How do you judge your system's neutrality?

Meanwhile, back in the on-topic world, I think I’ve come up with a theoretical explanation for Bryon’s observations. My earlier mention of entropy got me thinking about another kind of entropy: Shannon entropy in information theory. The entropy I mentioned previously was thermodynamic entropy, for which organization and entropy are inversely related (i.e., more entropy implies less organization, and vice versa). But Shannon entropy describes the predictability of a variable (or process).

The prototypical example to demonstrate Shannon entropy is of a “fair” coin. (A fair coin is one with an equal probability of coming up heads or tails when flipped.) Such a coin is maximally unpredictable and, because there are two possible outcomes, has one bit of entropy (i.e., you need one bit of information to communicate the result of the next flip). A coin that always comes up one way (either heads or tails), is entirely predictable, and therefore has zero bits of entropy. A coin that is biased (i.e., one result is more probable than the other) has entropy somewhere between zero and one, depending on how biased it is.

The main point here is:
Higher entropy => less predictability
Lower entropy => more predictability

What does this have to do with music and playback systems? Everything. Consider the information in the source (the music) to have some amount of entropy, X. (Interestingly, and perhaps helpfully, X will be a measure of how much the source can be compressed without loss.) The colorations/distortions are processes that reduce that entropy. Why? Because those processes are predictable. This is not to say they are fixed, or constant (we’ve discussed processes that are frequency dependent, for example), but they are predictable in that their effect on a signal may be known. And because they conceal/corrupt/eliminate some source information and replace it with predictable information, they reduce (at output) the original entropy of the source to something less than X.

Consider a system that when you play a source, it puts out a 60Hz hum. This system delivers a zero-entropy playback. It is maximally predictable. If you improve the system so that some of the source material starts poking through the hum, the entropy increases. Entropy is maximized when the source is played back with minimal predictable content, (and the only source of unpredictable content is the source itself).

So, getting back to Bryon’s observations, the reason that a more neutral system causes timbres/songs/albums to sound more unique and their ranges sound more diverse, is because they literally are more unique/diverse upon delivery to the ears. Which is to say they have higher entropy.

This also explains our intuitive notion that while some colorations may be desirable, they will still tend to homogenize the music.

This also helps put to rest my concerns over the issue of excess contrast requiring a modification of the terms of the operationalization. The Rube Goldberg machine (as Bryon put it) that I proposed was meant to be one endpoint in the continuum of contrast (the sine wave generator being the other). But to enhance contrast my machine replaced sounds from the source (and more generally the set of all recorded music) with sounds from the (larger) set of all recorded sound. So, I effectively increased the entropy, but I did it by bringing non-source information into the system. Which is cheating because real audio systems don’t do that. The only source (of which I am aware) of outside information (other than the source) that enters an audio system is the power. Power fluctuations and noise on the line, to the extent that they are stochastic processes, would act to increase entropy (and to the extent that they are not stochastic processes, would decrease entropy). But my guess is that their nature is such that they would not act to increase perceived contrast in the music. In any event, I think the notion that the operationalization would push us toward systems of excess contrast can be dispensed with.

Dgarretson – Thanks for clarifying your view on “embodiment.” It is a fascinating topic in its own right. I agree with you that a taxonomy of colorations would be very useful in these discussions. I will spend some time thinking about possible taxonomic schemes. BTW, you are one of funniest posters I’ve seen on A’gon.

Cbw wrote:

Consider the information in the source (the music) to have some amount of entropy, X. (Interestingly, and perhaps helpfully, X will be a measure of how much the source can be compressed without loss.) The colorations/distortions are processes that reduce that entropy. Why? Because those processes are predictable. This is not to say they are fixed, or constant (we’ve discussed processes that are frequency dependent, for example), but they are predictable in that their effect on a signal may be known. And because they conceal/corrupt/eliminate some source information and replace it with predictable information, they reduce (at output) the original entropy of the source to something less than X.

