curveSin =
#(lambda (x)
   (* 12 (sin (/ x 4))))

curveTan =
#(lambda (x)
   (tan x))

curveGauss =
#(lambda (x)
   (let ((sigma 0.028)
         (mu 127)
         (tau 6.283185307179586))
     (*
      (/ 1 (* sigma (sqrt tau)))
      (exp (/
            (- (expt (- x mu) 2))
            (* 2 (expt sigma 2)))))))

curveSqrt =
#(lambda (x)
   (* (sqrt x) 2))

curveSquare =
#(lambda (x)
   (expt x 2))

curveExp =
#(lambda (x)
   (exp x))

limit = #512

#(define notes
   (list
    (ly:make-pitch 0 0)
    (ly:make-pitch 0 0 1/2)
    (ly:make-pitch 0 1)
    (ly:make-pitch 0 1 1/2)
    (ly:make-pitch 0 2)
    (ly:make-pitch 0 3)
    (ly:make-pitch 0 3 1/2)
    (ly:make-pitch 0 4)
    (ly:make-pitch 0 4 1/2)
    (ly:make-pitch 0 5)
    (ly:make-pitch 0 6 -1/2)
    (ly:make-pitch 0 6)
    ))
sequence =
#(define-music-function (note function end)
   (ly:music? procedure? integer?)

   (define (safe-list-ref ls x)
     (let* ((z (length ls))
            (result (list-ref ls (remainder (abs x) z))))
       (if (negative? x)
           (ly:pitch-negate result)
           result)))

   (define (safe-inexact->exact x threshold)
     (let ((z (inexact->exact x)))
       (if (or (> z threshold)
               (< z (- threshold)))
           (- z)
           z)))

   (let ((music-list (list note))
         (start-pitch (ly:music-property note 'pitch)))
     (do ((x 1 (1+ x)))
         ((> x end))
       (set! music-list
        (append music-list
          (list
           (ly:music-transpose
            (ly:music-deep-copy note)
            (ly:make-pitch 0
              (safe-inexact->exact
               (round (function x))
               2000000000)))))))
     (make-sequential-music music-list)))

\markup \fill-line { \huge \smallCaps Sinus }
\new PianoStaff
  \autochange { \sequence c'16 #curveSin #limit }

\pageBreak

\markup \fill-line { \huge \smallCaps Gauss }
\new PianoStaff
  \autochange { \sequence c'16 #curveGauss #255 }

\pageBreak

\markup \fill-line { \huge \smallCaps Racine }
\new PianoStaff
  \autochange { \transpose c c,, \sequence c'16 #curveSqrt #limit }

\pageBreak

\markup \fill-line { \huge \smallCaps Exposant }
\new PianoStaff
  \autochange { \transpose c a,,, \sequence c'16 #curveSquare #11 }

\pageBreak

\markup \fill-line { \huge \smallCaps Exponentielle }
\new PianoStaff
  \autochange { \transpose c e,,, \sequence c'8 #curveExp #5 }

\pageBreak

\markup \fill-line { \huge \smallCaps Tangente }
\new PianoStaff
  \autochange { \sequence c'16 #curveTan #limit }