The Rollout of Linear Phase Crossovers

Over the past couple days, I rolled out the linear phase filters to my crossovers.

I first made the FIR cooefficient files on my Mac, running the Windows program RePhase (I've contributed to the European author, who is big at DIYAudio) but using the Wine emulator.  It all worked (though took multiple attempts to get it right and figure out how to successfully load on miniDSP and then better optimized--a process which could continue forever).

My first impression was, meh.

It was not clearly such an obviously big deal as my recent bass retuning and use of steeper and higher LR8 crossovers.  That was clearly, from the first moment, a big transformation, even bigger maybe than moving to the 2+2's.  Much more solid imaging, bass, dynamic range, freedom from strain.

But I think I'm hearing potential.  Other than slightly thinner sounding bass (which actually must be a good thing, actually it measures identically on pink noise) there seem to be no significant untoward effects.  No obvious "ringing" as I feared reading Linkwitz.  Maybe just the opposite

As I said, everything sounds thinner, almost everywhere in the room.  When playing pink noise the "flapping" sound I've generally heard before is all but gone, contributing to the sense that the bass disappeared.  But I've always wondered if that wasn't some sort of artifact, and indeed it may be, of group delay in the crossovers.  I have a lot of ways to increase the bass level if I ultimately find the "thinner" sound less enjoyable.

I found the new sound enjoyable on both Classical recordings from the Decca collection and Heavy Bass recordings like Grouse.

Now I need to reset the time alignment, and in particular the tweeter alignment possibly because it uses a different plugin for the 96kHz operation and that plugin has a far smaller set of FIR coefficients.  Doesn't really need more anyway, more are needed al lower frequencies.  But it could upset the time alignment by 30ms.  Which probably wouldn't be extremely audible since the supertweeter output is essentially inaudible nowadays anyway (crossed at 17kHz at 48dB/octave).  But wouldn't be good either.

The Acoustat response

The more logical descriptions of designing a crossover generally start with measuring the performance of the individual drivers.  Rather than my approach of adjusting the combined system.   Only rarely the Acoustats by themselves, and without the crossover.

I have an excuse.  For the last 6 years and up to last month, I had been using Behringer DEQ 2496 to perform the crossover functions for each way of the system, the subs, panels, and tweeters.  I use two high cut filters or low cut filters to make an LR4 lowpass or highpass crossover function.  Most EQ functions can be turned on or off without issue, but the high cut and low cut filters often "stick" so that if you turn them off, they stay on, and may stay on after more than one power cycle of the unit, though ultimately power cycling usually fixes it, sometimes I've tried certain button pressing like bypassing and unbypassing the EQ to achieve that same effect.

Now I have one setting on the OpenDRC-DI unit I use to perform crossover functions for the panels set to bypass the crossover functions.  Such a setting isn't safe on the bass or the tweeters.

However, for these measurements, I did not bypass the small number of EQ adjustments I make to the panels.

Also, I am interested in the acoustic crossover responses on the Acoustats, so I made measurements with the crossovers on also.

Acoustats, Both Channels, No Crossover

Briefly, the (lightly equalized) Acoustat response is reasonably flat within it's bandwidth, but limited on the low and high ends to some degree (mostly on the low end).  That's why I use subs and supertweeters.

Even without the crossover, my back-of-the-envelope calculation suggests this is close to 48dB/octave performance starting at 16kHz or 17kHz as the 6dB down point.  It actually looks even steeper than that, but you must account for the approximate 10dB error in the 20kHz band of the iPhone RTA.  In the 1/3 octave from 16kHz to 20kHz there should be 48/3 = 16dB rolloff, combined with 6dB at the crossover frequency, so it should be 22dB down, and here it appears to be 35dB down, but adding in the 10dB error it's only actually 25dB down, just a bit more than 48dB/octave if your reference is the default here, or less if your reference is a higher frequency that 1 kHz.

When the crossover is dialed in, the bottom end takes a hugh hit, with that bass peak being almost entirely suppressed, but the top end doesn't signficantly change (high ambient noise level makes the bass look worse than it probably is):

Acoustats, Both Channels, with Crossovers

There is some difference at 20kHz shown, a mere 1.6dB difference, despite the crossover subtracting 6dB at that point (the electronic lowpass frequency is 20kHz).  This is because we are hitting the noise level in the room the output is already so small.  So take all these measurements with a grain of salt.  Other differences in the highs are barely noticeable, the crossover might actually make it smoother at 14kHz, as we see in the combined response.  Basically I'm getting the benefits of the crossover (less wasted power, potential interference between speakers) at no visible cost--even actually some (though limited) benefits, as I've show in earlier measurements (the response at 14kHz is smoother with the crossover dialed in).

The above measurements used an uncorrelated pink noise, which I find more stable and accurate.  I also did the measurements with correlated pink noise.  Here's the speaker by itself (but with minor EQ):

Acoustats, Both Channels, Correlated Noise

Just looks a bit rougher than the one with uncorrelated noise.

Acoustats, Crossovers, Correlated Noise

The response with the crossover looks even more rougher than the one with uncorrelated noise, but otherwise basically the same.

Now take a look at the combined system response, with uncorrelated then correlated pink noise:

System Response, Uncorrelated Noise

The true response at 20kHz would be just slightly above the apparent peak at 18kHz.

System Response, Correlated Noise

Correlated noise looks rougher again.  Of course, everything is "interfering" with everything else.  Real stereo music is not like this.  Note that the dip around 100Hz is worse.  Bass changes as I move the iPhone mere millimeters with the correlated noise, features like that shift around.

I think I've done pretty well in making what appears to be nearly flat response, 20-20kHz, with deviations from that being harmless or even beneficial, in the uncorrelated pink noise response.

Streaming Radio Stations

This is one of those areas where there are too many choices, and one has to listen to 100 streaming radio stations before finding one that works, and then a month later it closes down and you have to start over.  I haven't much bothered with streaming radio ever.  The only thing that sort of worked for me was Pandora, which is auto-customized to my taste, but can also get boring, and isn't CD quality.  But I discovered more new-to-me artists on Pandora than any other source.

I moved to streaming libraries, like Tidal and Qobuz, where I can select any recording I know by name, artist, or genre, and simply play that.

But it's a pain too, not having a DJ of some kind to preselect music from the billions of titles available.  The convenience of having someone else pick the music for you is one of the reasons why I have always listened to FM and still do.  Meanwhile, many audiophiles have never even thought of FM as audio, just junk.

The DJ function is also of great social importance, as this is how most people discover music.  While you might wonder why even back when recorded music was socially costly (maybe a few hours of work to buy a 30 min LP) radio stations would play music for free, with some thought you see the promotional aspect is extremely important.  Radio play is exact what made the big hits big hits!  Otherwise, few people would have known.  Radio is advertising for recorded music!

