[CM] cmn factorize

Bill Schottstaedt bil@ccrma.Stanford.EDU
Fri, 7 Apr 2006 04:38:43 -0700

The "logic" in the 1/9 case
goes something like: if you ask for (say) triplets (i.e. n/3), you' re 
putting 3 (say 8ths) in a quarter, so you get, for example, q + e = q.
If you ask for 5 divisions in a quarter, that's q + s = q, (or is it h + e = q?) --
since the beat is closer to a 16th, this gets two beams, but the problem for cmn
is that in nested n-lets so to speak, you need to keep the beams
logical (say a triplet within a triplet = 1/9) so the outer triplet, the
unbroken beam, has one beam, and the inner triplet is considered
3 16ths in a triplet 1/8, so it ought to have 2 beams, but that means
a quarter at the outer level = h + s at the innermost level.  You'll
notice in the code (just below the point you mention) a long comment
about the problem, all brought about by rqq.lisp and its fancy nested
groupings.  I suppose we could add a flag to choose which style is
desired.  (The factorization was trying to catch these nested cases --
as you can see in the code I originally just chose the closest match
between flags and actual duration, but the experts disagree even on