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    The Computer Audiophile

    The Denafrips Design Philosophy Part 1

     


    Editor's Note: This series came about after I approached Denafrips distributor Alvin Chee about obtaining information detailing how Denafrips products work, how the digital processing is designed, and more about the company's thought process behind its highly regarded products.  What follows is part 1 of 4, in a series of essays written by Zhao, the Chief Engineer at Denafrips. 

     

    Audiophile Style is pleased to publish this series but neither endorses or opposes Zhao's views expressed below. Like most subjects we encounter in life, audio has many different approaches and even more opinions about each approach. I enjoy reading and publishing these differing views and am a firm believer that there are endless paths to audio bliss. The challenge is finding one's own path while enjoying the journey.  

     

    - CC

     


    On the insights of the design and development of digital audio equipment


    Chapter 1

     

    Does well measuring audio equipment, by today’s standards, really equate to good sound quality?

     

    Digital technology is a symbol of modern civilization. The developments of the past decade are especially astonishing. We have heard and experienced the big data artificial intelligence, augmented reality, digital twins, and virtual world, etc. These are the great achievements in digitization of the analog world we know, so much so that they are part of our daily lives now.

     

    In reality, the digital world doesn’t exist. The digital signal is not analog, it is a representation. It is a convenient way for us to digitize, record, and store data; present it close to the original.  In nature, what we see, hear, eat, almost everything, none of this information is digital. None of it can be expressed completely losslessly in digital form. 

     

    In the context of audio, to express and present the stored digital data in an analog signal, all we can do is use the techniques we know to convert the digital signal closest to the original analog signal, as much as possible. However, even if we believe this is arguably the closest approach, it must be built on the basis of Digital Signal Processing (DSP). Without DSP, the digital signal cannot be processed and converted into the analog signal at all. 

     

    Even with the advanced, sophisticated processing techniques, we can only achieve an approximate, closest to the original Digital To Analog conversion. It is impossible to achieve absolute losslessness. There are always various distortions, and unwanted signals introduced that do not exist in the original signal – as the conversion (AD/DA) take place.

     

    Therefore, the High-Fidelity definition that we often talk about, can’t actually be achieved. One may achieve fidelity in certain aspects, but there are always trade offs in other aspects. Hence, there is no real, absolute high fidelity, lossless in digital audio signal processing. There are always compromises. With regard to high fidelity, if the designer does not know how and what to focus on in the design, it poses great challenges in designing great audio products, especially so for the DACs.

     


    Industry Measurement Standards?

     

    Often, instead of a real music signal, we use a known, lab generated sine wave, square wave, triangle wave, multi-tone signal to test audio equipment performance. This is a compromised technique as we cannot possibly use the real music signal to measure whether the design of the equipment is performing as per the desired design because music signals are constantly changing. This has caused a lot of trouble for many audio engineers, even for some highly skilled, experienced engineers who are mistakenly lead to believe that the sine/ square / triangle wave test performance index data is the gold-standard and assume that test results can completely represent the entire audio signal. This is a big fallacy!

     

    As of todays’ technology, there is no signal that we can use to represent the audio signal we desire to hear. There is no device that can replace human ears to judge whether the sound is truly restored to the original recording, and there is no data indicator that can represent the quality of the audio signal restored from the DAC, amplifier, loudspeakers, and finally, to our ears.

     

    There is a vast variety of audio products on the market, but there are only a handful of truly amazing, great sounding audio components. One of the reasons is that there's no gold-standard for designing a good audio equipment per se. The standards we refer to (as above) are only elementary, entry-level, industry standards.

     

    How many industry standard makers have actually developed excellent audio equipment? The standards established today, are the basic standards, good for electronic equipment testing as a reference. These standards can only be used to determine whether the equipment is performing within specification or out-of-spec, but there is no way to judge whether the audio equipment is of excellent sound quality. The lack of a real standard causes much trouble and many challenges in the audio industry. 

     

    Talented audio designers of great audio products have their own set of design techniques up their sleeves. These techniques, often have nothing to do with the industry standard method mentioned above. The designers will never reveal to others what kind of techniques they've adopted. There are only a handful of great audio products and talented audio designers, and there are very few people who really understand and appreciate the secrets behind them. Even if the designer chooses to reveal the techniques and technologies behind certain designs, due to lack of standards, controversial debates and disagreements may arise, questioning the designer's choices. 
     
