Odd, distinctive rhythm? Compared to what?
The Harley is a V-twin -vs- most rice-rockets that are inline-4s.
The popular Harleys generally have more cc-(1300-1500, where inline-4s have 600-1100)
They do make smaller cc Harleys, but they are rather wimpy sounding.
An inline-4 fires 4 times in the same time a V-twin only fires 2, so the sound waves are closer together and tend to reflect off each other, where the V-twin has pauses.
So the engine has larger cylinders than inline-4s, thus you get a deeper tone. Compare a chevy 350 -v- Chevy 454, much deeper sound. An inline-4 with straight pipes makes a lawnmower type "bap bap bap", where the V-twin makes the "thump thump thump".
Suzuki makes a few V-twin sport bikes, and with a nice exhaust, sound sweet.
Here is a link, the exhaust clip is a Suzuki SV650 with a Renegade single exhaust pipe.
Sound Clip-on Renegade home page
Link to a picture of this sport bike->
SV650 with renegade exhaust