Getting beam subdivision working

[Jason Yip]

Hey all,

I'm currently way ahead of schedule with my GSoC project of fixing 
automatic beam subdivision, including any number of levels of nested 
tuples. I have implemented the structures necessary to support 
subdividing nested tuples and the only regression tests that "fail" so 
far are very few at the moment (attached as "make_check.png").

`beam-subdivide-tuplets.ly` concerns sextuplets, which my implementation 
treats the same as triplets. To implement a custom beatStructure that 
the user can specify for tuplets of a specific size, I may need some 
help (time-signature-settings.scm might be a good reference to provide 
defaults for tuplets with non-prime denominators).

The other "failing" regression tests concern the purpose of baseMoment. 
https://gitlab.com/lilypond/lilypond/uploads/9f968b929162a0d70d212ac2e99ec841/beam-subdivisions--notes-for-reimplementation--urs-liska.pdf 
points out the flaw of the current implementation's dependence on the 
value of baseMoment to subdivide beams. Currently, my implementation is 
much less dependent on baseMoment, generating the same subdivisions for 
the beams of test beam-subdivision.ly that only change the baseMoment 
value but not the actual note lengths. To allow better control of the 
intervals of subdivision and maintain backward compatibility, I suggest 
that there be 2 new options: minSubdivideInterval and 
maxSubdivideInterval. They are both Rationals. Their numerator and 
denominator must be a power of 2. For each power of 2 (including 
negative powers of 2 of course) between those two values, the beam can 
be subdivided by that interval. minSubdivideInterval can be 0 for no 
minimum limit, maxSubdivideInterval can be infinity for no maximum 
limit. For backward compatibility, when the subdivideBeams option is set 
to true, minSubdivideInterval can be set to baseMoment * 2. I have not 
implemented this yet so that the current regression tests at least 
compile under my implementation.

My implementation also successfully got the correct results (attached as 
"correct_nested_tuplet.pdf") of

```lilypond

\relative c' {
  \time 1/4
  \set subdivideBeams = ##t
  c32 c
  \tuplet 3/2 {
  \repeat unfold 4 c64
  \tuplet 3/2 { \repeat unfold 12 c128 }
  \repeat unfold 4 c64
  }
  c32 c
}
```

Note that the stable version doesn't even subdivide it all.

My implementation is available in a private fork, I'm not sure how I 
should share it if any other developers want to examine it (manual 
invite to each one who wants it?) It's a bit messy at the moment and 
definitely needs more code comments.

Does anyone have thoughts about my suggestions or want access to my 
implementation?

--
- Jason Yip

make_check.png
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correct_nested_tuplet.pdf
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