\version "2.19.47"

% format seconds as min:sec
#(define-public (format-time dur)
   (let* ((minutes (floor (/ dur 60)))
          (seconds (round (- dur (* 60 minutes)) ) ))
     (format "~2'0d:~2'0d" (inexact->exact minutes) (inexact->exact seconds))
     ))

% complete duration of scores - set after finalizing
duration = #'()

% markup command to display complete time
#(define-markup-command (duration layout props scoretag)(symbol?)
   (let* ((gauge-stencil (interpret-markup layout props "00:00"))
          (x-ext (ly:stencil-extent gauge-stencil X))
          (y-ext (ly:stencil-extent gauge-stencil Y)))
     (ly:make-stencil
      `(delay-stencil-evaluation
        ,(delay (ly:stencil-expr
                 (interpret-markup layout props (format-time (ly:assoc-get scoretag duration 0 #t)))
                 )))
      x-ext y-ext)
     ))

calcDuration =
#(define-scheme-function (tag)(symbol?)
   (define (calc-duration context)
     (let ((dur 0) ; duration in seconds
            (start (ly:make-moment 0)) ; last calc-time the duration was calculated
            )
       ; function to calculate duration in seconds since last calc-time
       (define (calc-dur)
         (let ((diff (ly:moment-sub (ly:context-now context) start) ) ; moment since last calc-time
                (tempo (ly:context-property context 'tempoWholesPerMinute (ly:make-moment 60/4)) )) ; current tempo
           (set! start (ly:context-now context)) ; set calc-time
           (set! dur ; add 60*(diff/tempo) to duration
                 ; if tempo is 120 BPM and 120/4 elapsed,
                 ; we have 60 * 120/4 * 4/120 = 60 seconds
                 (+ dur
                   (* 60
                     (exact->inexact (ly:moment-main (ly:moment-div diff tempo)))
                     )))
           dur
           ))
       (make-engraver
        (acknowledgers
         ((volta-bracket-interface engraver grob source-engraver)
          (ly:message "saw volta bracket @ ~A" (ly:context-now context)))
         ((bar-line-interface engraver grob source-engraver)
          (let ((bar (ly:context-property context 'whichBar)))
            (if (not (equal? "|" bar)) (ly:message "bar ~A" bar))
          ))
         )
        (listeners
         ((tempo-change-event engraver event)
          (calc-dur) ; calculate duration on every tempo-change-event (new tempo will be set after we listened to the event)
          (ly:message "duration: ~A" (format-time dur))
          )
         ) ; listeners
        ((finalize trans)
         (calc-dur) ; last calculation of duration
         (set! duration (assoc-set! duration tag dur)) ; set global duration (for the markup command)
         (ly:message "duration: ~A final" (format-time dur))
         )
        )))
   #{ \with { \consists #calc-duration } #}
   )

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% example

% TODO repeats are not included !!

meta = { \tempo 4=90 s1*4 | \tempo 4=120 \repeat volta 3 { s1*4 } \alternative { { s1 } { s1*2 } { \tempo 4=100 s1 } } s1*4 }

\score {
  \new Staff <<
    \meta
    \repeat unfold 32 \relative c'' { bes4 a c b }
  >>
  \layout {
    \context {
      \Score
      \calcDuration scoreBACH
    }
  }
  \midi { }
}

\markup {
  \box \duration #'scoreBACH
}