    We have seen some great audio designers, who do not use sophisticated test equipment. Simply, they make use of the basic oscilloscopes, signal generators, multimeters, as well as judging the sound with their ears, while designing the products. The products they developed, sounded much better than those developed with advanced equipment. 

     

    Why is that? As we discussed, there is no audio signal analyzer that can replace human ears to judge the sound quality of a device. And, there are no golden ears either, hence, all the measurement parameters in the industry standard may not represent the truth in terms of sound quality. Of course, it doesn’t mean that a designer can absolutely design excellent audio equipment just because he/she can hear and differentiate good/bad sound quality. Reason being, if the designer does not have a way to change poor sound performance in the direction of good performance, then it is impossible to make the equipment produce good sound.

     


    Dynamic Range

     

    Can the dynamic range we test, represent the dynamic range of the music signal we hear? Can the signal-to-noise ratio we test, represent the signal-to-noise ratio of the music signal we hear? Can the transient response we test with the step signal, represent the transient response of the music signal? Far from it.

     

    The music we hear is not just the specific measurements or parameters of the audio equipment itself. What we hear is the result of audio equipment that has processed the entire music signal. As such, we can’t judge the sound quality just by looking at the parameters of a piece of audio hardware. We should look at the measurement of the processed music signal. However, sadly, there is no standard available today to measure the processed music signal. Therefore, designers have to make do with compromises, using the limited measurement techniques available as a preliminary indicator of audio hardware performance.

     

    We use a sine wave to test equipment dynamic range. 130dB, for example, is a great one. But the real music signal may only be limited to 70-80dB. The signal-to-noise ratio we test is basically the signal-to-noise ratio of the audio equipment itself. What method can we use to measure the digital noise of the music signal unintentionally introduced, by the AD / DA conversion? With the lack of a converted digital noise measurement standard, how can the signal-to-noise ratio measurement be a good indicator? 

     

    This is one of the biggest reasons why many of the new DACs on the market, designed with advanced technology, sound "digital." The digital sound is related to the magnitude of the residual noise after digital conversion, so much so that the micro details of the relatively weak music signals will be covered up, inaudible, and adversely impact the sound quality. 
     
    Many engineers like to use square waves or triangle waves to measure the transient response of music. This isn't entirely correct. The transient response of this test, measures the transient response of the hardware device and cannot represent the transient response of the music signal. 

     

    You can do a simple test. Play a sine wave signal, a square wave signal, and a triangle wave signal with the same frequency and same amplitude. The transient response that most people hear will be a relationship of sine wave, greater than the triangle wave, greater than the square wave. 

     

    As such, how could it be possible to determine whether the transient response of the music signal is good or bad based on the square/triangle wave? Arguably, the use of a square wave signal to measure the audio equipment transient response is the most incorrect. The music signals in nature are continuous, varied in frequency and amplitude in a continuous, gradual way.  Even at 100KHz, the (inaudible) music signal is gradual and continuous. It is understandable to use an impulse signal to test equipment, but can we trust the measured data as an indication of a good or bad sound? It is the biggest fallacy! Audio equipment that perfectly reproduces square wave signals must have a lot of digital signal noise, and music will most certainly sound digital.

     

    It is puzzling and confusing at the same time. When we test the audio equipment with the industry standard, we have wonderful results, everything is great, to some extent amazing. We have the world's lowest distortion THD%, we have the highest dynamic range, and we have the best signal-to-noise ratio ever measured. Even if the equipment plays a 100KHz square wave, the equipment produces excellent transient response. But why does it sound so bad? The sound is fuzzy, heavy digital glare, poor dynamic control, and the micro dynamics aren't expressed.

     

    Because we use A signal instead of B signal to test the equipment. If the A signal is approximately equal to the B signal, then the test is meaningful. But if the test signals are very different, then the data tested with A cannot represent B, where the B signal is the music signal we desired.

     

    Sine waves, square waves, triangle waves, white noise, pink noise, none of these signals are remotely close to a music signal. Therefore, the measurements can only represent the hardware response to the specific, known signal. 

     

    It's like the audio equipment is a container, the music signal is water. The container itself is clean, but the container is covered with various kinds of paint. So, the water put in the container will be contaminated. The container, paints, and water are three kinds of substances, three different links, not just two substances.  Most audio engineers always mistakenly believe that container = container + paints. Because most of the paints in music are invisible and cannot be tested. To us, these paints, which contaminate the water, are digital noise.

