Hydrogen Audio are Good

I like Hydrogen Audio objectivists.  I am often disappointed with myself that I'm not an audio objectivist by their standards, or perhaps any.

One thing for sure, if you don't like spending money on unproven things, don't follow my approach, which pretty much guarantees that.

Arnold B. Krueger, despite his fame, works tirelessly and sympathetically to help find the best explanations for everything.  He is not the kind of in-your-face or casually hurtful person you might suspect from his reputation and his avatar.  But he is not the kind to surrender to subjectivism either.  He sticks to his reason, and I respect that.

I like doing what I do anyway.  I do focus a lot on things objectivists like, such a speakers and room acoustics.  But I also (waste?) a lot of time with electronics whose levels of performance should not be required for satisfactory reproduction.

I know that such things may not be important AT ALL.  I just enjoy working them anyway.  I try not to make big claims (but sometimes I do anyway, such as my recent war against sigma delta).  Whatever I might say, you can be sure that I do also always harbor considerable doubt at my own ideas.

I stay away from things where I have no understanding of how it's supposed to make things sound better, look better, or be more fun.  I think that is the wrong approach to audio.  If you don't have a hypothesis you are exploring, can understand roughly, or measure, I don't think it will be easy to make progress in a sound improving direction.

Many people think "science" is all about observation.  But actually, it always has to start with a plausible story.  Without a story, it's just all shots in the dark.

Jitter in new Toslink/SPDIF link

Now that I've finally implemented a digital link from the kitchen Mac computer to the living room stereo, I'm a bit worried about jitter.  So far I haven't noticed any loss of digital lock, or any bad sound (in fact, it sounds better than anything) but as an audiophile with obsessive tendencies (like most) I nevertheless worry about such things (though not as uselessly as some people, I like to think).

The link is not as simple as I might like.  At minimum, it has to convert the Toslink output of the Mac (conveniently combined with the headphone jack) into coax to run across about 65 feet of coax to the living room (50ft running through ceiling reaching wall jacks, and an additional 15 feet of patch cords…or the ceiling wire might also be 75 ft, I provided both lengths to the electricians and don't remember what they actually used).

Probably most of the degradation would come from conversion into Toslink inside the mac, and then conversion from Toslink to coax, and maybe in the Toslink cables themselves.

But actually, it's more complicated than that, because I need to run the Toslink from the Mac into at least a 3 way splitter.  Currently I use a INDAY 4 way Toslink splitter, which splits off one line for the living room (which gets converted to coax as described above), one line for the kitchen system (a Yamaha AV receiver), and one line for the hard drive recorder (which only accepts analog inputs, so therefore goes through an EMU audio interface repurposed as a DAC).

As I said, everything seems to work perfectly, but the line going to the living room has to pass through these interfaces:

1) The Mac Toslink output
2) 1 foot very high grade plastic Toslink cable
3) INDAY active splitter
4) 12 foot high grade plastic Toslink cable
5) MAudio CO2 converter
6) 2 foot precision coax
8) 50 feet in-wall coax with F terminations
9) F-to-RCA adapter
10) 6 foot RG-6 patch cord with RCA terminations
11) RCA-to-RCA barrel adapter
12) 6 foot Monster Video 3 patch cord with RCA terminations

Now the easiest thing to fix would be 9-12, I can simply get a 10 foot precision video cable terminated with F connector on one end and RCA on the other.  I will be ordering that next month.

But what actually worries me more are the Toslink conversions.  First the digital signal is emitted through a Toslink LED in the Mac.  Count that as 1 hop.  Then in the INDAY splitter, the digital is received and retransmitted.  Count that as 2 hops.  Then, in the CO2 adapter, it goes through one more Toslink receiver.  So count this as 4 optical "hops."  A minimal Toslink connection involves only two hops: sender and receiver.  Each optical hop limits rise time and therefore makes jitter possible.

I could easily change this by running the Toslink from the Mac through a different kind of splitter.  The best kind is the one that I haven't yet found, which would have two optical outputs and one coax output.  Instead, the typical kind of "splitter/converter" has one coax output and one optical output.  That would work just dandy for the living room connection, which would be reduced from 4 hops to 2 hops.  But meanwhile, it would increase the number of hops for the kitchen receiver from 4 to 6, because I'd still have to use the INDAY splitter on the Toslink output of the first converter to get the two Toslink outputs that I need, and likewise the number of hops to the EMU audio interface would increase to 6.  They might not even work with that many hops (though, I expect they would), but at best they would see increased likelihood of jitter, despite the use of very short 1 foot very high grade Toslink cables.

