Re: Automatic beaming fails with tuplets

[Urs Liska]

Am 11.11.2017 um 22:11 schrieb Hans Åberg:
> > On 11 Nov 2017, at 21:32, Urs Liska <address@hidden> wrote:
> >
> > AFAICS a tuplet suspends/shadows/interrupts the beatStructure. The regular 
> > processing of the measure should ignore a tuplet, and the tuplet should be 
> > handled separately.
> Each full tuplet group behaves like a mini-measure with its own beaming 
> pattern, though the general structure is the same. The beaming is then as of 
> the written notes values, not the actual timing values implied.

Exactly. And that's what LilyPond currently (explicitly) does wrong.

> >  From the results I assume that the beaming code suffers from the same misconception as 
> > the code in beaming-pattern: tuplets are recalculated and processed according to their 
> > *absolute position* in the measure. That means that an event that happens to occur on a 
> > beat of the measure's beat structure is treated like an event on a beat, which is 
> > incorrect. Instead the tuplet should get a "virtual" beat structure.
> >
> > In the example we have a 3/2 tuplet giving three crotchets over two. So any 
> > beaming (and subdivisions) should be based on an assumed beatStructure of three 
> > crotchets. That way the eight notes would automatically beamed together because 
> > they represent one crotchet.
> Each tuplet should have its own local beatStructure. A sextuplet should have by 
> default a 3 3 beatStructure, if not explicitly overridden.

With sextuplets I've come to the conclusion that it's possible to 
shorten the fractions - together with the tupletSpannerDuration.

\tuplet 6/4 4 is equivalent (in terms of beaming) to \tuplet 3/2 8. The 
same is true for \tuplet 12/8 4 => \tuplet 3/2 16, so I think it's a 
general rule.

> > Generally speaking a tuplet should be treated according to the 
> > visible/generic/unscaled durations of the content while the remaining parts of 
> > the measure simply ignore it, i.e. pick up at their usual Moment after the 
> > tuplet.
> Indeed, the beaming is as if the tuplet group did not exist but with a local 
> beatStructure, taking up the amount notation space as indicated by the tuplet 
> total time.

This local beatStructure can be inferred from the tuplet definition. If 
the tuplet is \tuplet 3/2 4 (as in my initial example) the resulting 
local beatStructure is:
- baseMoment 1/4 / 2 = 1/8
- beatStructure #'(3)
A single tuplet always has such an unary beatStructure whose baseMoment 
is derived from the tuplet denominator and span, and whose repetition 
(beatStructure entry) is the tuplet numerator.

Multiple identical tuplets can either be considered as sequential 
elements or as a larger "local measure":

\tuplet 3/2 4 {
  c8 c c c c c
}

can also be seen as
- baseMoment 1/8
- beatStructure #'(3 3)