     

    For vinyl lovers, do the pops/clicks noise produced by the turntable effect the listening pleasure? Does the inherent pops/clicks noise of vinyl records really worsen the signal-to-noise ratio of the music signal we hear? Why, in the music produced by vinyl, is the background noise often so dark and dead quiet? Are we not disturbed by pops/clicks noise? Is it because our human ears can easily distinguish pops/clicks and the background noise of recorded music?

     

    If you were to factor in the pops/clicks noises, vinyl dynamic range may not exceed 20dB. If the obvious pops/clicks don’t effect / correlate to the music background noise, how does the standard signal-to-noise ratio measurement represent the music background noise level?

     


    DAC – Digital To Analog Converter

     

    Terminator2Internal.pngIn the era of digital music, a DAC is the soul of the audio equipment. The quality of the DAC determines the quality of the entire audio system. On the market, there are low-cost, economical DACs, often measuring much better than high-cost DACs. Does the low-cost DAC sound better than the higher cost DAC?  

     

    Thanks to technological advances, in today’s world, the electronic and hardware performance far exceed the needs of music signals reproduced. Therefore, in general, most of the audio equipment meets the needs of high-end audio equipment in terms of measurements. However, the digital noise in the music signal exists, it contaminates the entire music frequency band, completely superimposed with the music signal. There is no way for the human ear to distinguish and to separate the digital noise and the music. The human ear can only regard it as a part of the music signal – digital glare. 

     

    Without proper measurement, the digital noise is often ignored. We should not underestimate it. One of the key goals of DAC design is to reduce the digital signal noise after DA conversion, as much as possible.

     

    In fact, the negative impacts of amplitude distortion, phase distortion, transient response, frequency response, etc., can be regarded as digital noise, and, these distortions are present in the entire audible frequency band. A common misinterpretation of the digital noise is, when we test the equipment with a sine wave sweep, the noise level of the entire audible frequency band was very low. One may mistakenly assume that the test result has little or no digital noise. 

     

    But DA conversion of the music signals is not the same thing, there is no digital noise in the original analog music signal. When we use AD conversion during recording, digital noise is added inevitably, artificially. When we use DSP algorithms and DA conversion to convert the digital signal to analog, these processes generate digital noise too.

     

    Therefore, when we look at the digital signal converted by the DAC, it should be in such a relationship:

     

    • Music signal after DAC conversion = Original analog recording + Digital noise generated by each process (AD/DA, etc)


    Hence, the design focus of digital audio equipment must be to reduce the digital noise generated by each process. This has also led to different level of DSP algorithms, DAC conversion architectures, etc., which directly affect the digital noise, thereby affecting the music reproduction itself. 

     

    We can have sophisticated, advanced analyzers to test the amplitude distortion, phase curve, frequency response curve, transient response, etc. separately. But these tests are independent, isolated to each other, they do not tell us the sum of the total digital noise, or the music reproduction of the entire audible frequency band as a whole. Which is the biggest reason why all these tests, measurements, cannot be used to judge the quality of music reproduction.

     


    Take Away

     

    The reason why I say that the standard measurements cannot determine the sound quality in a definitive way is as discussed above. It is not to say that the test standards, nor measurements are meaningless. These are means, methods and tools for us to determine the basic hardware design performance. But we must have a clear understanding of the total digital noise caused by various conversions stages in the equipment, these shall be the focus of concerns.

     

    When we design or purchase audio equipment, we are always distracted by the specification, measurements, and the test methods. If the better specification equals better sound quality, we may have hit a home run – to design the best measured audio equipment and call it the day. If these measurements can determine the sound quality, then all audio equipment will be easier to design (for audio engineers) and easier to choose (for consumers) – just buy the one with the best measurements. 

     

    Unfortunately, it’s not. Almost all the audio equipment with great sound quality does not necessarily have the best measurements. Almost all equipment with the worst sound does not necessarily have the worst measurements either. To some extent, some bad sounding equipment may measure very well.

     

    If we change a capacitor, a resistor, an interconnect, or a power cord, the sound we hear has changed. But do these changes affect the measurement of the equipment? Truth is, the measurements remain vastly unchanged, but the sound quality changes tremendously. Do the measurements really have a lot to do with the sound? If so, why is the sound greatly changed, but not the measurements?

