You can measure (and hear) all the distortion by subtracting the input from the output. The difference is just the distortion. Studio gear has little similarity to home audio.If we consider whether it is possible to measure something, we must define what are we measuring.
Regarding distortion, which is a non linear phenomenon, the plot thickens a lot.
You can quote a distortion figure in percentage for an amplifier. You must quote the frequency of the signal being measured (ok, we assume a sinusoid), its level, and we obtain a figure. A figure is a single dimension. How much information can a single figure portray?
Two different pieces of equipment with the same measured frequency response and distortion can sound radically different.
What is the harmonic content of that distortion, it, its spectrum?
How does it vary with level?
How does it vary with signal frequency assuming a sinusoid?
Do other complex products such as intermodulation appear when we are not playing a humble sinusoid but real music?
So, you can measure it. But good luck trying to obtain a measurement that can really characterise it in a useful way.
What is a useful way? Well, let's imagine that we devise a way to measure and characterise that somehow yields a vector magnitude such that two different pieces of equipment with the same "distortion vector" sound "the same".
And that's the problem. When recording music (except classical) it's not uncommon (especially for voices) to choose microphones that have a valve preamplifier that distorts a bit when pushed hard. And some of the coveted mastering equipment, especialy passive equalisers and dynamic compressors, do distort in a pleasant way. Or a way that most people will consider pleasant.
For dynamics processors you could boldly say that they "macro distort" (applying compression or limiting to a signal is non linear distortion) and also "micro distort" (inherent distortion to the components and circuit path unrelated to the settings applied on the control panel such as ratio, make-up, attack and release times, etc).
There's nothing wrong about it. We use our audio equipment to play music, not to reproduce laboratory measurements.
Is there anything wrong about the measurement first approach in fhis forum? Of course not at all, I am not claiming that. There is some performance any good piece of equipment must satisfy not to be considered junk. But beyond that some designers can make some adjustments in order to obtain that "something else".
When photography was invented I guess some people thought it would be a guarantee of absolute truth. That said, no matter how faithful photography is, just by composing a frame you are deciding how you want reality to look like. When recording music you choose microphones and their placement.
When mixing and mastering you make tons of decisions about equalization (which can be corrective or somewhat creative) and surely you will tweak dynamics. You can do it in an obvious, blatant, creative way, or you can be subtle and do it in a way that people won't notice. But you are altering reality.
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