Agree the Avanti has a particularly distinct, loud, and unpleasant sound. Though the reasons are (mostly / probably) different than you suggest.
The pusher configuration places the propellers in the path of both the engines’ exhaust and the wings’ outflow field. Both of which flow fields are very asymmetrical and high energy. On every revolution of the propeller, each of the five blades transits through the very different top-of-wing outflow, one exhaust port flow, the bottom-of-wing flow, then the other exhaust port flow. Which triggers lots of vibration and high-frequency turbulence. AKA “noise”.
The B-36, another famous pusher design, also had a weird thrumming noise unfamiliar to other big piston airplanes of the era. And for much the same reasons.
I only saw / heard a Starship in flight once or twice. But it was a memorable noise.
Here’s something semi-related to the above you might find interesting …
A bunch of the cruise drag of a carefully streamlined airplane design comes from the so-called boundary layer (“BL”) and the turbulence associated with it. The millimeter or two of air closest to the skin of the airplane is nearly stationary. And as the freestream air slides past that stationary air, lots of turbulence results. The depth of the turbulence in a large airplane is on the order of a few inches mid fuselage and grows to be a couple feet deep near the tail. That turbulent energy has to come from somewhere and appears from the airplane designer’s POV as drag needing to be overcome by engine power. The faster you go, the worse it gets.
With that background … one of the efforts for research is how to actively reduce BL drag. We’ve already gone about as far as possible with passive BL drag mitigation efforts. Although exotic textured nanomaterials show promise if only they could be economically produced in vast sheets to be applied to (most of) the airplane surface.
One idea for active BL control is to actively suck the fuselage boundary layer into engines partly buried in the aft fuselage. Which leads to the problem of something like a large turbofan engine with 80% of the arc of the fan in the freestream, and 20% down in the slowed turbulent air.
Preventing vibration and noise and fatigue-driven wear on the fan blades as each of them dips in and out of the differing flow every 10-ish milliseconds is an unsolved problem. So far.