Playback from optical media involves an intermediate analog stage. The digital representation of the amplitude data on the CD is actually read as analog information by your CD player, which then interprets this analog information to create a digital data stream representation. In effect, there's a digital-to-analog-to-digital conversion in the chain at this point. And, while the information is in its analog form at this intermediate analog stage, involving pit edges and eye patterns, it is naturally vulnerable to analog degradation by analog factors, factors like quality of pit edges and quality of eye pattern.
      But playback directly from a hard disk gets rid of this type of analog stage, by not having the pit edges and eye pattern play any role nor be any factor at the real time of playback. Therefore, playing back music directly from hard disk frees your music from degradation by the less than perfect quality of these analog factors that affect the vulnerable analog intermediate stage of playback from optical media. And, thus freed from degradation by these analog factors at this analog intermediate stage, music winds up sounding better than when played from optical media, indeed even better than when played from a CD copy with freshly laser cut pit edges.
      This of course is striking, dramatic further evidence that the quality of the analog pit edges and of the analog eye pattern does indeed affect (and adversely affect) the quality of the final sound you hear. Get rid of these degrading analog stages and factors, and the music sounds even better.
      Note that playing back music directly from hard disk is not magic, and still has its own potential pitfalls. There still is an analog intermediate stage (analog magnetic flux changes read by the hard drive), which should be just as vulnerable to having the ultimate sound quality affected by external analog influences as the analog optical eye pattern in CD players evidently is. Furthermore, computer clocks are not noted for being as jitter free as CD player clocks should be. But the fact that the sound of music is different and better suggests strongly that the potential pitfalls in computer hard disk playback are not as degrading of music as are the analog stages and factors in CD playback.
      Ever the curious scientific probers, we naturally have a follow up side question. Why? Why should the analog magnetic stage of a hard disk readout be any better than the analog optical stage of a CD readout? If anything, magnetics are inherently more sluggish (and therefore with more poorly defined transition slopes at more poorly defined points in time) than optics are.
      The answer to this mere side question may give us yet another important clue about what goes wrong with CD playback, to make its optical analog stage so vulnerably sensitive, yielding poorer sound far away at the output of a CD player when there's just a slight degradation in the quality of the analog optical signal all the way at the beginning of a CD player. Why, then, does a computer hard disk yield superior sound, when its magnetic analog stage should be inferior to a CD player's optical analog stage? Here's our hypothesis, based on what we discovered so far.
      In most PCs, the input reading of the hard disk is completely asynchronous, relative to the computer's master clock timing of all the computer circuits that later will do the computational processing of that data coming in from the hard disk. Computers generally must make this input reading asynchronous, because the CPU might have other, more important tasks to perform in real time, so it should not have any temporal commitments to the inputting of data (from a storage medium, from an internet connection, etc.). In a well designed PC, there is absolutely no timing link between the master clock and the reading of the hard disk. Instead, an independent circuit (with its own independent timing) reads the data from the hard disk into a small memory bank called a FIFO (first in, first out) buffer. The whole point of this buffer is to act as just that, an isolating buffer between the hard disk read-in circuitry before the buffer and the computational circuitry (governed by the master clock) that's after the buffer. The computational circuitry empties this buffer at the rate dictated by the master clock and the software that's running, in this case software that plays your music at the proper sampling rate. The hard disk read-in circuitry, that reads data from the hard disk into this buffer, never needs to know how fast the master clock and software are running and thereby draining the buffer, so never needs to be tied into the timing of the music playback in any way. All the hard disk read-in circuitry does need to know, and all it looks at, is whether the FIFO buffer is starting to get empty - and, when the buffer gets to a certain point near empty, then this circuit reads some more data from the hard disk into the buffer, in order to replenish it.
