\version "2.19.80"

centerBeam =
#(define-music-function (pitch1 pitch2 dur)(ly:pitch? ly:pitch? ly:duration?)
   (let*
    ((num-beams (- (ly:duration-log dur) 2))
     (slope-dir (if (ly:pitch<? pitch1 pitch2) -1 1))
     (ratio (/ 4 (ly:moment-main-denominator (ly:duration-length dur))))
     (left-dir (* -1 slope-dir))
     (right-dir slope-dir)
     (left-pos (* left-dir (/ num-beams 2)))
     (right-pos (+ left-pos (* right-dir 1)))
     )
    (ly:message "Ratio: ~a" num-beams)
    #{
      \temporary \override NoteColumn.ignore-collision = ##t
      <<
        {
          \override Stem.length = 7
          #(make-sequential-music
            (list
             (make-music
              'OverrideProperty 'pop-first #t
              'grob-value left-dir
              'grob-property-path (list (quote direction))
              'symbol 'Stem)
             (make-music
              'NoteEvent
              'duration (ly:make-duration 2 0 ratio)
              'pitch pitch1)
             (make-music
              'OverrideProperty 'pop-first #t
              'grob-value right-dir
              'grob-property-path (list (quote direction))
              'symbol 'Stem)
             (make-music
              'NoteEvent
              'duration (ly:make-duration 2 0 ratio)
              'pitch pitch2)))

          \revert Stem.length
        }
        \\
        {

          \once \override Beam.positions = #(cons left-pos right-pos)
          %\once \override Beam.positions = #'(-1.5 . 0)
          #(make-sequential-music
            (list
             (make-music
              'OverrideProperty 'pop-first #t
              'grob-value left-dir
              'grob-property-path (list (quote direction))
              'symbol 'Stem)
             (make-music
              'NoteEvent
              'articulations (list (make-music 'BeamEvent 'span-direction -1))
              'duration dur
              'pitch pitch1)
             (make-music
              'OverrideProperty 'pop-first #t
              'grob-value right-dir
              'grob-property-path (list (quote direction))
              'symbol 'Stem)
             (make-music
              'NoteEvent
              'articulations (list (make-music 'BeamEvent 'span-direction 1))
              'duration dur
              'pitch pitch2)))

        }
      >>
      \revert NoteColumn.ignore-collision
    #}))

{
  \time 3/8
  \key a \major
  \centerBeam gis' e'' 16
  \centerBeam fis' e'' 16
  \centerBeam e' e'' 16
  \time 3/16
  \centerBeam gis' e'' 32
  \centerBeam fis' e'' 32
  \centerBeam e' e'' 32
  \time 3/4
  \centerBeam gis' e'' 8
  \centerBeam fis' e'' 8
  \centerBeam e' e'' 8
  \time 3/8
  \centerBeam gis'' e' 16
  \centerBeam fis'' e' 16
  \centerBeam e'' e' 16
}