Let me first say: This is impressive. I think it offers a very plausible theory for the effects of neutrality specified in my operationalization, namely, distinctness and diversity. Given your theory, here are some things I believe you would agree to:

(1) Decreasing entropy = Increasing predictability.
(2) Increasing predictability = Increasing coloration.
(3) Increasing coloration = Decreasing neutrality.
.....Therefore:
(4) Decreasing entropy = Decreasing neutrality.
.....And also:
(5) Preservation of entropy = Preservation of neutrality.

Is this correct?

Cbw, my interpretation of Bryon's posts has been that he wants to find common ground on neutrality among all audiophiles and all systems, not just within each individual's own system. Please correct me, Bryon, if I am wrong, but I don't think I have been the only one putting that interpretation on the original post! By the way, Cbw, that is a fascinating discussion of entropy in your last post.

Dgarretson has some interesting additions, as well, though much of it I either don't understand or would disagree with. For instance, when you say that "continuousness" is "consistency of musical expression throughout the frequency range." Not sure what you mean by this. My first reaction on reading it is to say that no acoustic instrument (including the voice) has consistency of "expression" (assuming you mean things like timbre? volume?) throughout it's full range. If they were made to sound as if they did, it seems to me this would be a violation of what you guys are calling "neutrality?"

I am also not certain that your concept of "organization" is not another form of "coloration," since you are speaking of "small corrections to pitch and timbre, improved transients and decay against a quieter background." Corrections from what, exactly?

While I would agree with you that "warm" and "analytical" are not mutually exclusive, I would strongly disagree with the notion that there is no such thing as too much resolution. Just one example. Almost all orchestral recordings made today are done with too many microphones set up, in the musician's opinions, far too close to our instruments. The vast majority of the mix uses these mikes instead of any placed overhead, and many engineers don't even put any out in the hall anymore. The resulting sound of the recording is nothing like what a concertgoer actually hears, no matter where they are seated in the hall.

I realize that you are speaking of the resolution of the system, but many high end systems I have heard create a very similar effect on a recording that was done well. And whether this bothers someone or not would be down to their personal preference as well (so is the statement that the recording was "done well," for that matter). This has been discussed in a different thread before, the idea that many audiophiles assume that some "colorations" they are hearing are caused by their system, when in fact they are on the recording itself. I have seen more than one situation where two people could not agree on which was the case ("Well in MY system, it doesn't sound like that!" etc). This is yet another reason why I don't think there could ever be much agreement on any two people's sense of "neutrality." There are far too many subjective variables, no matter how well we could define colorations on the page.

A little while back, Al suggested substituting another term, such as ‘accuracy,’ for the term ‘neutrality.’ More recently, Cbw mentioned that, when reading my posts, he tends to substitute the term ‘distortion’ for ‘coloration.’ And Learsfool has argued in many different ways that ‘coloration’ is a subjective category.

I believe that these three points of view are related, in that they all identify the same shortcoming in my definition of coloration, namely: It makes ‘coloration’ too OBJECTIVE a category. Here is the definition of ‘coloration’ I have been working with:

COLORATION: Additions, subtraction, and alterations to the playback chain that conceal or corrupt information about the music.

I think Al was correct in his view that the above definition is close to a definition of ‘inaccuracy.’ I think Cbw was also correct in his view that the above definition is close to a definition of 'distortion.' And I think Learsfool was correct in his view that the above definition is not subjective enough.

For these reasons, I would like to propose four things:

(1) Following Al’s advice, we make my former definition of ‘coloration’ the new working definition of ‘inaccuracy.’

INNACCURACY: Alterations to the playback chain that eliminate, conceal, or corrupt information about the music.*

*There are two other slight changes to this definition. I have changed “additions, subtractions, and alterations” to simply “alterations,” since all additions and subtractions are necessarily alterations. I have also included “eliminate” with “conceal and corrupt,” since the former seems to be just as much a possible type of inaccuracy as the latter.

(2) In the spirit of Cbw’s substitution, we identify distortion as one of the determinants of inaccuracy:

DETERMINANTS OF INACCURACY: Various kinds of distortion, loss, and noise, such as jitter, crosstalk, intermodulation distortion, speaker cabinet resonance, phase shifts, room modes, comb filtering, flutter echo, etc.