      Consider the following analogy. Say you're driving across flat Kansas on a nonstop highway. Your car's engine is processing gasoline molecules under the command of electronic circuits feeding the fuel injectors, and therefore is also draining them from the tank, at a certain clock rate of X molecules per microsecond (this rate is pretty constant in our example, just like the constant sampling rate required for music playback). But you don't need to know what that clock rate is, or exactly how many gasoline molecules your car is consuming with each microsecond tick of the sampling clock. The electronic circuits do need to know exactly when in time (when in each piston cycle) to squirt the next charge of fuel into each cylinder, but you don't need to know that either. And while driving you have no way of knowing these things anyway, since you are isolated from all these precisely timed processes. All you do need to know, and all you need to pay attention to, is what the gas tank gauge says. When it gets down to a certain level, then it's your job to replenish the car's gas tank, to input more data. That tank is like a buffer between the precise timings of the engine's electronic circuits and you as driver. Thanks to the tank and the fuel gauge, you are isolated from all the timings of the engine's electronics (you can't know about these timings, and you don't care about them). The timing of your action process, inputting more gas into the buffer tank, occurs when you see the gas gauge nearing empty, and then when you happen to find a gas station - and the timings of this process (e.g. exactly when you find a gas station) obviously are not directly tied to the microsecond timing of the engine's control electronics.
      Even more importantly, the converse is also true. Just as your inputting process is not tied to the exact timings of the engine electronics, so also the timing of the engine electronics is not tied to the exact timing of when and how you input more gas to the tank buffer. The engine electronics can't know and don't care exactly when you refill the tank buffer; the engine will run fine regardless (provided only that the tank buffer hasn't run completely empty). The timing of the engine electronics doesn't know and doesn't care about the variety of analog timing factors that surround your refilling process: whether you input more gas into the tank buffer frequently or rarely; whether you fill the tank with the nozzle set on fast flow or slow flow; whether the gas pump pumps a steady even flow or a herky jerky flow that jitters over time. Thus, the timing of the engine electronics is not vulnerable to being affected by these external analog timing factors that do affect the refilling input to the buffer tank. Thanks to the fact that the buffer tank acts as an isolation barrier, your refilling process and all its timing variables are completely asynchronous with the timings of the electronics controlling your engine operations. And therefore your engine can continue to provide you with smooth, even, optimum driving performance, unaffected by the timing variable factors surrounding the process by which you input more gas into the tank buffer. Likewise, digital electronic playback circuits, which literally create and shape the music signal you hear in real time, can continue to provide you with smooth, even, optimum musical sound only when they are unaffected by any variable timing factors surrounding the process by which data is input from a storage medium into an isolation buffer, and this invulnerability can only be achieved by making that input process completely asynchronous in time, relative to the timings of the later electronic playback circuits..
      Because the reading of a hard disk is totally asynchronous in a PC, the circuit reading in the analog magnetic waveform and interpreting it into digital 1's and 0's, to put into the FIFO buffer, has no idea about the timing of the later processing circuitry that is draining the buffer and processing the musical bit stream. When exactly in continuous analog time is each clock pulse that is responsible for exactly placing each musical amplitude sample along the horizontal time axis, that can't be even a few picoseconds early or late, on pain of causing distortion of the music waveform? The circuit reading in the analog waveform from the hard disk has no idea, and couldn't care less.
      And the converse is also true, since the isolation of asynchronicity cuts both ways. The later circuitry processing your music after the FIFO buffer has no idea (and couldn't care less) about the timing of when (or how) the circuit reading in the analog waveform from the hard disk did its job of replenishing the FIFO buffer. Holy tempus fugit! Do you realize what that means? The real time in which you're listening to music is determined by the timing of the master clock governing the later circuitry processing the music. And now we see that this circuitry has no idea when anything occurs in the isolated circuitry reading in the analog signal from the magnetic hard disk (this read-in circuitry operates in a whole different time zone, with its own rules of buffer replenishment, and no connection at all to the master clock). This means that the real time in which you hear music, and the processing circuitry delivering this music to you with hopefully picosecond precise timing in this real time, has no connection to, and thus cannot be adversely by, any possible timing anomalies in that earlier read-in circuitry. If that circuitry reading in data from the hard disk has analog temporal instability (is early or late in its timing), the later circuitry actually delivering the music to you in real time won't know it and therefore can't be affected by it. Thus, it won't make any difference if the analog magnetic signal from the hard disk is sluggish, sloppy, weak, strong, early, late, jittery, etc.
