I do have an answer and the results surprised me even though I've done a bit of NVH before. At this juncture I should point out that all vibration is assumed to come from the crankshaft torque fluctuations. The rubber engine mounts are assumed to absorb all engine vibrations so any vibration must come from the crank and be transmitted to the driveline.

I compared the torque fluctuations from at the following speeds:

4 pot @1500 RPM vs 6 pot at 1000 RPM

" 3000 RPM " 2000 RPM

" 4500 RPM " 3000 RPM

This represents the engine speeds that a typical drive would use for 90% of their driving.

At low engine speeds, the inertial forces are trivial compare to the firing pulses. At about 4000 RPM the inertial forces become comparable to gas forces and rapidly romp away at higher speeds.

The 6 pot wins at very low and very high engine speeds. But the 4 pot proves to be remarkably smooth in it's mid range of 2000-4000 RPM.

In fact in this region it blows the blows the 6 pot away in terms of refinement. So running a 4 pot at 3000RPM is smoother and largely more efficient than running the 6 pot at 2000 RPM. Bear in mind that the two engines are making identical power so the 4 pot is making the same progress as the 6. That is a real surprise.

V6 friend is gutted!

Well my ancient Triumph with it's straight six is both beautifully smooth and sounds glorious into the bargain. Yes I am biased, but given the choice it's a six pot every time!

I can't remember the last time I drove a (petrol) car where engine vibration was even an issue, modern engine mounts, the common use of balance shafts and the lack of misfires given modern fuel and ignition systems have almost rendered this a non-argument. Engine smoothness is taken for granted, you can't feel most engines these days regardless of configuration.

Yes-but a single balance shaft running at crankspeed is mechanically straight forward-and virtually universally applied. The I4 requires twin contra rotating balance shafts running at twice crank speed-and are often not used because the implementation is problematic.

The point I didn't emphasise-and I should have done, is that the imbalance is what makes the I4 so unusually smooth in its mid range. The inertial forces are out of phase with the torque flux from successive compression and expansion strokes so the resulting torque output is smoothened.

This only really occurs with the I4. The I3 and I5 cannot put their unbalanced couple to good use.