(3) Acknowledging Learsfool’s objections, we make the definition of ‘coloration’ more subjective:

COLORATION: Inaccuracies audible as a non-random** sonic signature.

This new definition entails that COLORATION IS A TYPE OF INACCURACY, the type that results in an audible, non-random sonic signature. It is consistent with the existence of other types of inaccuracies that do not result in an audible, non-random sonic signature.

This new definition also makes the term ‘coloration’ somewhat more SUBJECTIVE, since it includes FACTS ABOUT THE SUBJECT, by employing the concept of ‘audibility' (more on this below).

**I almost said “constant” sonic signature, rather than “non-random,” until I read Cbw’s recent post where he reminded me that many colorations vary with frequency, and so are not, strictly speaking, "constant." So it is more precise to say that colorations are non-random, or what Cbw calls, “predictable, in that their affect on a signal may be known.”

(4) The definition of 'neutrality' stays the same, namely, the degree of absence of coloration.

There are two advantages to the proposals expressed in (1)-(4). The first is that these definitions more closely reflect audiophile usage. This is evidenced by Stereophile’s audiophile dictionary. It is by no means definitive, but it is a relevant data point concerning usage:

Accuracy: The degree to which the output signal from a component or system is perceived as replicating the sonic qualities of its input signal. An accurate device reproduces what is on the recording, which may or may not be an accurate representation of the original sound.

Neutral: Free from coloration.

Coloration: An audible "signature" with which a reproducing system imbues all signals passing through it.

You can see these definitions at the following link:
http://www.stereophile.com//reference/50/index.html

The second advantage of these new proposals is that they bring the conflicting views of the Objectivist and the Subjectivist one step closer together. It is only a step, though, since the new definition of ‘coloration’ I am proposing is only subjective in the sense that it includes facts about the subject, facts that, I believe, are themselves largely OBJECTIVE. So this is not a retreat from Objectivism, so much as it is an acknowledgement that understanding coloration and neutrality is partly a matter of understanding HOW INACCURACIES ARE PERCEIVED.

(1) Decreasing entropy = Increasing predictability.
(2) Increasing predictability = Increasing coloration.
(3) Increasing coloration = Decreasing neutrality.
.....Therefore:
(4) Decreasing entropy = Decreasing neutrality.
.....And also:
(5) Preservation of entropy = Preservation of neutrality.

Is this correct?

Yes, that is essentially the argument. #1 and #3 are by definition. The reason for #2 is I am asserting that the coloration processes are not stochastic. This assertion is consistent with the definition you quoted from Stereophile:

Coloration: An audible "signature" with which a reproducing system imbues all signals passing through it.

Which is to say that colorations are replacing/concealing/corrupting musical information with a "signature" (i.e., more predictable information).

This understanding of the entropy-neutrality relationship is somewhat in contrast to something I wrote earlier (first quoting Dgarretson):

Relating to continuousness, movement toward neutrality implies a more organized presentation.

This is an interesting notion. If we consider the source as maximally organized information, then each stage in the audio chain has the potential to disorganize some information. The extent to which we don't corrupt the information determines the organization of the final presentation. So for a system, the greater its neutrality, the lower its entropy.

Here I was talking specifically about the entropy of the musical organization. However I failed to consider that the colorations were, in fact, more organized than the music. So while the music was becoming less organized *as music*, the overall presentation was actually more organized (i.e., it had lower overall entropy). So I had mistakenly reversed the neutrality-entropy relationship.

Bryon writes:

INNACCURACY: Alterations to the playback chain that eliminate, conceal, or corrupt information about the music.

My only problem with this definition (aside from the typo) is a nit pick: "Alterations to the playback chain..." sounds like you are talking about changes to the hardware. More precise might be something like, "Alterations to the source (or music) as it passes through the playback chain..." and then drop "...about the music." Or maybe just change the word "to" to "within."

COLORATION: Inaccuracies audible as a non-random** sonic signature.

I very much like this definition as it closely matches my thinking about what a coloration is, without the restrictive "narrow band" constraint that I was considering.