      This digital system employing a magnetic hard disk still goes through an analog signal stage, just as a digital system employing an optical CD does. And this analog signal stage is still vulnerable to external influences. But if those external influences cause any timing degradations (indeterminacies, jitter, wander, etc.) in the analog signal coming in from the magnetic hard disk, those timing degradations die at the FIFO buffer, since the later circuits processing and delivering your music in real time are isolated from, have no knowledge of, and pay no attention to the timing of when data entered the FIFO buffer.
      Thus, the key to the sonic superiority of hard disk playback logically seems to be the total asynchronicity and temporal isolation of the read-in process, and in particular of that stage where the signal is actually in fully analog form and is thereby very vulnerable to timing degradations.
      From this, we can infer that CD playback could sound a lot better, as good as hard disk playback (or even better, since CD player clocks have lower jitter), if CD players were only built so that the transport, and the early circuitry that interprets, decodes, and assembles the incoming data, were totally asynchronous and isolated from the system master clock (instead of being tied into the master clock via PLL or some such linking circuitry). If the CD transport and early circuitry were temporally isolated in this manner, then even commercially pressed CDs with molded pit edges and average quality eye patterns should sound as good as freshly laser cut copies, and as good as hard disk playback.
      From this we can also infer again that the mechanism, causing the sonic degradation of music by inferior quality pit edges and eye patterns, must relate to timing errors they introduce into your CD player, and not to amplitude errors they might produce. The asynchronous isolation afforded by your PC's FIFO buffer topology would inoculate your music from timing errors originating in the analog intermediate stage (magnetic for the hard disk, optical for the CD), but not from amplitude errors. So the very fact, that PC hard disk playback with its asynchronous feature sounds superior to CD playback, in itself strongly suggests that the sonic inferiority of CD playback must be due to timing error and not amplitude error. If feature X fixes only timing errors but not amplitude errors, and a playback technique A with feature X sounds better than another playback technique B without feature X, then we can safely infer that the sonic inferiority of playback technique B is caused by timing errors and not amplitude errors.
      Recall too that CD players and of course PCs have heavy duty parity checks and error correction redundancy algorithms, to catch and correct any digital coding errors that could produce amplitude errors. So amplitude errors are unlikely except on rare occasions, and thus amplitude errors certainly cannot be responsible for the constant ongoing inferiority or superiority we hear in the sound of one playback setup vs. another.

-- Nature of Contaminating Error

      Thus far, we've seen abundant anecdotal evidence that the quality, of the analog input eye pattern signal to a CD player from the CD, somehow propagates all the way through the digital circuitry innards of a CD player to the output, to thereby make itself known in the  quality of the final sonic output of the CD player. For many of you who simply care about getting the best sound from your CD player, this is valuable knowledge, and is all you want to know. But for purposes of a thorough scientific analysis, we should also enquire exactly how the better or worse quality of the analog input eye pattern can possibly manage to propagate all the way through all that digital circuitry. This is a thorny question, and the jury is still out on a convincing answer.
      The answer might lie in the amplitude domain, or it might lie in the time domain. We don't think the amplitude domain is a likely candidate, for the following reasons.
