Pattern-generating Scheme function challenge

[Urs Liska]

Hi all, the Schemers in particular,

you surely know by now that I am writing a series of posts that demonstrate how elegantly and efficiently we can recreate a portion of a book that obviously has been produced with many pains in Finale.
I'm confident that it will be an impressive display of LilyPond's power :-) but I would love to go even one step further.

In the post published yesterday I showed how easy it is to typeset that polymetric example from Aldridge's book.
In the second post (finished but scheduled for monday or tuesday) I show a Python function that generates the LilyPond code for a complete set of patterns.
The third post will set up the files to finally print the whole set.

I would be happy to include an alternative approach if I can get the necessary input from the list (of course I will credit it correctly): Instead of generating the patterns' code with Python I would like to see a Scheme function that achieves the same directly from within the LilyPond files. Probably such an approach could even simplify a few other things.


The Python code I used is here: https://github.com/openlilylib/aldridge-patterns/blob/master/pattern-generator.py
and the resulting LilyPond file here: https://github.com/openlilylib/aldridge-patterns/blob/master/pattern-definitions.ily
and you can of course inspect the whole repository if you want.

The task is to print these examples in five parallel metric contexts (see http://lilypondblog.org/wp-content/uploads/2013/07/aldridge-ex-19-score.pdf),
therefore I had to do some things about those virtual time signatures.
If the patterns are generated by a Scheme function we can do better and handle this specification 'at source level'.

I have added a dummy file that should hold that function: https://github.com/openlilylib/aldridge-patterns/blob/master/pattern-definitions-scheme.ily

So:
The function should take three arguments (as already in the dummy):
- start and
- end of the range (which in my Python function is hardcoded)
- denominator of the time signatures

For each number in the range it should:
- produce a LilyPond pattern corresponding to the binary representation of the given number
- chose note/rest duration to be 1/denominator (which is an improvement over my Python approach because we can omit the \shift- and \scaleDurations process
- beam from the first to the last note if there is more than one note and if denominator > 4

Additionally the function should:
- Insert a manual break after four patterns or if the length of the pattern increases (which happens when the number is a power of two) (don't forget to reset the counter in that case)
- after that break re-print the time signature (calculated from the length of the pattern and the given denominator) and insert a \mark \default

Modifications in the main file I would expect:
- The \newExercise function is obsolete (it was necessary because the patterns themselves weren't aware of the denominator)
- Instead of the \shiftDurations - \scaleDurations steps (which can be dropped) I'd move the Timing to the individual staves, that is I don't use the timeSignatureFractions anymore but real time signatures.
- the \noBeamForLongerNotes function would become obsolete (as we don't generate those beams in the first place)
  (Sorry Harm, but it's not in vain because I'd of course also present my first approach)
- the patterns are called with \patterns start end denominator.
- As the \shiftDurations are obsolete I don't need that I-II-III-IV-V stuff anymore but can place the call of \patterns directly in the \score


I'm sure this would deliver even one more deep hit in our "notation battle", therefore I'm really looking forward to your suggestions.
They can be discussed here, or I'd happily accept them as pull requests.

Urs