How do you judge your system's neutrality?

A while ago Bryon produced some equations. Among them:

1. CA = (1/L+N+D). A COMPONENT’S ACCURACY is determined by the amount of loss, noise, and distortion within the component. More specifically, a component's accuracy is INVERSELY PROPORTIONAL to its loss, noise, and distortion.

Just a nit pick here: operator precedence being what it is, the equation as written would be evaluated as CA = (1/L) + N + D. But your intent to have all component accuracy be inversely proportional to all three of loss, noise, and distortion would be better written as CA = 1/(L+N+D).

3. CR = CA + FR. A COMPONENT’S RESOLUTION is determined by the accuracy of the component and the format resolution of the source. Specifically, a component's resolution is DIRECTLY PROPORTIONAL to its accuracy and the format resolution.

I've been wrestling with this one because I don't think of a component's resolution as limited by the resolution of the source -- that is, the output at any given moment may be limited by the source, but that is not be the component's inherent resolution limit. It is only when the source resolution exceeds the component resolution that you can know anything about the component resolution, at which point the source resolution ceases to be a factor. Or maybe I'm missing your point.

4. SA = SoCA. A SYSTEM’S ACCURACY is determined by the sum of its components’ accuracy. Specifically, they are DIRECTLY PROPORTIONAL.

5. SN = SoCN. A SYSTEM’S NEUTRALITY is determined by the sum of its components’ neutrality. Specifically, they are DIRECTLY PROPORTIONAL.

I have a couple of thoughts on these "sum of" relationships. 1) Some types of errors may not be simply propagated through downstream components, but may actually be reinforced by them. This kind of error may result in an exponential relationship, rather than a simple additive one. This would be an example of bad synergy among components. 2) In some cases, the entire chain may be limited by a single component. Resolution, for instance, may well be a function of the least resolving component in the chain, rather than the sum of small losses in several components. Neutrality, on the other hand, is likely the sum of the components contribution.

I realize that you did not intend these to be strict mathematical relationships, but these are some ideas that occurred to me about other types of relationships among components.

Cbw – Those are excellent observations. Taking them one at a time…

(1) RE: Component Accuracy, expressed as CA = 1/L+N=D,* Cbw wrote:

...your intent to have all component accuracy be inversely proportional to all three of loss, noise, and distortion would be better written as CA = 1/(L+N+D).

*Where…
CA = Component Accuracy
L = Loss
N = Noise
D = Distortion

You are absolutely correct that the equation should be CA = 1/(L+N+D). It was an oversight on my part.

(2) RE: Component Resolution, expressed as CR = CA + FR,* Cbw wrote:

I don't think of a component's resolution as limited by the resolution of the source -- that is, the output at any given moment may be limited by the source, but that is not be the component's inherent resolution limit.

*Where…
CR = Component Resolution
CA = Component Accuracy
FR = Format Resolution

I should have distinguished two different types of Component Resolution, namely, LATENT Resolution and OCCURRENT Resolution.

LATENT RESOLUTION: The amount of information about the music that a component can POTENTIALLY produce.

OCCURRENT RESOLUTION: The amount of information about the music that a component ACTUALLY does produce.

My equation for Component Resolution, CR = CA + FR, was intended to express the OCCURRENT resolution of a component. Occurrent Component Resolution is limited by Format Resolution, because a component cannot produce more actual resolution than it receives at its input. You are quite correct, however, that LATENT resolution is not limited by Format Resolution, as is illustrated in cases where a low resolution source is fed into high resolution downstream components.

I think you are also correct in that, when audiophiles talk about the resolution of an individual component, they are usually referring to its LATENT resolution, that is, how much resolution the component IS CAPABLE OF. The exception to this is when audiophiles talk about the resolution of the SOURCE component. In that case, resolution seems to refer to OCCURRENT resolution.

Also, when audiophiles talk about the resolution of a whole system, I believe that they are usually talking about its OCCURRENT resolution, that is, how much resolution the system ACTUALLY PRODUCES. Hence the inclusion of Format Resolution in my equation for System Resolution, expressed as: SR = SA + FR.

The value of distinguishing Latent Resolution from Occurrent Resolution is that it highlights the difference between System Accuracy and System Resolution, which I believe are two distinct virtues in an audio system. A highly accurate system passes the signal from software to ear with very little alteration to the musical information. But it need not be highly resolving, if the format resolution is low. Think: A $100K system playing MP3’s, and you have the idea of a highly accurate but not highly resolving system. A highly resolving system, on the other hand, presents a large amount of information about the music to the listener. To do this, it must start with a large amount of information about the music (high format resolution) and preserve that information through the playback chain (high system accuracy). Think: The same system playing a well recorded SACD.

