Re: compound time signature with non duple denominator

[mclaren]

I have an even more diabolical question, related to the one at the start of
this thread. 

But let me first answer the original question, which was: "Is there a way to
implement a non-binary time signature like 4 + 1/3?" I think I know a way to
do this.

This seems like an entirely valid question. 1/3 would be a single triplet
note, right? That is, if we're dealing with (4 + 1/3)/4, then what we want
is 4 quarter notes + 1 triplet quarter note, correct?  In that case, can't
we get the same effect by doing [X number of triplets equivalent to 4
quarter notes] + 1 triplet quarter note?

The number of triplet quarter notes = 4 quarter note is of course 12,
therefore the total is 12 + 1 triplet quarter notes, and therefore the time
signature should be 13/3.

Fortunately, the Lilypond snippets show us how to get a non-binary time
signature like this. The solution is two fold: first, set te time signature
to 13/4 and erase the time signature so it doesn't plrint and then insert an
artificial time signature which gets printed but not used. Second, use
\scaleDurations to get triplets for all notes in each measure.

Here's my Lilypond code:

\version "2.18.2"

\header { 
  tagline = ""  % removed 
} 

#(set-default-paper-size "a4" 'landscape)
%\layout {}

indent=0
<<
  
\new Staff { \clef "treble"
             \relative c''
               \override Staff.TimeSignature #'stencil = ##f 
  \time 13/8
% We need this time signature to get the beat
% structure, but this time signature won't print.
% Now we insert the time sig that does print. 

% This is the time signature that will print

 \override Staff.TimeSignature.stencil = #ly:text-interface::print 
  \override Staff.TimeSignature.text = 
  \markup \override #'(baseline-skip . 0) \center-column \number { 
    \concat { "4 + 1" } 
      \hspace #-0.1 
      \override #'(offset . -32) 
      \override #'(thickness . 1.6) 
       "3"}


\set Timing.measureLength = #(ly:make-moment 1364/780)
% This sets the barline locations. I had to play around with this
% make-moment value to get the barlines to place properly. AFAICT
% this make-moment vlaue is a by-guess-and-by-God "magic" value
% that has to be fiddled with by trial and error to get it right.
\relative c''
\scaleDurations 3/2 {

   c4 d f e \tuplet 3/2{b4} c4  b a  c  \tuplet 3/2{b4} c4 d f, g  \tuplet
3/2{b4}  c4 d c f, \tuplet 3/2{b4} e4  f g  d  \tuplet 3/2{b4} c4 d f, g 
\tuplet 3/2{b4}  c4 d f e \tuplet 3/2{b4} c4  d f  e  \tuplet 3/2{b4} c4 d
f, g  \tuplet 3/2{b4}
\bar ""
\break
c4 d f e \tuplet 3/2{b4} c4  b a  c  \tuplet 3/2{b4} c4 d f, g  \tuplet
3/2{b4}  c4 d c f, \tuplet 3/2{b4} e4  f g  d  \tuplet 3/2{b4}

} 
}

%\new Staff { \clef "bass"
%             \relative c,
               
%  \time 4/4
%\set Timing.measureLength = #(ly:make-moment 4/4)
 %{a,4 b, c d  a,4 b, c d   a,4 b, c d   a,4 b, c d   a,4 b, c d}
%}
>>  

And here's an example of the score output on imgur:
http://imgur.com/a/cSyML

Now here's my even more diabolical question:
How do you get Lilypond to do a meter and print barlines properly on a time
signature like
4 + (square root of 3)? And get valid page breaks?







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