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There's been a discussion in several threads here on the issue of the audibility of polarity reversal (let's define that to mean the effect of reversing the speaker cables on each speaker, or anything else equivalent) during music playback. I've done a few little experiments with it, and I thought some inmates might be interested in the results and discussion.
I want to preface this by saying that anecdotal evidence one way or the other isn't going to add very much to this discussion. Double blind results and a theory that accounts for them are the only thing that's going to advance this issue. I think that's clear from the recent history - 50 years of anecdotal evidence hasn't gotten anyone to take this seriously.
The first question to address is whether polarity reversal is EVER audible. Many people believe it is not, but they are mistaken. Let's see how we can make it as easy to hear as possible. First of all, it's obvious that only for an asymmetric signal (meaning one which is significantly different when inverted) can we expect to hear something. On a steady pure tone, for example, polarity can not possibly be audible because the inverted signal is identical to the original, time shifted by one-half period. So let's construct a very asymmetric signal and listen for the effect there.
To do this, take any audio program (Audacity is a good free example) and generate a pure tone at, say, 400Hz. Now generate another at 800Hz, but shift the phase by 90 degrees relative to the first. Summing those two signals gives a very asymmetric waveform. If you want to make it even more asymmetric, add another signal at 1200Hz with phase 180 degrees shifted from the first (etc.). If you look at that signal, the negative parts are of higher frequency but lower amplitude than the positive parts. The DC offset is zero. Note that it's crucial that these components be harmonic - anharmonic combinations (meaning combinations of pure tones where the frequencies are not integer multiples of some base frequency) are phase incherent (the polarity reversed signal looks the same, at least when averaged over a few cycles), and so polarity reversal can not be audible for them.
Now take that summed signal, call it test1, and make a new signal which is inverted (the invert function in Audacity does that for you). Call that test2. Now download a player with an ABX comparator (foobar2000 with the ABX plugin for example) and see if you can hear a difference.
After a little practice I found that quite easy. It sounds like one tone has a higher frequency than the other. Now let's say on a particular trial A sounds higher pitched than B. Here's where it gets really interesting - my headphones (Grado's) can be rotated so that the speakers are facing outwards, away from the ears, rather than inwards. When I wear them like that, I can still hear the difference (10/10 correct on ABX), but now B sounds higher than A!
This result has several implications. First of all, it proves that the difference I'm hearing is in my ears, not to anything in the playback chain like the computer or the phones. If the difference was due to distortion in the phones, for example, inverting them wouldn't change anything.
Second, it supports the hypothesis that the reason polarity is audible is that the ear acts roughly as a half-wave rectifier - that is it chops off the part of the signal that is a rarefaction, say, but not the part that's a compression (it might be the opposite, I don't know - one could actually find out by determining which way the phones are moving and checking which way sounds higher pitched). The pitch change is evidently due to the fact that this signal, when rectified one way (keeping the positive part), will have higher frequency than when rectified the other way (keeping the negative part).
So polarity reversal is audible on certain asymmetric test tones, and the likely explanation is that the ear/brain acts to a first approximation as a half-wave rectifier.
Now the question of interest to this forum (and presumably audiophiles in general) is whether polarity is audible for recorded music. I think the answer is almost always no on a system with low distortion, but I'll come to that in the next post.
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