tangential modes, the nulls are all at the 25% distance from the walls (dashed lines in the illustration), and there are some areas that are relatively free from these problems. The subs must be identical, driven with the identical bass-managed signal, and in specific locations. Three of the most effective and efficient arrangements are shown. In general the four-corners solution tends to be preferred. Other arrangements work, but all are less efficient – see my book or the Welti paper. The best listening locations are in the center area of the room, but because few rooms are perfectly symmetrical from a wall construction perspective, including doors, windows, fireplaces, etc., there will be variations. On site measurements and equalization are recommended but the situation has been greatly simplified.

Rectangular Room Sub Layouts

Figure 13.17 Rectangular Room Sub Layout Options

For a more detailed analysis of multi-sub location options, see: Optimum Room Locations for Subwoofers

How to Interpret Waterfall Graphs

I have seen some number of those photogenic waterfall diagrams lately. Figure 13.23 in my book, shown below, shows several ways of portraying exactly the same room. In waterfall diagrams there is a trade-off. You can have high resolution in the frequency domain, or high resolution in the time domain, but not both. This gets forgotten, or is not known by those making the measurements, or - cynically - is used to mislead.

Waterfall Graphs

Figure 13.23 Waterfall Graph Comparison

Waterfall graphs: you can have high resolution in frequency or time domain, but NOT both.

The top curve is a high-resolution steady-state frequency response, reasonably smooth, a good result for an unequalized room. This is from my first exercise in mode cancelling, shown earlier. The cancellation notch is present.

The first waterfall (b) shows a room that appears to be out of control, with numerous "resonances" ringing forever. This is the one with high resolution in the frequency domain, showing lots of detail, but as you move forward from time=0 the curves change only very slightly, maintaining their shape out to 350 ms. This looks alarming. But every curve moving forward is an average of events over 142 ms, so rapid change is impossible to see even if it is there. We are not seeing what is happening in the time domain.

The next waterfall in (c) has less resolution in the frequency domain, but more in the time domain, and now we see that the events in the time domain are more interesting, changing. In (d) with even less frequency resolution we see that moving forward from t=0 the curves start changing immediately, quickly taking on very different shapes. It is clear that there is only one resonance of any consequence and it is about 10 dB below the initial sound level, i.e. not likely to be a problem. All that was done here was to change the settings on the analyzer. It is the same room. Yet we have seen what could be portrayed as an uncontrollably boomy room, through to one that is very well controlled. Fortunately, that is the message conveyed by the steady state room curve, and that is precisely how it sounded - good.

Global EQ benefits multiple seats if seat-seat consistency is improved via a multi-sub- scheme.

Waterfalls can be useful, but many I see are just ornaments. Because of the ambiguity in what they show, they convey little or no information that cannot be inferred from a simple frequency response curve. But they are pretty.

The last illustration, Figure 13.24 in my book, shows things very clearly in a frequency response and a time response. It is clear that a properly matched parametric filter (a) is superior to an unmatched one (b). So, all equalization is not equal, but when properly done, it works in both the frequency and time domains. These data came from a hands-on measurement/equalization training session at a CEDIA event, and all present had no difficulty hearing the differences that are displayed here.  In (b) the nice looking “after equalization” data described a system that was audibly inferior to the one in (a). Science works.

In a normal loudspeaker/room system these results can only be expected at the measurement location. However, with multiple subwoofer schemes that yield similar frequency responses at several seats, global equalization can then benefit all of those listeners.

EQ and Ringing

Figure 13.24 EQ and Ringing

 

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Recent Forum Posts:

andy_c posts on April 08, 2016 15:23
Floyd Toole, post: 1124354, member: 73854
If you are measuring the steady state room curve (i.e. amplitude but no phase) for each sub separately at a listening location, the summation cannot work predictably. I may be wrong, but I sense that some people, and maybe some algorithms are doing this. Maybe somebody knows . . .

There have been some interesting new developments in this area with the Room EQ Wizard (REW) measurement freeware. Traditionally, it could make measurements that preserve the relative delays between different subs at the measurement position only when using an analog mic and a loopback timing reference. But in the last few years, USB mics have become the measurement mic of choice because of increased simplicity and decreased total cost. A loopback timing reference is not possible with a USB mic. Until recently, when not using a loopback, REW would shift each computed impulse response so that its peak is at t=0. This effectively removed the relative delay information between sub measurements at a given listening position, rendering attempts to form their complex (phasor) summation at that position in other software invalid. However, as of 5.15 beta 3 and later, it added an “acoustic timing reference”, a chirp starting at 5 kHz from a chosen full-range speaker, whose impulse response peak is shifted to t=0. This forms a timing reference for the other impulse responses, restoring the relative delay information that would otherwise be lost. This feature restores the ability of third-party software to correctly compute the phasor sum of multiple sub measurements at a given listening position. More information can be found here.
nathan_h posts on April 04, 2016 17:42
More than enough.

