Here is the official word from Triumph as found in the manual.
"All Triumph engines must be filled with a 15W/50, semi-synthetic or fully-synthetic motorcycle oil which meets API SG (or higher) AND JASO MA specification."
By "All Triumph engines", I'm quite sure they mean Hinkley Triumphs. I really doubt 15W/anything would work well in a Speedtwin with half million miles on it.
So, as long as it meets the spec, anything should work, but some will work better than others in any particular engine.
