No, Harley-Davidson does not have a patent on the sound of its motorcycle engines or the internal construction that creates the sound. The distinctive sound produced by Harley-Davidson motorcycles, often referred to as the "Harley sound" or "potato-potato sound," is a result of several factors, including the V-twin engine configuration, firing order, exhaust system design, and other engineering aspects.
While the sound of Harley-Davidson motorcycles is iconic and often associated with the brand, it is not protected by a patent. Sound itself generally cannot be patented, as patents are granted for inventions or processes rather than natural phenomena like sound.