This was, from the beginning, a big avenue for corruption.  Not only would record producers give records to radio stations to play for free, they would even make payments, called payola, for the DJ's to actually play them.  Payola was specifically made illegal, but you can bet the complicated interests involved have never gone away.

So all the online radio AND online libraries promote some music more than others, in various ways, corresponding to back door agreements and ongoing corporate relationships.

Synchronous vs Asynchronous transmission of digital audio

Another friend has just "discovered" the endless hype surrounding asynchronous digital audio transmission.  Once again, I must write a clarification, as follows:

Asynchronous is best if:

1) You are using USB (this usually means isochronous/asynchronous..the DAC clock drives the advance gathering and buffering of USB data packets from the source...so the source clock is irrelevant)

AND/OR

2) The destination is a DAC.

Hardly anyone but me thinks about the cases where you are transferring data from one digital device to another, such as a chain of digital audio processors (as I have) or a digital recorder (we are not supposed to do that anymore, just buy and listen) through which audio is transferred in real time.

In those cases, if you are using SPDIF (which is almost certain for several reasons), synchronous is better, because the data is not altered, and the timing is best corrected at the ultimate DAC endpoint (which should have asynchronous receiver) rather than at every intermediate point.

Nobody talks about this and I find it infuriating that nobody talks about it.  I post one essay after another.

I can measure the difference in distortion levels at the Emotiva DACs when I switch between synchronous and asynchronous.  It is the smallest amount I can measure, distortion increases from 0.0003% to 0.0004% when I switch to Synchronous mode.  That's not ordinary harmonics but some kind of low level grundge, resulting from jitter, which is being removed by the asynchronous receiver, the accumulation of many little spikes mostly below -130dB rising above the noise floor.

The benefits of asynchronous recevers are very small, IMO, and I wonder if they aren't being endlessly touted by corporate fascists primarily to shut out people like me who like to do loudspeaker experimentation, equalization, recording, editing, and other "dangerous" things, that work better with synchronous receivers.

With a digital recorder hooked up to my living room system, I can record unprotected analog sources such as vinyl records.  (The digital recorder will not allow the recording of protected digital streams like streaming audio or from DVD-Audio discs.)    I used to use a Masterlink, which has a synchronous digital receiver, and records exactly the bits sent to it.  The best recording method was to attach the Masterlink to the output of my Lavry AD converter.  Then I would record exactly at the quality level of the Lavry itself, which is very high.  But the Masterlink is incredibly cumbersome to use and CD's must be burned simply to transfer the data to my computer library.  My new Marantz recorder (PMD 580) is far more convenient as I can record audio files up to 2.1G onto flash memory, without having to mess with extraneous details.  Then I just walk the memory chip over to the computer and copy it (I gave up with the dated network archiving system).  But the Marantz slightly lowers the quality of the recordings, it uses ASRC so all the recorded audio is "interpolated" from the original.  In this case, there is no benefit to me, and in fact a slight loss, from the fact that an asynchronous digital receiver is being used.

Supertweeter Crossover

I have long been disturbed by an 18kHz peak that appears in my iPhone RTA measurements of the living room system:

Left Channel with all LR8 crossovers

Right Channel with all LR8 crossovers

Testing over the past two days suggests I can't fix that peak, or make other significant changes, by simple improvements to the supertweeter crossover.  From long experience I highpass the supertweeters at 17330 Hz and lowpass the Acoustats at 20kHz.  The result is fairly flat with a slight peak in the response at 18khz.  But it seems the peak is caused by my supertweeters themselves.  (Or, it could be an artifact of the iPhone RTA measurement.)  It is visible in the response curve of the supertweeters by themselves, or with just the Acoustats turned off, as in this RTA snapshot:

When I switched to 48dB/octave crossovers on both sides two weeks ago, the same crossover frequencies still seemed to be optimum.  I have now reconfirmed that with some new measurements.

The Acoustat naturally rolls off above 17kHz very steeply, possibly 48dB/octave or more.   I have to lowpass the supertweeters at 17330 Hz or lower, or there is a widening depression above 17kHz.

I don't actually need to have an electronic lowpass on the Acoustats since I am relying mostly on their acoustic rolloff.  But the electronic lowpass I use at 20khz seems to make very little difference in the frequency response either when the supertweeters are running or they are not.  It actually seems to improve the response slightly when the supertweeters are running, curiously reducing a depression at 14kHz.  This suggests to me the 20khz lowpass  is improving the curve of the 17kHz rolloff so the phase change more closely approximates the acoustic crossover at LR48.  When the supertweeters are running, lowpassing the Acoustats has always made the sound better, I have always believed.  I figured because it reduces the high frequency reactive loading on the amplifier, but it may be because frequency response is actually improved, or interference patterns reduced.

Both Channels, 19kHz lowpass on Acoustats, note broad 14k dip

Both Channels, 17330 Hz lowpass, 14k dip more pronounced

Both Channels, Lowpass bypassed

Both Channels, 20kHz lowpass, flattest of all around 14kHz

The 18kHz peak should be investigated at the tweeters, possibly removing the rears.

I also have capacitors on the supertweeters that reach -3dB at 40kHz.  The effect of this should be to boost the HF response gradually in their 17kHz to 40khz bandpass region.  But I always seem to see the reverse in my measurements, with response rolling off either at 20kHz or slightly higher, rather than going higher and higher.

These capacitors eliminate amplifier hum and protect the supertweeters.  I could possibly increase their value so that the the highpass frequency is lower, taking them more "out of the picture."

I had always figured that the relatively rising response at the supertweeter amplifier inputs up to about 40kHz would be an advantage, a +8dB rise compensating for their decreasing energy transmission from beam narrowing.  But it should also be re-investigated.  It may be having counterintuitive effects caused by phase changes near the acoustic crossover.

I measure the exact same peak at 18kHz, with 16kHz and 20kHz lower, with the iPhone placed as close as possible to the supertweeter.

The listening position measurements from ARTA using my calibrated microphone are much less useful, or I haven't figured out how to give them the kind of detail I see with the iPhone RTA.  I've been contemplating other devices, programs, and techniques to see what's going on higher up.  In my vast collection of audio junk, I have a never used Mighty Mike, based on a 1/8 panasonic capsule, which I believe does have response to 40kHz.  It's complicated, and the manual and calibration file are not at hand, if they ever existed.  I'd have to figure out how to wire the 1/4 phono plug, etc.

Update: Additional testing on the RTA app suggests it has about 10dB rolloff at 20kHz, but is fairly flat below that.  That somewhat changes the picture.  Essentially the peak at 18kHz is not a peak.  It's a reflection of the rising frequency response above 16kHz.  In actuality 18kHz is NOT higher than 20kHz, it may be somewhat lower.  The ARTA display, which shows response rising to just above 20kHz, and then falling, may be correct, or that measurement setup may have a similar problem (response falls off beyond some frequency) but just a higher cutoff.

