MUSINGS: Speaking "As If..." claims are truths, Attribution Theories, and the Numerical Madness of Chord (Mojo 2 and 104-bit DSP)? (And quick note on Multichannel "Kind Of Blue".)

As you've seen, recently, I measured the Chord Mojo DAC and we discussed the imminent release of the Mojo 2 which was formally unveiled on January 31 (2022). With that of course comes the flurry of media posts, reviews and advertising material hyping the new features which might or might not be useful depending on your needs.

An interesting interview (and I'm sure one of a number in the days ahead) is the one Darko conducted with designer Rob Watts released on February 1st. As much as I've been critical of Darko over the years (like this), I appreciate the interview, the questions, and perhaps showing some guarded skepticism; good stuff John for letting Watts speak.

The DAC infrastructure of the Mojo 2 is basically an "evolutionary" upgrade to the custom sigma-delta design of the Mojo 1 which is already very good. Watts admits to this evolutionary step (12:50). As suspected, they needed to keep Poly compatibility (2:15) - a shame because I think the retention of micro-USB is a real turn-off in 2022. These days, Bluetooth in a premium product I think is a basic mobile feature. At this kind of price point >US$700 for the Mojo 2, I think it's a little silly to also have to pay another >US$700, tolerate the added bulk, just to get wireless options but still limited to Bluetooth 4.1 A2DP/SBC last I looked; no aptX, LDAC, or even AAC codec support for higher fidelity (lossless Bluetooth would not be high on my priorities, but aptX Lossless is good I guess). As a general rule-of-thumb in consumer electronics, I think expensive add-ons like this usually don't make much sense, much less insist on ongoing compatibility across generations of products in the mobile space.

I got a chuckle from Watts saying that he listens to the Hugo 2 DAC + M-Scaler on a plane with a battery pack (4:30) - that's hardcore "audiophile" man. Given the limited leg-room these days, and the crying babies disrupting hi-fi listening in Economy, he must be referring to First Class perks. IMO, that seems more than a little bit out of touch with what reasonable passengers would do, no matter how "high end"! ;-)

Whether intended or not, the fact that Chord's advertising materials and interviews with Watts focus heavily on technical specs and numbers invite audiophiles to think about how these numbers might translate to sound quality.

We've talked about digital filter "taps" (9:30) already in the previous Mojo post so let's not worry about that here. The interesting discussions around new features of the Mojo 2 are mostly centered around the DSP. Chord is claiming that its design is now "lossless" (19:30) as opposed to presumably every other DSP in existence. As best I can tell, the belief  here is that if a signal of -301dBFS (27:30) can be demonstrated to have no noise floor modulation and no phase shift, then it's "lossless". He believes that this results in less harshness (which seems to be defined as brightness and "aggressive" sound [7:45]) due to the clean noise floor and improved soundstage ("perception of depth") due to phase accuracy. He claims that the brain is "incredibly sensitive" to noise floor and transient anomalies (10:45) at such low magnitudes.

Throughout this interview, he claims that these little things (like maintaining the vanishingly small -301dB signal resolution) are audible (21:30) based on work with the Chord DAVE. "Perception of depth got better" as the noise shaper went down to -350dB even, so he says! Note that this kind of talk and these numbers are not new, in fact he used them in the RMAF2017 talk.

Basically, the message is that the limits of typical 64-bit floating point math are not good enough. Realize however this is all in the digital domain of the DSP subsystem. While I have not seen a block diagram of the Mojo 2 published, based on previous stuff on the Hugo DAC and a diagram like this for the DAVE, I think what we're looking at is likely something like this:

Computer/Streamer 24/32-bit integer up to 768kHz data sent over USB --> 64-bit (floating point vs. fixed point? Could be 56-bits internally like M-Scaler.) WTA oversampler to 16fs (705.6-768kHz, 40,960-taps FIR filter) --> DSP @ 104-bit floating point (EQ & Crossfeed) -->  Linear interpolation to ~100MHz (2048fs), 5-bits SDM with "enhanced" 5th order? noise shaper --> "4-element Pulse Array" converter --> single-ended headphone amp output

From computer to the WTA oversampler to the DSP, we see an increase in number of bits, higher precision, which is good. However, to get the computed data out of the DSP and fed to the DAC portion itself, the floating point values need to be converted into the interpolated, noise-shaped, 5-bit ~100MHz SDM format.

The question then becomes, within this scheme, what practical difference in precision is there between 64-bit and 104-bit floating point calculations?

We know that 64-bits floating point ("double-precision floating point") as per conventional IEEE 754 provides for 52 bits of precision (also known as the "mantissa"). 2^52 values can be represented, which works out to log10(2^52) = 15.65 decimal digits of precision. So Watts is saying that such a tiny variation (precision down to around 15-16 decimal places) in the value of the DSP calculations, would significantly change the sound coming out of the single-ended headphone output which no doubt will ultimately be of far lower resolution than those lofty digital numbers.

