Noisewreck is right, DC offset and waveform asymmetry are NOT THE SAME THING. Nor am I saying the are. Those sax waveforms noisewreck is showing are asynnetrical but they have no DC offset. the "rest point" at the beginning and end is still 0DC.
What I am saying is that if you take those waveforms and invert their phase (not their polarity), that the entire waveform will be flipped, but will stay in place on the Y axis; i.e. it will be upside down, but will not move overall in the vertical scale.
But since the waveform is asymmetrical, the "centerline" around which that wavefrom will flip is not the same as the actual centerline of the chart (ithe wave is not centered around 0DC.) The offset, if you will, is in the location of the mirror itself.
Therefore, the rest line of that waveform waveforms WILL move when the phase alone is changed, and an offset will therefore be
created by the phase flip.
Flip the polarity, however, and the offset is not created because the flipping is around that 0DC rest line.
All I've been trying to say all along is that because of this offset in the location of the "mirror" depending upon whether one is changing phase by flipping polarity or whether one is changing phase irrespective of polarity, that the results are different; that they are two different physical processes.
Upon reflection (bad pun extremely intended

), there may not be anythng more than an incedental difference in sound because of physical loudspeaker limitations like have been mentioned earlier. But let's assume there is no theoretical difference in sound whatsoever:
That doesn't change my basic argument that if one wants to understand what a phase switch actually *does*, they need to understand that it is flipping polarity, not just flipping phase like the nomenclature suggests.
THAT'S ALL I HAVE BEEN REALLY TRYING TO EXPLAIN!
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Here's further consideration that I'm admittedly a little shakey about, but it may add another dimension to the importance of the difference: While the wave itself may not sound different, the difference in average voltage levels will affect what can be done with the mix in which that track is used.
For an extreme example, imageine a 1kHz pulse wave with 10% pulse width modulation that ranges from 0DC at rest to +10dB on top of the pulses. While the signal decreases headroom by 10dB, actually 90% of the time the signal is at 0DC.
Now invert the phase. Now the pulse is inverted, but the voltage range remains the same. Now the signal is "resting" at +10dB and the pulses are "peaking" downwards to 0DC.
Let's assume we have the perfect loudspeaker that won't distort because of the new 10dB DC bias; the signal will probably sound the same (golden ears will argue against that, but let's ignore that angle for now). *However", there is an important difference if we use this phase inverted but not polarity inverted track in our mix. While the overall headroom between the two states remains the same, now that headroom is being taken away not 10% of the time, but 90% of the time. It kinda simulates a denser track (in a very loose way); the RMS does not change like it would in a denser track, but because of the new offset the amount of "space" is reduced.
G.