To test the RTA app, I measured my Revel M20's.  According to published response curve, the M20 is about 3dB down above 10kHz, but then has a slight peak just before 20kHz.  On a smoothed response like the 1/6 octave RTA, I would expect 20kHz to be around 1-2dB down from flat and 18kHz to be about 2-3dB down from flat.  Roughly the same.  Well that is not what I measure a centimeter from the tweeter

I'm showing a drop of 12dB from 18kHz to 20kHz.  That suggests 10dB of error in that step.  Above that, there may be some error in 18khz itself, perhaps another 3dB, then it begins to match the published response down to 4khz or so where the effect of measuring right in front of tweeter kicks in.

So there was no peak at 18kHz, but an artifact of the rising response of the tweeter above 16kHz and the falling response of the RTA app with iPhone 8 Plus microphone.  This could occur in any measurement system.  My tweeters may have far more extended response than I can measure now. (Dynaudio specs showed D21AF having essentially flat response to 40kHz, a rare marvel of a cloth dome tweeter.  I suspected this required microphone perhaps millimeters from the driver and on center, perhaps adjusted with calipers for best response.   The wavelength at 40kHz may be half the dome width, so there is strong cancellation off axis, but all the better for a peak response right at the center.)

I would have assumed the RTA app had some generic calibration for the iPhone, or maybe even each iPhone model.  Perhaps not.

Most likely, the real story is that both 18kHz and 20kHz on the living room system rising above 16kHz, and they might continue rising to 40khz if measured close enough and on axis.

I continue to believe that a rise in the on-axis response of a dome tweeter is a good idea to compensate for the falling dispersion causing less reflected energy.  The current level setting reflects
10 years of tuning by ear and by measurement with a goal of both making it fairly flat, somewhat tipped up, and not actually minding if the ultrasonic response as measured this way or that is above the midrange, such rises are most often associated with better sound, unlike rises in other areas, such as around 4kHz, where a dip is generally adviseable.

But it looks wise to be wary of the accuracy of the top two bands in the iPhone RTA response.  I am apparently already getting what I want, a rising resonse to 20kHz and somewhere above, without any further changes.

miniDSP clipping issue solved

It seems the best thing I can do, is turn down the input level controls in the miniDSP plugins which are performing my crossover functions.  Though -5dB would be adequate for my test music, I'm choosing -6dB as a probable "worst case" value fitting my theory of what causes this problem.

On Thursday night, after ruling out a few other possibilities, and repeating a previous test than had been erroneous, I determined that the crossover functions in the miniDSP plugins that I am using can add 4.8dB or possibly more to the output level, above the peak level in the input signal.  This does not occur with sine waves, only with very dense and compressed music.  (My test recording was the first track of Supertramp Crime of the Century.)  So if you feed in a recording that peaks near 0dB, as most albums do, the miniDSP will then will clip at the digital output, unless you apply attenuation somewhere in the miniDSP.  It seems to me that the safest place to do this is at the input level control, and there would be little advantage (given the 32 bit operation of the miniDSP chips) in doing it at the output level control instead of the input, even if that worked (which I have not bothered to test).

Leaving the 6dB attenuation in the miniDSP plugin, the output level peaked at -1.2 dB, as read by the Behringer DEQ plugged into the digital output of the miniDSP, while playing the first track of Crime of the Century.

When I disabled the crossover function by clicking the bypass buttons in PlugIn running on my Mac Laptop which was "synchronized" to the midrange miniDSP OpenDRC-DI, the clipping problem went away completely.  Since I had set the level controls to -6dB, the peak level at the output was then exactly -6.0dB reading from the display of the Behringer DEQ 2496 plugged into the output of the miniDSP.  This proved that it is not the digital input receiver, the ASRC I criticized in the previous post, that was causing the clipping problem.  Instead, the problem appears only when you are applying some crossover functions, and goes away when you turn the crossover function off.  (But turning the crossover and attenuation functions off DOES NOT turn off the ASRC, as the output is always 48kHz regardless of settings.)

Now it seems the subwoofer and supertweeter ways have never shown this problem.  On Thursday night I dialed in the subwoofer crossover frequencies to the miniDSP I was testing, and then the max level was -10dB or less, not even close to clipping.

I tried a few other crossover functions to see what aspects of the crossover caused the output level to rise above the input level.  It seemed to occur in all the cases I've tested other than the actual subwoofer and supertweeter crossovers.  Specifically it is unrelated to using solely 24dB/octave LR4 or 48dB/octave LR8 crossovers.  Both of those types cause the problem when utilized across a wide bandwidth.  I tested my now standard 125Hz to 20kHz bandwidth for the midrange, as well as 10Hz to 20kHz.  I tried only having the lowpass and only having the highpass. and they also reproduced the problem.

My current idea is that you may need a crossover output of considerable spectral width to evoke the problem.  It might not ever be an issue for my subwoofer and supertweeter responses, which are relatively narrow band.  It doesn't appear to be a problem with my test music (Supertramp, Crime of the Century) on the subwoofer and supertweeter crossovers.  But I haven't ruled out that some other music or test might evoke the problem in the subwoofer and/or supertweeter.  So I believe it's best to apply the 6dB input attenuation to all of them to be safe, and until I have a definitive test which proves they are never affected by the issue.

My theory of what is happening is this:  A bandpass function having a highpass frequency and/or a lowpass frequency cannot "add" energy to the signal, only reduce energy.  So you might think such a problem as I am describing would never happen.  But the crossover also adds phase shift, different amounts of phase shift at different frequencies.  It could possibly move a peak at one frequency into alignment with a peak at a different frequency that actually slightly occurred later.  This could double the peak voltage, or +6dB, in the worst case.

Why is it that I never saw this problem before???  It's possible the Behringer units I've used before hide this issue somehow, possibly by using slightly different IIR (or even FIR) crossover functions, or possibly by using some independent "attenuation" system that is automatically applied when you use a crossover (on the DCX units) or a high pass or low pass filter (on the DEQ units).

I have often observed a bug that when you try to turn a highpass or lowpass EQ function "off" on the DEQ units, it often doesn't just go off.  It seems you may have to power cycle the unit to get a highpass or lowpass function to turn off.  This might be consistent with some "behind-the-scenes" attenuation function that is applied when you use those highpass or lowpass functions which "doesn't want to let go."

Perhaps this issue even explains why Behringer did not make a DCX unit with digital outputs.

I am not totally happy with the solution described at top, but I have worked it into my system by compensating for the -6dB level adjustment.  I turned up the level on the Emotiva DAC feeding my Hafler 9300 from -7.5dB (set there to maximize resolution at the loudest level I used to listen at) to -1.5dB.  On the DAC for the Aragon 8008 BB, I turned up the level to +6dB (I didn't even know it had such a level, but it does, and I think it has enough output voltage to support this level, though I'm not sure--it's not in the specifications or any reviews online--so I should test it sometime).  The supertweeter and subwoofer DACS have been reset to -1dB and 0dB respectively (previous values were -7dB and -6dB).

