As far as I can tell, no. However, it would be great to have some more specialized people's input on this.

There are about 170 years between them. Leonardo da Vinci apparently had no descendants, and "Vinci" was not a last name ("da Vinci" means "from this place called Vinci").

Leonardo da Vinci was into music. He played the lira and had students (also was REALLY into acoustics and instrument making), but I cannot find a way to connect both of them this way.

There is a third "Vinci." Pietro Vinci, a well respected polyphonist working in Sicily in the 16th century. As far as I can tell, he was also not related to either.

I guess it won't hurt if I put here some links to some music...

Leonardo Vinci

• Vo solcando un mar crudele, from Artaserse

• In barccio a mille furie, from La Semiramide riconosciuta

Pietro Vinci

• Some ricercari per organo