# LSR/743/code

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```
%% http://lsr.di.unimi.it/LSR/Item?id=743
%% see also http://lsr.di.unimi.it/LSR/Item?id=835
%% see also http://lilypond.org/doc/v2.18/Documentation/snippets/rhythms#rhythms-compound-time-signatures
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% LSR workaround:
#(set! paper-alist (cons '("snippet" . (cons (* 210 mm) (* 220 mm))) paper-alist))
\paper {
#(set-paper-size "snippet")
tagline = ##f
indent = 0
}
\markup\vspace #.5
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\relative c' {
\compoundMeter #'(1 2 3 4 8)
\repeat unfold 10 c8 \repeat unfold 20 c16\break
\time 3/4
\repeat unfold 6 c8 \repeat unfold 12 c16\break
\compoundMeter #'((1 2 3 4 8) (2 4))
\repeat unfold 14 c8 \repeat unfold 28 c16\break
\compoundMeter #'((1 2 3 4 8) (2 4) (2 3 8))
\repeat unfold 19 c8 \repeat unfold 38 c16\break
\compoundMeter #'(1 2 3 4 8)
\repeat unfold 10 c8 \repeat unfold 20 c16\break
\compoundMeter #'((1 8) (3 8))
\repeat unfold 4 c8 \repeat unfold 8 c16\break
\compoundMeter #'((3 8) (1 8))
\repeat unfold 4 c8 \repeat unfold 8 c16\break
\time 4/4
\repeat unfold 8 c8 \repeat unfold 16 c16\break
\bar"|."
}
%{
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Formatting of (possibly complex) compound time signatures
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
#(define (insert-markups l m)
(let* ((ll (reverse l)))
(let join-markups ((markups (list (car ll)))
(remaining (cdr ll)))
(if (pair? remaining)
(join-markups (cons (car remaining) (cons m markups)) (cdr remaining))
markups))))
% Use a centered-column inside a left-column, because the centered column
% moves its reference point to the center, which the left-column undoes.
#(define (format-time-fraction time-sig-fraction)
(let* ((revargs (reverse (map number->string time-sig-fraction)))
(den (car revargs))
(nums (reverse (cdr revargs))))
(make-override-markup '(baseline-skip . 0)
(make-number-markup
(make-left-column-markup (list
(make-center-column-markup (list
(make-line-markup (insert-markups nums "+"))
den))))))))
#(define (format-complex-compound-time time-sig)
(let* ((sigs (map format-time-fraction time-sig)))
(make-override-markup '(baseline-skip . 0)
(make-number-markup
(make-line-markup
(insert-markups sigs (make-vcenter-markup "+")))))))
#(define-public (format-compound-time time-sig)
(cond
((not (pair? time-sig)) (null-markup))
((pair? (car time-sig)) (format-complex-compound-time time-sig))
(else (format-time-fraction time-sig))))
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Measure length calculation of (possibly complex) compound time signatures
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
#(define (calculate-time-fraction time-sig-fraction)
(let* ((revargs (reverse time-sig-fraction))
(den (car revargs))
(num (apply + (cdr revargs))))
(ly:make-moment num den)))
#(define (calculate-complex-compound-time time-sig)
(let* ((sigs (map calculate-time-fraction time-sig)))
(let add-moment ((moment ZERO-MOMENT)
(remaining sigs))
(if (pair? remaining)
(add-moment (ly:moment-add moment (car remaining)) (cdr remaining))
moment))))
#(define-public (calculate-compound-measure-length time-sig)
(cond
((not (pair? time-sig)) (ly:make-moment 4/4))
((pair? (car time-sig)) (calculate-complex-compound-time time-sig))
(else (calculate-time-fraction time-sig))))
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Base beat lenth: Use the smallest denominator from all fraction
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
#(define (calculate-compound-base-beat-full time-sig)
(apply max (map last time-sig)))
#(define-public (calculate-compound-base-beat time-sig)
(ly:make-moment 1 (cond
((not (pair? time-sig)) 4)
((pair? (car time-sig)) (calculate-compound-base-beat-full time-sig))
(else (calculate-compound-base-beat-full (list time-sig))))))
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Beat Grouping
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
#(define (normalize-fraction frac beat)
(let* ((thisbeat (car (reverse frac)))
(factor (/ beat thisbeat)))
(map (lambda (f) (* factor f)) frac)))
#(define (beat-grouping-internal time-sig)
; Normalize to given beat, extract the beats and join them to one list
(let* ((beat (calculate-compound-base-beat-full time-sig))
(normalized (map (lambda (f) (normalize-fraction f beat)) time-sig))
(beats (map (lambda (f) (reverse (cdr (reverse f)))) normalized)))
(apply append beats)))
#(define-public (calculate-compound-beat-grouping time-sig)
(cond
((not (pair? time-sig)) '(2 . 2))
((pair? (car time-sig)) (beat-grouping-internal time-sig))
(else (beat-grouping-internal (list time-sig)))))
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% The music function to set the complex time signature
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
compoundMeter =
#(define-music-function (parser location args) (pair?)
"Create compound time signatures. The argument is a Scheme list of "
"lists. Each list describes one fraction, with the last entry being the "
"denominator, while the first entries describe the summands in the "
"enumerator. If the time signature consists of just one fraction, "
"the list can be given directly, i.e. not as a list containing a single list."
"For example, a time signature of (3+1)/8 + 2/4 would be created as "
"@code{\\compoundMeter #'((3 1 8) (2 4))}, and a time signature of (3+2)/8 "
"as @code{\\compoundMeter #'((3 2 8))} or shorter "
"@code{\\compoundMeter #'(3 2 8)}."
(let* ((mlen (calculate-compound-measure-length args))
(beat (calculate-compound-base-beat args))
(beatGrouping (calculate-compound-beat-grouping args))
(timesig (cons (ly:moment-main-numerator mlen)
(ly:moment-main-denominator mlen))))
#{
\once \override Staff.TimeSignature.stencil = #ly:text-interface::print
\once \override Staff.TimeSignature.text = #(format-compound-time args)
\set Timing.timeSignatureFraction = $timesig
\set Timing.baseMoment = $beat
\set Timing.beatStructure = $beatGrouping
\set Timing.beamExceptions = #'()
\set Timing.measureLength = $mlen
#} ))
%}
```