Re: Automatic beaming fails with tuplets

[Hans Åberg]

> On 11 Nov 2017, at 22:29, Urs Liska <address@hidden> wrote:
> 
> 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.

I think the feature that one may enter just the note value and not a full 
tuplet group leads into the wrong track. If one should have that feature, for 
correct beaming, one should first reduce it to full tuplet groups, and then 
apply its local beatStructure.

>>> 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.

Hindemith, "Elementary Training", p. 116, suggests that 6 8th notes beamed 
together should be musically interpreted as two groups of three 8th notes, 
which also can be written as two triplets. However, one can also have the 2+2+2 
beaming, in which case it cannot be reduced to two triplets, instead it is a 
single one.

So, in LilyPond, I think would be more natural to have a local beatStructure 
where one can indicate different pattern like (6), (3 3), (2 2 2), etc.

>>> 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.

This is just an interpretation for standard CPP music. One can other patterns 
as well, if one so like, and that is the case to irregular tuplets, say a 
quintuplet could be (5), (2 3) or (3 2), just as for measures.

> 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)

I think suffices to implement beaming for full tuplet groups, each treated as a 
separate entity with its own beatStructure. Other things could be implemented 
later if so wanted, but for a start, it might just be complication.