Atomic clocks

September 30, 2016
 by Paul McGowan

We all understand that in digital audio, the better the clock the lower the jitter, the better the sound. We’ve seen it in DirectStream: both the DAC and the new Memory Player.

So, if what we’ve built into our products is low jitter, what about adding something even better? Like an expensive external clock? Like an atomic clock? Wow, that would be the be-all-to-end-all clock. Right? Nothing’s more accurate than an atomic clock and we see them available for more money than the DAC itself. We’ve even read how much better a particular DAC sounds when added.

Remember in yesterday’s post I gave some examples of how we think one way, but ignore something else and wind up with the wrong answer?

Atomic clocks are a perfect example of being wrong.

Our digital guru, Ted Smith, is here to set us straight. This is lifted from our forums in answer to a customer’s question.

Atomic clocks are addressing a problem that’s irrelevant to audio: Long term clock accuracy.  It doesn’t really matter for music listening if the clock is accurate for years.  What really matters is how much the clock jumps around during a second or so.  It’s that jitter in time that frequency modulates the audio.

Atomic clocks actually aren’t designed for low jitter  (at least that’s not their primary design.)  In fact they don’t use the atomic reference at all in the short term.  They have a free running clock and they push it around based on periodic reads of the atomic reference.  It’s the quality of that free running clock that matters for audio and whether varying its rate adds phase noise that will affect the audio…  If they sound better at all in a system it’s just because they are better built overall than another clock, not because they are better for audio.

The ability to change the frequency of a clock to match an external source is exactly at odds with a low phase noise clock.  That’s the primary reason that PLL’s have a bad reputation in audio.  The act of trying to control the frequency of a clock is adding jitter to that clock.

Conversely running a clock for any distance, going thru various impedance discontinuities (e.g. cables and their connectors), being subject to ground loops and other interference, going thru conversions to optical and back, etc. all add jitter.  There’s no method of distributing a clock that doesn’t add phase noise in the frequencies that matter to audio.

Then there’s the issue of having multiple clocks in a system.  If a new clock is added to a DAC what’s the DAC supposed to do when that new clock runs at a slightly different rate than the incoming data?  Asynchronous sample rate conversion is the standard answer, but what really does is encode the clock rate differences into the output audio, making it impossible to separate that jitter downstream…  Not a good design for audio at all.

So, what sounds like a good idea, an external clock of the highest accuracy should be better, turns out to be worse. And, when it is better, that only means the internal one it replaced wasn’t very good to start with. So, adding the atomic clock is better – but only better than what was not good enough in the first place.

Myths we cherish are often broken by science.

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47 comments on “Atomic clocks”

  1. Myths are created for those who lack deep insight and knowledge, Paul. But who are the guys that create these myths? Look at the myths about the power cords improving sound due to better shielding (antenna myth?) or due to better handling of internal wave reflections or due to marginally improve the speed of the cloud of free electrons? All these myths seem to detract from the major problem that most power supplies pollute the system via the power bar with RF created by the rectifier. But again my question: if your findings concerning the improvement of digital audio are that crucial shouldn’t these improvements be introduced urgently first of all in the recording and mixing gear. Otherwise your products will even produce a sound quality that reveals the improper recording and mixing?

    1. Indeed they are. The A/D conversion step in the studio is crucial to the sound. Recording and mastering folks banter about Myteks, Burls and Sonomas in a similar fashion to the way we discuss our D/A gear. Well, maybe a little more rational… 😀 but not much.

      1. Indeed? You are only kidding, don’t you? What about power cords in the studios? Or do they produce their own current based on batteries delivering DC? 🙂

        1. Powercords, not so much. 🙂 Clocks and A/D conversion more so. I looked at your reply a second time and realized that I was only speaking to part of a broader subject that you were addressing. Just an observation after seeing articles and comments by pros. Perhaps some of them who hang out here could clarify but there seems to be agreement that the quality of the converter makes a difference. Clearly in a complex studio environment a master clock of high quality makes a difference (beyond just having everything not hiccup) but the internal clocking of A/D converters comes up in discussion of hardware preferences.

          1. Thanks! The MK2 version of TacT Audio’s digital amp offered a master clock output for the CD transport being connected. However the MK3 version skipped this master clock output as an outdated technology. That was some 12 years ago. Thus I wonder which studios are using cutting edge technology and which relying on proven concepts.