(3) RE: System Accuracy, expressed as SA = SoCA,* Cbw wrote:

Some types of errors may not be simply propagated through downstream components, but may actually be reinforced by them. This kind of error may result in an exponential relationship, rather than a simple additive one.

*Where…
SA = System Accuracy
So = “sum of”
CA = Component Accuracy

I agree that the “sum of” relationship expressed here is, in many cases, unlikely to be a simple sum. It may be multiplicative or exponential, depending on the type of inaccuracy in question. That is what I meant when I said that these were merely mathematical “analogies.” Having said that, it would nice to improve this equation so that it reflected the various types of inaccuracies that collectively determine System Accuracy. Do you have any ideas?

Hi Bryon - I think there is still some misunderstanding here. I am not disputing that there is a fact of the matter about whether there is coloration or not; as I have said before, I believe that colorations are ALWAYS present, and that an absence of them is not possible in music reproduction. When I made the analogy about coloration being in the ear of the listener, I meant that each listener will perceive these colorations differently, and that this is ultimately subjective no matter how much agreement can be made on terms. Taste comes into play here as well - which trade offs does one want to make, etc.

I also did not mean to imply that there is no such thing as an inaudible coloration. One obvious example is a digital processor designed to remove all frequencies above the range of human hearing, as many still are - this is clearly information that has been eliminated (it has also been proven that although the ear does not hear these frequencies, the brain does sense them and does perceive their absence).

Another clarification - I did not mean to imply that variety of tastes make it impossible to come to an agreement on quality. As you say, taste is not a static phenomenon at all. That is one of the main points of my brother's paper, in fact. That said, it still can be very easy to confuse taste with quality. For example, an audiophile who will refuse to own a tube amp, no matter how well made and how good it sounds because they consider them too "colored," a bias very often expressed here on this forum - insert your own favorite bias in place of this example. Almost none of us are as open minded as we would like to think we are.

Learsfool wrote:

I believe that colorations are ALWAYS present, and that an absence of them is not possible in music reproduction.

Learsfool - I understand that you believe that colorations are always present in music reproduction. About this point we are in agreement. I have a four questions for you:

(1) Do you believe that colorations can be either increased or decreased?

(2) Do you believe that colorations can be evaluated as to their euphony or “dysphony” by individual listeners?

(3) Do you believe that judgments about euphony/dysphony have ANY consistency across multiple listeners?

Learsfool wrote:

When I made the analogy about coloration being in the ear of the listener, I meant that each listener will perceive these colorations differently, and that this is ultimately subjective…

In introductory philosophy classes, a thought experiment is often discussed called “spectral inversion.” It asks students to consider the logical possibility that what I see as red, for example, you see as blue. Many people wonder about this possibility outside the context of philosophy classes. But unlike most of them, philosophers take the problem quite seriously.

The possibility of spectral inversion is just one example of a whole class of thought experiments designed to highlight the PRIVACY OF SUBJECTIVE EXPERIENCES and the INACCESSIBILITY OF OTHER MINDS. Your suggestion that “each listener will perceive colorations differently” strikes me as a version of this attitude, except that, rather than being agnostic about the percepts of other minds, you believe that the percepts of other minds are sufficiently different from person to person to make agreement about colorations impossible. In a way, you are saying: What I hear as “red,” you hear as “blue.” So, my last question for you is:

(4) Is this your view?

Hi Bryon - interesting questions, and I am sorry I can't take more time to answer them at the moment. The very short answer to the first one would be that that of course would depend on the specific coloration in question. The second question is a little puzzling to me, as I am not sure why anyone would answer that in the negative. Surely we all are always evaluating the euphony of our systems, even including Dgarretson's extreme objectivist?

As for the third question, sure, multiple audiophiles with similar tastes will often agree completely on that sort of judgement. I think there would rarely be complete agreement among a large number however, except perhaps in extreme cases, such as Al's $50,000 system vs. a Wal-mart boom box. Some colorations bother certain people much more/less than others. The digital distortions vs. analog distortions debate is a classic example.

As for the fourth question, I must admit I am completely unfamiliar with the "spectral inversion" thing, so I really can't say. Using your color analogy, perhaps a better example of what I meant than red/blue might be light purple/dark violet? Or perhaps back to my two high-end preamps in the otherwise same exact system example? One person might say that they prefer preamp A's warmer sound, where another will insist that it is too "colored." This would be a subjective judgement, EVEN IF THEY WERE IN AGREEMENT. Another example - one of the oldest types of audio component that has been in continuous production is the horn speaker. Many would say that clearly the longevity alone means that there is something fundamentally correct about the design. But of course there are a HUGE number of audiophiles who can't stand them, and completely write them off as an outdated, hopelessly "colored" design. Both opinions are frequently expressed on audio forums. This is a subjective judgement. I don't know if these brief answers help or not, but there they are.