How to annotate staff with beat numbers in Lilypond?

Question

I would like to annotate a RhythmicStaff with Beat Numbers - as in the following picture:

Perhaps, one could use the '_' character after a note to add numbers connected to a note at the beginning of the beat, but how about empty beats - where there is no note or rest, but the beat still needs to be shown - like the last measures in the example image.

What would be the correct way to do this? Ideally, so that - every measure, every bar in the score is automatically annotated with the beat numbers at the correct places?

Answer 1

Some way to get this automatically:

#(define (Beat_counter_engraver context)
   (let ((measpos #f) (grouping #f) (basemom #f) (beatmom #f))
     (define (mom->dur mom)
       (let ((pair (moment->fraction mom)))
         (/ (car pair) (cdr pair))))
     (define (is-beat-moment? count gping beatcount)
       (if (= (* count (mom->dur basemom)) (mom->dur measpos))
           (+ 1 beatcount)
           (if (> (* count (mom->dur basemom)) (mom->dur measpos))
               #f
               (if (null? gping)
                   #f
                   (is-beat-moment? (+ count (car gping)) (cdr gping) (+ 1 beatcount))))))
     (make-engraver
       ((process-music engraver)
          (set! measpos (ly:context-property context 'measurePosition 'noof))
          (set! grouping (ly:context-property context 'beatStructure 'noof))
          (set! basemom (ly:context-property context 'baseMoment 'noof))
          (set! beatmom (is-beat-moment? 0 grouping 0))
          (if beatmom
            (let ((grob (ly:engraver-make-grob engraver 'TextScript '())))
                  (ly:grob-set-property! grob 'text (number->string beatmom))
                  (ly:grob-set-property! grob 'direction DOWN)
                  (ly:grob-set-property! grob 'padding 3)))))))

\layout {
  \context {
    \RhythmicStaff
    \consists #Beat_counter_engraver
  }
}

\new RhythmicStaff
{
  \set RhythmicStaff.baseMoment = #(ly:make-moment 1 16) % manually make sure base moment is 1/16
  \set RhythmicStaff.beatStructure = 3,3,3,3 % manually make sure that beats always have 3 16th
  \time 6/16
  16 16 16 16 16 16|
  r16 16 16 8.
  \time 3/16
  16[ \once\set stemRightBeamCount = 1
      \once\set stemLeftBeamCount = 1
       r16 16]
  \time 6/16
  16 16 r r8. \bar "|."
}


%% with different moments:

\new RhythmicStaff {
  \time 2/4
  8 16 16 8 16 16
  \time 3/8
  16 16 16 16 16 16
  \time 6/8
  8 16 16 8 16 16 16 16 16 16
  \time 9/7 \tuplet 7/8 { 8 8 8 8 8 8 8 8 8 }
}

which results in

One issue here is that this only works when these is some event on the beat, so if you have something like \time 4/4 8 4 8 this will not output anything on the second beat, since there is nothing there. So you might want to do something like

<< \music \repeat unfold #(floor (/ (/ (car (moment->fraction (ly:music-length music))) (cdr (moment->fraction (ly:music-length music)))) 1/16)) s16 >>

EDIT: To achieve something like your example you can also do something like this:

#(define (Beat_counter_engraver context)
   (let ((measpos #f) (grouping #f) (basemom #f) (beatmom #f))
     (define (mom->dur mom)
       (let ((pair (moment->fraction mom)))
         (/ (car pair) (cdr pair))))
     (define (is-beat-moment? count gping beatcount)
       (if (= (* count (mom->dur basemom)) (mom->dur measpos))
           (+ 1 beatcount)
           (if (> (* count (mom->dur basemom)) (mom->dur measpos))
               #f
               (if (null? gping)
                   #f
                   (is-beat-moment? (+ count (car gping)) (cdr gping) (+ 1 beatcount))))))
     (make-engraver
       ((process-music engraver)
          (set! measpos (ly:context-property context 'measurePosition 'noof))
          (set! grouping (ly:context-property context 'beatStructure 'noof))
          (set! basemom (ly:context-property context 'baseMoment 'noof))
          (set! beatmom (is-beat-moment? 0 grouping 0))
          (if beatmom
            (let ((grob (ly:engraver-make-grob engraver 'TextScript '())))
                  (ly:grob-set-property! grob 'text (number->string beatmom))
                  (ly:grob-set-property! grob 'direction DOWN)))))))

\layout {
  \context {
    \Dynamics
    \consists #Beat_counter_engraver
    \override TextScript.font-shape = ##f
    \override TextScript.Y-offset = #-0.8
    \consists Instrument_name_engraver
  }
}

sixteenth-grid-during =
#(define-music-function (m) (ly:music?)
   #{
     \repeat unfold #(floor (/ (/ (car (moment->fraction (ly:music-length m))) (cdr (moment->fraction (ly:music-length m)))) 1/16)) s16
   #})

\paper {
  ragged-last = ##f
}

musI = {
  \mark "In 3"
  \time 3/8
  8 8 16 r |
  8 16 16 8 |
  16[ 16 8 r16 16] |
  4. \bar "|."
}

>

musII = {
  \mark "In 4"
  \time 4/8
  \set Score.beatStructure = 1,1,1,1
  8 16 16~ 8 r8 |
  r16 16[ r16 16] r16 8.~ |
  4 ~ 16 8 16 |
  16 r16 4 r8 \bar "|."
}

>

which gives you

Answer 2

Try

<<
  \new RhythmicStaff
  {
    \repeat volta 2 {
      \tempo "in 3"
      \time 3/8
      8 8 16 r |
      8 16 16 8 |
      16[ 16 8 r16 16] |
    }
    \repeat volta 2 {
      \tempo "in 4"
      \time 4/8
      8 16 16~8 r |
      r16 16[ r16 16] r16 8.~ |
      4~16 8 16 |
      16 r16 4 r8 |
    }
  }
  \new Lyrics \lyricmode {
    \repeat unfold 3 { "1"8 "2" "3" | }
    \repeat unfold 4 { "1" "2" "3" "4" | }
  }
>>

The basic trick here is to use Lyrics without \addlyrics or \lyricsto, allowing you to explicitly specify the duration: "1"8 is a syllable of "1" with a duration of 8 and that duration is then used as default for everything else.