In doing this, there is a loss, though it's somewhat hard to explain.   Since the entire 24 bit dynamic range is no longer being as well used, the resolution and the apparent dynamic range in the DAC is reduced.  I was thinking it might fall from about 115dB to about 110dB.  Now it turns out the S/N of the DAC chip in the Emotiva Stealth DC-1's is about as good as the Volume Control chip in dynamic range.  So substituting one for the other in achieving an approximate 6dB of attenuation would likely make little or no measureable difference at all.  But then there is still no getting around the loss of attempted resolution from 24 bits to 23 bits, but likely that has little or no measureable difference at the DAC outputs either, and all of this is entirely swamped by the distortion levels in my amplifiers themselves, which is around -92dB and might as well be buried in noise which is generally less bothersome than distortion.

It only hurts my feelings, a little, as I've spent the last 2 years trying to do the opposite: to increase the digital dynamic range by adjusting the gain structure of my system so it reaches the peak digital value right at my peak listening level, thereby getting all 24 out of 24 bits of resolution available, even at the cost of suffering some loss from the attenuators in the DACs themselves.

Now I have to give that up, to get the steeper crossovers which sound vastly better, and ultimately the linear phase steeper crossovers.

I'll get over it, and/or eventually figure out a better solution.

Actually, the first test I did on Thursday was to connect the coax from my Oppo UDP 205 directly to the input of the midrange openDRC-DI.  I was worried the aging Tact might have some issue that was causing the clipping problem--something I had not tested on Wednesday night.  I was relieved to reproduce the exact same problem with a direct connection from the Oppo as from an AES connection from the Tact (through a Henry Engineering AES splitter too).  There is no evidence of any problem with the Tact or the Henry Engineering.

minDSP digital I/O adds clipping

I like the fact that I was able to buy general purpose IIR and FIR DSP modules for my living room audio system having AES digital I/O, which is the kind I use mostly because of flexibility, extensibility, and robustness.  Using AES digital I/O, I can have endless digital processors in series with essentially zero added noise and distortion.  Because AES is balanced, it is immune to being affected by ground loops, which otherwise can be problematic in large complicated systems.

These are the miniDSP OpenDRC-DI units.  ("DI" means "Digital Interface.")  My system uses 3 of them, one for the subwoofer, one for the electrostatic panels, and one for the supertweeters.  Each one is loaded with a plugin that is programmed to perform my crossover functions, currently using IIR type DSP only, but with a more advanced FIR rollout intended real soon now.  The FIR approach will permit me to have what is impossible in the analog domain: phase linear high order crossovers.

However, I have never liked the idea that these OpenDRC-DI modules use ASRC (Asynchronous Rate Conversion) digital interfaces.  In my analysis, this kind of interface is only preferable for the endpoints of a digital domain--the DACs.  With intermediate digital processors, like the OpenDRC-DI, the jitter at their inputs is converted to changes in the digital values (THD and IM) which cannot be removed from the signal later.  Meanwhile, the consequence of putting digital modules with synchronous interfaces in series is inconsequential.  Any number of modules in sequence is more or less equivalent to a single module, whose performance is largely determined by the clock of the source device and the transmission protocol itself, and which can be de-jittered at the ultimate endpoint (the DAC).  All the ultimate DAC has to do is approximate the clock of the source device, everything else in between can be washed out at that point (using buffering or ASRC).

I would have VASTLY preferred that OpenDRC-DI use synchronous interfaces and adapt to the sampling rate in the input signal.  This is what my Tact RCS 2.0 preamplifier does, and also what the Behringer DEQ 2496 which I still use for general purpose equalization and limiting and level/RTA displays.  I use both of these with full digital I/O so analog conversions are nowhere in sight (until the final DACs, which connect straight to the amplifiers).  The sequence of digital processors is now

Source Digital -> Tact -> miniDSP -> Behringer -> DAC

If I had my druthers, the Behringer DEQ's would have programmable FIR capability, and then I wouldn't need the miniDSP's.  But I have to live with the devices I can buy and afford because scratch building the thing I want would take years.  Or maybe I could just have one big box that performs all the functions of all of these devices, but it would have to have 3 separate DSP paths and 3 digital outputs for the 3 ways of my system.  I use the Tact only to select input devices and adjust system level and balance and test polarity for the whole signal, then the signal gets divided 3 ways by the 3 OpenDRC-DI units.

I believed the THD/IM caused by intermediate ASRC in the miniDSP would be nearly unmeasurably small, so it wasn't going to be a problem, I just would have preferred something different for intellectual/aesthetic reasons (I like things to be as "good" as possible, in objective terms like THD and S/N, whether I can provably hear a difference or not).

But now I have discovered a problem that is less than trivial.  Clipping !!!

[Update July 17.  Apparently it was wrong to blame the ASRC for the clipping.  It appears, in fact, that the miniDSP crossovers introduce a higher peak level.  It is therefore necessary to compensate the level for that, which is weird, but not the kind of nonlinear evil I was thinking.  These original experiments were wrong because I was testing the "no crossover" possibility by selecting setting #4, and in fact setting #4 was not set to "no crossover." Today, I repeated the experiments, but with laptop connected to the miniDSP to change the crossover possibilities onscreen.  I may post this next.  My earlier conclusions, unedited below, are therefore wrong.  And the crossover doesn't even have to be LR8 to have this problem.  LR4 does it just as well.  I still don't like ASRC, but I was wrong to blame the clipping on ASRC.]

I discovered this problem because the new steeper LR8 crossovers I am using allow me to play much louder than ever before without any strain from my speakers.  So I was playing one day close to 0dB (which means about 95 dB peak SPL, which is loud but not harmful), and then I discovered the clipping problem, which appears to be entirely caused by the ASRC.

I was playing Crime of the Century by Supertramp at  -0.6dB (on the Tact volume control) and noticed that the red lights on the Behringer DEQ for the midrange way were flickering.  Taking a closer look at the peak holding level display on the Behringer for the Source Input (which is the OpenDRC-DI crossover for the middle way), it was showing CLIP as the peak level.

I tried setting the Tact level to -2dB and still got clipping.  Then I tried setting the Tact level to -4dB and still got clipping.  Finally I decided that there was probably a maximum need for 6dB ASRC headroom, and I have never seen the clipping happen with the level set to -6dB or lower.  I believe that is a safe value, and I wouldn't want to use less attenuation because there might be some different album that pushes it even farther than Crime of the Century.

It may be hard for digital novices to understand how this is even happening.  If the digital audio data were transmitted without change through the system, this COULD not be happening (I think, though I  am not entirely sure of the consequences of using an LR8 crossover--that might be partly involved, although my experiments have already demonstrated it cannot be the entire story, as I will describe below).