            1. In an environment with multiple digital inputs and processors a master clock is necessary to keep everyone in line. It is said by some that the quality of this clock can have an influence on the sound. Single A/D units do not need external clocking and some say it can actually degrade the recording. With my tiny studio and prosumer equipment, I have no opinion on this. Most of the units that I have seen being discussed in this detail are way out of my budget.

    2. Myths are what we all buy into, you and me included, Paul. We may not realize it because our myths resonate with us and we believe them to be true. For example, one of your personal myths seems to revolve around the idea that everything’s measurable – don’t get too literal on me – I am not trying to criticize nor argue whether you’re right or wrong or even if that’s accurate. I just want to point out we all have belief systems. We all believe our belief system is, of course, the correct one.

      This observation of personal bias—call it worldview—is not spark more controversy, just to point out we all have our biases.

      1. “True” or “false” are precisely defined for mathematical logic. Right or wrong have a precise definition too. In Common language or communication these terms are most fuzzy or ambiguous and I try to avoid them. Better: appropriate or inappropriate. Constructive or destructive. I also would discriminate between myths, beliefs, assumptions and speculations. I rather would prefer to trust somebody than to believe in things that never can’t be proven or falsified! In the end everybody creates his own truth and is right within the limits of his information base!

        1. @paulsuirrel

          You’re right when to speak about “true” and “false” in the area of maths. Within the physics most do not speak of “true” but of “bewahrheitet” – excuse me for the German term. I think in English it is best translated to well-founded proved. This does mean no other than “we think it is true until there is a better proof”. That has nothing to do with “believe” because we recognize that it can not be equated with “true” and “false” as taken from the mathematical models.

          To return to the subject of this post – precision clocking has also to do with the magnitude. We know that a certain manufacturer of DACs uses a “Femto-Clock”. I wonder why? Within a femtosecond (10^-15s) the light travels just a halve wavelenght of red light which is about 0.3 μm. So what the heck?


          1. I agree, Bernd, and I am most sceptical concerning marketing claims. Why should a manufacturer disclose his relevant findings? Better to repeat some established myths or pretentions misleading the competition! Concerning the problem of perception and ‘validation’ it would be a big progress for the culture of the discussion if everybody could agree that our ears as our eyes are part of a most complex pattern recognition system that is characterised by lifetime learning. Everybody is familiar with optical illusions. Watching changing structures of clouds we sometimes ‘detect’ (recognize) faces or animals. You can bet that children will recognize different things compare to adults due to their limited database. Stereo now is based on aural illusions and on a similar learning based pattern recognition process. Thus true or false are inappropriate terms here concerning the most subjective perception. I recently could compare two big speakers systems in a dealers show room. The first system was designed by a young guy just having made his degree and profiting from the latest textbook knowledge and simulation technologies. The other system was designed by a guy building speakers for some 55 years now, a guy who never had calculated a crossover. We listened to a concert and the track started with big Chinese gongs standing back on stage. The stage depth was jaw dropping for both systems. But listening to the old man’s speakers the initial percussion sounds were clearly kettledrums! I addressed the artist and he confirmed that this track started with kettledrums! Thus the latter speakers allowed to detect the correct patterns learned – despite the confusion caused by a stereo system due to the crosstalk phenomenons. I bet the experienced designer never would disclose his know-how and voicing strategy! 🙂

      1. In my experience power cords make a difference. But every designer of an amp I had the chance to ask about power cords negated any positive effect on “his baby”. And there are many power cord designers that turn their assumptions, theories or speculations into myths! 🙂

  2. I brought up the topic of cesium clocks being used by the National Bureau of Standards and by an international standards organization some posts back. These clocks are used as a reference for many engineering and scientific applications. Ultimately whether you have a built in clock for an electronic circuit or an external clock it is going to be free running depending on some physical phenomenon whether it’s the natural oscillating frequency of a quartz oscillator in your TV set, radio, or cesium atoms kept at controlled temperatures. These ultimate stable time bases are used for example to keep the telecommunications network including all of the data transmission in synch. They are used in the GPS system. Do you have to build your own atomic clock? No. You can use the National Bureau of Standards clock signal by radio or over the internet. Of course on the internet you are subject to the jitter that system introduces. But radio transmission does not.

    A PLL is a phase locked loop. It is a very clever circuit that locks on to an external reference through a feedback loop that detects the difference between the phase of an incoming oscillator signal and a local variable frequency oscillator and locks them together. A narrow band tracking filter at the input of the external source is usually added. It limits noise so the local oscillator doesn’t get side tracked by noise and lose lock on the desired signal. The output can be whatever you want, a square wave, triangle wave, sine wave, pulse output.

