How to set phase correctly:
Since it's easier to hear a null than a peak do this. Reverse the polarity of one speaker (swap + and -) and play a test tone from 20hz to 200hz. Next, from the listening position, ask someone to adjust the phase so you hear a DIP in sound level at some point during the test tone. This creates a null point. Swap your speaker cable back and you're done!
What does a phase issue sound like?
Simply put, there will be an audible dip in the crossover range. Again, only IF there is a phasing issue, will this be noticeable. Importantly, a phase induced dip may lead you to set the sub volume level too high causing, "bloated bass."
Back to the OP's point: If one believes inverse speaker polarity causes a drop in low frequencies, then one must also believe phase of a subwoofer vs. main speakers may cause a similar drop. No, polarity and phase are not the same at all, however, for demonstration purposes, the drop of sound level IS similar.
Subwoofer phase adjustments are simply (very small) timing delays applied to ONE of two speakers attempting to producing the SAME frequencies. A subwoofer phasing problem is a timing issue. A few posts stated the problem well: AT THE CROSSOVER POINT of the main speakers to the subwoofer, phase matters. The goal is to slightly delay the subwoofer's sound wave to match the main speakers' phase and have these competing signals reach the listener simultaneously. How much it matters depends entirely on your specific set up. (Eg. room dimensions, LF capability of the mains, location of the sub to listener) WHERE the sub is located in relation to the main speakers affects phase. Specifically, subs located close to mains = little phasing problems, whereas, subs positioned CLOSER to the listening position and FURTHER from the main speakers = larger phasing problems.
As was also pointed out, subs often reach up to 100 or 200hz and phasing issues become more noticeable, complicated and real. I agree with MC that under a certain frequency it cannot matter.
Lastly, one cannot "invert the phase." This makes no sense. Adjusting the phase 90 degrees, 180 or 270 of a subwoofer is adding a small delay in the timing of the sound wave. There is no way to do the opposite and speed the sound wave up, hence no such thing as, "inverted phase."
Smooth LF augments all music performances and movies, at loud volumes or quiet volumes. LF done well is glorious.