The MAudio CO2 can be used as that new kind of splitter/converter.  By changing some switches, I could change it to take Toslink input and produce both Toslink and Coax outputs.  And there are also other similar splitter/converters available, including one from Calrad.  (MAudio no longer makes the CO2, but there is a Calrad replacement which can also be used as one Toslink to Toslink and Coax.)

But I have seen nothing doing exactly what I want: 1 Toslink to 2 (or 3) Toslink and 1 coax.  There are other variations, however.  Calrad makes an adapter that takes Toslink input and gives as output 1 Toslink, 1 Coax, and one stereo output.  With that unit I would put living room at the minimum of 2 optical hops, and keep the kitchen receiver at 4 optical hops (where it is now).  And I would eliminate the need for the EMU interface.  But that's also a rub, because I doubt the DAC in the Calrad adapter would be as good as the one in the EMU interface (which is professional grade, >110dB S/N, etc) and would also lack the convenient volume control.  Plus, I'd need to use a stereo audio isolation transformer on the analog outputs because otherwise I'd be connecting the grounds of my kitchen hard drive recorder and my living room audio system (very undesirable!).  That isolation transformer would not be as perfect as the optical isolation now used, AND it would further slightly degrade the analog audio sent to the hard drive recorder.

There might be some sort of switch that would do the trick.  This one looks like it might work, except it's unclear whether it actually converts Toslink to coax or merely switches Toslink to Toslink and Coax to Coax.  Plus it's way overcomplicated for what I need, since it also switches and distributes 4 component video inputs, though surprisingly inexpensive also (which raises other doubts).

And I haven't even begun to consider adding yet another digital link to the master bedroom.  I could easily add that on to the system I have now (simply by adding another CO2 converter to the currently unused 4th Toslink output of the INDAY splitter) but it would not work with any of the other adapters or switches I've mentioned so far.

In assessing new digital audio distribution strategies, it might be useful to measure the digital transmission system itself or the jitter it produces.  Here's the best discussion of measuring jitter I've seen.

Here are some very expensive digital analyzers I won't be buying.

Here's a long discussion of transports and jitter--but also looks closely at the SPDIF and Toslink interfaces.

Here's a discussion of Jitter that claims audibility based on AES analytics (not ABX testing) to 120pS for 16 bit and 20pS for 20 bit.  (The ABX testing shows much lower sensitivity up to 10nS, 100 times larger.)  Here's a further discussion of the importance of characteristic impedance by the same author (Steve Nugent of Empirical Audio).

Here is Toslink vs Coax measurement, and the coax is said to be 7 times better.

Here is MSB paper on jitter.

FINALLY, I found what I need, a Toslink splitter with extra coax output, the Inday TLDA-22.

Actually, what would be really perfect would be if it had two galvanically isolated coax outputs, so I could send coax digital to two different rooms.  Given that two galvanically isolated outputs would be pretty hard to do anyway, one coax output is ok.

Dirac

Here's a review of Dirac pc-based equalization system and other equalization systems.

Interesting.  However I wouldn't like having to run everything through my Mac for correction.

My last time around (in 2010) with automated room eq didn't turn out well.  Optimizing the center room sweet spot made the room boundaries in a huge boom zone.  Next time, I plan to only correct the subwoofer bass, and I plan to do a multipoint correction which takes into account boundary positions as well as the current less central sweet spot.  I still plan to use the DualCore DSPeaker to do this.  It's hard to know how the DSPeaker algorithms compare with Dirac, but DSPeaker is sure more convenient for me.

Other software for room eq includes Audiolense, Acourate, and REW.  REW creates filters that you load onto a PEQ device (I still have the one they suggested in factory box).

Here's a quick summary of DRC, Acourate, Audiolense, Ultimate Equalizer 2.0 HT, Dirac, and MathAudio.

Audiophile Information Model

A musical event, either live, or the sum total of pre-recorded takes, consists of a very large amount of information, though perhaps much of it redundant.  A produced album consists of a huge reduction in the original information, but presumably selected or translated as to concentrate the musical information from the redundant, and have a particular style.

Listening to a recording, and audiophile gathers information of many kinds, originating from the recording,  constructed (interpolated or stylized) mentally from information in the recording, and caused by the interaction between the recording and the reproducing system.

