I'm guessing since you have a BA you don't have a tach, but if you experience the same vibration when winding out in lower gears, have your carbs balanced. Triumphs like ours are susceptible to engine vibration in the 3000-4000 rpm range (right about 55-65 mph in top gear) when the carbs go out of synch. My SM had exactly the same problem which disappeared after I synched the carbs, and while I know the crank offset is different on the BA vs. the SM, the problem is the same.