    If the cesium clock had much jitter it would limit the speed of packet switching since the timing of packets being reassembled is critical to getting the sequence right. Here are some links to cesium clocks and PLLs.

    PLLs have been around for a very long time. The first one I saw was hand built for a scientific measuring instrument that cost many tens of thousands of dollars and a lot of skill to design and build. That was around 1970. It wasn’t long afterwards that you could buy one on an integrated circuit chip for a few dollars.

    Okay, enough chatter. I challenge Ted to produce actual performance specifications for Jitter comparing his oscillator and that of the National Bureau of Standards cesium clock. I also challenge him to specify the threshold of audibility where the effects of jitter becomes inaudible. Don’t snow me with nonsense that the decrease in jitter that can be detected in the end result by ear is infinite. It isn’t winter yet and I don’t have my boots on.

    1. I have some personal experience and expert friends and colleagues on both sides of this equation. I worked with Dr. Albert Benjaminson, the HP clock guru, on a differential quartz clock with a baseline stability of E-13. It was extremely low power (a few nanoWatts) to keep the temperature precisely at the “turning point” inside a double oven that was stable to .01 degree.

      This does, in fact, increase the phase noise as Smith details. The low power made the circuit sensitive to noise despite minimized conductor length, extensive shielding and grounding. I was working on the differentiator circuit and made several improvements in the hardware and software to compensate for the phase noise.

      My former boss Rob Billinger builds the atomic clocks at NIST Boulder, which are the leading edge of long term accuracy. They have essentially the same problem – any perturbation of the system changes the frequency and temperature is the enemy. They keep a single Rubidium atom in a laser cage with laser cooling. I never asked him about the phase noise, but the same principle applies – a trade-off between short term and long term precision.

      OTOH, it has been proven that human perception beats the tradeoff between time and frequency, with well trained individuals able to hear ten times better than is “mathematically possible” according to the Fourier Uncertainty Principle, a well established theorem of information theory. This was proven by Physicists because Audiologists use the rules of Physics too literally in modeling hearing!

      If you read blogs by the best ears in the recording biz or follow them on facebook, they all report picoseconds of jitter are audible. This includes Tim de Pavaricini, Barry Diamant, Allen Farmelo, Morton Lindberg, Andrew Lipinsky, the Cheskys and their current and former engineers, etc.

      I live at the intersection of music and digital technology, keeping my ears trained with daily doses of acoustic music, never listening to digitally compressed files and limiting my exposure to digitally processed files (mixed and mastered) to an hour or two a week. This is critical because every knob in a recording studio adds phase noise and distortion, and distortion compounds geometrically.

      My solution to clocking is DSD. At 2.822MHz, the phase noise averages better. It is further impossible to process a DSD file, it is exactly what the microphones heard. This is why the recording biz abandoned SACD’s – you can’t mix, balance, splice, overdub, EQ, compress, auto-tune or add reverb. I see that as a FEATURE, not a bug.

    1. If all folks had an education in science or engineering they might know the right questions to ask and wouldn’t be so gullible as to take all claims at face value. They might also be skeptical to ask for anyone making claims to offer credible evidence that what they say is both true and matters. But that requires a lot of work acquiring that knowledge. It’s a lot easier to just accept whatever people tell you. How do you think the world has gotten to the sorry state it’s in?

      1. Yes….if only the world were all engineers and scientists. What a wonderful world that would be.

        What I often talke issue with, in regard to your view, Mark, is that you seem to assume everyone here, and indeed, everyone but those with a proper scientific education (yourself included, natch) are ALL, “so gullible as to take all claims at face value” and “just accept whatever people tell you”.

        I challenge you to put 100 scientists into a room and see if they all agree on a given aspect of the science and art of audio.

        I would also tend to disagree about the state of the world, but that’s for a different sort of blog.

  3. This is claimed to be the most stable clock in the world.

    It is 40 times as stable as NIST’s clock

    The world’s most stable optical atomic clock resides in the Ye lab in the basement of JILA’s S-Wing. The strontium-(Sr-)lattice clock is so stable that its frequency measurements don’t vary by more than 1 part in 100 quadrillion (1 x 10-17) over a time period of 1000 seconds, or 17 minutes.