In no single listening can all the information be fully gathered originating from the recording, in each listening only a subset of information originating from the recording is actually gathered, and the subset gathered on successive listenings differs, though usually with large central overlap.  But while the subset of information gathered originating from the recording may vary little, the impact on mental reconstruction may be discontinuously huge, because the construction process is itself highly discontinuous and non-linear.  The information gathered resulting from interaction with the reproducing system may also vary only slightly, but have large discontinuous impact upon mental reconstruction.

Now many audio reproducing systems are simplifying systems.  They simplify the information available from the recording.  A classic and ubiquitous way is by limiting frequency response.  Few reproducing systems do not restrict frequency response in some way, though most ubiquitously in the very deep bass.  So while we may hear to 20 Hz and feel to 16 Hz, few reproduction systems do a good job of reproducing the octave below 32 Hz.  Meanwhile, systems with 32 Hz response may have high end response to 22kHz, which is actually a violation of a longstanding rule of frequency response bandwidth limiting…low frequency restriction should be matched by high frequency restriction to sound balanced, and response to 20kHz corresponds with low frequency response to 20Hz.

But simplification in other forms is actually more serious.  Most of these are simplification by obscurity.  Resonances draw attention to themselves and their intermodulations with the music, but obscure adjacent details.

Systems involving dynamic compression are another type.  The worst of those can simplify by reduction.  MP3 is an example of such a system, the missing information is simply gone.

I maintain that DSD is such a dynamic compression system, as are all PWM and delta sigma systems.  They often rely on reduced human sensitivity to high frequency dynamic range.  Canonical DSD has 1 bit of resolution at 64fs, which means little more than 65^2 possible states at 20kHz.  Redbook 16 bit 44.1kHz digital has 65536^2 possible states at that frequency.

Now you can see from the vast amount of information potentially available at just one cycle of the highest frequency we can hear…we can never hear it all, but only a subset.  But if there is vastly reduced information in the recording itself, then more overlapping subsets of information may be heard on each listening.  Ultimately making it boring.

More evidence from a big test and upgrade

Now believing that ladder DACs are better than Sigma Delta DACs, I am disappointed by the fact that the way I was playing high resolution media necessarily involves passing through one set of sigma delta DACs.  Those are the Burr Brown 1790's in my Denon 5900 universal disc player.  The analog output of that player gets resampled to digital (via a professional grade Lavry AD10 analog to digital converter) for level, crossover, and eq processing, and converted to analog the last time by the Burr Brown 1704's in my Onkyo RDV-1 operating as a DAC.

Onkyo RDV-1 (on bottom) running as DAC

Unfortunately, I can't simply play DVD-Audio discs on the RDV-1 and use it as a DAC at the same time.  Even if I were to give up the crossover and EQ parts of my system (and therefore the subs and super tweeters), I would still have no way to set the level on the RDV-1 output.  I use no analog attenuators (and I generally find that passive attenuators make the sound dark, dead, and closed-in).  The RDV-1 is simply connected to my main power amp via short audiophile grade interconnects.  As complicated as my system looks, the analog domain past the digital converters is very simple--just wires connecting to a well designed amplifier.

But what I could do, and what I did, was take the RDV-1 offline for awhile (Saturday and Sunday) and  use it as the analog source for the Lavry AD10, and record the Lavry digital on my Alesis Masterlink.  I could then burn those new digital files to a DVD-Video disk at 24/96, and play that in the Denon using digital output.  In the whole process, I would be using the ladder DACs in the RDV-1 twice, first for making the new digital files, and finally as my main system DAC.  And I would not be using sigma delta DACs at all, all other transfers would be digital.

Recording tracks on the Masterlink was a relearning experience and it took quite a bit of time to record tracks in groups of three, burn them to CD24 discs with the 24/96 digital information unaltered, and copy them to my Mac mini.  After I had copied over about 6 songs from the DVD-Audio of Santana Supernatural, it occurred to me that rather than burning DVD's with the new digital files to play on the Denon 5900, it would take about the same effort or less to create a SPDIF digital connection from my Mac to my living room system.  And then, I would also be able to play other digital files from the Mac without burning discs…including the Audiogon Sampler I just downloaded from HDTracks over the last week (but without any actual means to play it).  And then I could get more albums from HDTracks, possibly including the official high resolution files from Santana Supernatural, which are likely to be even better than my resampled versions.  (I will NOT be getting any DSD files, which I have no means of playing and I strongly believe are inferior anyway.)

