Reversing Polarity -- Voodoo or Easy Tweak?

Herman...You are a bit hasty in saying that the drum sound will be compression followed by rarefaction. It depends on which side of the drum the mic was on. Also, as a disturbance propagates the wave shape changes. Consider, for example a Tsunami, where the initial disturbance is always that the sea recedes, followed by the flood. I have observed a similar effect of a ship bow wave while going through a canal. There must be an explanation, but I don't know it.

Do you have any scope pictures of a mic signal from a drum?

I see we are still confused, and I don't blame anybody for being that way since it is a bit confusing even without the years of improper use.

AC, which has no + or - poles! Only DC has a + or - polarity. Speakers can have only an absolute phase inversion

This is incorrect. Absolute phase inversion makes no sense. I know what you mean, but it is an incorrect use of the term phase. Phase has to do ONLY with time, and you cannot invert time.

AC does indeed have a polarity at any given given point in time. It may be incorrect to say that a given AC signal is overall positive or negative, but at some points in time it is positive and sometimes it is negative.

A clear example is a balanced system. You have 2 signals. One is the same as what a single ended system would have, and the other is inverted. This second signal is also commonly described as being "180 degrees out of phase" with the other one, but it is not. It's polarity is inverted, not it's phase. In a sense they are mirror images of each other.

When one is going more positive the other is going more negative.
If one has a value at a given point in time of +2 volts and headed more negative, the other one will be -2 volts and headed more positive. As an aside, I see this as a major problem with balanced systems. They must take 2 signals of equal amplitude but opposite polarity and amplify them through 2 different chains of amplifiers with the exact same gain and phase shift in both chains.

A phase shift occurs when different frequency ranges are shifted [delayed] by milliseconds

This is correct. Speaking to Eldartford's earlier point about the phase shift in crossovers being inconsequential, I disagree. At the -3dB (half power) point of a first order filter the phase shift is 45 degrees. This is a significant amount, especially if the fundamental frequency from an instrument falls in the passband and the first harmonic falls outside.

Am I the only one who thinks this thread reads like Abbott & Costello's "Who's On First"?

I thought Who was on second.

Eldartford, perhaps you are correct about mic placement, but if you are listening to a live kick drum you will surely be out in front of it unless you are the drummer and the sequence will always be one way or the other, and if you reverse it when playing it back it will sound different.

Herman...Both Hi and Lo signals are shifted 45 degrees at X/O, so the woofer/tweeter discrepancy is 90 degrees (for first order). In fact the discrepancy is constant at 90 degrees for all frequencies, but causes most problems around the X/O frequency where both drivers are emitting sound. With a second order crossover, 180 degrees of phase shift, there will be a deep sharp notch in frequency response unless one driver is connected with inverted polarity (or, as some might say, out of phase).That's why I like 24dB crossovers, where the shift is 360 degrees, so that sine waves are back in "phase" if you will pardon the term. Sine waves are a pretty good approximation of musical sounds, at least for a few cycles.