     

    So, does a well measured audio equipment by today’s standards, really equate to good sound quality?


     
    Zhao, Chief Engineer
    DENAFRIPS
     

     

    FormMore about Denafrips, visit https://www.denafrips.com 




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    1 hour ago, Rcanoe said:

    I have dodged the bullet many times by auditioning systems with good reviews and manufacturing pedigree


    Interestingly good reviews and manufacturing pedigree are subjective, nothing to do with measurements.

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    1 hour ago, The Computer Audiophile said:

    Excuse?


    In the sense that sometimes a designer or engineer will opt for a particular topology or technology that may not produce excellent technical performance/measurements but or because it may sound good to him. The “to him” is crucial here because there is no universal good/pleasing sound and thus it makes his choice a personal subjective one. What sounds good to him may not sound good to me or you.

     

    Think Vandersteen’s phase coherence banner technology which is achieved at the expense of as good as possible performance in other parameters, some recognised by the majority of experts as being at least as if not more important/audible.

     

    I am still giving Denafrips the benefit of the doubt until I read the remaining parts. Thanks for pulling this through.

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    On 8/27/2021 at 10:55 AM, firedog said:

    Especially expectation bias.:D. Very hard to measure.

     

    Your expectation bias here is easy to spot 😉.

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    1 hour ago, Summit said:

     

    Your expectation bias here is easy to spot 😉.

     

    Do you actually no what the term means? Apparently not, as no expectation bias of mine has been expressed. But your bias has.

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    9 hours ago, toddrhodes said:

    Music is an experience that engages multiple senses, states of mind, and evokes responses from all over our bodies, in the ideal scenario. And it may sound trite but these could include foot tapping, air guitar, tears, goosebumps, meditative states - how could one ever try to predict those responses with a set of numbers?

    Well stated, and this is far from trite!  This IS what it all comes down to and IS what one should strive for in the end.  Being this is so purely an individual "thing", everyone at some point has different acuity "levels" (think beginner listener vs mastering engineer) throughout their audio journey.  Those levels give us experience which then formulates our preferences which ultimately changes how each we get to that end result

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    On 8/27/2021 at 1:09 AM, firedog said:

    Bruno Putzey has talked about how he can do a suite of measurements on amps - including some unconventional ones that test the amp in various extreme or unusual scenarios - and can tell which ones will sound good. And those are amps of all types - Class D, Class A/B, even tube. He says if you actually know how to measure the true performance, the measurements are a good predictor.

     

    He's also talked about how you can voice an amp to get the sound you want - for instance, he said he could make his Class D amps have a "Macintosh" sound if he wanted to.

     

     

     

    This reminded me of Bob Carver's transfer function:  https://www.hifianswers.com/2020/04/amp-modelling-bob-carver-transfer-html/

     

    Bruno is a math first guy, but also gets feedback from listeners to understand what they are hearing.  If I remember correctly, he has stated that there are listener responses that he considers legitimate that cannot be understood from measurements alone.  

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    On 8/27/2021 at 5:06 AM, sdolezalek said:

    I hope that in Parts 2, 3 and 4 we will hear more about how Alvin Chee thinks about those tradeoffs in a way that allows us to decide whether that results in something that should sound better to all ears rather than just to Alvin Chee's ears.  ;-) 

    Firstly Chris, thanks for publishing these 4 articles and based on what appeared I am looking forward to the next 3. It was interesting to read his thoughts on measurements and listening, given that he produces one of the best measuring R2R DACs. I am sure we can forgive the minor problems of language and I can confirm that my Chinese is non-existent. 😁

     

    Just a picky point, Alvin Chee is the owner of Vinshine Audio, the worldwide distributor (and a great guy for service) and not Zhao,  who is the designer at Denafrips.

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    Thanks @The Computer Audiophile. Interesting article and good discussions.

     

    Just one thing I hope we see in the follow-up articles. Can Mr. Zhao show us some graphs and diagrams so we can appreciate more clearly what is being discussed, particularly the magnitude of the effect he's talking about as an engineer where possible?

     

    Too often in the audiophile world, we're fed words which can only go so far. While I agree that small differences might leave measurements "vastly unchanged", why not focus on the measurements that actually could and do change (eg. "digital noise generated by each process", jitter, distortion, etc. that Denafrips might be trying to address)? My concern is that if it's all "subjective" and totally unobjectifiable, then I think that's a bit problematic from an engineering perspective; we don't need an engineer to write an article about this if that's all it is!