So that was the big upgrade--I added Hirez file playing capability to my living room and kitchen systems.  I had been behind the curve a few years on this.  To allow the Mac to actually play high resolution audio files, I downloaded and installed Amarra Hifi for $49.  If the Mac natively plays high resolution files at all (and I'm not sure it does anyway), it does so by resampling them to 44.1 kHz and 16 bit resolution.  Amarra bypasses that operation and makes the Mac play back files up to 96kHz in their native sampling rate, and in bit clear fashion so all the bits get through.  The digital connection uses my new in-wall network, which has a Belden RG-6 line running from the kitchen to the living room.  I take the Toslink output from the Mac, run it through a 12 foot Toslink cable, convert to coax with a M-Audio CO2, then run through 75 ohm coax cables and a couple F-to-RCA adapters, and plug that into my Tact preamp as one of the coax digital inputs.  I had all the needed cables and adapters on hand, though I also needed to use one RCA barrel connector to join two RCA terminated 75 ohm cables.  I should get better quality cables cut to the correct length later.  Even with the adhoc whirring, the digital connection from Mac to living room works perfectly, and there is no detectable ground loop though the CO2 is powered in the Kitchen through it's own transformer which has a two wire AC connection.  Though some audiophiles may frown at such a "complex" system because of all different wires, I see only a direct digital connection without any synchronous or asynchronous conversion or modulation.  The clock being used is the one in the Mac Mini, and bit buffering is done right there--by hardware and Amarra, and that is the best possible place.

I wasn't actually expecting to be able to play Hirez in the kitchen, but to my delight the Yamaha 5790 receiver takes the 24/96kHz digital input and plays it just fine.  I have never heard such good sound being played in the kitchen.  I also understand iTunes much better, and that I can simply select a bunch of songs and put them into a playlist.  If you don't play from playlists, iTunes will simply proceed to play every song available, which could be dangerous.  And adding songs to iTunes is most simply done just by clicking on them.

Playing the new Hirez files, the added resolution from bypassing the sigma delta converters in my Denon 5900 was obvious.  There is much more resolution now!  Sometimes I felt the highs were a bit strident, and the brass extra brassy, but the sound was much more interesting and involving and worth putting up with the blemishes.  Better cabling might help the stridency.  It had a neutral and transparent sound with layer upon layer of stuff going on in audio that was audible for the first time.  By comparison, the original path through the 5900 was like rose colored glasses--it always had the passion, and it always sounds pleasant, but it's missing many of the details.  That's the signature of sigma delta converters, and what would be expected from the information loss that is inevitable from them.

One thing I hadn't been expecting was the newfound bass tightness.  Although sigma delta converters should work fine in the bass, they might work "too well."  I think they were halving the bass sometimes, working like a subharmonic synthesizer.  Now the bass is deep and tuneful at the same time.  Far more tuneful.

Of course the differences I'm describing are the differences between starting with the Denon 5900 and the new Onkyo RDV-1.  The differences could be caused by other aspects of the circuitry.  But I think both of these machines are well engineered, and that most of the differences come from the differences between the digital to analog converters they use, which are fundamentally different (though ironically both made by Burr Brown).

Sonos Line-In levels

I use the line-in feature of my Sonos system more than anything else.  It's incredibly convenient and sounds good.  The main things I listen through Sonos line-in are my two FM tuners (Kenwood KT-6040 and Pioneer F-26) which are set to Jazz/Indie KRTU and Classical KPAC.

But I often wonder about setting the input level.  Unfortunately Sonos provides no visible feedback of clipping through the line input.

Well here is what Sonos Support says about the line input levels.  Interpolating for levels 3-5 and 7, here are the max input levels as best I figure them now:

2.2V  Level 1 (low)
2.0V  Level 2
1.8V  Level 3
1.6V  Level 4
1.4V  Level 5
1.2V  Level 6
1.1V  Level 7
1.0V  Level 8
0.8V  Level 9
0.6V  Level 10

My Kenwood KT-6040 specs say output is 0.8V at 100% FM modulation.  Since modulation can go a bit higher than 100% in practice, this corresponds to a max output of about 1.0V, which was a standard line level before CD players were introduced (CD players have output of 2.1V).  Allowing a further bit of headroom, I've just set the Sonos to Level 5 which is 1.4V.  Previously I had been using Level 1 or 2, which is a waste of dynamic range.

