\version "2.19.6"
#(define ((custom-time-signature one two) grob)
   ;; derived from
   ;; http://lilypond.1069038.n5.nabble.com/Mixed-Time-Signatures-Non-regular-alternantion-between-5-8-and-8-8-td18617.html
   (let ((numOne (number->string (car one)))
          (denOne (number->string (cdr one)))
          (numTwo (number->string (car two)))
          (denTwo (number->string (cdr two))))
   (grob-interpret-markup grob
     (markup #:override '(baseline-skip . 0) #:number
       (#:line ((#:column (numOne denOne))
                (#:column (numTwo denTwo))))))))


alternatingTimeSignatures =
#(define-music-function (parser location timesigs)
   (list?)
   (let* ((sigOne (car timesigs))
          (sigTwo (cadr timesigs)))
     #{
       \override Score.TimeSignature.stencil =
         #(custom-time-signature sigOne sigTwo)
       \time #sigOne
     #}
     ))

\relative c' {
  \alternatingTimeSignatures #'((3 . 8) (4 . 8))
  c8 d e
  \omit Score.TimeSignature
  \time 4/8
  f g a b
  \time 3/8
  c g c,
  d e f
  g a b
  \time 4/8
  c b a b
  \revert Score.TimeSignature.stencil
  \time 5/8
  c b a g f
  
}

\relative c' {
  \override TupletNumber.text = #tuplet-number::calc-fraction-text
  \alternatingTimeSignatures #'((3 . 4) (4 . 7))
  c4 d e
  \omit Score.TimeSignature
  \time 4/7
  \tupletSpan 4*16/7
  \tuplet 7/4 {
    f e f fis
    g a ais b
  }
  \time 3/4
  c4 g c,
}