     

    Also, more specifics would be useful. For example:

     

    "We have seen some great audio designers, who do not use sophisticated test equipment. Simply, they make use of the basic oscilloscopes, signal generators, multimeters, as well as judging the sound with their ears, while designing the products. The products they developed, sounded much better than those developed with advanced equipment."

     

    Can we have an example of what this means? Does this apply to DACs? Any hint as to which one(s) specifically are being suggested here? I think enquiring minds need to know (and perhaps to check out for ourselves!).

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    In the article,

     

    Quote

    If we change a capacitor, a resistor, an interconnect, or a power cord, the sound we hear has changed. But do these changes affect the measurement of the equipment? Truth is, the measurements remain vastly unchanged, but the sound quality changes tremendously. Do the measurements really have a lot to do with the sound? If so, why is the sound greatly changed, but not the measurements?

     

    This is the heart of the matter, and relates to something that those of an objectivist stance won't, or aren't able to understand - the vital significance when we listen to reproduced sound of our, human, hearing systems to be able to compensate for some anomalies, or deficiencies in the sound field, and not to others. Changes in frequency response? Easy peasy ... if it were not so, then listening to, say, a live piano would be a nightmare - every time you turned your head, moved around, or something came between you and the instrument, the sound of the playing would be yo-yoing in a very disturbing degree - which of course it doesn't; your mind, automatically, compensates for all these variations - and the sense of the instrument in action retains its smoothness, and integrity.

     

    The same applies to audio replay ... if the integrity of the sound heard is adequate, then this automatic, internal compensation kicks in - and the integrity of what is heard is maintained - this, "internal illusion", is key to the experience of a heightened, subjectively satisfying SQ.

     

    Changing of a single, tiny part of a system - like a capacitor, or a power cord - may be just enough to nudge the integrity of the system as a whole into the zone where the anomalies that disturb our hearing systems are low enough in level to be safely ignored, discarded - completely unconsciously. This is why it can work as a literal switch, and the "tremendously" adjective does indeed apply, to the sense of change in the presentation.

     

    This was made obvious to me over 30 years ago, by the behaviour of my rig at the time - and this is still exactly how it works today, with the current state of audio design - one thing 'wrong' with an otherwise perfectly measuring component will mean that it will be a failure as a means of conveying what's been captured in a recording in a satisfying way - and there's no way around this, except by tracking down the issue by whatever means you prefer, and resolving it.

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    Maybe, just maybe, certain audio phenomena need to have a whole article devoted to what the perception is, what the measurement is AND IS NOT, for both qualitative and quantitative characteristics.

     

    There are things I've have heard while comparing DACs (very recently for several weeks) that are very, very difficult to put into words, and have made me appreciate even more the subjective nature of this hobby. I tire of the measurement debate as much as the next lurker, but I would also like to see progress made in this hobby so that maybe, just maybe, we can all just get along. 

     

    ("Aim High" -USAF advertisement)

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    4 hours ago, feelingears said:

    Maybe, just maybe, certain audio phenomena need to have a whole article devoted to what the perception is, what the measurement is AND IS NOT, for both qualitative and quantitative characteristics.

     

    There are things I've have heard while comparing DACs (very recently for several weeks) that are very, very difficult to put into words, and have made me appreciate even more the subjective nature of this hobby. I tire of the measurement debate as much as the next lurker, but I would also like to see progress made in this hobby so that maybe, just maybe, we can all just get along. 

     

    ("Aim High" -USAF advertisement)

    The difficulty is that basic research is very expensive and the audiophile community/market is just too small to generate significant funds.

     

    Research into new drugs and how they affect the human body and mind costs $millions but the payoff can be $billions.

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    Oh, I'm certainly not naive enough to think any industry or company is going to do this, for exactly your reason. But I don't think Edison or Tesla or most others had much backing going for them either. 

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    On 8/29/2021 at 12:08 PM, George47 said:

     

    Just a picky point, Alvin Chee is the owner of Vinshine Audio, the worldwide distributor (and a great guy for service) and not Zhao,  who is the designer at Denafrips.

    Thanks for making this clear.

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    Mr. Zhao is also the owner of Denafrips and the designer/manufacturer of Musician.

