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This is silly. LUFS does not tell you if a model is perceptually close.Null tests and LUFS measurement of the results have well-known shortcomings, but I don't think there's much evidence that it's a misleading methodology when used for properly done real-world guitar amp capture comparisons. Most criticisms I've seen are rather theoretical in nature and don't really point to any cases where a properly done null test leads to incorrect or misleading conclusions.
You could argue it's hard to do a null test correctly, and I agree with you, but that's taking issue with the tester, not the test.
I haven't seen anything that improves on using integrated LUFS to objectively measure the results of the test. You want to know the magnitude of the discrepancy and LUFS is a pretty good way to measure that in a way that is meaningful for human hearing.
And you don't want a 1D measurement for comparing amplifier tonality - models, or otherwise.
You want as many dimensions as possible.
The problem is that a guitar amplifier is not a linear playback device. It is a nonlinear, input-dependent transformation system.
A null test fundamentally answers only one question:
“Are these two signals identical for this exact stimulus?”
That is a very narrow question.
An amp comparison needs to answer a completely different question:
“Do these two systems behave the same when a human plays a guitar through them?”
Those are not equivalent.
Two nonlinear systems can produce extremely small error residuals for one input, and behave radically differently for slightly different inputs. And guitar is nothing but slightly different inputs.
Pick attack
string choice
pickup inductance
note decay
intermodulation between strings
palm muting
dynamic impedance interaction with the speaker
A null test collapses all of that into a single fixed stimulus.
So you are not measuring the amplifier anymore.
You are measuring the amplifier's response to one specific waveform.
LUFS then makes the problem worse, not better. Integrated LUFS is essentially an energy-weighted loudness estimate over time. It is a scalar. But amplifier tone is not a scalar phenomenon.
The perceptual differences players react to live in:
dynamic compression behaviour
attack transient shaping
intermodulation products
harmonic distribution vs input level
bias shift / memory effects
speaker-interaction damping
None of those map cleanly to integrated loudness.
Two amps can have a −45 LUFS null residual and still feel completely different to play because the error is structured, not energetic. And the ear is far more sensitive to structure than magnitude.
A 40 dB-down transient distortion at note onset is perceptually obvious. A −40 dB broadband noise floor is not. LUFS only measures magnitude. Players respond to behaviour.
To evaluate an amp model you need multidimensional measurement:
level-dependent transfer curves, dynamic response, intermodulation behaviour, and time-variant response - essentially system identification, not waveform comparison.