    Both this clock and NIST’s clock are located in Colorado.

    Anybody got the correct time?

  4. Let me try to bring some clarity to this discussion. Before I start on what role an atomic clock can play let me first be sure everyone here understands the difference between accuracy and precision. In everyday speech we often use these terms interchangeably, but in the scientific and engineering world they have very different definitions. “Accuracy” is the ability to measure something and get a result that is very close to the accepted value. “Precision” is the ability to measure something and repeatedly get almost the same value over and over again. Thus, a precise measurement that has very little scatter in repeated measurements may be inaccurate because the average of those measurements is noticeably off from the accepted value (the standard). And an accurate measurement may have a large amount of scatter in repeated measurements and thus is not very precise.

    Now atomic clocks achieve great accuracy because they are so very precise. Let me explain exactly what that means. The clocks that the standard bureaus use are based on the element Cesium. They measure the frequency (cycles per second which is a Hertz (Hz)) of an atomic transition (an oscillation) that takes place in the Cesium atom. The precision of that frequency is 2 to 3 parts in 10 to the 14th power. The inverse of that frequency (1/Hz) is the period of the transition (or oscillation) and has the units of time. That time interval has the same precision as the frequency. Thus by counting those very precise time intervals you get a very accurate answer to how much time has elapsed since a given starting time. It is, however, the very precise nature of the frequency of the atomic clock transition (oscillation) that in principle makes it the ultimate internal clock in any piece of gear that requires precise timing.

    So why isn’t it a good idea for everyone to go out and spend $15K – $20K for an atomic clock for you digital devices (it would be a Rubidium clock not a Cesium clock, but Rubidium is almost as precise as Cesium and Cesium would cost $50K or more). It isn’t a good idea for two reasons. The first is all of the reasons that Ted Smith gave in Paul’s post above. The second is that the best man made clocks (based on temperature controlled crystal oscillators) have a precision of a few femtoseconds. This is 2 or 3 parts in 10 to the 12th power. Now if you do not understand how exponents work, please trust me when I tell you that an atomic clock is 100 time more precise than the best man made crystal oscillator clocks. Now, all of those things that Ted talked about in Paul’s post also have imprecisions of at least a few femtoseconds if not larger depending on the design and build of the piece of gear.

    The ultimate precision (or jitter) of the gear is the combination of all the various imprecisions in the gear. There a two ways to add up those imprecisions. If it can be shown that the various imprecisions are correlated (one depends on the other) then you add them up arithmetically (meaning the same as you would add up 1,2,3, and 4 to get 10) including the precision of the internal clock which if it is an atomic clock is 1/100 the size of all the other imprecisions. If it can be shown that the imprecisions are not correlated then you square each of them, add up the squares and take the square root to the sum. And if some of the imprecisions a correlated and others are not you have to use a combination of the two methods.

    The bottom line on all of this is the atomic clock is overkill. Money that would be spent on an atomic clock is better spent figuring out what is the largest imprecision in the list that Ted gave and work on reducing it and then work on the second largest and so on. I hope this helps all of you understand why we do not need an atomic clock in digital gear.

    1. I just realized a made a huge name mistake. I said that a clock that is good is a few parts in 10 to the 12th power is good to a few femtoseconds. The correct name is good to a few picoseseconds. A femtosecond would be a few parts in 10 to the 15th power. My bad!

  5. Your statement that atomic clocks have nothing to do with the quality of audio is correct, of course. I ran into the problem of jitter in communications in the early 70s when updating the computer network that controlled the power distribution network of Belgium. It took less than an hour of engineering to solve with a 1 bit deep memory buffer added to the software at the interrupt level with a fixed instruction path (no conditionals) and a low jitter high accuracy clock circcuit of programmable frequency. It always amazes me how the audio industry makes a well known issue documented in a combination of communication and digital circuit textbooks hard by hacking at it. Just make sure your digital circuit has low capacitance and high impedance to ground and is driven hard so that the transitions are very determinate in time. In the 70s that meant not much more than using well engineered CMOS electronics in a single layer board. Today you have to work hard to get it wrong. sheesh.

  6. dCS sells a very expensive outboard master clock. Reviewers certainly hear a difference in SQ but I find reviewers to be a bit partial to the industry. But, I’m guessing that customers can hear an improvement in SQ before they reach for the black card.

    How would you explain this?