      As we said above, your CD player actually creates or generates the digital data representing the amplitude of the music signal, and it creates this by interpreting the analog input signal (the eye pattern) that it actually receives from the CD. This digital data can be viewed as a single stream of 1's and 0's, which will later be assembled into 16 bit words representing the amplitude of the music signal, for each successive sampling period. In order to increase the storage capability of a CD, it's more efficient to translate the actual music data into a coded format, and merely store on a CD how many consecutive 0's there are between 1's at each point in the data stream of this coded format. Simply speaking, instead of having to store each and every 1 and 0 on the CD, they merely store a series of pit and land lengths saying how many consecutive 0's there are at each point between 1's. Thus, if there are four consecutive 0's, they only have to store one pit or land length saying 4, rather than four numbers saying 0.
      Now, how does your CD player do the interpreting of the analog eye pattern waveform, to then produce a digital stream of 1's and 0's? Your CD player looks at the zero crossings of the undulating analog input signal, and it makes its best guess as to how many integer whole time periods T have passed between the last zero crossing and the present zero crossing. If it decides that X whole time periods T have passed, then it freshly creates a digital data stream at that point that has the correct sequence of 1's and 0's (this is still coded). Thus, if your CD player looks at the elapsed time between the present zero crossing and the previous zero crossing of the analog input waveform, and makes its best guess that this elapsed time is closest to 7 whole time periods T, then it will create a certain digital data stream. The important point here is that your CD player will only pick a whole integer number of time periods T as its best guess.
      If the eye pattern is a high quality waveform, then the zero crossings will all be very well defined, and these analog zero crossings, which could occur at any moment on the continuous analog time scale, will all be very near to being exactly at one of the integer multiples of time period T, so it will be easy for your CD player to correctly guess the nearest whole integer number of time periods as the intended interval between zero crossings. On the other hand, if the eye pattern is a poor quality waveform, then perhaps its zero crossings will be more slanted (less vertical), and thus less determinate in time, or perhaps added noise will make the time of zero crossing less determinate, or perhaps its temporal jitter or wander in continuous time will put the zero crossing about halfway between two integer whole time periods T (elapsed since the last zero crossing). In this case, your CD player will have a much harder time guessing correctly what pattern of 1's and 0's to put in its newly created digital data stream. For example, suppose that the eye pattern quality is so poor that a zero crossing occurs 7.5 time periods T after the previous zero crossing. Then your CD player will have to guess: have 7 whole time periods T elapsed since the last zero crossing, or 8 whole time periods T? Which is correct, so I can generate the correct amplitude that the music is supposed to be for this sample? If the CD player guesses wrong, and generates the wrong digital data sequence, then it will ultimately output the wrong amplitude of music signal for this 16 bit sample (once the single stream of 1's and 0's is reassembled into a stack of 16 bits representing amplitude).
      It's worthwhile clarifying two potential sources of confusion at this point. First, the CD player is looking at an analog input waveform which could cross the zero line at any analog instant in the continuous ongoing march of time, but the interpretive decision the CD player must make relates to determining which is the nearest whole integer number of time periods T between this analog moment of zero crossing and the analog moment of the previous zero crossing. Thus, this early stage of your CD player has a continuous fractional analog input, but must output a discrete whole number, representing its best guess. Second, this early stage of your CD player is looking at and interpreting the time periods between zero crossings of the analog input signal, but its purpose in so doing is to generate only the digital amplitude of each sample of the music signal. Timing in is interpreted and becomes amplitude out. And hopefully only amplitude out. As we will see below, this early stage of your CD player should not also be involved in creating any timing information about the music signal it will later output to your ears. In other words, this early stage of your CD player might be looking at the timing of the analog input signal from the CD, but it should output only amplitude information about your final music signal from its interpretation of the eye pattern, and should not attempt to output any timing information for that final music signal. As we discussed above, the music waveform you hear is a two dimensional waveform, and amplitude is only one of its two dimensions, so its other dimension, time, has to be generated by your CD player somewhere within the CD player - but this other dimension, time, should not come from here, should not come from the eye pattern.
      So, what happens if the eye pattern is just slightly poorer in quality? We know from our research that even a slight degradation of reflectivity results in audibly degraded sound, so presumably

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