     

    Source

     

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    On 8/27/2021 at 9:53 AM, firedog said:

    Again, I made no comment about Denafrips equipment. I was reacting to the ideas expressed in the post, which were general and also didn't specifically reference his DACs.

    Zhao’s post really has very little to do with engineering. As was pointed out, the Denafrips DACs are properly engineered and measure very well (especially given that they use an obsolete fundamental design). This is really just an example of how to market audio products, and you can beak it down to see how he’s pushing all the right buttons that will trigger a ‘buy’ response from his marketplace. 
     

    We can see all the familiar tropes: ‘digital’ is really ‘analog’ (something Max Tegmark and the Mathematical Realists would fervently disagree with); ‘real music’ is different to sine waves; designers have to tinker with the product and listen to the changes; the noise and distortion you get from vinyl don’t really matter; and last but not least, making insignificant changes to passive elements (like power cords 😂) produces perceivable changes in sound quality.

     

    At the end of the day, a product’s success depends on getting people to buy it, so you can view this as a seminar on how to get people to open their wallets. It’s not an approach I would encourage or approve of (I’m trying very hard to be polite here, otherwise I’d have phrased that rather differently …). But we can point to other manufacturers who have managed to build successful companies without resorting to this sort of pandering.

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    ...and then there's sticking with what you know, specs or no specs. I'm about to start over. I do love the "house sound" of McIntosh, but have decided to stick my ears in front of other brands, both amplification and speakers. I tend to lean into established brands, at least ones that I can afford. I trust that they have jumped through the years of technical hoops and R&D expenses to arrive at what they feel is the sound for them. 

     

    I'm looking forward to the rest of the articles, mostly because the first one doesn't really say that much. Getting sound that isn't live, via analog or digital, to our ears is always a technical compromise. The amount of tweaking that can be done I assume is almost infinite, or else why continue to tinker? Remember in the good old days of tape? "Is it live or is it Memorex?" (I think I have that right) Live is always best; the rest is more or less satisfying to the prospective customer; and a challenge to the marketer. I just find it all fun and engaging! 

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    5 hours ago, JJinPDX said:

    Remember in the good old days of tape? "Is it live or is it Memorex?" (I think I have that right) 

    Sort of right. Usually when people say "tape", they mean Reel to Reel. The Memorex quote was in reference to Cassette tape.

     

    I remember the Memorex ads, where Ella Fitzgerald shattered a crystal glass with her singing. Then the Cassette version did the same. (Actually my memory said it was Aretha, but Wikipedia says it was Ella). Real life listening was less convincing. 😏

     

    Bay Bloor Radio did a McIntosh demo in the early 1970's. A live band, consisting mostly of store employees, played a simple jazz tune, then it was replayed through all McIntosh gear. I couldn't hear a difference, which demonstrates how reliable blind testing is. 

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    I'm in general agreement with this article. Relying on measurements exclusively creates diminishing returns. The other piece is equipment synergy.. what one piece does well, other pieces in the audio chain can enhance or obscure. 

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    Are the other parts posted somewhere else?

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    Interesting. Would love to see a more precise characterization of digital noise, I assume some of it is quantization noise (critical for low level signals), jitter, etc. It is interesting the point about vinyl noise and that the brain is able to separate it out, that is indeed my experience.

     

    I would say there are ways to make measurements better: Most music occurs at low volumes. Yet, we measure THD, SINAD, etc with max volume input signals. I would like to see these measurements with a large set of input signal levels, even just the sine waves normally used. In fact, my understanding is that the original AES spec was to measure THD with an array of input levels. I speculate the industry didn't like this because it showed the defects of crossover distortion in the first solid state amps - they would look a lot better if just the max input signal was measured.

     

    To illustrate the point, if you plot how much time a 2V sine wave spends at each level of signal, you get the yellow line below. But most music follows a distribution given by the red line.

     

    As for the argument that real music is not used because it is hard to characterize it - as opposed to predefined waveform which anyone can reproduce. We could come up with a complex set of waveforms, with level distributions that resemble music, and use that. As a scientist (I have a PhD in Physics) all of these things should be measurable. However, it is clear that the simplistic measurements we do today are not enough.

     

    Finally, the key arbiter of it all is what we hear: the ear is a very precise tool and it is after all the one we ultimately care about.

    87013D92-1A15-438D-8605-4CCFC59FE3CD.jpeg

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