It often takes a few minutes to get used to higher resolution, and that was true when I changed from Level 2 to Level 5.  But there is no audible clipping or harshness, just more information.

Recap on DSD information loss theory

In classic 1x DSD delta sigma modulation, canonically one has 1 bit at 64Fs.  Seen from the perspective of 1Fs, 44.1kHz, which itself is a bit more than twice the "standard" human hearing limit of 20kHz (most adults have less than 16kHz), all these bits are equal, regardless of order.  Therefore, the total information at 1Fs is 65--there are 65 possible states, simply the total number of "on" bits from 0-64.  Expressed as "dynamic range" this (64/1) is 36dB before noise shifting.  The dynamic range rises 6dB for each octave lower than 1Fs/2, so at 20kHz it is about 43dB.

Meanwhile, classic Redbook CD 44.1 kHz 16 bit has 65536 possible states at 1Fs--the same 98dB of dynamic range it has at all in band frequencies.  Just by these numbers, this means that standard 44.1k 16 bit has 65536/65  or about 1008 times more information than DSD.  No DSD or Sigma Delta system that I am aware of has more potential information per second in the audio band than Redbook CD.  Higher Resolution PCM systems do have easily calculable more information than Redbook and should be preferred even over Redbook CD, I think (though the complete argument for this--the encoding of frequencies believed too high to hear--is too long for this essay).

Does this matter?  Most of the frequencies in the Redbook vs DSD comparison are not beyond human hearing, and they determine the fine contour of waveforms, even if not hugely present.  Of course, the amount of information present matters!  I'm not saying it can be easily heard, but it is a form of dynamic distortion far larger than those is PCM, and DSD is supposed to be better, a successor to PCM.  So it should not have additional kinds of distortion, albeing this one a kind of "smoothing" distortion that is relatively pleasant…but is information losing.  When information is lost, the results are not good, even when you can't hear it all in one listening, more information makes successive listening session more interesting, and even the same listening session when the information loss itself has a predictable nature.

There are counterarguments.  (a) we are less sensitive to state limitation in the extreme highs, where it is particularly true (ironically maybe because of the "higher bandwidth") that DSD has the least state information.  (I don't buy this argument, I think clusters of high frequencies on a transient basis are found in many places even if they don't show up in averages.)  (b) Even within band, the ordering of the same count of bits matters, even at 1Fs.  (I can't see an easily defended argument for this.  1Fs is 44.1 kHz, more then twice the range of human hearing.  So modulations above 44.1kHz shouldn't be relevant, and that's all I would expect the ordering of bits to change.)

However, being somewhat unsure about (b), I came up with a factor of 16 to describe how much the ordering of bits might matter.  This was the minimum to satisfy the possibility I might hear the benefit of DVD-Audio recording over the sigma delta modulator in my Denon 5900, which is quite good.  So the factor of 16 has been quasi-empirically determined, and the actual adjustment factor may be higher (or nonexistent!).

So by this standard, using my 16x factor, the DSD information loss over Redbook drops to 1/64 instead of 1/1024.  I use this 16x factor below, but bear in mind the raw information loss numbers are far larger and may be more relevant.

Pure 1 bit 10x DSD as used in the new PS Audio gets to 1 / 6.4 times as much information as Redbook.  Quad DSD eels out 1 / 25.6.  But actually most Sigma Delta converters have far better information recovery than canonical DSD anyway, by virtue first of having more bits, then higher speeds also.  Still, however, none has more information than Redbook.  So for example the prehistoric sigma delta Burr Brown 1720's in my Denon 5900 are 3 bits run at 256Fs (quad dad rate, btw).  The 3 bits add 8x information.  This brings it to 1/2 times as much information as redbook, more than 3 times as much as the new PS Audio 10x DAC.  It's obvious that it's easier to get more information with bits than high rates of oversampling.  But strangely the audio world is moving in the opposite direction.

Dark Energy/Matter is Information

Thinking about information loss just led me to think that Dark Energy and Matter might well be Information.  It's something we know exists and is conserved under many situations, but it doesn't fit as a separate entity into the Standard Model.

I'm already known as being critical of official information theory (Shannon, Shannon/Hawkins) as it is applied to audio.

Home Sweet Home

Back home.  My own system is oh so special in so many ways.

1) Whole house coverage.  The combination of omni super tweeters (which contribute magic you don't directly hear so much…but take it away and the magic disappears), dipolar electrostats, and powerful stereo subs means that sound penetrates everywhere in the house.  Thankfully the bedrooms can be mostly cut off with the new soundproof doors and wall.  But open them up, and the party goes on everywhere.  The kitchen is a great place to listen to the living room stereo.

