dotted semicircle indicating harmonics

[sylvius]

Hi all,

I’m trying to draw a dotted semicircle above and below a note head to indicate harmonics (as shown in the picture).

This is what I’ve achieved so far with LilyPond but it’s far from perfect. (I didn’t manage to typeset a dotted semicircle. There still are some collisions…)

%%%%

\version "2.21.0"

semicircle = \markup { 
  \postscript #"2 0 moveto 1 0 1  0 
                180 arc 0.2 setlinewidth  stroke"
}
semicircleDown = \markup { 
  \postscript #"2 0 moveto 1 0 1  0 
                180 arc 0.2 setlinewidth  stroke"
}

semicircleUp = \markup { 
  \postscript #"0 0 moveto 1 0 -1  0 
                180 arc 0.2 setlinewidth  stroke"
}
music = { 
  \key g \major
  \time 6/8
  
  <fis'_3 d''^2>4 r8 
  %\once \override Script.script-priority = #-100
  <d'_3>4^\semicircleDown _\markup { %\rotate #180 %\halign #1 \semicircle
    \semicircleUp} 
    ^"harm:" r8
}

\score {
  \music
}

%%%%

Any hint is greatly appreciated!

Thanks

Sylvius