Is whatever difference significant enough that calling this the "world's first lossless DSP" means anything!? It's one thing to label the DSP in advertising material as being "UHD DSP" (Ultra-High Definition?), but it's another to call something like this "lossless" isn't it? After all, we are introducing EQ and other changes, plus digital data will always be quantized at some level, so the choice of the word "lossless", which has a traditional meaning in audio seems to be unnecessarily controversial probably as an advertising move. Is it just that they're increasing bit-depth from computer to DSP, therefore there's no risk of rounding errors in the digital calculations?

Throughout this interview, Watts keeps insisting "What I found was..." this and that subjective improvement in sound quality, whether it be lower noise, improved timbre, nicer transients, more depth, etc... These are the usual qualities Chord/Watts hammers on to make a case that their big numbers, whether it be tap length, or DSP bit-depth (40,960 taps and 104-bits in this case) can make a big difference. We already know that Watts thinks 1M-taps make a difference even though there's no reason to think the theoretical advantages are all that meaningful (oh yeah, from a precision point of view, notice that the M-Scaler has to output the data to 24-bits only!). As for the DSP, wouldn't then going to 128-bits math make it "even more lossless" because now we can theoretically achieve >750dB of dynamic range on the digital side? Is this "numerical madness" not at some point absurd? (Notice that he talks about a 140-bit DSP he's working on at 28:50 - "that is really scary this particular project!" - seriously folks, why so emotional with mere numbers and 40 decimal places!? So what?)

I speculate that 104-bits was chosen simply because they can claim a 3-figure bit-number. When you're trying to impress using specs, this looks good. I doubt there's a better reason why he's not using a more typical "extended precision" format like 80-bits (63-bit mantissa, 18-19 decimal places) for example; software like HQPlayer has been doing this for years.

Linking "What I found was..." with numbers like dB and bits of processing is an attempt to wrap a subjective belief with numerical properties as if they are reliably correlated, even suggesting they may be causal. It's no different from cable manufacturers saying as if their special winding for the wire or type of dielectric is what caused an unsubstantiated subjective "improved" sound quality. Or as if the special all-silver wire transformer is what improved the sound of a certain tube amp (which still is noisy at low power when measured!). These attribution theories can be interesting hypotheses to test out, but let's be sophisticated enough as independent audiophiles to show skepticism first before accepting the likely extreme claims as valid. By this point in history, with plentiful high-fidelity products in the market, it's well and good to hear from a manufacturer about "what was found", but just as important is that the manufacturer needs to help demonstrate to audiophiles "how I found it". It is only by doing the latter that a company can meaningfully contextualize such claims.

Maybe the Chord Mojo 2 DSP is truly awesome and I look forward to having a listen myself, reading insightful forthcoming reviews and more importantly, objective tests if someone actually bothers to spend time measuring the DSP feature at the analogue output.

I'd be careful with getting too excited though. IMO, what Rob Watts/Chord needs to do to make a strong case that 104-bits is meaningful is by showing us:

1. The digital difference between the Mojo 2's 104-bit DSP and an actual 64-bit DSP. By all means, use the -301dB test signal and show us the resolution and temporal difference through the processing including noise shaper. (This is a technical demonstration of the engineered precision since one cannot send a -301dB signal to a 24/32-bit USB DAC, nor is the analogue output even nearly this quiet.)

2. Show us what difference 64-bit vs. 104-bit DSP processing makes with the signal coming from the analogue outputs of the Mojo 2! (Curious to see what actual data is fed in and what EQ or Crossfeed settings used if there is a significant difference to be seen.)

3. Then show us the results of actual controlled human listening tests to demonstrate this supposedly significant improvement between 64 and 104 bits.

I'm sure he can show some nice graphs and waveforms with signals at very low dB levels directly fed into the DAC at ≥64-bit precision for #1. My bet is that he cannot show evidence for #2 and #3 . No, what his son at 29:45 claims he heard isn't impressive - this is just a less objectionable variant of the "My wife heard a difference in the kitchen!" motif.

Until there's plausible evidence, I hope each time Watts gives these kinds of interviews, it's just going to sound less and less meaningful for listeners who understand what the implications are of his claims. There's no need to be automatically impressed just because of big numbers!

In an implied way, there is this aura/mystique/miracle being promoted by large numbers like 1M-taps or >100-bits DSP processing from Watts/Chord, isn't there?

Even if we believe that the 104-bit DSP is necessary, I do have concerns from a potential user's perspective. Regardless of the internal precision, practically, notice that the EQ settings are limited by the rather "rough" overlapping 4-bands (called "lower bass"/20Hz peak, "mid-bass" shelf, "lower treble" shelf, and "high treble"/20kHz peak) set from +9 to -9dB, at +/-1dB steps. This limited way of setting EQ is not unexpected since the user interface does not include any kind of display to fine-tune EQ shapes nor provide detailed feedback. For example, say we want to implement a simple narrow parametric -2.5dB 4kHz "BBC Dip" (like in this discussion), but leave everything else unchanged, it would be impossible to set this on the Mojo 2. In any event, it would have been very nice to see the summed and subtracted EQ curves on a display. Interesting that the manual even suggests the user look at RTINGS.com headphone curves for compensation settings. As it stands, recommendation of looking at the complex measured curves "as a guide for experimentation with Mojo 2’s DSP feature" I guess could be interesting but only on a very gross level given neither precise EQ settings are available nor detailed visual confirmation of the resultant curve.

