Re: Automatically identify beats

[Aaron Hill]

On 2018-10-06 10:01 am, Daniel Sales wrote:
> Hi, is it possible to identify the beats on each different timing
> automatically, in order to set a different color for strong, medium
> and weak beats ?
>
> something like
>
> \coloredBeats <color_for_strong_beat> <color_for_medium_beat>
> <color_for_weak_beat> (black as default)
> ...
>
> For example, the expected output for
>
> \score {
>   \new Staff  {
>     \coloredBeats #red #green #black
>     \time 2/4 a4 b |
>     \time 3/4 a4 b c |
>     \time 4/4 a4 b c d |
>     \time 6/8 f8 g a b c d
>   }
> }
>
>  would be equivalent to:
>
> strongBeat = {
>     \override NoteHead.color = #red
>     \override Stem.color = #red
> }
> mediumBeat = {
>     \override NoteHead.color = #green
>     \override Stem.color = #green
> }
> weakBeat = {
>     \override NoteHead.color = #black
>     \override Stem.color = #black
> }
> \score {
>   \new Staff  {
>     \time 2/4 \strongBeat a4 \weakBeat b |
>     \time 3/4 \strongBeat a4 \mediumBeat b \weakBeat c |
>     \time 4/4 \strongBeat a4 \weakBeat b \mediumBeat c \weakBeat d |
>     \time 6/8 \strongBeat f8 \mediumBeat g \weakBeat a \strongBeat b
> \mediumBeat c \weakBeat d
>   }
> }

Hi Daniel,

The biggest hurdle as I see it is computationally determining what is 
meant by "strong", "medium", and "weak".  Those labels might have an 
intuitive understanding by musicians, but for computers they require 
additional input.

For instance, 6/8 timing could be thought of as "1 2 3 / 4 5 6" or "1 2 
/ 3 4 / 5 6".  Aside from other possible subdivisions, these two timing 
options each could have different degrees of emphasis applied (e.g. "S M 
W / S M W", "S W W / M W W", "S W / M W / M W" ...).  As such, the time 
signature alone is not enough information for a computer to be able to 
color note heads correctly.

So, let me propose an alternative to your original interface that will 
hopefully be both useful and easier to implement/maintain:

%%%%
\version "2.19.82"

#(define (rational-color-pair? x)
  (and (pair? x) (rational? (car x)) (color? (cdr x))))
#(define (rational-color-pair-list? x)
  (and (list? x) (rational-color-pair? (car x))
    (or (null? (cdr x)) (rational-color-pair-list? (cdr x)))))
colorizeBeats = #(define-music-function (args)
  (rational-color-pair-list?)
  "Conditionally overrides the color of the note head based on
   its position within a measure."
  #{ \override NoteHead.color = #(lambda (grob)
       (let* ((moment (grob::rhythmic-location grob))
              (matches? (lambda (m r)
                (eqv? 0 (ly:moment-main-numerator
                  (ly:moment-mod m (ly:make-moment r))))))
              (color (assoc (cdr moment) args matches?)))
        (if color (cdr color)))) #} )

{
  \colorizeBeats #(list (cons 1/2 (x11-color 'red))
                        (cons 3/8 (x11-color 'orange)))
  \time 4/4 \repeat unfold 16 { b'8 }
  \colorizeBeats #(list (cons 3/8 (x11-color 'red))
                        (cons 3/16 (x11-color 'orange)))
  \time 6/8 \repeat unfold 2 { b'8 8 8 8. 8. }
  \colorizeBeats #(list (cons 1/4 (x11-color 'red))
                        (cons 1/12 (x11-color 'orange)))
  \time 5/4 \repeat unfold 2 { b'2 \tuplet 3/2 { 8 8 8 } 4 8 8 }
}
%%%%

This approach does not attempt to parse the time signature but rather 
requires the user to provide a list of time intervals and their desired 
color.  Note that the first rule in the list that matches will be 
applied, so the ordering within the list is important.

In the example provided, the first section highlights in red every half 
note (or more precisely, every note that *aligns* to a half note) and in 
orange every dotted quarter.  The second highlights dotted quarters and 
dotted eighths in a similar manner.  The third example shows the effect 
working with tuplets by coloring so-called "twelfth" notes.

-- Aaron Hill

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