I suspect the caveat is: Smoothing beyond a certain point can be misleading, hence the notion of high-resolution.
mtrycrafts posts on April 04, 2016 17:28
Floyd Toole, post: 1126466, member: 73854
nathan_h and others - if you are able to make high-resolution steady-state LF measurements, you will find the resonances. …
Would a test disc with 1 Hz increment per track considered hi-rez?
nathan_h posts on April 04, 2016 12:11
Floyd Toole, post: 1126466, member: 73854
nathan_h and others - if you are able to make high-resolution steady-state LF measurements, you will find the resonances. It is very likely - based on my lifetime of experiences - that there are only a few, probably only one or two problem resonances (peaks) and a bunch of dips. You cannot equalize the narrow dips because they are non-minimum-phase destructive-interference phenomena. So you don't want an automated equalizer that might try to fill them - there are some “smart” algorithms that are programed to ignore them, but you have to know that. All you really need is a manually programmable parametric EQ that allows you to zero in on the problem peaks, adjust the frequency, the Q (bandwidth) and dial the peaks down to a moderate level. That's it.

I'm going to assume that you prefer not to talk about specific commercial solutions, which is fine/understandable.

For other folks in this thread, I will comment that I have found the DSPeaker Anti Mode products to be just about he only “automatic” tool that tames key peaks in the subwoofer realm, without doing harm or getting overzealous.

http://www.dspeaker.com/en/products/anti-mode-8033.shtml

But the MiniDSP, if one is comfortable with translating REW measurements into filter parameters, seems to achieve very similar results. Pros: You can visibility into exactly what the EQ is doing with the MiniDSP because YOU are doing it. Cons: If you blindly follow the REW recommendations about filter parameters, you may not get what you want.

I have one of each and depending on what I am trying to achieve, I use one or the other. If it is simply taming a sub's in room response, the DSPeaker Anti Mode is quick and easy. The MiniDSP, on the other hand, lets me do other things, like take a stereo signal and do bass management with it (pulling the low frequencies to a separate output) and EQ a little, a lot, etc, whatever I want.

As for equalizing above the transition frequency (the Schroeder calculation is designed for large reverberant performance spaces and yields the wrong frequency in small rooms), it is a good thing - up to a point. Above the subwoofer frequency one enters the domain of adjacent boundary effects (Chapter 12 in my book), which includes what some people call the Allison effect. These can be equalized, and often show up as dips, but they are broad, low-Q dips when you do the necessary spatial average over the listening area. So, knowledgeable equalization is useful up to a few hundred Hz if used with restraint. I would advise reducing the Q of the filters at higher frequencies though.

When I first read your book, I'll bet I completely did not grok this. I need to go revisit it. Thanks for the reminder/pointer.

So, equalizing resonances for the benefit of the sweet spot needs one mic location, while identifying the adjacent boundary issues requires multiple mic locations. Only with multi-sub solutions will the EQ reliably work for multiple listeners.

I have finally got the ‘multi subs’ religion. I first heard / read about the idea nearly 10 years ago. I bought a second sub, put it on the front wall with the first and said “Well, that doesn't seem to have made any difference!” and sold that second sub.

Some time after that I read the summary of Welti's research/articles (there was a nice PPT making the rounds that summarized the AES paper, I believe) and understood my error. It wasn't just about dropping a second sub into the room at random but doing so in a deliberate fashion. I got a second sub, again, and placed it in the opposite corner of my rectangular room from the first sub, and that made a ton of difference. A little EQ to tame peaks and one is golden.



Thanks for sharing your learnings. I'm off to do my homework.
Floyd Toole posts on April 04, 2016 11:20
nathan_h and others - if you are able to make high-resolution steady-state LF measurements, you will find the resonances. It is very likely - based on my lifetime of experiences - that there are only a few, probably only one or two problem resonances (peaks) and a bunch of dips. You cannot equalize the narrow dips because they are non-minimum-phase destructive-interference phenomena. So you don't want an automated equalizer that might try to fill them - there are some “smart” algorithms that are programed to ignore them, but you have to know that. All you really need is a manually programmable parametric EQ that allows you to zero in on the problem peaks, adjust the frequency, the Q (bandwidth) and dial the peaks down to a moderate level. That's it.

If you want to look at waterfalls, this will be confirmed. But really, if you look at the back curve in a waterfall and see a peak, you will see ringing. No peak, no ringing. Waterfalls do not add information, they confirm what can be inferred from the room curve in a photogenic way. This assumes that the parameters of the waterfall are set right.

As for equalizing above the transition frequency (the Schroeder calculation is designed for large reverberant performance spaces and yields the wrong frequency in small rooms), it is a good thing - up to a point. Above the subwoofer frequency one enters the domain of adjacent boundary effects (Chapter 12 in my book), which includes what some people call the Allison effect. These can be equalized, and often show up as dips, but they are broad, low-Q dips when you do the necessary spatial average over the listening area. So, knowledgeable equalization is useful up to a few hundred Hz if used with restraint. I would advise reducing the Q of the filters at higher frequencies though.

So, equalizing resonances for the benefit of the sweet spot needs one mic location, while identifying the adjacent boundary issues requires multiple mic locations. Only with multi-sub solutions will the EQ reliably work for multiple listeners.
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