Is this important?  Audio purists say no, you want to hear only the speakers in the sweet spot, and nothing but the speakers.

But nearly all of my listening is "non-serious", the music is background to other activities, or I am not sitting in the sweet spot.

2) Whole living room coverage.  On return from vacation, I first sat in the couch.  The sound was surprisingly good, in fact--possibly more positive feeling bass than the sometimes anemic sweet spot bass.  Way off axis, but there was still an image…with all parts playing.  For enjoying music--it was surprisingly close to the sweet spot…and without the need for perfect centering as in the sweet spot.

3) Multilayered depth, and especially at the sweet spot.  I've readjusted sweet spot chair in both axes a bit, a couple inches farther back, and the centering is now right on.

Frequency balance, especially the highs, is superlative, Class A.

Bass deep and incredible, but still a bit lumpy.  Class A-.

Imaging wide and multilayered.  Class A.

Grade A-+ (just a tad short of Grade A).

That's listening to the DVD-Audio of Santana Supernatural, which I've been spinning since arriving in San Antonio in the wee hours of Saturday morning.  Stereo track of course, which is 96kHz 24 bit, played through Denon 5900 (a top of the line product once, with separate power for the Burr Brown 1720 powered outputs) into a Lavry AD10, then on to digital preamp, crossover, and equalizers, expressed back into analog through Burr Brown 1704 powered Onkyo RDV-1 for the Acoustat powering Aragon 8008 BB.

It occurred to me that I'm not getting the full potential information because of the lossy sigma delta conversion in the Burr Brown 1720 DACs.  Estimating this to be a 4 bit sigma delta converter operating at 256fs, we have this much information at fs:

256 * 16 = 4k

A lot more than DSD's 64 (!) but still not good.

Whereas 16 bit PCM gives us:

65536

So, for awhile I connected to the PCM output of the denon, which gives me 48kHz 16 bit apparently because of DVD-Audio operation without the manufacturer setting the hires digital output allowed flag.  But I didn't figure that out until a few hours of listening to this 16 bit quality.

I didn't like it.  Yes, in some ways, I could hear superior inner definition.  I heard a great deal more harshness too.  But big stuff, like the deepest bass, is merely sliced off.  In a strange way, you get more micro detail without the macro detail that makes it meaningful.

This suggests to me that there are issues with my way of calculating information.  DSD might actually have more than 64 units of information at Fs.  Of course this is certainly true if DSD has higher than Fs/2 bandwidth, which it does.  To me, it's not clear how to adjust the formula.  But I'd say we have one datapoint here:

DSDei is around 16 * 64

Because the between the translated sigma delta, at 4k previously calculated information, seems better overall than pure pcm at 64k.  Of course the underlying information stream is far richer too.  But if it were really choked off at 4k units of information vs the 64k of 16 bit PCM, that shouldn't matter.

I may be able to preserve the information by making a master link recording of the analog output of the Onkyo RDV-1 which uses a full 24 bit ladder DAC.  I'd use the Lavry AD-10 for digital conversion, feeding the AES/EBU inputs of the Masterlink.  Then I could edit that into a DVD-Video disk with unprotected digital output at 96kHz.  That does require the more expensive version of Diskwelder Bronze 1000m.  Then I could play through existing system w/o loss from sigma delta converters, whatever it actually is, via the digital outputs of the Denon 5900, or through a future SPDIF connection from kitchen.

DSD loses information, but what is lost? [extended June 14]

It's easy to see that sigma delta systems and/or DSD lose information.  Consider "canonical DSD" as a purely 1-bit system (which is not actually how the encoders and decoders work, but still describes the datastream well).

At Fs, the standard sampling rate frequency (44.1kHz I believe, or perhaps it's 48kHz), a 16 bit system has 65536 "states."  A 1 bit system operating at 64Fs has 2 states per bit times 64 or 128 states--thus it has 65536 / 128 or 1/512 as many possible states.  Now that is huge information loss!  (Quad DSD has 1/128 as many states as 16 bit digital.  The new PS Audio DAC has 10x the DSD rate or 1/51 as many states as 16 bit digital.)

