Technical question on phase inversion.

If the issue is really bothering you, buy a copy of the  'CHESKY RECORDS
JAZZ Sampler
and
Audiophile Test Compact Disc
VOLUME 1'.  It includes a few Absolute Polarity tests, to enable you to see if you can detect the difference(s) with phase inverted, along with other tools to help you properly set up and test your system.  If you can't audibly discern phase inversion with this CD: don't worry about it.    If you can: it will enable you to make the corrections necessary for your greatest listening pleasure.  Of course, then you'll have to listen to every recording in your collection and mark some for phase-reversed listening(if there's a reversal switch, somewhere in your system).   A number of recording in my collection sound the same both ways.  Most don't.  .   http://www.amazon.com/Chesky-Records-Sampler-Audiophile-Compact/dp/B000003GF3

I have phase inversion switches on the rear of my Reflection Audio preamplifier and remote button for my Velodyne subs. With the subs off it's difficult to hear the differences of inverting the phase with most recordings partly because of the getting up to make the switch and my acoustic memory.

On the other hand changing the phase of the subwoofers extra low frequencies with the remote while remaining in the listening position the out of phase can be quite audible on recordings with forwardly mixed kick drums. In fact the phase can change from track to track. 

My speakers are inverted, judging by direction of woofer's membrane movement when small DC voltage is applied. My DAC and amp are non-inverting.  I switched wires and sound changed, becoming tighter in the bass.  It was also mentioned in few Stereophile reviews including this one (Dali MS5 paragraph):
http://www.stereophile.com/content/fifth-element-22-page-older#TGueSFxlbl7YX344.97

I'm not sure why speaker designer decided to make it with inverted polarity, but I like it.  These speakers, in my room, sound better that way.  Of course it can be just the opposite for other CDs or it could be only my imagination - a placebo effect after reading Stereophile reviews, but I don't see a reason to change.

To complicate matters, the drivers in many loudspeakers are wired in various states of inverted polarity relative to one another. Vandersteen famously are not, all drivers in them being wired in the same polarity and crossed-over with 1st order filters, which maintains the speakers phase (at x/o frequencies at least). Many planars are of single-polarity design, of course. When you have speakers whose drivers are in opposite polarity to each other, good luck trying to correct for source material! I guess getting the midrange driver to move positively to a positive signal is the thing to prioritize.

bdp24, that might be the case in my speakers.  Somebody stated that midrange drivers are in the opposite phase to woofers.  It would explain why designer wired/marked woofers in opposite phase in order to preserve proper midrange polarity.