Since everybody wants to be serious and we are REALLY going to have another oil thread
Triumphs new spec is 10w-50 for the 675
Yes yes I know a bunch of owners manuals say 10w-40 but that is because Mobile didn't have a 10w-50 MC oil when they where the "official" Triumph oil partner.
They fill with Castrol 10w-40 semi-synthetic at the factory and recommend (but not require) that you go 10w-50 full synthetic after the first oil change.
I run ELF MOTO 4 XT Tech 10w-50 (available under Kawasaki private label branding in the US) in all my bikes and to fry my chips.