So those spikes and ripples on the square wave are just the missing terms above 48kHz? I've often thought how ironic this is, that you filter something and it comes out less smooth, not to mention the overshoot always staying the same magnitude. (I can't remember the name of that effect though I was talking about it just a few months ago. Urgh! 😏)
I have to say that I have managed to find near zero correlation between time coherence and sound quality and these days you are unlikely to find an actual Bessel filter in anything I'm working on. I remember you always saying how soggy they were and how they didn't really do very much actual filtering. I now have exactly that view and almost marvel at how little they do. Even in pre amps, what was my 70kHz final 3rd Order Bessel filter has been replaced by a 100kHz 3rd Order Butterworth which is almost indistinguishable for phase linearity but does more filtering and doesn't encroach into the passband nearly as badly. In speakers it's all odd-order Butterworths, at least as a framework. I would say keeping the power response flat (and there's more to this than just the Butterworth summing) is vastly more important and contributes to the sense of timing more than any linear phase-ish shape. I also think it's important to have the two responses in quadrature so that the outputs don't interfere with each other and a L-R definitely doesn't provide that.
Designing any of these listening tests is fraught with scope for misinterpretation. Even Floyd Toole's work on dispersion is flawed by so many other things being affected by moving the crossover frequency. I'm in agreement with him that keeping discontinuities out of the dispersion characteristics is important but we're never going to know whether what his listening panel liked was lower distortion from the mid-bass (being mostly below breakup), less chance for it to beam certain frequencies at you, or missing out contributions from the dust cap (which often produces a last dying peak at around 5k).
I think the use of Bessels in crossovers did bring a benefit but it was more one of competent design. So many speakers pre- the Personal Computer, and especially outside the competent manufacturers, were just plain flawed, with actual design mistakes in them. The Bessel couldn't be knocked up on a pocket calculator quite as easily and obviously as a 2nd Order Butterworth and if it was, it was so heavily damped that changes in component values hardly made a difference - and you certainly didn't get any surprises. But I'm yet to be convinced that it actually brought any positives because of its linear phase nature.
I'm a bit puzzled as to how the L-R is performing quite decently on the power response front since it's one of the very worst for that with its notch at crossover. For me it gives that ultimate "domestic sound" with the band members trotting across the top of your mantlepiece and never being able to muster up any sense of scale or power. Guess i'll have to wait for your next piece. :)
So those spikes and ripples on the square wave are just the missing terms above 48kHz? I've often thought how ironic this is, that you filter something and it comes out less smooth, not to mention the overshoot always staying the same magnitude. (I can't remember the name of that effect though I was talking about it just a few months ago. Urgh! 😏)
I have to say that I have managed to find near zero correlation between time coherence and sound quality and these days you are unlikely to find an actual Bessel filter in anything I'm working on. I remember you always saying how soggy they were and how they didn't really do very much actual filtering. I now have exactly that view and almost marvel at how little they do. Even in pre amps, what was my 70kHz final 3rd Order Bessel filter has been replaced by a 100kHz 3rd Order Butterworth which is almost indistinguishable for phase linearity but does more filtering and doesn't encroach into the passband nearly as badly. In speakers it's all odd-order Butterworths, at least as a framework. I would say keeping the power response flat (and there's more to this than just the Butterworth summing) is vastly more important and contributes to the sense of timing more than any linear phase-ish shape. I also think it's important to have the two responses in quadrature so that the outputs don't interfere with each other and a L-R definitely doesn't provide that.
Designing any of these listening tests is fraught with scope for misinterpretation. Even Floyd Toole's work on dispersion is flawed by so many other things being affected by moving the crossover frequency. I'm in agreement with him that keeping discontinuities out of the dispersion characteristics is important but we're never going to know whether what his listening panel liked was lower distortion from the mid-bass (being mostly below breakup), less chance for it to beam certain frequencies at you, or missing out contributions from the dust cap (which often produces a last dying peak at around 5k).
I think the use of Bessels in crossovers did bring a benefit but it was more one of competent design. So many speakers pre- the Personal Computer, and especially outside the competent manufacturers, were just plain flawed, with actual design mistakes in them. The Bessel couldn't be knocked up on a pocket calculator quite as easily and obviously as a 2nd Order Butterworth and if it was, it was so heavily damped that changes in component values hardly made a difference - and you certainly didn't get any surprises. But I'm yet to be convinced that it actually brought any positives because of its linear phase nature.
I'm a bit puzzled as to how the L-R is performing quite decently on the power response front since it's one of the very worst for that with its notch at crossover. For me it gives that ultimate "domestic sound" with the band members trotting across the top of your mantlepiece and never being able to muster up any sense of scale or power. Guess i'll have to wait for your next piece. :)