Here are some new preparatory studies for working with samba cruzado, and for getting this third surdo thing happening with the bass drum- I’ve refined my methods a bit as I’ve been working with this in my own practice.
To briefly explain what we’re about to readers who haven’t been following me on this: in a samba bateria, the first and second surdos provide the structural bass drum parts, and the third surdo plays a more syncopated solo line. In samba cruzado, played on the drum set, the left hand crosses over the right to play the first and second surdo parts on the toms (often suggesting the third as well), while the right hand emulates the tamborim or caixa on the snare drum. The bass drum usually plays a generic ostinato, which is actually made redundant by the left hand part.
So what we’re developing here is the use of the bass drum as that independent third surdo voice, while using the right hand effectively. If we were strictly trying to copy a bateria, the right hand could play a two-measure tamborim part, with variations, while the bass drum plays a four-measure semi-improvised third surdo part. Realistically, you’re probably going to have to choose between concentrating either on the right hand, with simplified bass drum accompaniment, or on the bass drum, with the right hand filling in where it can. And that usually makes the most musical sense as well- you will often want to emphasize one over the other.