Adjusting slur positions vertically

Using \override Slur.positions it is possible to set the vertical position of the start and end points of a slur to absolute values (or rather, forcing LilyPond's slur algorithm to consider these values as desired). In many cases, this means a lot of trial and error until good values are found. You probably have tried the \offset command next just to find out that it doesn't work for slurs, emitting a warning instead.

The code in this snippet allows you to tweak the vertical start and end positions by specifying relative changes, similar to \offset.

Syntax: \offsetPositions #'(dy1 . dy2)

\version "2.24"

offsetPositions =
#(define-music-function (offsets) (number-pair?)
  #{
     \once \override Slur.control-points =
       #(lambda (grob)
          (match-let ((((_ . y1) _ _ (_ . y2))
                       (ly:slur::calc-control-points grob))
                      ((off1 . off2) offsets))
            (set! (ly:grob-property grob 'positions)
                  (cons (+ y1 off1) (+ y2 off2)))
            (ly:slur::calc-control-points grob)))
  #})

\relative c'' {
  c4(^"default" c, d2)
  \offsetPositions #'(0 . 1)
  c'4(^"(0 . 1)" c, d2)
  \offsetPositions #'(0 . 2)
  c'4(^"(0 . 2)" c, d2)
  \bar "||"
  g4(^"default" a d'2)
  \offsetPositions #'(1 . 0)
  g,,4(^"(1 . 0)" a d'2)
  \offsetPositions #'(2 . 0)
  g,,4(^"(2 . 0)" a d'2)
}