What's happening is that the ASRC is "interpolating" new digital data points from the existing signal.  The interpolated points are in reference to the internal clock of the miniDSP, whereas the input signal data points are created by the clock of the source device.  The two clocks not only have small amounts of random jitter between them, they may also be at altogether different sampling rates.  This is how ASRC works.  The interpolation is not linear, but uses higher order (curved) functions.  So if you are interpolating between two points that are nearly at the maximum level, the interpolated point on the curve in between may actually be above maximum level.  Hence, clipping.

This problem of going above maximum level is well known (or should be) to the designers of DACs. Albums are often compressed as far as they can be compressed.  During playback, most digital to analog converters use oversampling and digital filters for reconstruction, and these reconstruction filters also interpolate between the input data points.  And, because once again the reconstruction filters are not linear, but curved, you may have interpolations that go above the maximum level.  These are called intersample overs, and are common in highly compressed digital music.  Well designed DACs are already designed to handle this.

But the digital transmission system is not designed to handle this.  There is a maximum peak output level which cannot be exceeded.  And that is equivalent to the peak level at "0dB."

The Big One: A Steeper Crossover (LR8)

In previous post, I was just speaking of a friend who doesn't has to retest "A" because "B" is so much better than anything before...  That's exactly what I now feel about the new steeper crossover I have set up between my SVS subwoofers and Acoustat 2+2 electrostatic panels.

This is the biggest improvements I've made in years, vastly exceeding such things as wire changes, DAC changes, amplifier changes, and individual EQ changes, and even the vast improvements I made from Time Alignment using ARTA last month.

Changing from the  1+1 speakers to the 2+2 speakers would not have been as big, except in combination with the actual fact that I had never adjusted the treble on the 1+1's properly, so that was also an equivalent upgrade.

Seeing the many issues on both sides in the 100-200 Hz region, I was thinking steeper crossover was what I needed.  I had tried setting the crossover frequency from 100 Hz up to 140 Hz, which had eliminated the suckout around 106 Hz called by front wall reflection cancellation.  That had merely exchanged one problem for another, a depression from 160 Hz to 190 Hz caused by rolloff in the subwoofer.  THAT depression was just about as bad sounding as the suckout.

I could not move the crossover frequency downwards without the 106 Hz suckout reappearing.

So, on to steeper crossover, which the plain vanilla miniDSP plug-ins let me do easily (I could not do this with my Behringer 2496 DEQ's, and though the DCX's I used to use could do it, I never tried, and I haven't used DCX's in ages because they don't have digital outputs).

I started at 130 Hz with a 48dB/octave Linkwitz Riley crossover alignment (or LR8, as it is abbreviated, because 8 poles).  My previous crossover had been 24dB/octave, LR4.

I then tried 120 Hz, which was better on top but worse on bottom.

125 Hz seemed to split the difference perfectly, resulting in relatively flat response (flatter than ever before) from 20 Hz to 200 Hz, shown on 6th octave RTA 16k bins.

Upon listening, jaw dropped.

The front center of the image, which always seemed a bit iffy, was more solid than ever.  Far more solid, and with more easily front to back.  The entire image left to right is more solid with front-to-back depth.  The bass is far more solid.  There's no sound of strain--in fact, I can crank up 6dB louder than before without sense of strain.  A terrible resonance I believed I was going to have to tear down one speaker to fix, has just disappeared, at higher levels.

This is just so much better.  It's huge.

I never tried this before because of concern about the added phase shift.  Linkwitz himself generally stuck with the LR4 because of reduced phase shift.  And he therefore chose wide bandwidth drivers, and built his speakers around the requirements of the LR4 crossover.

I don't have that option with electrostats.  They have given me a situation for which, in many cases, I NEED the steeper crossover for my system to work well.

I think now the front wall cancellation reflection needs to be removed either by crossing over to another speaker before it occurs (and with a steep crossover), or by moving the speakers way way far back from the front, as in fact my late friend Alan did with his Magnepans (which he said had been inspired by some guy in Japan).

Or perhaps it could be aligned with a room mode, which sort of seems to have been the case in the right channel.  This is why I had ignored this problem so long...I did most of my subwoofer EQ testing on the Right Channel.  And I had been somewhat obsessed by cancellation above 200 Hz.  But I now know the 220 Hz suckout was the second-order cancellation.  The fundamental was the 106 Hz suckout which was only clear in the left channel, where it was devistating to bass solidity, and image solidity generally, as bass would always shift right to where there was no suckout (in fact, uncorrected, a big peak) because of the room mode.

But I have very little wiggle room in the placement of my speakers, giving my living room is also a functioning part of the house.  I'd already moved my electrostatic speakers further and further out from the wall, over years, as it was clear it was important to improving the sound.  The point I reached here seemed now seemed to be about as good as it got, and needed to be.  But remember I did this testing, in particular, on the right channel because the left channel is so tightly constrained by other furniture it's hard to move.  I assumed similarity in the wall distance thing, it turns out, which wasn't so similar.

Since the speakers are already as far out as they can be, I have to make the best of it, but the current distance (45 inches to center of speaker)  turns out to work remakably well, fantastically well, with a 125 Hz LR8 crossover.

At some point, I can push it further, and turn the LR8 into a digitally corrected phase linear LR8.  Linkwitz himself didn't much do the linear phase thing, he suggested issues with it, which he even described to me in person, and still on his website.

I intend to give the linear phase crossover thing a good staging, but I want to take awhile to get the immense advantages of the regular LR8 to sink in, and perhaps make some other adjustments first, including to the supertweeter crossovers.

(Tested music included: Supertramp Crime of the Century, which presented some other issues, to be discussed in future posts.)

Avoid Jumping to False Conclusions

To get the 140 Hz crossover producing a decent RTA, I had added a 7dB boost at 174 Hz in the sub response.  I figured this was "OK" because of the 140 Hz crossover, certainly by 174 Hz the crossover was already applying more than 7dB of attenuation, this was just providing a bit of boost in this region where the sub itself was starting to roll off, but not hugely rolled off yet.

But when I was listening to the Saturday night program featuring local concert performances called Performance Saturday on KPAC, announcer Nathan Cone's voice seemed to have a lot of added upper bass delayed resonance.  The kind you might imagine, say, from a 1930's large cabinet radio.

OK, I immediately figured this had to do with the boost.  So I dialed back the boost, and re-listened to the radio program I had recorded digitally from my FM radio onto my Marantz state recorder.  (Pity me having to listen to the preceding 5 minutes of music over and over for these tests--marvelous music--but anything gets tiring in a situation like this.)

I thought it sounded better, but the upper bass resonance had NOT entirely gone away.