But what information is lost?  DSD with noise shifting has standard specifications superior to 16 bit digital in almost every way.  It has higher frequency response, lower midband noise, etc.  So how can information be lost?  And given this huge information loss, how come so few audiophiles notice it and so many audiophiles strongly believe, nevertheless, that DSD is a superior system to 16 bit PCM--and even high resolution PCM (which has far more states than 16 bit digital)?  Surely DSD is not a "lossy compression" system like MP3, which has issues which are far clearer on a technical or listening basis.  Strangely, DSD is a "lossy expansion" system which uses more bits to encode less information about amplitude, and it's very hard to see what is actually being lost.

The reason the limitations of DSD systems go unnoticed is that human hearing and most technical measurements don't actually deal with small changes in amplitude that do not cause detectable differences in continuous waveforms.  At best, humans can only reliably hear differences in overall amplitude down to 0.1dB in the midband, and they are far less sensitive to differences in overall amplitude very high frequencies close to the bandwidth limit of digital systems.

The 128 states that canonical DSD has at Fs represent a dynamic range of about 44dB.  16 bit digital systems have the same dynamic range across the audible spectrum--98dB.

Clearly what is lost with sigma delta systems is dynamic range at the higher frequencies down to about the middle of the frequency spectrum.  This is not easy to hear, but many things audiophiles obsess about are not actually that easy to hear either.  In a complex recording, high frequency dynamic range is what makes it easier to separate different sounds.

In a photograph, the smallest details represent something called "resolution."  That is analogous to what is lost with sigma delta systems, which should also be called resolution.

June 14 further thoughts:

One of the problems with observing this difference in information is that it may not be audible over one listening.  There is only so much information a human listener gathers in each listening.  Subsequent listenings may gather a slightly disjoint set of information.  Possibly never is the sum of all information completed, except for standard recordings.

But clearly the larger the initial amount of information, the more likely variance between the information gathered in the first listening and each subsequent one.  This difference makes a recording sound "real" as opposed to "canned."  A canned sound may be fine the first time, but then it gets boring, precisely because there is no more information to be gathered, it was all apparent the first time.

So we definitely want a recording to have as much information as possible, particularly in audible ranges, and extending to lesser degrees beyond.

By stepping back from the information available even with far earlier PCM systems, DSD deprives us of information, as of course to lesser degrees generally all sigma delta devices (I' do calculations in a later essay).

The superiority of ladder DAC's

Here's another essay on the superiority of ladder DAC's.

At the 2014 Newport T.H.E. Show, two exhibits had ladder DAC: MSB and Audio Note.  They both seemed to have superior resolution to other systems, except for 15 IPS tape used for the MSB Extreme system.  (Other tape systems shown were not as good as the UHA--by far.)

Curiously MSB used cheap speakers, nevertheless achieved Class B performance.  Audio Note was Class C, likely because of high distortion SET amplification and NOS, it sounded a bit harsh.  (When I previously heard Audio Note at the 2009 T.H.E Show in Las Vegas, I put it in Class F--very harsh sounding.  Ironically, that was the top end Audio Note system of the time, whereas the 2014 T.H.E. show had a mid level Audio Note system--which I thought sounded better.)  Also, I believe that No-Oversamping-Or-Filtering is a bad approach which leads to harshness.

Newport Beach T.H.E. Show Ratings

[within classes, ordered by preference, Class A is the best available period]

Class A

MBL Extreme system, 4 MBL amps, 6 MBL subwoofers, MBL Preamp, UHA tape deck
(Mind blowing.  I listened to this system for a total of 6 hours during two evenings without fatigue. They had evening demonstrations after 8pm on Friday and Saturday.  I got the sweet spot on Friday evening and was in heaven.  I moved around in the back on Saturday and full stereo wasn't as good as my own system off axis, but that was mostly because of all the people in front taller than me.  Transparency, clarity, dynamics, power, freedom from noise and distortion, this system has all I look for.)

MBL Extreme

U.H.A tape deck and MBL electronics

4 MBL monoblock amplifiers

One of several room tuning devices (against wall)

[At 2009 CES show, I heard two Class A systems, the Force dipole line source speakers from Perfect 8 with Bridge amplifiers, in the same price range as MBL Extremes, and a demonstration of actual "safety" master tapes played by the Hollywood recording engineer who made them--he refused to identify loudspeakers.  None of the 2009 Las Vegas T.H.E. show exhibits were Class A, except for my last brief encounter with the late James Bongiorno.]

