Re: Autobeaming

[Hans Aberg]

On 30 Dec 2009, at 00:17, Carl Sorensen wrote:

> > I find the current LilyPond structure hard to cope with when wanting
> > subbeaming.
>
> Yes, right now there is no sound method for dealing with subbeaming  
> (or beam
> subdivision, as I think it's called).  I hope to fix that.

That would be good. I think that the beaming structures without the  
meter concept are essentially the same, so it might fix the beaming  
problem altogether.

> > The smallest units is "in one", where one only has a time segment
> > which should be beamed as much as possible - on the time level
> > subdivision it expresses.
>
> Ross and Read talk about this smallest unit as a "beat", and it is not
> necessarily the denominator of the time signature.

I got the term "in one" from Steve Latham, who said it was used in  
Finale, and also by musicians when performing for example Beethoven's  
5th, which is written in 2/4, but normally played "in one", that is,  
with only one metric accent per measure. A strict time signature would  
have been 1/2, but apparentlty, that is not used in CPP.

There is the Bulgarian "Eleno Mome" which the Bulgarian musicologists  
write in 13/16, 13 = 4+4+2+3, but the 3 here indicates a time bend  
which is performed typically very close to 4. So I think a correct  
writing would be 7/8, where 7 = 2+2+1+2, or (2+2)+(1+2) if subaccents  
should be displayed.

I then avoid the use of "beat" because it is ambiguous here. The time  
units can be so short it is not possible to count on them. (Here the  
quarter note is at about 144 bpm.)

> In fact, in what they
> refer to as "compound time" or "compound meter", the beat is three  
> times the
> denominator of the time signature.

Such terms are ambiguous: there seems to be a divide between a "Latin"  
and a "Germanic" tradition, going down in the middle of Europe, with  
the Netherlands on the dividing line.

In the Latin tradition, "duple" and "triple" time refers to how the  
notes of the piece are subdivided. So 4/4 is duple time. In the  
Germanic tradition, it has to with the time signature. So 4/4 is  
quadruple time.

This then affects the interpretation of "compound time".

I stick to essentially Germanic tradition. Meters that can be written  
without a + are simple, others are compound. So 6 = 3'+3' is compound.  
4 is simple, but compound when interpreted as 2+2.

Meters that are built up in a regular way I call regular, the others  
irregular. So 9 = 3'+3'+3' is regular and compound (can be rewritten  
as a 3, which is simple), but 9 = (2'+2')+(2'+3'), common in the  
Balkans, is irregular and compound.

English speaking may find this confusing, but is close to the Germanic  
tradition.

> > Then one can repeat that either equally by an integer multiple or a
> > "+". For example, 6/8 calls for a "in one" 3+3 division of the time
> > unit which is the 1/8th note, which at the same time is the same as 2
> > times the dotted 1/4th note. So doing some pseudocode, it might be
> > written
> >   (3+3) x 1/8
> > or
> >   2 x 3/8 = 2 x 1/4. (dotted 1/4th)
> >
> > However, in the first one, the 3's should be "in one", and not be
> > beamed as "in three", expressing metric subaccents. So perhaps one
> > needs to distinguish between these two types of integers, say write
> > "in one" as 3'. Then the first one should be written
> >   (3'+3') x 1/8
>
> So if I understand correctly, you mean that all the notes in each of  
> the 3'
> sections should be beamed together, thus avoiding metric subaccents?

Yes, I think that is the lowest level, and also default if there are  
no conventions.

Take tuplets. If there are quintuplets, then it should be a 5' unless  
specified as typically 2'+3' or 3'+2'.

For sextuplets, there is a convention that the should be in 3, so  
there is an implicit rule 3'+3' - there should be no subbeaming of the  
3'. But a compose might want to change that.

Triplets are by convention in 3 - the 3 not the 3'

> > Then take a time signature like 4/4. It has i fact two common
> > interpretations:
> >   (2'+2') x 1/4
> >   4 x 1/4
> >
> > Now one might also use tuplets tied to the metric. For example, in
> > Macedonian 7/16, one may normally play as
> >   (3'+(2'+2')) x 1/16
> > But one may shift to using quadruplets on the 3s divided as 2'+2',
> > which one might want to express in the subbeaming. So one might  
> > want a
> > second rule like
> >   (3:4 (2'+2') + (2'+2')) x 1/16
> > So the \meter should have a sequence of such rules.
>
> I believe that these rules are exactly what the current autobeaming  
> rules
> can express (although the rules that express this are not in the  
> current
> default beam settings).

I have had problems in the past when doing subbeaming. So I have no  
problems getting the 3'+2'+2'. But strange things tend to happen when  
doing subbeaming. For example, getting the quadruplet subbeaming 3:4  
2'+'2 might be hard. Unfortunately, there is a very popular Macedonian  
meter (Ibraim Odza, for example)
  ((3:4 (2'+2') + (2'+2')) + 3:4 ((2'+2') + 2') x 1/16
or 12/16.

> > When writing a time signature, some may want to just adding it all in
> > one number, and other want to write a "+", Bartok style. That might  
> > be
> > described by replacing some of the (..) with [..] on one of the  
> > rules.
> > For example
> >   [3'+(2'+2')] x 1/16
> > would be written as
> >    7
> >   16
> > But there is a problem already here, as one might want to writ it as
> >   3+2+2
> >    16
> > even though the beaming is (3'+(2'+2')). Writing
> >   [3'+[2'+2']] x 1/16
> > would strictly speaking lead to a time signature
> >   3+(2+2)
> >     16
> > though it is probably uncommon to have (..) in the time signature.
>
> I believe we currently have the capability of writing compound time
> signatures (which governs the display of the time signature).  With  
> the new
> properties, we'll be able to set the measure grouping and the beaming
> characteristics, so I think the full flexibility will be there.

Are probably referring to what you have in the development stage, and  
not in a current version?

Anyway, I am willing trying it out.

> > I think some may then want to write a different time signature than
> > what is strictly implied by the beaming.
> >
> > Together with the defined has defined a \meter structure, one needs  
> > to
> > also specify how it should be rendered. On the top level, it might
> > express a meter change between measures, using various dotted bars
> > ":", then comes space break, and after that some subbeaming.
> >
> > So that is roughly how I think about it. - LilyPond has some of it,
> > but I think cannot express that hierarchy properly in a suitable  
> > human
> > interface.
>
> The human interface in LilyPond is likely to continue to be sub- 
> optimal at
> least for the near future.

It is not really necessary to do all subbeaming, but it is being able  
to do it.

> But I believe that in the near future the
> capability to display the appropriate time signatures, measure  
> grouping,
> beaming, and subbeaming will be present.

This might then fix the general autobeaming problem then

You get my admiration for doing this work - I had some ideas on how to  
do it more than a year ago, but haven't gotten around doing a better  
description.

  Hans