I tried it with the boost again.  I thought it was worse again, but now it was getting really hard to tell. That's the way it goes, for me, with A/B audio tests.  If I even listen to B at all, I start getting confused, and by the time I've listened to A/B/A, I am really confused.

When I just want to move forwards with something I know is an objective improvement, I don't bother trying to do an A/B test at all.  I just set up B--which often takes awhile--and start listening to it.  Days later, if there's clearly something wrong with B, I may go back to A or try to move on to some further refinement of B which is C.  And so on.

I find listening tests so inconclusive I don't put much faith in them.  I'd also hate to predjudice my judgement against what is likely to be a step forwards with a quick but possibly false snap judgement against it.  But I've known people who take the opposite stance, intended to do A/B/A  test, but finding B so much clearly better they don't need to go back.  Just forwards.  I find that very suspicious actually.  Strong result claims need better, not lesser, validation.

Anyway, as I was dialing back the A, I noticed something.  As part of the previous day's testing, I had never re-enabled the midrange EQ on one channel.  It was bypassed.  I completed the A/B/A test sequence anyway, which I felt had some internal validity even if the conditions were way off.

Then I went back to re-enable the midrange EQ, and I noticed something else.  I had never restored the 140 Hz crossover for the subwoofer, I had left it with the 300 Hz crossover I had dialed in for testing purposes.

It was THAT which had distorted the sound of Nathan Cone's voice the most.

What may be happening in the subwoofer as the frequency rises above 160 Hz or so, the subwoofer's 13 inch cone starts becoming directional.  It measures fairly flat to 300 Hz...but only on-axis.  Of axis, the increasing directionality means that midbass in that region is less radiated toward the listening position, but more towards a wall reflection.

Well, that's another theory I have but not really well established yet.

But concluding the boost was THE problem was wrong.  It's even hard to know how much it was a factor.  I generally don't like to boost anyway, but it's unclear how much bad this experience shows it to be a problem.  I could have just been mistaken.

I have often found longstanding "conclusions" to have been caused by some mistake, exactly like this, but sometimes long after.

For that reason, things would need to be tested and retested for firm conclusions.  I avoid that problem by resisting firm conclusions generally, especially in things that don't make sense to me.

Emotiva Stealth DC-1

I bought three more of these Emotiva DACs after I found that my first one measured far better than all my dual differential 1704 based DACs.  As I recall, it measured 0.0003% distortion, which is identical or better than my Juli@ measurement card itself in loopback, so the Emotiva might even be better than that.  I needed 4 identical DACs with AES inputs and Balanced outputs and level control, so these inexpensive Emotiva DACs fit the ticket at a reasonable price.  They have always sounded sweet and pure to me.

I was shocked to see bad things written about this DAC after that.

  But now I go back to the original ASR review, and in fact it's pretty actually pretty good, beats the highly touted original Topping DX7 in THD but not linearity.  It would get a 2dB better SINAD score than the DX7.  It has other unimportant issues, like an -104dB idle tone at 17kHz with USB input playing J-Test.  Amir rightfully dismisses this as audibly unimportant, though not a good sign.

Elsewhere, and possibly at ASR,  I read something worrisome about a grounding issue and running rather hot.  I had to cancel a ground loop by plugging the Emotiva into the same circuit as my Amplifier...suggesting it IS grounded, but may lack isolation through the AES input which a professional unit should have.

Because of heat, I avoid stacking them, and in the one case I do, I use 3 rubber feet to separate them.

There are complains of failures at ASR, but I have had my original unit over 5 years, and no problems.

I continue to think about upgrading to the latest Topping, a D90 would be unequivocally better (unlike the DX7) but it hardly seems worth it for likely inaudible improvements, and I have more important things to think about.

Looking at individual drivers

I had reached the conclusion the dips in the left channel midbass response starting at 180 Hz are occurring because the subwoofer doesn't have flat response to there.  Measurements below show I was mostly correct, but as usual, the story is a bit more complicated.  The panels do also have a bit of relative difference, with the right channel actually peaking at 180 Hz, cancelling some of the sub dip there.  It does appear like the subs might have enough response to work more or less OK at 140 Hz with a steeper crossover like LR48, which I am pondering.  Whereas if I move the crossover any lower, I might expose the panel cancellation at 110 Hz, which a 140 Hz crossover mostly but not entirely suppresses.

The measurements I made today are not necessarily the quietest.  It is 106F outside and my air conditioner is running near its top speeds.  I decided to leave it running, and just accept that as a given.  The rough range of the subwoofer response should be apparent anyway.  There are some slightly audible tonalities in the operation of the air conditioner, but they do not appear to introduce any notable spikes in a background noise measurement.

Here is the left channel sub (and supertweeter) without any EQ.  Notice the large dip below 140 Hz, and especially at 180 Hz.

Here is the left sub with all the current EQ dialed in.  Notably I have significantly suppressed but not eliminated the dip.  This is with 5.5dB of boost at 174 Hz, and I wouldn't feel safe dialing much more in.  The dip at 225 followed by a huge peak just above is very tricky to fix with EQ, though I could probably suppress the peak without making the dip too much lower.

The right channel subwoofer with EQ is similar at low frequencies but does not have the boost at 180 Hz, therefore 180 Hz is down but about 40% less than in the left channel without EQ.  This seems to explain some but not all of the difference at 180 Hz the combined responses of both channels.  Note also it has no peak at 225, only higher at 260.

Some of the remaining difference might be caused by the Acoustat response.  Here is the left channel Acoustat response, with EQ, with the super tweeters turned off, but no crossovers (which does not make an easily visible difference at high frequencies).  There is just a tiny dip at 180 Hz compared to the surrounding frequencies, though in the midst of the second highest plateau.

With the current panel EQ turned back on, there is very little difference there but you can tell the unmitigated peak at 4kHz right where Linkwitz calls for a dip.  I think this could be the error that kept the Acoustat from becoming a market leader, instead of being displaced by Martin Logan and Sanders.  This is somewhat tuneable with the HF level control, but not without making it less flat higher up.  I keep the HF level control nearly perfectly centered.  The Absolute Sound had the temerity to criticize the sound of the Acoustat 2+2, which could still be considered a feat of modern engineering, that perhaps lowlifes like me dare not criticize--it's far more amazing as a total package than anything I have come up with, and probably ever will.  But, there may have been some truth in TAS whining.  If Strickland could just have been persuaded to make it just a bit better sounding somehow, with a little nicer tuning of the response.  The speaker sounds "coarse" like sandpaper playing pink noise without EQ, with EQ it sounds smooth despite the slighly more irregular looking response curve.  The excess output with no EQ is centered right at the 6kHz "metallic" range.  I concede my "smoothing" may not yet be perfected...and perhaps it's even "too smooth" sounding, once again proving you can't naively judge sound from the response curve picture.

Here is the right channel channel Acoustat with EQ.  Notice there is actually a slight peak at 180 Hz, helping reduce the dip in the combined response on the right.

