%% Creates a (optionally rounded) bracket with a gap in the middle.
%% lx = left x position, ly = left y position, rx, ry similar for right
%% p = the length of the protruders
%% th = line thickness
%% gap-w = horizontal width of the gap
%% rounded? = whether to create a round bracket
#(define (make-bracket-gap lx ly rx ry p th gap-w rounded?)
   (if rounded?
       (let* ((width (- rx lx))
              (height (- ry ly))
              (sep-width (/ (- width gap-w) 2))
              (sep-height (* height (/ sep-width width)))
              (line-left (make-path-stencil
                          `(moveto ,lx ,(+ ly p)
                            curveto 
                             ,(+ lx (* sep-width 1/5)) ,(+ ly (* sep-height 1/5))
                             ,(+ lx (* sep-width 2/3)) ,(+ ly (* sep-height 2/3))
                             ,(+ lx sep-width) ,(+ ly sep-height)) th 1 1 #f))
              (line-right (make-path-stencil
                          `(moveto ,rx ,(+ ry p)
                            curveto 
                             ,(- rx (* sep-width 1/5)) ,(- ry (* sep-height 1/5))
                             ,(- rx (* sep-width 2/3)) ,(- ry (* sep-height 2/3))
                             ,(- rx sep-width) ,(- ry sep-height)) th 1 1 #f)))
         (ly:stencil-add line-left line-right))
       (let* ((width (- rx lx))
              (height (- ry ly))
              (sep-width (/ (- width gap-w) 2))
              (sep-height (* height (/ sep-width width)))
              (line-left (make-line-stencil th lx ly
                                            (+ lx sep-width) (+ ly sep-height)))
              (line-right (make-line-stencil th rx ry
                                             (- rx sep-width) (- ry sep-height)))
              (prot-left (make-line-stencil th lx (+ ly p) lx ly))
              (prot-right (make-line-stencil th rx (+ ry p) rx ry)))
         (ly:stencil-add line-left line-right prot-left prot-right))))

%% create bracket with text in gap. Take text, direction, rounded from grob
#(define (center-text-gap L R p th grob)
   (let* ((text (ly:grob-property grob 'text ""))
          (direction (ly:grob-property grob 'direction UP))
          (lx (+ (car L) (* 2 th)))
          (rx (- (car R) (* 2 th)))
          (p (* p direction))
          (dir (if (< p 0) -1 1))
          (ly (- (cdr L) p))
          (ry (- (cdr R) p))
          (outside-staff-p (ly:grob-property grob 'outside-staff-priority))
          (is-outside-staff (number? outside-staff-p))
          (ly (if is-outside-staff (* dir (min (* dir ly) -4)) ly))
          (ry (if is-outside-staff (* dir (min (* dir ry) -4)) ry))
          (det (ly:grob-property grob 'details))
          (rounded? (assoc-get 'rounded det #t))
          (texs (grob-interpret-markup grob text))
          (ctex (ly:stencil-aligned-to (ly:stencil-aligned-to texs X CENTER) Y CENTER))
          (texex (ly:stencil-extent ctex X))
          (tex-width (interval-length texex))
          (brack (make-bracket-gap lx ly rx ry p th (+ tex-width 0.7) rounded?))
          (tex-tr (ly:stencil-translate ctex (cons (/ (+ lx rx) 2)
                                                   (/ (+ ly ry) 2)))))
     (ly:stencil-add brack tex-tr)))

%% print a slur as bracket with text
#(define (slur->bracket grob)
   (let* ((cpts (ly:grob-property grob 'control-points))
          (L (first cpts))
          (R (last cpts)))
     (center-text-gap L R -1 0.15 grob)))

#(define* ((from-details symb #:optional default) grob)
   (let ((det (ly:grob-property grob 'details)))
     (ly:assoc-get symb det default)))

hbracketStart = \tweak direction #(from-details 'direction DOWN)
                \tweak stencil #slur->bracket
                \tweak outside-staff-priority #(from-details 'outside-staff-priority)
                \="hb"(
hbracketStop = \="hb")

hb =
#(define-music-function (text rounded music) (markup? boolean? ly:music?)
   #{
     {
       <>\tweak text #text \tweak details.rounded #rounded \hbracketStart
       #music
       <>\hbracketStop
     }
   #})

hbT = \hb "T" ##f \etc
hbS = \hb "S" ##t \etc

%%% EXAMPLE

\paper {
  indent = 0
}

\score {
  \relative {
  \omit Score.TimeSignature
  \omit Score.BarLine
  \hbT c'1 
  \hbT d
  \hbS e
  \hbT f
  \hbT g
  \hbT a
  \hbS b
  \hbT c 
  \hbT d
  \hbS e
  \hbT f
  \hbT g
  \hbT a
  \hbS b
  c
  \break
  
  \override Slur.details.direction = #UP
  \hbT c,,1 
  \hbT d
  \hbS e
  \hbT f
  \hbT g
  \hbT a
  \hbS b
  \hbT c 
  \hbT d
  \hbS e
  \hbT f
  \hbT g
  \hbT a
  \hbS b
  c
  \break

  \override Slur.details.outside-staff-priority = #500
  \hbT c,,1 
  \hbT d
  \hbS e
  \hbT f
  \hbT g
  \hbT a
  \hbS b
  \hbT c 
  \hbT d
  \hbS e
  \hbT f
  \hbT g
  \hbT a
  \hbS b
  c
  \break
  
  \revert Slur.details.direction
  \hbT c,,1 
  \hbT d
  \hbS e
  \hbT f
  \hbT g
  \hbT a
  \hbS b
  \hbT c 
  \hbT d
  \hbS e
  \hbT f
  \hbT g
  \hbT a
  \hbS b
  c\break
  
  \override Slur.font-series = #'bold
  \override Slur.font-shape = #'italic
  \hbT c,,1 
  \hbT d
  \hbS e
  \hbT f
  \hbT g
  \hbT a
  \hbS b
  \hbT c 
  \hbT d
  \hbS e
  \hbT f
  \hbT g
  \hbT a
  \hbS b
  c
  }
  \layout {
  }
}