\version "2.20.0"

#(define (make-autosplit-chord chord . ref-pitch)
   "Return a pair of lists, containing the pitches of @var{chord}, splitted at
a reference pitch.  The reference pitch is derived from @var{ref-pitch}.
If @var{ref-pitch} is empty, @code{c'} is regarded as reference.
  "
   (define ref-pitch-steps
     (if (and (pair? ref-pitch) (car ref-pitch))
         (ly:pitch-steps (car ref-pitch))
         0))

   (call-with-values
    (lambda ()
      (partition
       (lambda (note)
         (> (ly:pitch-steps (ly:music-property note 'pitch))
            ref-pitch-steps))
       (event-chord-notes chord)))
    (lambda (x y) (cons x y))))

autoSplitChord =
#(define-music-function (stem-dir staff-names pitch chord)
   ((ly:dir? 0) (pair? '("up" . "down")) (ly:pitch?) ly:music?)
   (_i "Split @var{chord} at optional @var{pitch}.  The default of @var{pitch} is
@code{#f}, which is interpreted by the called procedure
@code{make-autosplit-chord} as @code{c'}.

The splitted chords are distributed to named staves, relying on optional
@var{staff-names}.

The optional @var{stem-dir}, determines the direction of the stems and whether
the chords may be connected by a cross-staff stem.
The default results in unconnected chords.
If the @code{Span_stem_engraver} is consisted, the chords may be connected by a
cross-staff stem.")
   (if (music-is-of-type? chord 'event-chord)
       (let* ((skip (make-duration-of-length (ly:music-length chord)))
              (devided-pitches (make-autosplit-chord chord pitch))
              (upper-chord
               (if (pair? (car devided-pitches))
                   (make-event-chord (car devided-pitches))
                   (make-skip-music skip)))
              (lower-chord
               (if (pair? (cdr devided-pitches))
                   (make-event-chord (cdr devided-pitches))
                   (make-skip-music skip))))
         #{
           <<
             \context Staff = #(car staff-names)
             \context Voice {
               $(if (negative? stem-dir)
                    #{
                      \once \override Stem.cross-staff = #cross-staff-connect
                      \once \override Flag.style = #'no-flag
                      <>\noBeam
                    #})
               $(if (not (zero? stem-dir))
                    #{ \once \override Stem.direction = #stem-dir #})
               #upper-chord
             }

             \context Staff = #(cdr staff-names)
             \context Voice {
               $(if (positive? stem-dir)
                    #{
                      \once \override Stem.cross-staff = #cross-staff-connect
                      \once \override Flag.style = #'no-flag
                      <>\noBeam
                    #})
               $(if (not (zero? stem-dir))
                    #{ \once \override Stem.direction = #stem-dir #})
               #lower-chord
             }
           >>
         #})
       #{ \context Staff $chord #}))

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% TESTS
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Pippo = <c e g c' e'>1
PippoDue = \chordmode {c1:/g}
PippoTre = c1
PippoQuattro = {<c e g>}

\new PianoStaff
\with { \consists #Span_stem_engraver }
<<
  \new Staff = "up"
  {
    \key c\major
    \autoSplitChord #UP <f a a' f'>2
    \autoSplitChord <g c' e'>4
    \autoSplitChord #DOWN <g c' e'>
    \autoSplitChord <c g e' c''>1
    \autoSplitChord \chordmode {c:/g}
    \autoSplitChord {<c g e' c''>}
    \autoSplitChord {<c e g> <d	 f a>}
    \autoSplitChord c
    \autoSplitChord <c'>
    \autoSplitChord <<c\\e'\\g''\\g,>>
    \autoSplitChord <<c1\\e'2\\g''\\g,>>
    \autoSplitChord <<c1 \\ {e2 f}\\d'1>>
    \autoSplitChord <<
      {c4 d e f}
      \\
      {c' d' e' f'}
    >>
    \autoSplitChord \Pippo
    \autoSplitChord \PippoDue
    \autoSplitChord \PippoTre
    \autoSplitChord \PippoQuattro
  }
  \new Staff = "down"
  {
    \key c\major
    \clef bass
    s1 %bass staff appear only at the beginning, then reappears as another staff with treble clef
  }
>>

\new PianoStaff
\with { \consists #Span_stem_engraver }
<<
  \new Staff = "up"
  {
    \key c\major
    \autoSplitChord #UP <f a a' f'>2
    \autoSplitChord <g c' e'>4
    \autoSplitChord #DOWN <g c' e'>
    \autoSplitChord <c g e' c''>1
    \autoSplitChord \chordmode {c:/g}
    \autoSplitChord {<c g e' c''>}
    \autoSplitChord {<c e g> <d	 f a>}
    \autoSplitChord c
    \autoSplitChord <c'>
    \autoSplitChord <<c\\e'\\g''\\g,>>
    \autoSplitChord <<c1\\e'2\\g''\\g,>>
    \autoSplitChord <<c1 \\ {e2 f}\\d'1>>
    \autoSplitChord <<
      {c4 d e f}
      \\
      {c' d' e' f'}
    >>
    \autoSplitChord \Pippo
    \autoSplitChord \PippoDue
    \autoSplitChord \PippoTre
    \autoSplitChord \PippoQuattro
  }
  \new Staff = "down"
  {
    \key c\major
    \clef bass
    \repeat unfold 16 s1 %bass staff is shown correctly
  }
>>