    1. I tried to in the post. Let me try here in the comments section. As Ted mentioned, if you add an expensive outboard master clock that improves performance, the one thing we can quickly ascertain is that the original it replaced wasn’t anywhere near as good – and we know that because adding external clocks has problem because they are external – so the new one has to be a LOT better than the internal one.

      The best place to make a clock work properly is inside the DAC.

      The fact that an external one works better than an internal one only demonstrates that the internal one wasn’t up to par and I don’t say this to be critical. But, the fact remains, connecting an external clock to an internal DAC is fraught with problems.

      1. First you say in your posting that atomic clocks are not designed for low jitter. Now you say the fact remains, connecting an external clock to an internal DAC is fraught with problems. Which is it, one, the other, or both?

        One of the articles I referenced said there are two criteria for clocks, accuracy and stability. Stability has to do with the degree of deviation of the clock’s frequency from its nominal value. NIST’s Cesium clock beat’s Teds by a factor of almost ten million that’s 10 E6. (2* 10E-10 to 10 E -17) The Strontium clock is at least 40 times better. Also, it is so accurate that its estimated long term error is one second in 15 billion years, longer than the universe is believed to exist. How could it achieve that degree of accuracy if it had any instability?

        It takes a different specialized set of skills to design receivers that lock on to a clock rf signal and generate a clean local signal synchronized to it. But it is done all of the time in high technology. What kinds of systems rely on such accuracy and stability? Think of the problem of aiming the Hubble space telescope at a galaxy 10 billion light years away knowing where it will be at precisely the right time and keeping it on target to get a sufficiently exposed sharp clear image of it. If the clock that keeps the telescope on target wavers in frequency even minutely the image would be blurred. The entire object is only a tiny fraction of one second of one degree angle of arc and is so faint it can’t be seen with even the sharpest eyes in a living creature.

        1. Why do you continue to bring up these outrageous atomic clocks. Do you have any idea what a Strontium atomic clock would cost? Esoteric make a G-01 master clock which uses a Rubidium atomic clock. Its frequency precision is +/-0.05 ppb (this means the period is good to about 50 picoseconds, 50 parts in 10 to the 12th power). It cost $22K. This is as good an external masterclock as there is in audio.

          1. First of all it was Ted Smith who brought it up months ago when the new DAC first appeared on the market. He said at the time that a Rubidium clock was not good enough. He said that clocks with jitter of two parts in ten billion weren’t good enough. He said the people who manufactured the chip told him they thought he was bonkers.

            Look at the title of this blog entry. Do you think I wrote it? Nope, wasn’t me. Guess who? It was the who. Why do I bring up these “outrageous” atomic clocks? Because they are not only far more accurate but have far less jitter than the clock chips you can buy and all you need is a receiver with the right circuit to lock on to them. In fact they are also available on the internet and for many downloads on the internet are their ultimate source material.

            I really don’t understand your problem. If you don’t like my postings, I suggest you don’t read them.

    2. You might find this interesting. Here is a link to the Stereophile review of the dCS Vivaldi stack by John Atkinson. As you probably know John holds a degree in engineering and is a very respected audiophile. The link is to the measurements page and please read the third to last paragraph. The external clock had no impact on the jitter measurements, but JA thought the system sounded a little better with it. And, the Vivaldi master clock is not the big of a deal, it is a dual crystal oscillator that they claim when stabilized is good to 0.1 ppm. That is 100 nanoseconds.

      Here is a link to an interesting comparison of master clocks. This article says that my estimates of how good the various clocks are in my post above may have been too optimistic, but the idea of waht I posted stil is good.

        1. Well that is true but I have even stronger opinions about his inabilities. I don’t ever recall him claiming he had a degree in engineering or was an engineering student. I do recall him saying he had a background in physics and chemistry. If he is a degreed engineer, I’d be happy to write a letter to the Chancellor of his University claiming a full refund of his tuition. John Curl who used to never respond to anyone who was not an electrical engineer was not an engineer himself. Although he had taken some engineering courses, his degree was in physics. This is why all he talked about when it came to cables was the Fermi Velocity of electrons. When you’re a hammer, every problem is a nail. When you’re a physicist, every problem is too small to see or if large too far away to see. That’s why they can get away with their preposterous theories and when one doesn’t work out they just invent another. Nobody ever knows if they got the right answer. The only ones who understand them and what they say are other physicists. From everyone I’ve ever met and I roomed with one in college for two years, they’re all bonkers. Atkinson believes in demagnetizing phonograph records. I’m sure he’ll have some preposterous theory like iron atoms in the black dye.

