Some good examples of very unsymmetrical waveforms can be found on some of the minimally-processed Sheffield recordings, ideally one of the direct-to-disc LPs of Harry James. However the asymmetry of James' trumpet and one of the trombone solos survives nicely on the CD.
These are, as noted, hell on wheels for potentially clipping things throughout the signal chain and of course present terrible problems for broadcasting if not alleviated. But oh my goodness do they add to the realism if accurately reproduced!
These sorts of material are likely to allow absolute polarity detection, although what that perception is due to is questionable---is it the effect the signal is having on the system, on your own ears/brain (the so-called Wood* effect), or both?
A little story I may have related elsewhere:
When the UCLA Electronic Music Studio director decided he had to have Dolby B noise reduction on a tight budget (this was circa 1969), he purchased some consumer boxes (branded Advent IIRC?). They worked o.k. for some program material and horribly for others. It turned out that the polarity of specific waveforms common to the synthesizers made an enormous difference. Internal to the boxes were amplitude detection circuits that, to save a few nickels were strictly half-wave. They and the level control circuitry they served were faked out almost completely if the sawtooth had a slow rise and rapid fall versus the opposite. You get what you pay for. And for most heavily processed consumer audio the boxes worked fine. For amateur recordists I wonder though.
To save the day, in collaboration with a physics grad student who was an amateur musician and hung around the studio, we devised an add-on that would not per se require surgery on the boards, but would merely be tacked on in parallel to make the detector circuits symmetrical. It worked. The downside was that the edge connectors for the stock boards were unbelieveably cheap and good for at most a few mating cycles, so the result was a plague of intermittencies.
As so often was the case, the engineers were initially praised and ultimately reviled. After dealing with the prima donnas and getting completely fed up, I quit to work full-time for the Astronomy Dept., where I remained until 1985.
*no relation that I know of