Now Glen old buddy, I like your summation. Q - Is the phase switch on a balanced microphone properly or improperly named?
Assuming that the switch is simply inverting the sign of the voltage (which is what I think the microphone is actually doing - correct me if I'm wrong there) I think the "proper" (so to speak) short answer is that it's truely a polarity inversion and not strictly JUST a phase inversion, because there is something more going on than if the phase were the only thing that was changing.
While the phase of the signal is also inverted, on an asymmetric waveform the values of the voltage envelope are also changing, which wouldn't happen on a pure phase shift only. The range of the envelope stays the same, but the actual values differ.
For a hypothetical example, let's say you're record a drum hit that, because of the actual action of the drum skin, peaks at (after preamping to normalize around 0VU) +16VU and -12VU. Flip the phase *only*, and those peaks remain the same with a DC offset on the waveform of +4VU. Flip the polarity, however, and ther is no DC offset, but the peaks now range from +12VU to -16VU. In both cases, the envelope range remains the same (28dB), but there is a DC offset of 4dB between the actual peak voltages between the two methods.
I think possibly (this is only a theory) that the reason that historically "phase inversion" and "polarity inversion" are semantically used interchangably, is because that's assuming a default symmetry around zero Volt reference. For example, when talking about an AC current, we're basically talking about a theoretical sine wave (not including noise) centered around a 0V reference. In such a case, there is no difference in result between a polarity inversion and a phase inversion; they quack the same. That default terminology has been inherited from basic electrical theory and is a basic concept that everybody pretty much understands.
The problem with that "understood" terminology comes in when we move into the world of audio and information theory where the desired waveforms are not simple symmetric waveforms. At that point, technically speaking, the equality between polarity and phase inversions starts to break down.
It's easy to just accept the intercahngability of the titles "phase inversion" and "polarity inversion", we all (including me) find ourselves using them interchangably all the time (the "Kleenex" effect). HOWEVER, when it comes to actually understanding and explaining the actual mechancs in forums like this one, the technical difference IS a real difference, and is important to understand in the long run.
The Qs I have, which I don't really know the answer to is, what do the various brands of digital software do when you click their inversion switches? Do they simply change the sign of the value, in which case they would truely be polarity inverters, and *technically speaking*, not just phase inverters? Or do they actually perform a time-independant (or instantaneous) phase shift or inversion, in which case they'd truely be phase inverters and not polarity inverters? I've never really looked at that in any kind of etail, so I'm not sure. It'd be easy enough to test on the various applictations, though.
G.