\version "2.20.0"

#(define (split-music dir music ref)
   (let ((es (ly:music-property music 'elements))
         (e (ly:music-property music 'element))
         (p (ly:music-property music 'pitch)))
     (if (pair? es)
         (ly:music-set-property!
          music 'elements
          (map (lambda (x) (split-music dir x ref)) es)))
     (if (ly:music? e)
         (ly:music-set-property!
          music 'element
          (split-music dir e ref)))
     (if (ly:pitch? p)
         (if ((if (> dir 0) >= <)
              (ly:pitch-steps p) (ly:pitch-steps ref))
             p
             (ly:music-set-property! music 'name 'SkipEvent) % works, but produces warnings
             ))
     music
     ))

splitMusic =
#(define-music-function (parser location dir ref music )
   ((ly:dir? 1) (ly:pitch? (ly:make-pitch 0 0)) ly:music? )
   (split-music dir music ref))

%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Examples

someMusic = {
  c d e g c' d' c''
  <c e' g'>
  \chordmode{d:7/a}
  << {c' d' e' f'} \\ {c d e f}>>
  d'2.
  \relative c' {c1 b a g}
  << \chordmode { c4 d e f} \\ \transpose c c, \chordmode {c d e f}>>
  << {c' b e' f'} \\ {c, e, c2} \\ {g2 a4 b}>>
}

\markup "Some music"
{\someMusic}

\markup "\SplitMusic result on piano staff"
\new PianoStaff
<<
  \new Staff {\splitMusic \someMusic}
  \new Staff {
    \clef bass
    \splitMusic #DOWN \someMusic
  }
>>

\markup "\SplitMusic result on SATB (with arbitrary split-points)"
\new StaffGroup
<<
  \new Staff {
    \clef soprano
    \splitMusic #UP f' \someMusic
  }
  \new Staff {
    \clef alto
    \splitMusic #DOWN f' \splitMusic #UP a \someMusic
  }
  \new Staff {
    \clef tenor
    \splitMusic #DOWN a \splitMusic #UP d \someMusic
  }
  \new Staff {
    \clef baritone
    \splitMusic #DOWN d \someMusic
  }
>>