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.
