Best way to center beam between upper/lower staff?

[Andy Bradford]

Hello,

This has to be a FAQ, yet all my searching turned up a mixed bag.

I'm trying to have some notes cross from the lower staff to the upper staff but 
want the beam to automatically center.  In my example this is accomplished in 
measure 3 with much manual work.  Is there a better way?


%%%%%%%
\version "2.22.2"

\score {
  <<
    \new PianoStaff {
      <<
        \new Staff = "up" {
          <<
            \new Voice {
              \relative c'' {
                R1 
                a4 g f e
                e f g a
              }
            }
          >>
        }
        \new Staff = "down" {
          <<
            \clef "bass"
            \new Voice {
              \relative c {
                \voiceOne
                d4 e f g
                r8 a \change Staff = "up" c \change Staff = "down" a \change 
Staff = "up" d \change Staff = "down" a \change Staff = "up" e' \change Staff = 
"down" r
                r8 a, \change Staff = "up" \stemDown c \change Staff = "down" 
\stemUp a \change Staff = "up" \stemDown d \change Staff = "down" \stemUp a 
\change Staff = "up" \stemDown e' \change Staff = "down" \stemNeutral r
              }
            }
          >>
        }
      >>
    }
  >>
}
%%%%%%%

Thanks,

Andy