Here is the right channel Acoustat response with no EQ.  Notice again the peaking from 4-8 kHz which I have imperfectly (but simply) reduced with EQ above.

The New Crossover Frequency

In the last episode, I determined that the 100 Hz crossover frequency between the SVS subwoofers and the Acoustat panels was too low, because front wall cancellation reflections appear to be centered around 110 Hz or so.  (One friend wants me to investigate the reflections further, from multiple angles, etc., but I'm satisfied my story is essentially correct.  100 Hz can't and won't work.)

Early indications were a crossover frequency of 140 Hz might work.  I first set up a highpass at 147, but a lowpass remaining at 100 because it seemed to have an approximate 140 Hz acoustic rolloff anyway.

I was troubled by that assymmetry for various reasons.  When I ultimately go to linear phase crossovers, such an approach might not work at all.  And even more immediately, it seemed that I was still suffering a depression around 100 Hz anyway, just like before.

I was thinking of setting up my fancier measurement rig with calibrated microphone and ARTA to first do a full analysis of the subwoofer response, and the panel response, and find the exact best crossover frequency from that.

But instead, after a day of distraction, I decided to go ahead and try setting both sides to 140 Hz, with normal 24dB/octave, and see how that worked.

And of course, once I had done that, I couldn't help but keep fiddling with parametric EQ's on the subwoofer side to get it straightened out.

(Plot spoiler: I looks indeed like I will have to go back and determine the actual Subwoofer response after all, because it seems to be a factor in how the 140 Hz crossover works.  There is considerable weakness around 180 Hz which may be caused by subwoofer already starting to roll off where the crossover is still expecting some output from the sub side.  Curiously this only seems to happen in the left channel.  I'm thinking the left subwoofer, which is very hard to get behind, may have some sort of internal crossover enabled which is interfering with my attempt to do a good 140 Hz crossover.  This needs to be checked by playing the sub with a much higher crossover like 300 Hz.  In past experience, it's not good to play pink noise full range into my SVS without any subwoofer.  That generates scary sounding noises that make you wonder if the subwoofer isn't going to self destruct.  So it needs some crossover, or some other way of ensuring that all testing is below about 300 Hz.)

After first setting up 140 Hz for both the panels and the subs in my miniDSP OpenDRC's I measured what looked like much higher bass than before:

My first impression was that the subwoofer level was too high.  (I had long suspected this.)  But I quickly took a look at the sub response by itself,  but with the 140 Hz crossover enabled).  That looked like this:

That looked like there might be some peaking at 140 Hz, but not enough to explain the huge bulge at 140 Hz.  So I turned the sub level down and down.  From -3dB to -13dB.  That looked a little flatter, but there was still that peak at 140 Hz!  If I remembered correctly, I already had a big cut there.  At that point, not remembering that I had an hour earlier turned down all the PEQ's above 90 Hz on the principle this would be a whole new EQ game because of the new crossover, and I'd best start from scratch.  As a result of that memory failure, I started with a huge sub level change rather than first restoring the old EQ's.  With a 10dB reduction, the last LF plateau around 32 Hz was clearly lower than the 18kHz peak on top, and generally I like those more-or-less at the same level, intuitively and otherwise (though the true HF response is not revealed by these or any other measurements I have yet done, and on ARTA with my calibrated mike the HF peak appears to be about 15dB higher, which I think partly has to do with my cal microphone's lack of omnidirectionality at those frequencies, or some such factor, even perhaps the way the software works.  I think for an RTA long term average type response, it's hard to beat the iPhone running the  RTA app I have, and the iPhone simulates a true omnidirectional microphone response with two microphones and sophisticated internal processing.)

Finally I realized I had previously zeroed out the 125 Hz notch and even a 105 Hz notch I had zeroed out last week or before, but left in the PEQ list set to 0dB.  I actually took the time to run the oscillator and retune all 3 points.  And then back to the RTA and back to the oscillator.  I slowly raised the subwoofer level as seemed to work best, but not back to the original -3dB which may indeed have been too high.

(Having the sub level too high, or a substantial "room curve," is very destructive to transparency across the audio range, and also limits dynamic range.  You can't turn the level up too far without everything in your house rattling, or even the sub itself sounding off, on very bassy music.  You can sort of make a too high level work by having deep notches at the room modes.  Or you can lower the sub level and use less-deep notches.  It's never exactly clear where the optimal point is between deeper notches vs lower sub level.)

Finally, after endless adjustment, I got to this:

The deepest bass up to just pass 125 Hz is as flatter and nicer than it has ever been.  There is zero notch at 100 Hz, though a slight depression that includes 90 Hz.  But look, now there are some too-large depressions starting at 160 Hz, and also just above 250 Hz, that I didn't recall from before.  I tried fixing the lower one with as much as 7dB boost at 170 Hz without much success.  If I remember correctly, the measurement above is the one with the boost already added, it looked even worse before.  I figure the boost is OK because at 140 Hz response is already rolled off by 6dB by the 140 Hz crossover, and the fairly high q peak I'm adding at 170 Hz doesn't much extend that low.  I generally have more headroom in the bass too, meanwhile the midrange headroom is deliberately limited so as not to waste digital dynamic range and "information"...it's always playing close to 0dB.
(This kind of tradeoff is called "gain structure.")

Still, even with the boost, I'm not happy with this response as it looks.  I think it sounds OK, with much punchier bass than before, and the pair of lower midrange depressions aren't immediately obvious to me.  On oscillator sweeps they don't sound so much like the null at 110 Hz I was aiming to eliminate with these changes, they sweep better than they look in the RTA.

Opening more cans of worms

At the end of my last week-long session of Time Alignment using ARTA, I made a list of future improvements to put ahead of expriments with linear phase crossovers.

During that "Time Alignment" I also made some adjustments to the bass in the left channel, using only ARTA as a tool.  Now ARTA is very good in many ways, but relying only on one kind of measurement to make important adjustments is like trying to map a mountain from one picture window view.

It disturbed me since than that I had probably reduced the bass too much to make it look flat in the ARTA measurement.  This seemed to be confirmed when I did my first new iPhone measurements on Sunday July 5.  But then I realized I had the weighting switched to A.  I switched it to C to make this measurement (though it's actually better if I use "Flat" which is an option in this app, and I remembered to use Flat for all measurements after this one):

Left Channel, as last adjusted using ARTA

The bass below 63 Hz was rolled off more than it appears here.  I brought out my oscillator and resumed doing hand sweeps.  It was clear the left channel was audibly lower at 30 Hz and below especially, which seemed to almost disappear.

That was relatively easy to correct simply by dialing back a little the cuts I had made when using ARTA.  I experimented with changing the position of the wide 3/4 octave cut, there really seem to be two separate resonances involved in addition to a broad area of excess (without EQ).  But I finally left the low EQ frequency more-or-less unchanged, because if I set it precisely to the center of the lower resonance, it tends to cut the lowest frequencies too much.  So it's at a compromise frequency that works for both resonances AND the whole area pretty well, as currently adjusted.