      1. re the specifications of the vivaldi equipment which Atkinson was unable to verify

        “dCS Vivaldi Master Clock: Class 1, temperature-compensated master clock with dual VCXO. Clock frequencies: 44.1, 48, 88.2, 96, 176.4, 192kHz. Clock accuracy: better than ±1ppm when shipped (guaranteed for 12 months from shipping date), typically ±0.1ppm when shipped and stabilized.

        Well that’s not even remotely in the same league as Ted’s whose clock is as good or better than 2 parts in ten billion +/- (.0000000001) or in other terms +/-.0001 PPM. So what do you have to say Vivaldi dCS? What do you expect for just $108,000? More proof brains beats money.

  7. Very interesting topic. Everything has a perfectly logical explanation it’s just that we do not know it always and thus myths are born. This problem is perpetuated further when we are so in love with the myths that we keep trying to prove them to be right and refuse to face the facts which point to the contrary. That is described as going round and round in a circle. How colourless life would be if there were no myths. Enjoy the myths. Regards.

  8. So I have been wanting to ask this question of the esteemed commentators of this blog for some time, but have not been sure where to ask it. Maybe it is a clock and jitter question, so here goes:

    I have all my files on a NAS in my home, and have the NAS set up to be able to stream to my iPhone via JRemote, from anywhere on the web via the dyndns service. The files are converted and sent as constant bitrate 320kb mp3 files by JRiver and/or are stored that way on the NAS so no conversion is needed. These are primarily CD rips I have done myself.

    I also listen to Spotify on the phone and stream songs the same way. I have a premium account so am supposed to be receiving the Spotify files at 320 mp3 as well.

    However, when I do a comparison of the same song via the JRemote stream of my personal file, with the same song from Spotify, the difference in clarity, dynamics, etc. is noticeably superior from my file than Spotify. This is repeatable time after time with any song. Can anyone explain why this might be so? Does Spotify use some kind of additional compression over and above the mp3 format (perhaps to keep bandwidth down) that my streamed file does not? I have wanted to get to the bottom of this as I am quite curious about it. If anyone could shed light on this. Thanks. I suppose maybe it is not jitter or clock but who knows. Thanks in advance.


    1. I don’t have a knowledgeable answer to offer you but I can suggest the following. MP3 compression is rather variable – variable depending on user settings – and the type of compression scheme used.

      Spotify relies on the Ogg Vorbis compression algorithms that may well be different than what you used.

      Bottom line, all compression schemes are not the same and you can certainly hear the differences.

      1. Thanks Paul. I have tried Googling this query ad nausea and found no discussion of it at all. I rip all my stuff using LAME in JRiver but I honestly have no idea what algorithms are used by any of the ripping programs and I am also sure I am not technical enough to understand them anyway! However, I would imagine from the home server there is no additional compression and decompression to send the file whereas Spotify may be doing so to keep file sizes down for streaming.

    2. My best guess is this is a timing issue. Internet transmission is subject to burst errors and delays. The information is sent in packets, and they can even arrive out of order. The Spotify app that plays their files is not optimized for jitter, but for gapless playback when the transmission has gaps and reducing CPU loading.

      JRiver probably paid more attention to playback timing because they are selling sound quality, not quantity. Further, the transmission over your relatively low traffic household network is closer to real time than any WAN feed.

      1. Thank you for the input, it is always great to get new perspective on how these apps and programs function. I was driving a lot yesterday and listening to the new John Prine album, first via Amazon Music which I know was only 256 KB and then through the JRiver app. Even over Verizon’s data network and then Bluetooth to my car stereo the sound quality differences were striking.

        Everyone have a great day and happy listening.

  9. It would truly be sad if scientists and engineers who have by comparison limitless resources and who are focused on only one thing, building the best clock they could, couldn’t build one that far outperforms one in a $6000 DAC where only one of the elements is a clock. Why would such an extraordinary clock be needed? Because there are far more complex and important systems than home audio systems that use that clock signal as a reference by tying into it and locking on to it.

    1. The question here is not million dollar clocks, it is “Atomic Clock” products that have audio relevant frequency outputs. You can beat tradeoffs by throwing money and time at them, but making a timing box that improves sound is a very limited market. The laws of physics say there is a trade between short term and long term accuracy, and that timing accuracy degrades over distance. The laws of economics say you get what you pay for, sometimes, but you never get more.

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