It can be tough to find the right audio clips, but here's one that isn't bad.
In this case it's the 5.2L Lambo V10's uneven firing order caused by the two banks being 90 degrees apart vs. the 144 crankshaft rotational degree spacing of exhaust pulses on a given 5-cylinder bank and opposing cylinders sharing a common, non-offset journal. In effect, this is two 5-cylinder engines sharing a common crankcase and crankshaft.
The musical third is lurking in this uneven timing and the heavy high harmonic content comes about when you have two banks that are even firing unto themselves.
A cross-plane American V8 is not even-firing on each side of the vee, but a bundle-of-snakes (180-degree) exhaust like in a Ford GT40 will get you some of that octave scream too.
Comes down to a couple reasons - 1) the increased pollution reduction technologies (i.e the catalytic converter and muffler) used, which in the video you linked to doesn't have any of those and is just straight headers and 2) the timing of those older motors is mechanical and set to be optimal when the motor is at a peak (or near peak) performance.
Not true with mechanical variable valve phasing/timing/shifting systems, famed (and defamed) as VTEC for Honda, but available in other alternative forms (and often recently and in milder forms probably due to Honda and Toyota patents gradually expiring), like Toyota: VVT-i (famous as VVT in AE86's 4A-GE engine), Suzuki: VVT (e.g on Swift Sport M16A engine), Ford: VCT...
Or it can be completely electronic thanks to direct injection gasoline engines, like Fiat MultiAir.
I get what you mean though, I heard a Ford RS200 being ragged around a track last year and it sounded amazing.
Are you really trying to discredit Lamborghini because they're now owned by Audi? The passion you're referring to comes from the design. Most people couldn't care less about the sound. The other day a Ferrari 599 GTB passed by a restaurant and my friend said it was an obnoxious sounding car.
How about Pagani? Their engines are made by Mercedes/AMG. Does that mean it's any less Italian?
Maybe this will change you stance on Lamborghini
Supercars cars that use other manufacturer's engines:
-Maserati (Ferrari engines)
-Rossion Q1 (Ford engine)
-Noble M600 (volvo engine)
-Aston Martin (DB9 uses Ford-based engine)
-Ariel Atom (Honda and Suzuki engines)
-TVR Cerbera (originally a TVR engine, switched to Jaguar)
-Spyker (Audi engines)
-Koenigsegg CCX (Ford engines)