Question, if you are going to use the fan by placing it up against the fins of a heat sink, shouldn't those fins generate some tonality? Is not, to some extent, the struts substituting themselves for the tonality that would be generated if you placed the fan up against the fins of a water radiator (without the use of a plenum).
At least with the struts, the fan manufacturer gets a chance to tune the fan to minimize the problem? Would that not be so.
Does the nexus pick up tonality when paced against different types of heat sink fins?
It's the regularity of the radially placed "spokes" which generates tonality as the fan spins. In a typical heatsink, even though the fins are butted right up against the fan, the positional relationship between each fin and each blade varies quite a lot as the fan spins. There isn't the same kind of regular metronomic pass by each fin across each strut. The spacing between the HS fins is also way too tight, so rather than one or two tones, many are generated.
Which answers your last question, no, mounting any fan on any heatsink increases turbulence noise, not tonality. The latter sometimes occurs, usually when a fan is spinning pretty fast, but its caused by vibrating fins on the heatsink, not the regular air-borne interaction between blades and fins.
As for the second question, I'm not sure. But... Taking away the tonality that is caused by the extra struts doesn't necessarily eliminate tonality that might be caused by external impedances in actual usage.