If you were to reverse the speaker connections, that ENTIRE waveform (including the initially negative-going tweeter output and the initially positive-going woofer output) would be inverted.
Ahhh! Now I get it, Al. The sentence above is what made it click for me. And yes, that does clarify your befuddlement, and it intensifies mine!
I was not saying the two box speakers were out of phase with each other, they are not. I was saying the two drivers housed inside each box speaker are wired out of phase with respect to one another.
Jea48 - Sorry, I misunderstood you. You are correct - the tweeter and the woofer, in each speaker, are wired with opposite polarity. This is common practice with a Linkwitz-Riley crossover with a 36 dB slope, as described here. As Al pointed out in his last post, the inversion is necessary to provide a flat frequency response.
By chance have you listened to the Focal 1007be speakers, wired both ways, with the JL Audio Fathom F113 sub turned off?
Yes, I have. The results are the same. So I don't believe the sub is a factor. And the sub polarity is the same as the woofers on the mains (both negative). I switched the sub polarity at the same time I switched the speaker cable leads to the mains, changing them both from positive to negative. Now that the woofers on the mains are negative polarity, failing to change the sub to negative polarity results, as you would expect, in a significant diminishment of bass due to cancellation. But I have not been listening to it that way, so that is also not a factor.
If you want to get a better idea what's going on, then at some point, after getting completely used to the way things are now . . . you need to put the connections back the way they were originally, and leave it that way long enough to form some new impressions all over again. The perceived change in sound should then of course be the opposite of what you first experienced. This is an important step - it will help rule out side-effects from the dismantling (i.e. tightening up the speaker drivers, refreshing connections), as well as confirm again that you're hearing what you think you're hearing.
This is a good suggestion, Kirkus.
...then the most likely explanation is that the loudspeakers' drivers/cabinet and crossover interact with each other differently when the phase is inverted...
This was my original theory. But I thought that Al just explained how any improvement due to driver/crossover/cabinet interaction would only apply to recordings with a particular absolute polarity, positive or negative. But the improvements I've experienced seem to be constant regardless of the absolute polarity of the recording. Does that refute the driver/crossover/cabinet interaction theory? Now I'm confused again!
So I'm guessing that in your case, where you have strong speaker magnets and a complex crossover, all stuck together in a small loudspeaker, that by reversing the driver lead phasing you're changing the electromagnetic interaction between all of thse components.
Fascinating. But would this effect be constant across all recordings with different absolute polarities?