Jarman will have a chance of another medal in the final for the vault (15:24 BST on Sunday), an apparatus on which he is the world champion.
There are also other medal chances for Great Britain on Saturday, with Max Whitlock seeking to defend his pommel horse title (16:16 BST) and Harry Hepworth competing in the rings and vault finals.
Jarman, from Peterborough, trains at the same Huntingdon gym that produced Louis Smith, whose pommel horse bronze at Beijing 2008 was the first time a British gymnast had placed in an Olympic event for 80 years.
That medal marked the start of this successful period for the nation’s gymnasts, who have now won medals at every Games since.
In Paris, Jarman’s floor medal came the day after trampoline gymnast Bryony Page won gold.