Does anyone here know the details of this "highly complex" relationship calculation? Yes? Please explain it.
Simply explained, the signal is put through a K-weighted filter and the RMS of the result is measured. The important part is the k-weighted filter, which was designed by the ITU after compiling and averaging many decades of studies. The thing to remember is that it's a relative rather than an absolute measurement of loudness and even then, as it's based on a broad average, it may or may not align with any particular individual's perception. Furthermore, it only works under certain conditions, in relatively small rooms.
Are you saying that soundstage in recordings is ALWAYS manufactured? I doubt you mean this.
Why do you doubt this? Soundstage is always manufactured.
By "not an audio characteristic" do you mean that it's a figment of our imagination & not based on some characteristics contained in the signal stream?
Effectively yes, it's a figment of our imagination and not based on a property or characteristic contained in the sound waves.
OK. Can you show a set of such measurements that define a real (not studio manufactured) soundstage?
No, you're not getting it, there is no such thing as a "real" soundstage. Soundstage is a human concept, an artificial construct of the brain, a perception. It's not a physical property of the sound waves! What you are asking for is akin to asking for a set of measurements which define a real dragon. The only way we could create a set of measurements for a dragon would be to get a bunch of people to draw a dragon next to something of a known size, say a car, then work out the dimensions of each of the drawn dragons and finally calculate an average. Then we would have a set of measurements. This is, in effect, how we measure loudness. Soundstage is a more tricky problem though, because there's not even consensus on what soundstage actually is, and until we have that, we can't even start to think about a way of creating an averaged model to measure it. That's why I used loudness as an example, there's general consensus over what loudness is, although not general consensus over exactly what loud is and that's why we can only model relative loudness and not absolute loudness.
You are going to struggle to grasp these concepts until you understand that perception and reality are two different things which are either unrelated or related in a complex way which varies between individuals. Our brains create complex perceptual structures or models, the functional design of which is allow us to make sense of the world around us. The mistake made by many is a failure to understand this principle design goal and instead believe that the design goal of perception is to represent reality as accurately as possible and there are some/many who don't even believe there is any difference between perception and reality. The difficulty facing these latter groups of people is that perception is all they have ever experienced, reality cannot be experienced and therefore we can't compare reality and perception, except indirectly, through knowledge and understanding of the concepts, rather than through physical experience. At it's heart this is what science is; in an attempt to model reality, science attempts to separate reality from perception. Perception is easy, so easy we barely have to think about it and so common we invent labels to describe shared perceptions but if we want to really understand what's going on, we only have two choices; accept that reality and perception are two different things or invent some "magic" in an attempt to justify that they're the same thing! Science dictates that sound waves only have two intrinsic properties, amplitude and frequency. What we perceive when we listen is only loosely related to these two intrinsic properties, sometimes not related at all or related so complexly it's near impossible to work out if there's any relationship and because it's a perception rather than reality it can vary significantly from person to person.
Much of what is attributed to properties of sound waves does not exist in reality, regardless of how trivially easy to accomplish or how commonly shared those perceptions are. We've already mentioned loudness and soundstage, to these we can add a whole host of other commonly shared and labelled perceptions such as; pitch, musicality and even "music" itself, to name just a few, none of which exist in reality! Audiophiles are commonly unable to understand this difference, relying solely on personal experience rather than on knowledge/understanding and that's why the response when trying to justify personal experience against the science must ultimately must come down to "magic". Of course the response to that accusation is always along the lines of; It's only magic because science isn't yet able to measure properties beyond just amplitude and frequency but when it does, it will cease to be magic and it will become science. Unfortunately for audiophiles, we are not talking about the type of theoretical scientific model which we know is flawed but is just the best we currently have, we are talking about a precise, proven mathematical understanding of sound waves which has been around for nearly 200 years. So in this case, for magic to become science, this mathematical proof would have to be proved incorrect, a feat which nearly 200 years worth of the world's top mathematicians have failed to achieve. There's additionally a simple logical proof, borne out of the practical application of the mathematical proof; As amplitude and frequency are the only properties of sound waves we know about, they are the only properties of sound waves which we are able to measure and therefore record. In other words, if there is some other "magic" in there, we can't record (or reproduce) it! So, as this "magic" cannot and does not exist in the recordings these audiophiles are listening to, the only logical conclusion is that if it exists at all, it must exist somewhere other than the recording and the only logical place that could be is in their perception!
G