[I rate my living room system as Class A- on good days, Class B on lousy days, depending on music, media, and minor setup details like chair position.  I combine line source electrostatic full range electrostats with ribbon omnidirectional super tweeters and massive subs--that's not all that different in concept from speakers like The Force.  I continue to believe that for the very best sound, you have to break away from the box speakers--though box speakers can be quite good.  I need more work on room and speaker integration---but what I've already done with time delay correction and minor eq is not too bad.]

Class B+

Yg Speakers, Kronos Turntable
(totl Kronos may be best turntable I've ever heard.  Both quiet and dynamic.  Brubeck played with jaws dropping and total silence from listeners.)

Class B

German Physiks speakers

Exceedingly transparent, great bass, good sound off axis

Usher Speakers, Usher Subs, Pass Labs X and XA Amps
(excellent but lacking ultimate deep bass)

Usher speakers and subs, Pass X and XA amps

Von Schweikert VR100 XS  (lacking only ultimate deep bass, and often played too loud)

Wilson Sasha, Audio Research Electronics, guided by famous recording engineer who always set levels perfectly, playback used Amarra but set levels via Audio Research preamp)

Walker Proscenium Turntable, Pass Labs 300 Xs Amps
(Totally quiet, non-resonant, and perfect decay of notes, but seemingly lacking leading transient dynamics.  Makes me think that other belt drive tables, like Linn Sondek, use resonance to add pseudo dynamics, and this is why Linn has only slowly adopted anti-resonance features which many people, including me, thought they should have had in the beginning.  Unfortunately with total resonance control like Walker Proscenium, belt drive can lack dynamic sound.  One anomaly in this hypothesis is how the Walker presented the decay of sounds perfectly.  One would think that if heavy platter belt drives had a problem with dynamics it would show up mostly in the decay of sounds, not in the leading transients.  Perhaps the Walker is the one that actually reads records correctly, and all other turntables with more assertive dynamics editorialize.  Also the speakers in the Walker demo did not look impressive and I only heard two scratchy classical chamber music album sides, perhaps not good enough for fair assessment.  And the only turntable I clearly liked better is the Kronos.  A friend argues that the Kronos is wrong and the Walker is right.  So I've moved this up to Class B.)

Class C+ or better (room issues prevented higher rating)

Magico Speakers (the big ones), VAC electronics, Tape
(room had echoes and weird imaging, phasey sound.  Can't fully judge speakers therefore.  Room had buzz from AC--needed to remove heat from the massive VAC amps.   But Kraftwork tapes had massive and effortless slam, best slam I've heard outside the MBL Extremes.  You might not expect massive slam from tube amps, but these looked as big as the MBL mono blocks--picture from back of room doesn't do them justice.)

Magico speakers, VAC amps, Tape

Big Mac Amps

(Massive sound, but somewhat lacking HF detail compared with D'Agostino amps)

Class C

(most other systems I heard)

Class C-

Audio Note System

E.A.R System

(both E.A.R. and Audio Note systems sounded harsh, though at least Audio Note had high resolution from ladder dac.  I've never heard good sounding SET's, they have always sound harsh to me.  Push pull tube amplifiers always sound fine to me, but not necessarily better than transistor amps.)

Class D

MBL surround system (and for that matter, ALL surround systems I've heard)
   no real imaging...all I heard was nearest speakers

Class F

Sound Reinforcement at T.H.E. live concert


*************************** End of Ratings

Special Mention

Believed to be Class A:  MSB DAC's....possibly best sounding DACs,  better resolution that sigma delta DACs.  The sound was highly resolved, but speakers+amplification+room were only Class C+, so hard to judge.  I have noticed this pattern before, people who make some super expensive component often pair it with cheap stuff in demos.

Disagreed with

Michael Fremer...who said that Quad DSD is identical to tape (nb, I haven't heard quad dsd), that DSD is better than PCM, and that DSD files are superior to SACD, all wrong IMO.  DSD at all speeds is inferior to R2R decoded Redbook CD on principles, and I have never heard either SACD or DSD to sound better than PCM, or DSD files to sound better than SACD discs.  Furthermore, the DSD bandwagon has destroyed the market for real PCM dacs since cannot economically keep up with inferior sigma delta DACS at increasingly higher speeds.  However MSB does offer 2x DSD with their ladder dacs, a great technical achievement.  DSD is a sorry legacy of Sony's "leadership" in digital, which took a wrong turn with sigma delta converters, leading to DSD

[Updated last on June 19, mainly adding pictures.]