Phase Coherence as a measure of Acoustic Quality

[Joe Gwinn]

Having read the two articles, they do not say that the linear approximation (just add the effects, or alternately, just ignore string stiffness) is wrong, only that the linear approximation is just that, an approximation. The various full nonlinear solutions give more accurate answers for sure, but approximate methods are far easier to use, and capture most of the important behavior.

More to the point, one should always start with the linear models and see if they suffice in practice before resorting to the far more complex nonlinear models.

If one really wants to capture the full nonlinear effects, it's hard to beat a full finite-element model of a practical string, and it's practical to program such a model given that strings are one dimensional. One breaks the string into a string of interconnected little cylinders, where each cylinder is small enough that its behavior is linear, and numerically solves the resulting system of coupled ordinary differential equations. I have a textbook on this, written by a researcher at Bell Labs, back when Bell Labs was riding high. With any luck, someone has already done this, and published their code.

[Mike Sulzer]

Umm -- a single resistor has linear phase, so counting components isn't a good metric.

Sure a pickup can have linear phase, or close enough. The classic example is an air core with ceramic magnets, with resonance well above audio range.

OK, but I think we are discussing real pickups in use by guitarists around the world. They are high impedance and have a resonant peak in the upper part of their useful response. It would take some components to straighten out the phase response.

Also, why would you want to do that? Who says a linear phase response would give the sound a guitarist wants?

[Ronsonic]

I may manufacture some loudspeaker boxes for him for drivers that will cleanly and accurately handle 130 Hz to 30 Khz with a woofer added. The only problem is that the drivers cost about $500.00 per in bulk. Manger...German... .

Shame Lambda Audio is now defunct. The head cat there, Nick McKinney was building some positively insane drivers for both high end audio and bass. He had 15" subs that without the crossover would go to 7K clearly, sopranos came through them sweet and clear. I don't recall what the FR of his bass cabs was, but it was extensive.

The stuff was extremely non-cheap, but they produced some amazing gear when they were in business.

[Joe Gwinn]

OK, but I think we are discussing real pickups in use by guitarists around the world. They are high impedance and have a resonant peak in the upper part of their useful response. It would take some components to straighten out the phase response.

Only if the resonant frequency is too low. Then things get complex.

Also, why would you want to do that? Who says a linear phase response would give the sound a guitarist wants?

It could be an icepick sound for sure, but I didn't claim it would yield a good sound, only that it would yield linear phase from a pickup, so it is possible to do this. In other words, a proof of principle in the form of a gedanken experiment.