Give me enough data points, and I could explain it all with the math.
We don't have enough data points. At a certain point, we perhaps can't have enough data points, just because the interactions are so complex.
Try reading Dekker's Drift into Failure. It's about failure analysis in complex systems (and why reductionist thinking is often a bad idea when trying to understand such failures), but it certainly applies to trying to "explain" the audible behavior of real-world sound reproduction with mere math.
edit: As a for-example... a speaker driver (like a headphone) is basically an electric motor attached to a spring (the diaphragm suspension). The suspension (spring) holds it at a zero point, and the motor moves it from the zero point, pushing air in the process. An electric motor consists of an AC-charged coil moving against a magnetic field. Now, if you look the other direction, a coil moving inside a magnetic field is an alternator, generating AC power.
So when the signal from the amplifier drives the motor that moves the speaker driver, energy gets stored in the spring - and then released back into the alternator, and pushed back into the terminals of the amplifier. That back signal is subject to serious nonlinearities from the suspension, including distortion, frequency response variations, and frequency-dependent group delay and phase shifts.
Most - but not all - of the back current from the speaker is absorbed by the output devices from the amp (which have high but not infinite impedance). What gets through is then picked up by the global negative feedback loop that is supposed to keep the amplifier linear, injecting it as phase-reversed signal into the input. Um.
This has a number of effects. First and foremost, it makes the amp/speaker interface much more sonically colored that it seems on the surface. Second, it blows up amplifiers when under enough strain - this is a real-world effect that any PA engineer has observed.
But go on, tell me again how my objections are just unscientific mystical hand-waving.
We don't have enough data points. At a certain point, we perhaps can't have enough data points, just because the interactions are so complex.
Try reading Dekker's Drift into Failure. It's about failure analysis in complex systems (and why reductionist thinking is often a bad idea when trying to understand such failures), but it certainly applies to trying to "explain" the audible behavior of real-world sound reproduction with mere math.
edit: As a for-example... a speaker driver (like a headphone) is basically an electric motor attached to a spring (the diaphragm suspension). The suspension (spring) holds it at a zero point, and the motor moves it from the zero point, pushing air in the process. An electric motor consists of an AC-charged coil moving against a magnetic field. Now, if you look the other direction, a coil moving inside a magnetic field is an alternator, generating AC power.
So when the signal from the amplifier drives the motor that moves the speaker driver, energy gets stored in the spring - and then released back into the alternator, and pushed back into the terminals of the amplifier. That back signal is subject to serious nonlinearities from the suspension, including distortion, frequency response variations, and frequency-dependent group delay and phase shifts.
Most - but not all - of the back current from the speaker is absorbed by the output devices from the amp (which have high but not infinite impedance). What gets through is then picked up by the global negative feedback loop that is supposed to keep the amplifier linear, injecting it as phase-reversed signal into the input. Um.
This has a number of effects. First and foremost, it makes the amp/speaker interface much more sonically colored that it seems on the surface. Second, it blows up amplifiers when under enough strain - this is a real-world effect that any PA engineer has observed.
But go on, tell me again how my objections are just unscientific mystical hand-waving.