Re: Questions about HorizontalBracket

[Lukas-Fabian Moser]

Hi Francesco,

> I’m trying to use HorizontalBracket to annotate the intervals between notes of 
> a scale.
>
> The example (perhaps not minimal, but almost working) attached shows something 
> very close to what I want to achieve.
>
> However there are a few things that need to be fixed, or improved:
> 1) the brackets remain outside the staff no matter how I fiddle with staff-
> padding and padding properties, while I would like them to stay closer to the 
> notes;
> 2) I cannot find an (obvious and) automatic way to have the ends of a bracket 
> to align with the center of the note heads. I found a manual workaround by 
> setting the shorten-pair property, which is a far from being an optimal 
> solution;
> 3) is there a way to create a V-shaped bracket? The hack I came up with is 
> ugly;
> 4) to have brackets both above and below the notes I have used two voices, one 
> with the notes hidden. Is there a faster/less verbose way to obtain the same 
> result?
>
> Besides these, it would be nice (but not essential) to have these bracket to 
> also follow the slope of an interval.
>

LilyPond's horizontal brackets are not very flexible, as far as I know. But it occurred to me that for everything you listed, the necessary mechanisms are in LilyPond as part of the mechanism typesetting slurs: 1), 2) is automatic for slurs, 3) is a matter of distorting a slur to a simple three-point line, and 4) is possible by virtue of the \=... construct.

Hence, how about:

\version "2.21.0"

% Some routines for calculating with 2D vectors (given as scheme pairs)
#(define (vector-sum v w)
   (cons (+ (car v) (car w))
         (+ (cdr v) (cdr w))))

#(define (vector-factor factor v)
   (cons (* (car v) factor)
         (* (cdr v) factor)))

#(define (scalar-product v w)
   (+ (* (car v) (car w))
      (* (cdr v) (cdr w))))

#(define (midpoint p1 p2)
   (vector-factor 1/2 (vector-sum p1 p2)))

#(define (normal p q)
   ; yields a normal vector to the line from p to q.
   ; the length of the normal vector will be proportional to
   ; the distance [pq].
   (cons (- (cdr p) (cdr q))
         (- (car q) (car p))))

#(define (side v normal start)
   ; A line through "start" with fixed normal vector "normal" cuts the plane
   ; into two half-planes. This function returns
   ; 0 if v lies on the line itself,
   ; +1 if v lies in the half plane that the normal vector points to,
   ; -1 otherwise.
   (let ((dist (- (scalar-product normal v)
                  (scalar-product normal start))))
     (cond ((> dist 0) 1) ; is there no "sgn" function in guile?!
           ((< dist 0) -1)
           (else 0))
     ))

% Shortcuts for using pairs inside a \markup \path ...
#(define (moveto p) (list 'moveto (car p) (cdr p)))
#(define (lineto p) (list 'lineto (car p) (cdr p)))

VShapeSlur =
\tweak stencil
#(lambda (grob)
   (let* ((control-points (ly:grob-property grob 'control-points))
          (start (first control-points))
          (1st-directional-point (second control-points))
          (2nd-directional-point (third control-points))
          (stop (fourth control-points)))
     (grob-interpret-markup grob #{
       \markup {
         \path #0.1 #(list (moveto start)
                           (lineto (midpoint 1st-directional-point 2nd-directional-point))
                           (lineto stop))
       } #})))
\etc

bracketSlur =
\tweak stencil
#(lambda (grob)
   (let* ((control-points (ly:grob-property grob 'control-points))
          (start (first control-points))
          (1st-directional-point (second control-points))
          (stop (fourth control-points))
          (normal (normal start stop))
          (scaled-normal
           (vector-factor
            (* 0.075 (side 1st-directional-point normal start))
            normal)))
     (grob-interpret-markup grob #{
       \markup {
         \path #0.1
         #(list (moveto start)
                (lineto (vector-sum start scaled-normal))
                (lineto (vector-sum stop scaled-normal))
                (lineto stop))
       } #})))
\etc

\relative c' {
  c1 \bracketSlur ( d) e \bracketSlur( f g a g f')
  c,1 \VShapeSlur ( d) e \VShapeSlur( f g a g f')
}

\relative c' {
  c4 \VShapeSlur \=0_( \VShapeSlur \=1^( d e \bracketSlur \=2_( f\=1) e d\=2) c b\=0)
}

Best
Lukas