But I became more and more bothered by the apparent notch at 100 Hz in the 6th octave RTA.  I'd "worked" that a little bit before and it seemed fairly intractible.  I tried, tried, and tried some more.

I reduced and even eliminated the numerous EQ cuts below and above 100 Hz.  That didn't remove the problem, though with a bunch of EQ changes it seemed to be a bit better.  Here I was using both hand sweeping the oscillator, AND the RTA app.)  Sometimes.  It was sounding nearly OK on the hand sweeps.  But not really enough better on the RTA, in fact making the surrounding regions more level with more finely tuned EQ seemed to make the notch at 100 Hz look worse.

Left Channel, after raising low bass and fine tuning EQ's around 100 Hz

Clearly something bad is going on right around 100 Hz, which is also the crossover frequency.  And clearly it has nothing to do with the EQ's I am applying nearby.

I first tried to get a handle on this by looking just at the bass response, which I figured was a factor:

There is a very little tiny dip around 100Hz, though it's hard to pay much attention to that when other things are not looking good.  (BTW, the I left the supertweeters on for these measurements.)  For one thing, the crossover doesn't seem to be really crossing over at 100 Hz, more like 140 Hz, and that's with two big notches dialed in to the subwoofer response above 100 Hz already.

I tried to do some more adjustments to fix the 100 Hz dip anyway, but nothing did much good.  I began to determine that the 100 Hz dip in the sub response is caused by a room mode.  When I've dialed in the frequency at maximum notch cancellation, I can walk around the room and the response varies enormously, going from way too much to just the little dip shown here at the listening position.

That's significant, but really not that bad.  A bigger problem must be elsewhere, notably in the Acoustat response (as rolled off by my crossovers and EQ adjusted, but with the supertweeter left on as before):

This doesn't look like it rolls off as much as it should, but the electrical signal as shown by the RTA on my Behringer 2496 DEQ shows the bass rolloff exactly as you would expect from 24dB/octave Linkwitz Riley.  The rolloff is flattened acoustically mainly by the high level of ambient noise.  So just ignore that.  The main feature here is the very large notch at both 100 Hz and 112 Hz.  Those notches would look even worse if the ambient noise (from air conditioner and stuff) were removed.

Interestingly enough, I had dialed in a 100 Hz cut in the Acoustats, which I determined necessary from the Right channel on which I spent more time EQ'ing in the recent past.  I had that same cut in the Left channel where it makes things worse, primarily because I had only done "stereo link" EQ's for the Acoustats previously.  Right here I decided to change that, and removed the 100 Hz cut from the Left channel, but it made little difference (IIRC, I had removed the 100Hz cut just before I took the above measurment.  Prior to that, 100 Hz and 112 Hz were more level.)

After playing around with this for far longer than should have been necessary, it finally began to occur to me that this 100-112 Hz notch was being caused by rear wall reflection and cancellation.

Somehow, my intuition had always been that the rear wall reflections would be a factor only at much higher frequencies, such as 220 Hz, or 160 Hz, where they had troubled me long ago.

After continuing to think wrongly about this problem, I finally figured out the right answer.  The rear side emission of a dipole radiator is already out of polarity with the front side.  Because of that, it has to make an entire wavelength (or none at all) of travel to have a cancellation effect.  So the distance from the wall is 1/2 of the wavelength of the cancelled frequency.  And not 1/4 of the wavelength, as it would be for a box speaker.

But calculating from the wall distance of the closest point of the speaker doesn't suggest 112 Hz at all.  The minimum distance perpendicular to the wall is 40 inches, and at the center of the 2+2 panel it rises to 45 inches.  Taking 45 inches as the distance, that would cause cancellation at 146 Hz.

Wavelength = Speed-of-Sound / Frequency
Frequency = Speed-of-Sound / Wavelength
(1100 * 12) / 90
146

But what's happening here is that not all the sound travels that minimum distance.  The dipole radiates in the back as the front across a 90 degree arc.  Nearly all of the reflected rear wave travels considerably more than 90 inches.  90 inches in the bare minimum, most of the reflected rear wave travels more like 120 inches before it reaches the plane of the speaker, and that is what corresponds to the cancellation at roughly 112 Hz.

Several times last year I moved my electrostats further from the wall to mitigate the cancellation notches.  When I reached the current distance, the notch seemed to completely go away in the right channel.  In fact I had added an additional cut around 100 Hz because there was too much energy there.  I hadn't paid much attention to the left speaker.

I should have paid more attention to the left speaker, which shows the cancellation notch much more clearly, and NO amount of EQ can get rid of it.  Even increasing the subwoofer output at 100 Hz doesn't help much because it is also a room mode for the monopole subwoofer.

I further confirmed the cancellation nature of the 100-112 notch in the panel response by measuring all around the room.  Unlike the room mode caused by the subwoofer, the larger notch in the panel response is only a little affected in magnitude by listening position.  There is no place where it gets louder instead of softer.  The notch pretty well sucks out all the signal everywhere.  But the center frequency of the notch shifts a bit, possibly because it also interacts with the room mode, OR because the angle from the speaker determines the rear wave travel distance.  At the listening position, the notch seems centered around 106 Hz, and on the side further back, it seems to center around 120 Hz.

So I had two problems not amenable to solution with EQ: a room mode (for monopole subwoofer), AND a rear wall cancellation notch.  But both are amenable to other solutions.

I was shocked at how much difference moving the listening position a mere 10 inches forwards made in the bass response from the subwoofer only.  There is no shortage of 100 Hz from the sub at that position, which I've decided to make permanent at least temporarily.  But this may mean way more readjustments of things like the speaker angles.  But I've decided to take on that challenge anyway.  Actually, the closer position might be better for stereo width anyway.

Fixing the panel response is done by opening another can of worms.  But it only makes sense that if a speaker has problems in the 100 Hz range, I should not be using that frequency as my crossover frequency.  I should cross over the panels higher then 100 Hz to push the rear wall cancellation effect way below the crossover frequency for the dipoles, not just above it!

Actually, however, I first though of this solution just from the fact that even with the existing crossovers and EQ's dialed in, the subwoofer response seems to naturally roll off around 140 Hz.  So, I decided that would be a good place to start, and I then adjusted the panel crossover to have a 140 Hz acoustic crossover frequency, or what looks like one on my RTA.

All my fine-tunings now need to be fine tuned all over again, given that I've changed both the listening position and the crossover frequency.  But it looks now like this is the only way to go forwards.  What I was doing before doesn't make sense.

Even without additional fine tuning, just crudely readjusting the listening position and the crossover frequency has made the sound much punchier and yet clearer at the same time.