Hi Bryon,
I agree completely with everything in your preceding post.
Assuming that the improvement I experienced really is constant across all recordings, regardless of their polarity, then surely we are right to conclude, as you and I both have, that the ABSOLUTE polarity of the recordings is irrelevant to the issue. But does it follow from that, that the RELATIVE polarity of the tweeter/woofer is irrelevant to the issue? I'm getting a little lost in the how that inference works.
BTW, I don't know if it's relevant, but the two drivers are not on the same plane. The woofer is recessed in the speaker cabinet, so that its center is slightly farther from the listener than the tweeter.
While the polarity inversion of the tweeter relative to the woofer is certainly relevant to the sound of the system (and I believe, although I'm not totally certain, that the inversion is necessary to flatten the frequency response of the speaker given the particular crossover design), the bottom line is simply that two inversions in the signal path (prior to the speaker) and/or in the recording = no inversions, regardless of how the tweeter and woofer are phased relative to each other.
Let's say that the speaker connections are reversed, and that a polarity-correct recording is being played, and that imaging is improved for that recording relative to what it was with the speaker connections not reversed. In that situation the tweeter's output will be polarity correct relative to the original event, and the woofer's output will be inverted relative to the original event.
If we now play a recording that has inverted polarity, with the speaker connections still reversed, the tweeter's output will be inverted relative to the original event, while the woofer's output will be polarity correct relative to the original event. Which is the same situation that we had with the previous recording when the speaker connections were not reversed, which resulted in inferior sound on that recording.
So the fact that reversing speaker connections provides improvement that is consistent regardless of the polarity of the recording is what is so baffling.
Another way to look at it is to consider Figure 7 of John Atkinson's measurements, linked to in earlier posts. That depicts the speaker's response to a positive-going pulse or step waveform, which by definition (or, more precisely, by Fourier theory) includes sinusoidal spectral components at both low frequencies and high frequencies. The initial response to the application of that waveform is a negative-going half-sine wave, since the (inverting) tweeter responds to the signal's high frequency content sooner than the woofer can begin to respond to lower frequencies (and also because the path length from listener to tweeter is slightly less than the path length from listener to woofer, as you noted). The response to that high frequency spectral component eventually oscillates to a positive-going half cycle, at which time the output of the woofer starts to predominate, beginning with a low frequency positive-going half-sine wave, and eventually oscillating to be negative-going.
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. If the polarity of the recording were then inverted, that ENTIRE waveform would then be re-inverted back to what it was for a non-inverted recording with non-inverted speaker connections.
I hope that further clarifies my befuddlement :)
Best regards,
-- Al
