jon - those ATC measurements are commendable and likely to produce very fine results in the frequency domain. For this Thiel thread, I will add a few comments.
Loudness: 4th order or any higher than 1st order slopes allow the driver to operate in its robust range and attenuate the out of band requirements, so they can play louder cleaner. Things get so much easier in that world; that's why most designers go there. Thiel's 01 used 3rd order and the model 02 used 2nd order slopes. The change for the 03 and after to first order increased the difficulty of the design undertaking by an order of magnitude, at least.
And as I have mentioned in the past, by removing phase and time coherence, the ear-brain gives a free pass to many other anomalies; they no longer are scrutinized as real and therefore can be ignored. Examples include the edge diffraction and soft-dome break-up modes. Diffraction isn't particularly audible with high order slopes because the brain doesn't associate the source with reality, and diaphragm breakup is attenuated to lower loudness and becomes less audible. Note that the literature considers 4th order Linkwitz-Reily filters to have 0 phase shift, but that is because they pretend that 360°, which rotates phase angle a full cycle, is exempt because 360° looks like 0 on a graph. Also, the speakers described do not look time-aligned, so the transient wave-fronts will reach the ear at different times as well as phase delayed relative to the input. Many commentators say that doesn't matter, which is because the ear-brain is so good at reconstructing the probable intended sound which has been scrambled by the speakers. Our work at Thiel demonstrated to our satisfaction how that brain-work of reconstructing the probable-intentioned waveform serves to decouple the listener from the emotional experience of the music. As I have said, most commentators disagree and deem higher order filters to be OK, and first order, phase coherent wavefronts to be unhearable and meaningless.
I suspect that Thiel lovers have identified the "trueness" of phase and time coherence and are willing to put up with the attendant compromises including less smooth frequency domain performance and higher audibility of many ancillary anomalies. Jim spent a lifetime identifying and reducing those anomalies (sonic baggage) and I am now stretching the envelope to include cleaner electronic performance which original budgets and materials science did not permit.
Loudness: 4th order or any higher than 1st order slopes allow the driver to operate in its robust range and attenuate the out of band requirements, so they can play louder cleaner. Things get so much easier in that world; that's why most designers go there. Thiel's 01 used 3rd order and the model 02 used 2nd order slopes. The change for the 03 and after to first order increased the difficulty of the design undertaking by an order of magnitude, at least.
And as I have mentioned in the past, by removing phase and time coherence, the ear-brain gives a free pass to many other anomalies; they no longer are scrutinized as real and therefore can be ignored. Examples include the edge diffraction and soft-dome break-up modes. Diffraction isn't particularly audible with high order slopes because the brain doesn't associate the source with reality, and diaphragm breakup is attenuated to lower loudness and becomes less audible. Note that the literature considers 4th order Linkwitz-Reily filters to have 0 phase shift, but that is because they pretend that 360°, which rotates phase angle a full cycle, is exempt because 360° looks like 0 on a graph. Also, the speakers described do not look time-aligned, so the transient wave-fronts will reach the ear at different times as well as phase delayed relative to the input. Many commentators say that doesn't matter, which is because the ear-brain is so good at reconstructing the probable intended sound which has been scrambled by the speakers. Our work at Thiel demonstrated to our satisfaction how that brain-work of reconstructing the probable-intentioned waveform serves to decouple the listener from the emotional experience of the music. As I have said, most commentators disagree and deem higher order filters to be OK, and first order, phase coherent wavefronts to be unhearable and meaningless.
I suspect that Thiel lovers have identified the "trueness" of phase and time coherence and are willing to put up with the attendant compromises including less smooth frequency domain performance and higher audibility of many ancillary anomalies. Jim spent a lifetime identifying and reducing those anomalies (sonic baggage) and I am now stretching the envelope to include cleaner electronic performance which original budgets and materials science did not permit.