In my quest to emulate an upright sound I stumbled upon this very simple question. Given the same gauge and tension, why (if at all) do flatwounds sound different than roundwounds?
Flats tend to be stiffer with less upper harmonic content in the sound. They are generally less flexible than rounds and you hear the thump because the higher harmonics are subdued. Having said that there are bright flats and dull rounds. For upright like tones old flats or nylon wounds get closer than rounds and your technique plays a big part so it pays to experiment with technique and mutes to get closer to that sound.
See picture above. Logic says that strings so different in construction will sound very different. If you want details... well, the physics is way over my head, but my non-technical answer would be that the core of a flatwound string is in full contact with the flat wrap wire, so the end result is that the upper harmonics are dampened/muffled/muted (whatever). The round wrap allows the core to vibrate more freely, and produce a lot more upper harmonic content. Of course as noted, there are differences in tone even between strings of the same type, which is a whole 'nother discussion. But the tonal differences between rounds and flats are dramatic IME regardless of those secondary differences within the same type.
The core type (round vs. hex) has very little bearing on the question as to why flats sound different from rounds. One thing to keep in mind is most bass strings, except for the ones with the smallest diameters (G's), have more than one layer of winding. Even with flats, the inner layers are round wires wrapped around the core wire with only the outer cover wire being a flat ribbon.
I see what you mean, but each corner of the hex core is in full contact, so the muting (?) still occurs, as it does when the flat wire wrap covers a roundwound wrap (see above).
You're asking this backwards. Flatwounds came first, so - why is that roundwound strings sound different compared to flats?
The shape of the wire affects the magnetic field differently: The flat surface of flatwounds will stay closer to the fundamental note, while the valleys in roundwounds will produce more harmonic content. The more jagged the wire, or deep the valleys, the more this is pronounced, & why folks enjoy the rough-feeling Rotosounds.