In article writes:

What I was getting
at was that, as far as I can figure, a polarity inversion is, in
practice, the same as 180° of phase shift for repeating waves. As in:
if you were to duplicate a track with a 'repeating' type of waveform and
zoom in and look at the two, the comparison of the two tracks would look
(and sound) the same (excepting the first 1/2-period of the wave)
regardless of whether you shift the phase 180° or invert the polarity.
With a complex waveform I wouldn't think this to be the case.

They would look the same if you picked the right "window" of time for
both. But if you picked the same window of time for both, one would be
going positive at the same time as the other was going negative. And
for a waveform that's symmetrical in time, you won't hear a difference
when listening to one waveform at a time. But sum them and they'll
cancel (you'll certainly hear that).

However if you have non-symmetrical waveforms, not only can you see a
difference in the appearance of the waveform, but there are cases
where the difference is quite audible. If you have a DAw program that
can generate a waveform, try generating a minute or so of a 20 Hz
sawtooth. Import that into your DAW and listen to it. Then invert the
polarity and listen again. You'll hear a difference. If you don't have
a convenient way to generate a waveform, you can download a short
demonstration file that has a few seconds of such a sawtooth, then the
polarity inverts. You'll be able to hear the change on just about any
speakers.

http://www.recordingmag.com/download...opolarity.html

A polarity inversion is a special case, the equivalent of 180 degrees
of phase shift at all frequencies.

I'm not getting this: probably because I'm having trouble not thinking
in terms of a DAW, where if I were to duplicate, say, a kick drum, and
invert the duplicates polarity, it would 'look' (and I dare say, sound)
very different than any type of phase shift I can imagine.

This is true, but if you were to duplicate a simple waveform and
invert the polarity, it would look exactly like a 180 degree phase
shift. It's really difficult to visualize phase shift on a complex
waveform because, other than for special cases, the phase shift of
each frequency that makes up that complex waveform will be different.
However, a polarity inversion is absolute. At any given time, what was
going positive, becomes negative by the same amount. This is what will
happen if in invert the polarity or shift the phase of a single
frequency (which is a sine wave, and only a sine wave) by 180 degrees.

As far as the sound of an inverted kick drum, you can certainly
try that and listen for yourself. A kick drum is a good example of the
kind of waveform that can sound different in opposite polarity, and in
fact, it's often a good idea to try inverting the polarity of the kick
drum to see which way it sounds best in the context of the mix. In
real life, when you have leakage between mics on a drum kit, inverting
the polarity also changes the phase relationship of leakage, which can
have its own effect on the sound of the drum kit.

But that's a digression.

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