It should be interesting watching in "real-time" over the next number of months how the audiophile advertising system and network of reviewers roll out the Mojo 2 news with various ads, notifications, and subjective reviews to capture consumer interest. Articles like this one: "Chord Mojo 2 review: this mini DAC is a huge upgrade for your headphones" is a great example of the push for labeling this device as "best-in-class" sound; it would not be surprising to see the Mojo 2 "destined" to be on "Best Of 2022" lists by year end. Despite superlatives around claimed subjective sound quality, what caught my eye in that review article was the statement: "Ergonomically, the Mojo 2 is a bit of a disaster". That seems honest looking at the video instructions. A nice LCD/OLED screen and graphics for the EQ settings would have just been too obvious, or maybe conventional, for Chord, I guess. Similarly, you'll see YouTube reviews like this one parroting a lot of the same Chord technical advertising claims but as usual, offers no independent objective testing.

While a new "UHD DSP" might be cool, I wonder whether engineering efforts could have gone elsewhere, finding opportunities to enhance other features. Balanced headphone out (significantly lower noise, improve dynamic range)? More headphone amp power? Better battery life (clearly the digital processing has substantially increased power consumption)? Bluetooth input? My suspicion is that any of these features probably would have either improved sound quality or usability way more than the difference between 64-bit and 104-bit DSP.

Classic Rube Goldberg (1931).

To be clear, I still think the engineering from Chord is excellent as already demonstrated by the Mojo 1 - but more than likely way over-engineered. That extreme level and accompanying advertising hype are cause for reflection as audiophiles and consumers when thinking about true value of a product.

Just as with the flowery prose of extreme subjectivism, I think as Rational Audiophiles, it's important to avoid being bedazzled with extreme technical specs and numbers. Consider what these numbers actually imply and ask oneself whether the company has done anything to demonstrate the claims; in this case a linkage of sound quality with perpetually larger FIR tap lengths, and now DSP bit-depth. I think it's important to only be excited with the specs when there's a sense that these numbers actually significantly represent progress within limits of demonstrable listening ability. For example, does it make sense that we need precision beyond a standard 64-bit DSP's 15 decimal places when high bitrate 320kbps MP3 actually sounds pretty good with all its "lossiness" or that harmonic distortion isn't all that audible at relatively high amounts, or that even the difference between 16 and 24-bit audio isn't all that perceptible? (Much less expressing exuberance over 140-bits and 40 decimal places for FIR coefficients!)

One last thing, I liked how Darko asked Watts at around 32:10 - "Do you have any go-to test tracks that you use that you can share?" Brilliant. Notice how Watts fumbles on that question and cannot even produce the name of a single track he uses to assess "depth" for example (apparently organ, electronica, guitar tracks, a Norah Jones track?). This is despite listening to "three tracks" he uses in particular and has heard them "thousands and thousands" of times. Reminds me literally of that quote from Alan Parsons about audiophiles using his music to listen to their equipment. ;-)

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Fun discussion. Here we are talking about better-than-64-bits floating point calculations with 15-16 decimal places calculated hundreds of thousands of times a second for 2-channel digital audio. It looks like 9 significant digits for the value of π likely was all that was needed to land a man on the moon back in the 1960's within feet if not inches of the intended target. The Apollo Guidance Computer software only used 30-bit fixed-point matrix and vector calculations. These days, even for interplanetary navigation, 3.141592653589793, within 64-bits floating point, is all NASA/JPL needs. It looks like pi to 40 decimal places would be precise enough for calculating the circumference of the universe down to the accuracy of the hydrogen atomic diameter.

Maybe Watts is onto something with that 140-bit DSP to accurately reproduce "Musica universalis"! But then again, this just means we need >140-bits for truly ultimate "multiversal" music quality! ;-)

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The other night I spent some time getting reacquainted with the 2001 5.0 SACD Kind Of Blue I digitally ripped (using PS3) a decade back as I continue to explore my library since installing the multichannel Roon endpoint discussed last week.

KoB was done on 3-channel tape so the 3 front speakers are put to good use plus some additional tasteful ambience in the rears. I think the clarity on the multichannel mix is fantastic, better than the 2-channel versions I've heard over the years. I agree with some comments I've seen online that the multichannel version does an excellent job highlighting Paul Chambers' bass in the center channel that can sound muddled when spread into the 2.0 mix-downs. I recommend KoB fans to at some point experience the multichannel version. I wonder if the Atmos mix of KoB will ever be released.

I listened to the KoB mono mix awhile back but am not a fan of mono in general. I get it that for very old recordings, perhaps the mono version was the "definitive" release back in the day that everyone heard over the radio and some folks "grew up" with. Given a choice, unless the 2-channel is done very poorly, I don't find mono sound interested due to the missing lateral soundstage and absence of the timing cues to signal spatial depth. 

Time to get into Nicholas Jaar's ambient electronica Cenizas (2020, DR10) this weekend as well. 

Hope you're all enjoying the music!