[JohnM]

The spectrum of the sine sweep does not have any "sub-harmonics" or other artefacts. There are 2 main sources of the features you describe: distortion due to overdriving the replay chain (your mention of "squarishness" hints of clipping occurring somewhere) and aliasing in a badly designed DAC (a DAC which does not oversample will require extremely tight filtering on its output if it is to correctly reproduce the input, without this filtering it will generate aliasing artefacts. Easing the filtering requirements was one of the drivers for the design of oversmapling DACs). Looking at the individual samples of a swept sine does not show you the true shape of the waveform unless the plotting function applies Nyquist filtering (as the DAC should do), without such filtering (e.g. with a simple join-the-dots representation) the displayed waveform will have an aliased appearance. Basically the same problem a DAC without over-sampling suffers from if it omits the (essential) output filters.