Take any two sustained frequencies and look at the sine wave summation. Now shift either of those two frequencies any multiple of 360 degrees and look once again at the summation. Both results will be identical. Thus, sustained notes, no matter how complex, will exhibit no overtone structure changes when one frequency is shifted a multiple of 360 degrees.

Second order Linkwitz-Riley crossovers have an electronic 180 degree phase shift and flat amplitude response summation. With one driver wired out of phase the total acoustic phase shift is 360 degrees. Fourth order L-R crossover have a 360 degree phase shift. Thus, both of these designs are "phase coherent" even though they don't preserve the original absolute phase. In practice, this means that there is some group delay present between high/low drivers, and that group delay has the effect of distorting transients. Whether this group delay transient distortion is audible or not is an area of ongoing research. Perhaps this is what you hear.

First order designs shift each speaker 90 degrees in phase, but have zero-degree phase summation at the crossover frequency. I've always been skeptical about this design route as tiny changes in head position relative to the speaker will destroy this zero-degree phase summation. In other words, first order designs with spaced drivers are

*very* sensitive to speaker/head relationships, and only have that magic "perfect phase" response for one small volume in space (incidentally, a volume smaller than the human head if you include the upper frequencies as being important).

Coincident drivers get around that problem very nicely. Even though each driver still has a 90 degree phase shift, the acoustic phase summation is 0-deg across the crossover frequency, and since their acoustic centers are coincident that means the effect remains off axis as well. Of course, coincident drivers bring to the table a host of other design problems. Thus the truth that speaker design is about compromises.

BTW, I have played trumpet now for about as long as you have played violin, though I get rustier as time goes on and I don't play as much as I should. The overtones you mention are present when two brass instruments play together, and are very rich in structure. Though the instruments themselves have mathematically defined pitch centers for each note, these are easily enough "bent" to accommodate even tempered tuning. When using my ears alone, I play a scale out of tune wrt an electronic tuner, but perfectly in tune wrt a reference pitch, whether that be a fundamental or not, much the same as you play a violin. My lips are equivalent to your fingers. Erm... something like that.

Oh, and I

*always* have my piano tuned using even tempered tuning. I would

*never* let anyone near my piano with an electronic instrument. Yuck! That makes me curious... I'm rusty on the theory of even tempered tuning; I think I'll go do some reading to refresh my memory of how the mathematics plays out.